Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant 9819962641, 9789819962648

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Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant

Changhe Li

Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant

Changhe Li School of Mechanical and Automotive Engineering Qingdao University of Technology Qingdao, Shandong, China

ISBN 978-981-99-6264-8 ISBN 978-981-99-6265-5 (eBook) https://doi.org/10.1007/978-981-99-6265-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Preface

Manufacturing industry is a pillar industry in national economy. Transformation and upgrading of traditional manufacturing industry to sustainable production through energy-saving and emission reduction are a key project in the strategic development to be a manufacturing power of countries around the world, especially developing countries. They are even the key development direction under the concept of sustainable national economic development. Moreover, International Organization for Standardization (ISO) has formulated standards for carbon emission ISO 14067-2018 and relevant laws like Cleaner Production Promotion Law for manufacturing powers. To meet the strict standards and laws, it proposes urgent and essential needs to green transformation and upgrading of traditional manufacturing industry. Mineral cutting oil has been used in manufacturing industry for hundreds of years, and it overcomes many technical problems, such as cooling, lubrication, and debris removal under the strong thermal-mechanical coupling effect on the cutting and grinding interface. Nevertheless, the abundant use of mineral cutting oil has caused serious environmental pollution, cost pressure, and threats to occupational health, thus failing to meet the principle of recycling economy and sustainable manufacturing. Quasi-dry manufacturing, that is, minimum quantity of lubricant (MQL), can decrease the consumption of cutting oil by more than 90%. As an effective substitution of traditional flooding cooling lubrication, quasi-dry manufacturing is applicable to manufacturing of parts with low cutting force and specific energy. However, it is easy to produce thermal damages to strong plastic materials with low thermal conductivity, such as titanium alloys, high-temperature nickel base alloys, and so on. Hard and brittle materials like zirconia ceramics for medical use are easy to cause cracks/ force damages. The technological bottleneck of anti-wear, anti-friction, and thermal dissipation through compressed air carrying the minimum quantity of degradable lubricant still remains. On this basis, the author proposed a new method of nanobiological lubricant MQL grinding. In this new method, solid nanoparticles are added into the degradable lubricating base fluid to prepare the nanofluids. The nanofluids are applied to MQL grinding by taking advantages of strong heat exchange capability, anti-wear, and anti-friction properties of nanoparticles. This not only inherits all advantages of v

vi

Preface

MQL grinding, but also overcomes the critical defect of traditional MQL grinding— insufficient heat exchange capability. Moreover, the excellent anti-wear and antifriction properties of nanoparticles are conducive to increase lubrication performances of grinding wheel-workpiece interface and grinding wheel-chip interface in MQL grinding, thus improving machining accuracy and surface quality (especially surface integrity) of workpieces significantly. Besides, they can prolong the service life of grinding wheel and improve the working environment. Hence, it is a new sustainable green grinding technique orienting to environmental-friendly, energysaving, and high-energy utilization. Due to the involvement of solid nanoparticles, the tribological behaviors of the grinding wheel-workpiece interface, oil film formation mechanism in the grinding zone, and thermodynamic action laws of grinding media on the grinding zone are changed. Chapters 1–5 of the book is arranged and compiled by Professor Changhe Li and Professor Yanbin Zhang, Chaps. 6–10 is arranged and compiled by Professor Changhe Li and associate professor Min Yang, Chaps. 11–15 is arranged and compiled by Professor Changhe Li and Ph.D. candidate Wenhao Xu. The whole book was compiled and finalized by Professor Changhe Li. Professor Bingheng Lu from Xi’an Jiaotong University, an academician of the Chinese Academy of Engineering, is responsible for the primary review of the book. He proposes many valuable suggestions which are highly appreciated. Otherwise, this book is financially supported by the following Foundation items: the National Key Research and Development Program, China (2020YFB2010500), National Natural Science Foundation of China (52105457, 51975305), the Special Fund of Taishan Scholars Project (tsqn202211179), the Youth Talent Promotion Project in Shandong (SDAST2021qt12), and the Natural Science Foundation of Shandong Province (ZR2023QE057, ZR2022QE028, ZR2021QE116, and ZR2020KE027). I’d like to express my sincere thanks to many experts, colleagues, and professors for their great supports, assistance, and relevant studies for reference during writing of the book. Due to the limited ability and time of the author, it is inevitable to have careless omissions and inappropriate expressions in the book. Your criticism and correction during reading the book are highly appreciated. Qingdao, China

Changhe Li

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Flooding Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Dry Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Cryogenic Cooling Grinding . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 MQL Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.5 Nanofluids MQL Grinding . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.6 Thermodynamic Action Laws in NMQL Grinding . . . . . 1.1.7 Measurement Methods of Thermal Parameters in NMQL Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Research Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Research Status in Thermodynamic Action Laws During Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Research Status in China . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Research Status in Foreign Countries . . . . . . . . . . . . . . . . 1.4 Research Status on Theoretical Modelling of NMQL Grinding Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Kinematics of a Single Grain and Material Removal Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Mechanical Model of a Single Grain . . . . . . . . . . . . . . . . . 1.4.3 Geometry and Kinematical Modelling of Ordinary Grinding Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Research Status on Theoretical Modelling of NMQL Grinding Heats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1 Definition of Grinding Temperature Field . . . . . . . . . . . . 1.5.2 Solving Method of Grinding Temperature Field . . . . . . . 1.5.3 Heat Source Distribution Model . . . . . . . . . . . . . . . . . . . . 1.5.4 Thermal Partition Coefficient Model in the Grinding Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Description and Explanation of Research Problems . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 5 5 6 7 7 8 13 14 14 20 22 22 24 25 26 26 27 29 31 33 34 vii

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2

3

Contents

Analysis of Grinding Mechanics and Improved Predictive Force Model Based on Material-Removal and Plastic-Stacking Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Grinding Force Model of a Single Grain . . . . . . . . . . . . . . . . . . . . . 2.2.1 Grains/Workpiece Interference Mechanism and Debris Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Cutting Force Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Ploughing Force Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Frictional Force Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Ordinary Grinding Wheel Models and Dynamic Active Grains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Protrusion Height of Grains in the Grinding Zone . . . . . 2.3.2 Static Active Grains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Dynamic Active Grains and Cutting Depth . . . . . . . . . . . 2.4 Grinding Force Models of Ordinary Grinding Wheel and Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Construction of Grinding Force Models . . . . . . . . . . . . . . 2.4.2 Prediction of Grinding Force . . . . . . . . . . . . . . . . . . . . . . . 2.5 Experimental Verification of Grinding Forces . . . . . . . . . . . . . . . . . 2.5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Comparative Analysis Between Predicted Values and Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Variation Trend Analysis of Grinding Force . . . . . . . . . . 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43 43 44 45 54 57 57 62 63 64 65 68 68 68 69 69 70 70 73 73

Velocity Effect and Material Removal Mechanical Behaviors Under Different Lubricating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.2 Material Removal Mechanical Behaviors of High-Speed Grinding Under Different Lubricating Conditions . . . . . . . . . . . . . 76 3.2.1 Grain-Workpiece Interference Geometric Model . . . . . . 76 3.2.2 Mechanical Action Mechanism and Material Strain Rate in the Cutting Zone . . . . . . . . . . . . . . . . . . . . . 84 3.2.3 Debris and Furrow Forming Mechanisms . . . . . . . . . . . . . 87 3.3 Experimental Method of Single-Grain High-Speed Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.3.1 Building of the Experimental Platform . . . . . . . . . . . . . . . 94 3.3.2 Discussion of Previous Single-Grain Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.3.3 Experimental Methods of Single-Grain High-Speed Grinding Under Different Lubricating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.4 Experimental Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . 101

Contents

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3.4.1

Debris Morphology and Material Removal Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Plastic-Stacking Phenomenon and Influencing Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Effects of Lubricating Conditions and “Velocity Effect” on Unit Grinding Force . . . . . . . . . . . . . . . . . . . . . 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5

Probability Density Distribution of Size and Convective Heat Transfer Mechanism of Nanofluid Droplets . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Research Status on Convective Heat Transfer Mechanism of Nanofluids Spray Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Research Status of Heat Transfer Mechanism of Nanofluids in the Grinding Zone . . . . . . . . . . . . . . . . . . 4.2.2 Research Status of Convective Heat Transfer Coefficient in Spray Cooling . . . . . . . . . . . . . . . . . . . . . . . 4.3 Mathematical Model of Convective Heat Transfer Coefficient Under Nanofluids Spray Cooling . . . . . . . . . . . . . . . . . 4.3.1 Nanofluids Atomization Mechanism and Probability Density Distribution of Droplet Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Effects of Airflow Field Around Micro-abrasive Tool on Droplet Distribution Pattern . . . . . . . . . . . . . . . . . 4.3.3 Theoretical Models of Spray Boundary . . . . . . . . . . . . . . 4.3.4 Probability Density Statistics of Size of Droplets with Effective Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . 4.3.5 Convective Heat Transfer Coefficient Model of Nanofluids Spray Cooling . . . . . . . . . . . . . . . . . . . . . . . 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design and Experimental Evaluation of Convective Heat Transfer Coefficient Test System in Nanofluids Spray Cooling . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Research Status on Measuring Device of Convective Heat Transfer Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 In-Pipe Transient Measurement of Convective Heat Transfer Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Measurement of Forced Convective Heat Transfer in a Narrow Annular Channel . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Measurement of Convective Heat Transfer in Helical Grooved Tube with Inner Helical Teeth . . . . . 5.3 Characterization of Thermophysical Properties of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101 107 109 113 114 117 117 118 118 120 123

123 126 128 131 134 135 138 141 141 142 142 144 145 147

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5.3.1 5.3.2

Preparation of Medical Nanofluids . . . . . . . . . . . . . . . . . . Characterization of Thermophysical Properties of Nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Design and Building of the Measurement System for Convective Heat Transfer Coefficient Under Nanofluids Spray Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Experimental Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Design and Building of the Measurement System . . . . . . 5.4.3 Measuring Errors of Experimental Device . . . . . . . . . . . . 5.5 Experimental Result Analysis and Discussions . . . . . . . . . . . . . . . 5.5.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 Analysis and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Research on Microscale Skull Grinding Temperature Field Under Different Cooling Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Definition of Grinding Temperature Field . . . . . . . . . . . . . . . . . . . . 6.3 Solving Method of Grinding Temperature Field . . . . . . . . . . . . . . . 6.3.1 Solving Grinding Temperature Field Based on Analytical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Solving Grinding Temperature Field Based on Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Type-I Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Type-II Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Type-III Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 6.5 Constant Heat Source Distribution Model in Grinding of Metal Materials with Ordinary Wheel . . . . . . . . . . . . . . . . . . . . . 6.5.1 Rectangular Heat Source Distribution Model . . . . . . . . . 6.5.2 Triangular Heat Source Distribution Model . . . . . . . . . . . 6.5.3 Parabolic Heat Source Distribution Model . . . . . . . . . . . . 6.5.4 Comprehensive Heat Source Distribution Model . . . . . . 6.6 Dynamic Heat Flux Model of Ductility Domain Removal of Hard and Brittle Bio-Bone Materials . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Statistics on Effective Grinding Abrasive Number of Spherical Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Energy Consumption for Plastic Shear Removal of Bone Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.3 Energy Consumption for Removal of Bone Material Powder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.4 Dynamic Heat Flux Model for Ductility Domain Removal of Hard and Brittle Bio-Bone . . . . . . . . . . . . . . . 6.7 Thermal Partition Coefficient Model in the Grinding Zone . . . . .

147 147

152 152 153 156 157 157 158 163 164 167 167 169 170 171 173 177 178 179 179 180 181 182 183 184 187 189 191 193 195 199

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6.7.1

Rated Heat Supply Coefficient Model at Grinding Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.2 Thermal Partition Coefficient Model of Grinding Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.3 Thermal Partition Coefficient Model of Abrasive/ Grinding Fluid Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.4 Thermal Partition Coefficient Model of Grinding Wheel/Workpiece System . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7.5 Thermal Partition Coefficient Model Considering Convective Heat Transfer of Grinding Zone . . . . . . . . . . . 6.8 Thermal Damage Domain in Dry Grinding of Bio-Bone . . . . . . . 6.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

8

Process Parameter Optimization and Experimental Evaluation for Nanofluid MQL in Grinding Ti-6Al-4V Based on Grey Relation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Experimental Equipments . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Experimental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Experimental Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Single-Index SNR Analysis . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Multi-Index Grey Correlation Analysis . . . . . . . . . . . . . . . 7.4 Verification Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Workpiece Surface Quality Analysis . . . . . . . . . . . . . . . . . 7.4.2 Grinding Efficiency Analysis of Workpiece Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature Field Model and Experimental Verification on Cryogenic Air Nanofluid Minimum Quantity Lubrication Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Numerical Simulation of Grinding Temperature Field . . . . . . . . . 8.2.1 Mathematical Model of Grinding Temperature Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Determination of Simulation Parameters . . . . . . . . . . . . . 8.2.3 Numerical Simulation Results . . . . . . . . . . . . . . . . . . . . . . 8.3 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Experimental Equipments . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Experimental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

200 201 202 202 203 206 207 208

211 211 212 212 213 215 215 215 222 224 225 230 231 232

235 235 236 236 240 245 247 247 248 250 250

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8.3.5

Comparison of Simulation and Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Experimental Results Analysis and Discussion . . . . . . . . . . . . . . . 8.4.1 Specific Grinding Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 Cooling Performance Evaluation Under Different Working Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.3 Boiling Heat Transfer Analysis . . . . . . . . . . . . . . . . . . . . . 8.4.4 Effects of Workpiece and Debris Surface Characteristics on Cooling Heat Transfer . . . . . . . . . . . . . 8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Convective Heat Transfer Coefficient Model Under Nanofluid Minimum Quantity Lubrication Coupled with Cryogenic Air Grinding Ti-6Al-4V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Experimental Equipments . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.2 Experimental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.3 Experimental Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Specific Grinding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Friction Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Experimental Results Analysis and Discussion . . . . . . . . . . . . . . . 9.4.1 Lubrication Performance Evaluation Under Different Working Conditions . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Effects of Temperature on Lubrication Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.3 Atomizing Angle Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.4 Surface Roughness and Surface Morphology . . . . . . . . . . 9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Effects of Cold Air Fraction in Vortex Tube on Heat Transfer Mechanism in CNMQL Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Numerical Simulation of Grinding Temperature Field . . . . . . . . . 10.2.1 Mathematical Model of Grinding Temperature Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Determination of Simulation Parameters . . . . . . . . . . . . . 10.3 Numerical Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 Experimental Equipments . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Experimental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

251 253 253 255 256 258 261 262

265 265 265 265 266 266 266 266 267 268 268 270 274 276 278 279 281 281 281 282 282 283 285 285 285 286

Contents

10.4.4 Comparison of Simulation and Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Experimental Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.1 Specific Grinding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.2 Effects of Nanofluid Viscosity on Heat Transfer Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.3 Effects of Surface Tension of Nanofluids on Heat Transfer Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.4 Effects of Atomizing Effect and Boiling Heat Transfer on Heat Transfer Performances . . . . . . . . . . . . . 10.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Effects of Nanofluid Concentration on Heat Transfer Performances in Cryogenic Nanofluid Minimum Quantity Lubrication Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Experimental Equipments . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 Experimental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.3 Experimental Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 11.3.1 Grinding Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.2 Specific Grinding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.3 Effects of Viscosity and Contact Angle of Nanofluids on Heat Transfer Performances . . . . . . . . . 11.3.4 Effects of Nanoparticle Dispersibility on Heat Transfer Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Performances of Al2 O3 /SiC Hybrid Nanofluids in Minimum-Quantity Lubrication Grinding . . . . . . . . . . . . . . . . . . . . 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 MQL Mechanism of Mixed Nanofluids . . . . . . . . . . . . . . . . . . . . . . 12.2.1 Thermophysical Properties of Al2 O3 and SiC Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.2 MQL Mechanism of Base Oil . . . . . . . . . . . . . . . . . . . . . . 12.2.3 Lubrication Mechanism of Mixed Nanoparticles . . . . . . 12.3 Performance Evaluation Parameters of Mixed NMQL . . . . . . . . . 12.3.1 Grinding Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.2 Micro-friction Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.3 Specific Grinding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.4 Removal Parameters of Workpiece . . . . . . . . . . . . . . . . . . 12.3.5 Workpiece Surface Quality . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 Research on Grinding Surface Homogeneity . . . . . . . . . . . . . . . . .

xiii

287 287 287 289 291 293 296 297

299 299 299 299 300 300 300 300 301 303 305 307 309 311 311 312 312 312 314 316 316 320 320 321 321 322

xiv

Contents

12.4.1 Autocorrelation Analysis of Workpiece Surface Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.2 Cross Correlation Analysis of Workpiece Surface Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.3 Power Spectral Density Analysis of Workpiece Surface Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Grinding Performances of Al2 O3 /SiC Mixed Nanofluid MQL with Different Mixratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.2 Experimental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.3 Experimental Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.4 Experimental Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Experimental Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.1 Grinding Force Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.2 Specific Grinding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.3 Surface Roughness of Workpiece . . . . . . . . . . . . . . . . . . . 13.4 Discussion of Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.1 Lubrication Mechanism of Pure Al2 O3 Nanofluid and Pure SiC Nanofluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.2 “Physical Synergistic Effect” Analysis of Al2 O3 / SiC Mixed Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.3 Workpiece Surface Morphology and Profile Supporting Length Rate Curve . . . . . . . . . . . . . . . . . . . . . . 13.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Lubricating Property of MQL Grinding of Al2 O3 /SiC Mixed Nanofluid with Different Particle Sizes and Microtopography Analysis by Cross-correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.1 Experimental Equipments . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.2 Experimental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.3 Experimental Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.1 Specific Grinding Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3.2 Removal Parameters of Workpiece . . . . . . . . . . . . . . . . . . 14.3.3 Surface Roughness of Workpiece . . . . . . . . . . . . . . . . . . . 14.4 Analysis and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

322 324 325 326 326 329 329 330 330 330 331 332 334 334 337 339 342 342 345 347 348 349

353 353 354 354 354 354 355 355 356 357 360

Contents

14.4.1 Lubrication Mechanism of Al2 O3 /SiC Mixed Nanofluids with Different Physical Encapsulation Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.2 Effects of Contact Angle Between NMQL Droplet and Workpiece Surface on Lubrication Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4.3 SEM Analysis of Grinding Debris . . . . . . . . . . . . . . . . . . . 14.4.4 Cross Correlation Analysis of Al2 O3 /SiC Mixed NMQL Under Different Size Ratios . . . . . . . . . . . . . . . . . 14.4.5 Cross Correlation Analysis of Profile Curves at Two Points of the Same Workpiece Surface . . . . . . . . . 14.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Spraying Parameter Optimization and Microtopography Evaluation in Nanofluid Minimum Quantity Lubrication Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2.1 Experimental Equipments . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2.2 Experimental Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2.3 Experimental Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.1 SNR Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.2 Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.3 Optimization Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.4 Experimental Verification and Discussion . . . . . . . . . . . . . . . . . . . . 15.4.1 Power Spectral Density Analysis of Surface Profile . . . . 15.4.2 Surface Morphology of Workpiece and EDS . . . . . . . . . . 15.4.3 Debris Morphology and EDS . . . . . . . . . . . . . . . . . . . . . . . 15.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xv

360

363 364 365 367 369 370

373 373 373 373 374 375 376 376 382 385 385 385 388 391 391 394

List of Figures

Fig. 1.1 Fig. 1.2 Fig. 1.3 Fig. 1.4 Fig. 1.5 Fig. 1.6 Fig. 1.7 Fig. 1.8 Fig. 1.9 Fig. 1.10 Fig. 1.11 Fig. 1.12 Fig. 2.1 Fig. 2.2 Fig. 2.3 Fig. 2.4 Fig. 2.5 Fig. 2.6 Fig. 2.7 Fig. 2.8 Fig. 2.9 Fig. 2.10 Fig. 2.11 Fig. 2.12 Fig. 2.13

Problems of traditional flooding lubrication technique . . . . . . . Different kinds of green manufacturing methods and their characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement method of grinding force [60] . . . . . . . . . . . . . . . . Measurement method of grinding temperature . . . . . . . . . . . . . . Schematic illustration of open-top approach . . . . . . . . . . . . . . . . Clip-type thermocouple [60] . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principle of infrared temperature measurement . . . . . . . . . . . . . Main contents and key difficulties of grinding force modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of surface temperature in grinding zone and grinding point temperature of grains [160] . . . . . . . . . Schematic diagram of heat source distribution model . . . . . . . . Diagram of grinding heat generation and transfer [165] . . . . . . Thermal partition coefficient model based on grinding wheel/workpiece system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grain shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cutting depth of a single grain . . . . . . . . . . . . . . . . . . . . . . . . . . . Interference actions of grains in surface grinding . . . . . . . . . . . . Plastic-stacking mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEM of grinding debris and cards model . . . . . . . . . . . . . . . . . . Schematic diagram of the grain stress state . . . . . . . . . . . . . . . . . Result of scratch tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation laws of cutting efficiency (β) . . . . . . . . . . . . . . . . . . . . Calculation principle of grain cutting force calculation principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frictional force on rake face and sides of grains . . . . . . . . . . . . . Experimental setup of tribological tests . . . . . . . . . . . . . . . . . . . Results of tribological tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Static and dynamic active grains in grinding zone . . . . . . . . . . .

3 4 8 11 12 12 13 23 30 30 31 33 45 46 47 47 48 50 51 52 54 58 61 62 65

xvii

xviii

Fig. 2.14 Fig. 2.15 Fig. 2.16 Fig. 2.17 Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 3.4 Fig. 3.5 Fig. 3.6 Fig. 3.7 Fig. 3.8 Fig. 3.9 Fig. 3.10 Fig. 3.11 Fig. 3.12 Fig. 3.13 Fig. 3.14 Fig. 3.15 Fig. 3.16 Fig. 3.17 Fig. 3.18 Fig. 3.19 Fig. 3.20 Fig. 3.21 Fig. 3.22 Fig. 3.23 Fig. 3.24 Fig. 3.25 Fig. 3.26 Fig. 3.27 Fig. 3.28 Fig. 3.29 Fig. 3.30

List of Figures

Maximum undeformed chip thickness of dynamic active grains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dynamic active grains and ag in grinding zone . . . . . . . . . . . . . Process of grinding force predictive program . . . . . . . . . . . . . . . Predicted values and test results of grinding force . . . . . . . . . . . 3D model of debris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3D model of debris and cross sections at different cutting depths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cutting depths and swing angle of a single grain . . . . . . . . . . . . The cross section shape of debris at different swing angles . . . . Diagrams of the cutting depth function, cross section area function of debris and grinding force signal . . . . . . . . . . . . . . . . The cross section area function of debris based on grain boundary model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The cross section area function of debris based on furrow model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material deformation mechanism in the cutting zone . . . . . . . . . Stress analysis of the workpiece material in cutting zone . . . . . Strain rate under different grinding parameters and friction coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stress–strain curve under “velocity effect” . . . . . . . . . . . . . . . . . Debris forming mechanism under quasi static condition . . . . . . Debris forming mechanism under high strain-isothermal condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Debris forming mechanism under high strain condition . . . . . . Plastic-stacking mechanism and 3D morphology of furrow . . . Deformation mechanism and stress analysis of workpiece material at the grain edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Influence of different lubricating conditions on the velocity effect of material removal . . . . . . . . . . . . . . . . . . Experimental platform of single-grain grinding . . . . . . . . . . . . . Surface morphology of single diamond grain . . . . . . . . . . . . . . . Clamping of single diamond grain . . . . . . . . . . . . . . . . . . . . . . . . Grinding force measurement method in the single-grain cutting test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental methods of single-grain cutting . . . . . . . . . . . . . . Experimental methods of spindle cutting . . . . . . . . . . . . . . . . . . One-step method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-step method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of debris between single-grain cutting and ordinary grinding experiments . . . . . . . . . . . . . . . . . . . . . . . Debris morphology at different cutting speeds . . . . . . . . . . . . . . Calculation method of shear frequency . . . . . . . . . . . . . . . . . . . . Shear frequency under different cutting speeds . . . . . . . . . . . . . Debris morphologies at different lubricating conditions . . . . . .

66 67 69 71 77 77 78 80 82 82 83 85 85 88 89 89 90 90 91 92 93 95 95 96 97 97 98 99 100 101 102 104 105 106

List of Figures

Fig. 3.31 Fig. 3.32 Fig. 3.33 Fig. 3.34 Fig. 3.35 Fig. 3.36 Fig. 3.37 Fig. 4.1 Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 4.5 Fig. 4.6 Fig. 4.7 Fig. 4.8 Fig. 4.9 Fig. 4.10 Fig. 4.11 Fig. 4.12 Fig. 4.13

Fig. 5.1 Fig. 5.2 Fig. 5.3

Fig. 5.4 Fig. 5.5 Fig. 5.6 Fig. 5.7 Fig. 5.8 Fig. 5.9 Fig. 5.10

xix

Furrow morphologies at different lubricating conditions . . . . . . Furrow morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cutting efficiency under different working conditions . . . . . . . . Effect of cutting depth on cutting efficiency . . . . . . . . . . . . . . . . Signal image of cutting force of a single grain . . . . . . . . . . . . . . Calculation method of unit grinding force . . . . . . . . . . . . . . . . . Unit grinding force under different working conditions . . . . . . . Heat transfer coefficient ranges for several typical heat transfer methods [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation trend of heat transfer coefficient of cooling medium with grinding zone temperature [7] . . . . . . . . . . . . . . . . Convective heat transfer area of workpiece/cooling medium [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The discrete probability distribution of droplet size . . . . . . . . . . The continuous probability distribution of droplet size . . . . . . . Diagram of gas barrier layer on the abrasive tool surface . . . . . Airflow field around micro-abrasive tool . . . . . . . . . . . . . . . . . . . Several typical spray experiments . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of circular spray boundary . . . . . . . . . . . . . . Schematic diagram of elliptic spray boundary . . . . . . . . . . . . . . Sketch of parabolic spray boundary . . . . . . . . . . . . . . . . . . . . . . . Probability distribution of spray droplets . . . . . . . . . . . . . . . . . . Variation trend of minimum and maximum spreading droplet size with viscosity, surface tension, density and velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of in-pipe measuring device of convective heat transfer coefficient [1] . . . . . . . . . . . . . . . . . . Schematic diagram of measuring device for forced convective heat transfer in narrow annular channel [4] . . . . . . . Schematic diagram of convective heat transfer measurement device in the helical grooved tube with inner helical teeth [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measuring instruments of surface tension, contact angle and viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermophysical properties of pure normal saline and nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of solid–liquid-gas equilibrium of droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement system for convective heat transfer coefficient of nanofluids spray cooling . . . . . . . . . . . . . . . . . . . . Test curve of convective heat transfer coefficient . . . . . . . . . . . . Test curve of convective heat transfer coefficient of SiO2 nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measured and calculated values of convective heat transfer coefficients of nanofluids . . . . . . . . . . . . . . . . . . . . . . . .

107 108 109 110 111 111 112 121 121 122 124 125 127 127 128 129 130 130 133

136 144 145

146 149 150 151 154 155 157 158

xx

Fig. 5.11 Fig. 5.12 Fig. 5.13 Fig. 5.14 Fig. 5.15 Fig. 5.16 Fig. 6.1

Fig. 6.2 Fig. 6.3 Fig. 6.4 Fig. 6.5 Fig. 6.6 Fig. 6.7 Fig. 6.8 Fig. 6.9 Fig. 6.10 Fig. 6.11 Fig. 6.12 Fig. 6.13 Fig. 6.14 Fig. 6.15 Fig. 6.16 Fig. 6.17 Fig. 6.18 Fig. 6.19 Fig. 6.20 Fig. 6.21 Fig. 6.22

List of Figures

Dmin and Dmax of pure normal saline and nanofluids . . . . . . . . . Schematic diagram of liquid adsorption layer on the nanoparticle surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of energy migration due to micro-motion of nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of rotation motion of nanoparticles with different shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of rotating fluid microelements in nanofluids [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of heat transfer channels among nanoparticles [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overall research map for the dynamic model of temperature field in bio-bone micro-grinding with nanofluids spray cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of grinding tool-bone contact states . . . . . . Schematic diagram of instantaneous point heat source . . . . . . . Schematic diagram of mesh lines and mesh nodes in finite difference method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of thermal conductivity microelement . . . . Schematic diagram of heat conduction model and convective heat transfer in grinding interface . . . . . . . . . . . . Surface temperature in grinding zone and grinding point temperature of grains [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of heat source distribution model . . . . . . . . Comprehensive model of heat source distribution [19] . . . . . . . Schematic diagram of different heat source distribution models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy generation and consumption form in micro-grinding of bio-bone material . . . . . . . . . . . . . . . . . . . . Schematic diagram of effective cutting part of micro-grinding tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material removal volume by grains . . . . . . . . . . . . . . . . . . . . . . . Critical debris formation state of hard and brittle materials . . . . Surface area of materials newly formed by crack propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of cutting force for micro-grinding of bone materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Micro-grinding geometric model and temperature field model of bone materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature field model on the x–y surface . . . . . . . . . . . . . . . . Temperature field model on the x–z surface . . . . . . . . . . . . . . . . Heat distribution in grinding zone . . . . . . . . . . . . . . . . . . . . . . . . Diagram of grinding heat generation and transfer [25] . . . . . . . Thermal partition coefficient model based on grinding wheel-workpiece system [29] . . . . . . . . . . . . . . . . . . . . . . . . . . . .

159 160 161 161 162 163

168 170 172 174 175 178 181 182 185 186 188 190 192 192 194 196 197 198 198 199 200 203

List of Figures

Fig. 6.23 Fig. 6.24 Fig. 6.25 Fig. 7.1 Fig. 7.2 Fig. 7.3 Fig. 7.4 Fig. 7.5 Fig. 7.6 Fig. 7.7 Fig. 7.8 Fig. 7.9 Fig. 7.10 Fig. 7.11 Fig. 7.12 Fig. 7.13

Fig. 8.1 Fig. 8.2 Fig. 8.3 Fig. 8.4 Fig. 8.5 Fig. 8.6 Fig. 8.7

Fig. 8.8 Fig. 8.9

xxi

Flow chart for solving dynamic temperature field of bio-bone micro-grinding under nanofluids spray cooling . . . Thermal damage zone on x–y surface of bio-bone dry grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal damage zone on x–z surface of bio-bone dry grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental device setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of experimental data measurement process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main effects plot of S/N ratio for T . . . . . . . . . . . . . . . . . . . . . . . Main effects plot of S/N ratio for Ft . . . . . . . . . . . . . . . . . . . . . . Main effects plot of S/N ratio for U . . . . . . . . . . . . . . . . . . . . . . . Main effects plot of S/N ratio for Ra . . . . . . . . . . . . . . . . . . . . . . Main effects plot of S/N ratio for grey relational grade . . . . . . . Profile supporting length ratio curve tp (c) under different grinding parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEM morphology of workpiece under different grinding parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EDX analysis scheme of group 2–2 and group 2–6 . . . . . . . . . . Workpiece material removal mechanism under NMQL condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEM images of grinding debris under different conditions . . . . Histograms of material removal rate (Λw) and specific grinding energy (U) of workpiece under different grinding parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heat transfer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plane uniform gridding structure . . . . . . . . . . . . . . . . . . . . . . . . . Heat transfer state at node (i, 1) . . . . . . . . . . . . . . . . . . . . . . . . . . Effects of grinding surface temperature on the boiling heat transfer under NMQL condition . . . . . . . . . . . . . . . . . . . . . . Simulation phase diagram of grinding surface temperature field under NMQL condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation curves of grinding surface temperature field under different conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental equipments. (1) delivery pipeline, (2) oil storage cup, (3) Lubricants, (4) pressure regulator, (5) intake valve, (6) pressure control valve, (7) plunger pump, (8) grinding wheel, (9) Workpiece, (10) Dynamometer, (11) Staging, (12) temperature control valve, (13) hot end outlet, (14) gas inlet, (15) cold air outlet, (16) cold air nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of grinding force and grinding temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measuring equipments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

205 206 207 213 214 219 219 220 221 224 225 226 227 228 230

231 237 238 239 242 246 246

247 248 249

xxii

Fig. 8.10 Fig. 8.11 Fig. 8.12 Fig. 8.13 Fig. 8.14 Fig. 8.15 Fig. 8.16 Fig. 9.1 Fig. 9.2 Fig. 9.3 Fig. 9.4 Fig. 9.5 Fig. 9.6 Fig. 9.7 Fig. 9.8 Fig. 9.9 Fig. 9.10 Fig. 9.11 Fig. 10.1 Fig. 10.2 Fig. 10.3 Fig. 10.4 Fig. 10.5 Fig. 10.6 Fig. 10.7 Fig. 10.8 Fig. 10.9 Fig. 11.1 Fig. 11.2 Fig. 11.3

List of Figures

Relation curves of grinding temperature and time under different conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum grinding temperature under different conditions . . . Comparison between simulation and experimental results of workpiece surface temperatures . . . . . . . . . . . . . . . . . . . . . . . Specific grinding force under different conditions . . . . . . . . . . . Schematic diagram of boiling heat transfer in grinding zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface microtopography of workpiece . . . . . . . . . . . . . . . . . . . . Bottom surface topography of debris . . . . . . . . . . . . . . . . . . . . . . Specific grinding energy under different conditions . . . . . . . . . . Friction coefficients under different conditions . . . . . . . . . . . . . Lubrication effect of Al2 O3 nanoparticles in grinding zone . . . . Maximum grinding temperature under different conditions . . . Viscosity-temperature curves of Al2 O3 nanofluids . . . . . . . . . . . Contact angle measurement under different conditions . . . . . . . Two definitions of the atomization angle . . . . . . . . . . . . . . . . . . . Measurement of atomization angle under different conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ra and RSm values of workpiece surface under different conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEM images of surface microtopography of workpieces under different conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spreading and infiltration of nanofluid lubricants on the pipelines of the workpiece surface . . . . . . . . . . . . . . . . . . Heat transfer coefficients at a cold air fraction of 0.45 . . . . . . . . Phase diagram of simulation changes of the grinding zone at a cold air fraction of 0.45 . . . . . . . . . . . . . . . . . . . . . . . . . Simulation and experimental curves of maximum temperature in grinding zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . The simulation and experimental results of maximum temperature in grinding zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific grinding energy under different cold air fractions . . . . Temperature and viscosity curves of nanofluids sprayed into grinding zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of contact angle . . . . . . . . . . . . . . . . . . . . . . Curves of surface tension and contact angle of nanofluids . . . . . Gas flow sprayed into the grinding zone . . . . . . . . . . . . . . . . . . . Variation curve of grinding temperature under 0.5% of Al2 O3 concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum temperature of the grinding zone under different Al2 O3 concentrations . . . . . . . . . . . . . . . . . . . . . Specific grinding energy under different Al2 O3 concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

252 252 253 254 257 259 260 267 268 269 270 272 273 275 275 276 276 278 284 285 287 288 289 290 292 293 294 301 301 302

List of Figures

Fig. 11.4 Fig. 11.5 Fig. 11.6 Fig. 11.7 Fig. 12.1 Fig. 12.2 Fig. 12.3 Fig. 12.4 Fig. 12.5 Fig. 13.1 Fig. 13.2 Fig. 13.3 Fig. 13.4 Fig. 13.5 Fig. 13.6 Fig. 13.7 Fig. 13.8 Fig. 13.9 Fig. 13.10 Fig. 13.11 Fig. 13.12 Fig. 13.13 Fig. 13.14 Fig. 13.15 Fig. 14.1 Fig. 14.2 Fig. 14.3 Fig. 14.4 Fig. 14.5 Fig. 14.6

xxiii

Viscosity of Al2 O3 nanofluids with different concentration at 0 °C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contact angle of Al2 O3 nanofluids with different concentration at 0 °C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of “hot short circuit” of nanoparticle lap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of “filling blocking” effect of nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Antifriction mechanism of Al2 O3 /SiC mixed NPs on the grinding zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model of conical grinding grain . . . . . . . . . . . . . . . . . . . . . . . . . . The probability distribution of grain size . . . . . . . . . . . . . . . . . . Autocorrelation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross correlation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a Plane grinding setup and b MQL-fluid delivery system . . . . . Measurement of grinding forces . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of grinding force measurement signals under five working conditions . . . . . . . . . . . . . . . . . . . . . Grinding forces under different Al2 O3 /SiC mixing ratios . . . . . Grinding force ratios under different Al2 O3 /SiC mixing ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific grinding energies of MQL grinding using different nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Profile curves of workpiece surfaces under five different working conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Workpiece surface roughness (Ra) and SD of MQL grinding using different nanofluids . . . . . . . . . . . . . . . . . . . . . . . Workpiece surface roughness (RSm) and SD of MQL grinding using different nanofluids . . . . . . . . . . . . . . . . . . . . . . . The morphology of Al2 O3 in SEM [2] . . . . . . . . . . . . . . . . . . . . The channel of Al2 O3 in TEM [3] . . . . . . . . . . . . . . . . . . . . . . . . Atomic structure of SiC [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Physical encapsulation” of Al2 O3 and SiC . . . . . . . . . . . . . . . . Workpiece surface morphologies of MQL grinding using different nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Profile supporting length rate (Rmr) curve of Mix(1:2) and Mix(2:1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific grinding forces of different size ratios of Al2 O3 / SiC mixed nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Workpiece removal parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . Ra and SD of MQL grinding using different nanofluids . . . . . . RSm and SD of MQL grinding using different nanofluids . . . . . Profile supporting length rate curve . . . . . . . . . . . . . . . . . . . . . . . “Physical encapsulation” phenomenon of the Al2 O3 /SiC mixed nanoparticles with different grain sizes . . . . . . . . . . . . . .

304 304 306 307 315 317 318 323 324 330 331 335 336 336 338 340 341 341 344 344 345 346 348 349 356 357 358 358 360 362

xxiv

Fig. 14.7 Fig. 14.8 Fig. 14.9

Fig. 14.10

Fig. 15.1 Fig. 15.2 Fig. 15.3 Fig. 15.4 Fig. 15.5 Fig. 15.6 Fig. 15.7 Fig. 15.8 Fig. 15.9 Fig. 15.10 Fig. 15.11

List of Figures

Contact angle between nanofluid MQL droplets and workpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEM images of grinding debris in different working conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross correlation function curves and cross correlation coefficient curves of profiles among different workpiece surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross correlation function curves and cross correlation coefficient curves at two different points on the same workpiece surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Utilization of experimental equipments and visualization of the experimental sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mean and SD of grinding force in 9 groups of experiments . . . Main effect diagram of S/N ratios for tangential sliding force F t, sl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main effect diagram of S/N ratios for normal sliding force F n, sl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main effect diagram of S/N ratios for micro friction coefficient μ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main effect diagram of S/N ratios for surface roughness Ra . . . Main effect diagram of S/N ratios for surface roughness RSm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PSDF curves of five experimental conditions . . . . . . . . . . . . . . . The air barrier layer on grinding wheel surface . . . . . . . . . . . . . SEM morphology and EDS of workpiece surface in five experiments for verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SEM morphology and EDS of grinding debris in five experiments for verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

363 365

366

368 374 377 378 379 380 381 381 387 389 390 392

List of Tables

Table 1.1 Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 2.6 Table 3.1 Table 3.2 Table 4.1 Table 4.2 Table 4.3

Table 5.1 Table 7.1 Table 7.2 Table 7.3 Table 7.4 Table 7.5 Table 7.6 Table 7.7 Table 7.8 Table 7.9 Table 7.10

Common test methods of grinding temperature . . . . . . . . . . . . Elemental composition of 440C material . . . . . . . . . . . . . . . . . Parameters of β(ag) (95% confidence bounds) . . . . . . . . . . . . . Grain stages and force equations . . . . . . . . . . . . . . . . . . . . . . . . Parameters of corundum grinding wheel disk . . . . . . . . . . . . . Parameters of Tribological tests . . . . . . . . . . . . . . . . . . . . . . . . Input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fitted values of parameters and confidence interval . . . . . . . . . Experimental scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convective heat transfer coefficient values in different heat transfer areas [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input parameters for the calculation of spray convective heat transfer coefficient of SiO2 -saline nanofluids . . . . . . . . . . Output parameters for the calculation of spray convective heat transfer coefficient of SiO2 -saline nanofluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermophysical properties of nanoparticle block materials and base fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grinding experimental parameters . . . . . . . . . . . . . . . . . . . . . . Elemental composition of Ti-6Al-4 V . . . . . . . . . . . . . . . . . . . . Physical properties of Al2 O3 nanoparticles . . . . . . . . . . . . . . . Factors and levels of grinding process parameters . . . . . . . . . . L16 Orthogonal experimental table . . . . . . . . . . . . . . . . . . . . . . Experiment values and their corresponding S/N ratios (dB) of each factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Response table for S/N ratios of each factor . . . . . . . . . . . . . . . The calculated grey relational grade among S/N ratios of different indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Response table for S/N ratios of the grey relational grade . . . . Experimental design for verification . . . . . . . . . . . . . . . . . . . . .

10 50 53 54 61 62 70 83 100 123 136

137 149 214 214 215 215 216 217 218 223 223 224

xxv

xxvi

Table 7.11 Table 8.1 Table 8.2 Table 8.3 Table 8.4 Table 8.5 Table 8.6 Table 8.7 Table 8.8 Table 8.9 Table 8.10 Table 8.11 Table 10.1 Table 10.2 Table 10.3 Table 13.1 Table 13.2 Table 13.3 Table 13.4 Table 13.5 Table 14.1 Table 15.1 Table 15.2 Table 15.3 Table 15.4 Table 15.5 Table 15.6 Table 15.7 Table 15.8 Table 15.9 Table 15.10

List of Tables

The mechanical properties under different grinding parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Given parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature and heat transfer coefficient of grinding zone under different conditions . . . . . . . . . . . . . . . . . . . . . . . . . Parameters of K-P36 grinder . . . . . . . . . . . . . . . . . . . . . . . . . . . Dressing parameters of grinding wheel . . . . . . . . . . . . . . . . . . . Element composition of Ti-6Al-4 V . . . . . . . . . . . . . . . . . . . . . Physical characteristics of Ti-6Al-4 V . . . . . . . . . . . . . . . . . . . Composition and boiling point of the synthesis lipid . . . . . . . . Physical properties of Al2 O3 nanoparticles . . . . . . . . . . . . . . . Grinding experimental parameters . . . . . . . . . . . . . . . . . . . . . . Fluid temperature and gas flow at nozzle outlet . . . . . . . . . . . . Given parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grinding experimental parameters . . . . . . . . . . . . . . . . . . . . . . Chemical components of Ni-based alloy chemical composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristics of Al2 O3 and SiC particles material . . . . . . . . Grinding process parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . Dressing parameters of grinding wheel . . . . . . . . . . . . . . . . . . . Experimental design for the effect of Al2 O3 /SiC mixing ratio on lubrication performance of nanofluid MQL . . . . . . . . Experiment schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Levels of grinding factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L9 orthogonal array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corresponding S/N ratios for the observations . . . . . . . . . . . . . ANOVA results for F t,sl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ANOVA results for F n,sl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ANOVA results for μ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ANOVA results for Ra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ANOVA results for Rsm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental design for verification . . . . . . . . . . . . . . . . . . . . . The area coefficients (S) and proportionality coefficients (K) of PSDF curves in different frequency bands . . . . . . . . . .

225 241 242 245 247 249 249 249 249 250 251 251 283 284 286 331 331 332 332 333 355 375 375 376 383 383 384 384 384 386 387

Chapter 1

Introduction

1.1 Introduction Grinding is one of the most basic machining forms. It is particularly important that the ultimate precision and surface quality of most parts are guaranteed by the grinding process. High circumferential velocity of grinding wheel and high energy consumption (specific grinding energy) are the most characteristic features of grinding. Grinding is negative rake cutting with the grains on the grinding wheel surface and its energy consumption for removal of unit volume of materials is far higher than those in other machining techniques [1, 2]. Most energy produced in the grinding zone are transformed into heats and dissipated onto debris, grinding wheel and workpiece [3]. Since grinding is different from other machining forms, each grain contact with workpiece for an extremely short period under the high circumferential velocity of grinding wheel and the volume of debris produced during grinding is very small, thus resulting in the significantly low proportion of produced heats carried away by debris [4]. The high energy density of grinding zone has significant influences on surface quality and usability of workpiece. In particular, it may cause thermal damages (oxidation, burn, residual tension and cracks of surface) of the workpiece surface when the grinding zone temperature exceeds the critical value. These will lead to reduction in anti-fatigue and anti-wear performances of parts, thus shortening service life and decreasing reliability of parts, accompanied with reductions in the grinding performance and machining precision of grinding wheels [5, 6]. With the heat accumulation on workpiece surface, the size precision and shape precision are significantly poor due to influences by the grinding heats [7]. Grinding is generally the ultimate machining procedure of parts. Grinding technology and technique determine the ultimate precision and surface quality of parts. Hence, it is necessary to adopt effective measures to lower and even eliminate influences of grinding heats on machining precision and workpiece surface quality. Controlling grinding zone temperature and decreasing thermal damages of the workpiece surface effectively are important topics to study the grinding mechanism and improve surface integrity of the processing parts. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_1

1

2

1 Introduction

1.1.1 Flooding Grinding To lower grinding zone temperature effectively, injecting grinding fluid into the grinding zone at a mass flow is called flooding cooling. Due to the existence of a layer of “air barrier” surrounding the grinding wheel which moves at a high speed, flooding liquid supply is often difficult to enter into the grinding zone [7, 8] and the “effective flow rate (the ratio between the liquid volume actually entering into the grinding interfaces and the total liquid supply)” is on 5–40% [9, 10]. As a result, most of grinding fluid actually cannot arrive at the grinding interface, but only serve for cooling the workpiece base at surrounding zones. As a result, the traditional fluid supply mode has insufficient cooling ability, thus resulting in grinding burns and degrading surface integrity of workpieces [8, 9]. Besides, a lot of the supplied grinding fluid may form fluid introduction force and hydrodynamic pressure at the wedged spaces between grinding wheel and workpiece [11], thus triggering deflection deformation of the grinder spindle and further decreasing the practical cutting depth [3]. Hence, the traditional flooding liquid supply method not only brings great shape and size errors of the processing workpieces [12, 13], but also incurs a considerable waste of grinding fluids. With the issuing and enforcement of environmental protection laws in countries around the world and establishment of the ISO14000 environmental management system, new requirements are proposed to processing techniques and levels of the machining level. Moreover, the industrial circle and scientific researchers are forced to re-evaluate the flooding cooling lubricant grinding technique. Danobat, a Spanish grinding machine manufacturer, investigated the costs of grinding fluid (Fig. 1.1). Results [14] showed that machining cost, cutter cost and cooling liquid cost accounted for 75, 7 and 18% of total costs of part machining, respectively. Clearly, the cooling liquid cost accounted for nearly 1/5 of total costs and it was 2–3 times that of cutter cost. In the total cooling liquid cost, the cooling liquid supply and filtering devices accounts for 40%, accompanied with 22% of sewage treatment cost, 10% of labour cost, 14% of coolant base fluid, 7% of energy cost, and 7% of other costs. Obviously, the proportion of coolant base fluid in cooling liquid cost is very small, but other costs related with cooling liquid account for a very high proportion. Due to perfection and strict requirements of environmental protection laws, the expenses for cooling liquid treatment is going to climb up continuously. As a result, the proportion of cooling liquid cost in the total machining cost will increase gradually. What is more serious is that the abundant oil mist and PM2.5 suspended particles which are produced in many process, such as violent impacts between cutting fluid and high-speed rotating cutter and high-temperature evaporation, have caused terrific harms to the natural environment and human health [15, 16]. The technological difficulties caused by traditional flooding lubrication are shown in Fig. 1.1. Green development is an international trend. Resource and environmental issues are challenges that human beings are facing with together, and sustainable development is increasingly becoming a global consensus. In particular, facilitating green growth and implementing new green policies are common choice of the global major

1.1 Introduction

3

Fig. 1.1 Problems of traditional flooding lubrication technique

economic entities to cope with international financial crisis and climate changes. Developing green economy and seizing the commanding heights of global competition in future have become important national strategies. Developed countries begin to implement the “re-industrialization” strategy successively, and re-create new competitive edges of the manufacturing industry. The influences of green concepts, policies and regulations, such as cleaning, high efficiency, low carbon and recycling, are improving continuously. The resource and energy utilization has become an important factor to measure competitiveness of the national manufacturing industry. Green trade barrier also becomes an important mean for some countries to seek competitive edges. Green manufacturing is an essential way to realize industrial transformation and upgrading. As a manufacturing power, China is still struggling with the high-input, high-consumption and high-emission development mode, and it still has great gaps with international advanced level in resource and energy consumption and pollutant emissions. SO2 , nitric oxides and dust emissions from industries account for 90, 70 and 85% of total emissions, and the carrying capacity of resources and environment has reached its limits. It is urgent to accelerate and facilitate green development of the manufacturing industry. Driven by green manufacturing project, implementing green manufacturing comprehensively not only has important practical effects to relieve the current resource and environmental bottlenecks and constraints and accelerate to train new economic growth points, but also has profound historical significance to accelerate transformation of economic development mode, promote industrial transformation and upgrading, and improve international competitiveness of the manufacturing industry [17–20]. The key task in green transformation of traditional manufacturing industry lies in cleaning transformation in the production process. Based on reduction of pollutant production from the source, the traditional production technological equipments are reformed and enterprises are encouraged to adopt the applicable advanced cleaning production techniques and technologies for upgrading and transformation. The green

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1 Introduction

transformation of basic manufacturing technology advocates green machining techniques with few or no cutting fluids. By the end of 2020, it can save energy by more than 30%, and save materials and decrease wastes by more than 20%. The Made in China 2025 Initiative stimulates clearly that green manufacturing engineering is one of five key construction projects. (1) Implement specific technological transformation of traditional manufacturing industry, such as improving energy efficiency, clean production, water-saving pollution control, recycling, and so on. (2) Set examples of great energy-saving and environmental protection, comprehensive resource use, remanufacturing, and low-carbon technological industrialization. (3) Implement the plan to improve clean production level in key areas, river basins and industries, and promote solidly special projects of atmosphere, water and soil pollution source control. (4) Establish standard systems for green products, green factories, green parks and green companies, and make green evaluation. (5) By 2020, a thousand green demonstration factories and a hundred green demonstration parks have been built. An inflection point occurred in the energy and resource consumption of some heavy chemical industries and the major pollutant emission intensity of key industries decreased by 20%. (6) By 2025, the green development of manufacturing industry and unit consumption of major products will reach the global advanced level and the green manufacturing system will be established basically. Traditional flooding lubrication machining no longer fits the concept of sustainable development and even becomes a technological bottleneck [21, 22] against high-efficiency and high-quality machining of emerging materials (e.g. difficultto-process materials [18] and medical ceramics [19, 20]) due to its disadvantages, including environmental pollution, threats to physical health of operators as well as high expenses for use and disposal. Therefore, research and development of new green machining methods have become a hotspot and a key challenge since the new century. Nowadays, researchers have proposed many green machining methods (Fig. 1.2) based on two ideas: one is to decrease the consumption of cutting fluid or abandon it, and the other is to replace cutting fluid with “green media”.

Fig. 1.2 Different kinds of green manufacturing methods and their characteristics

1.1 Introduction

5

1.1.2 Dry Grinding Dry cutting is a green process technology and it is firstly applied to the automobile industry. In the beginning, Professor F. Klocke from the Aachen Polytechnic University in Germany made a keynote speech on CIRP conference in 1997, which claimed that the successful application of dry processing in machining brings new prospects to green processing technology [23]. Dry processing do not use cutting fluid in the machining while guaranteeing the service life of cutter and precision of parts [24, 25]. Now, researchers have carried out experimental studies on dry processing of multiple workpiece materials, including cast iron, steel, aluminium and even titanium (Ti) alloy /aluminium (Al) alloy [26–28]. These studies cover many basic machining forms, such as turning, drilling, milling and grinding. Some research results demonstrate that dry processing has following advantages, improving environmental protection during processing, decreasing processing costs, avoiding harms to physical health of operators, etc. Due to the lack of direct lubrication with cutting fluids, it proposes higher requirements to the cutter and machine tool for dry processing to replace the cooling lubrication effect of cutting fluid and achieve equivalent workpiece surface quality. Cutters for dry cutting often need higher tenacity, hardness and anti-wear properties, and are able to get a low friction coefficient on the cutter surface. Nevertheless, dry processing has irreparable shortcomings that restrict its further application to machining. In dry processing, friction and adhesion of the cutterworkpiece interface occur due to the lack of lubrication [29]. The workpiece temperature increases due to the production of abundant frictional heats, thus shortening the service life of cutter and degrading processing quality of workpiece significantly [30, 31]. In particular, the processing zone temperature of dry grinding with abundant frictional heats is above 500 °C and even can reach 1000 °C [32, 33], which is inevitable to cause serious burns on workpiece surface [34]. With the development of machining technology, the cutting/grinding speed increases and processing requirements of new workpiece materials (e.g. high-temperature Ni-based alloy [35] and Ti alloy [36]) are increasing continuously. The dry processing technology has to be further studied [37].

1.1.3 Cryogenic Cooling Grinding According to current literature review, low-temperature cooling lubrication mainly includes following modes: low-temperature pre-processing of workpiece, indirect low-temperature cooling, low-temperature gas jet, low-temperature treatment, etc. Low-temperature gas jet is a cooling lubrication mode which is extensively studied at present. In low-temperature gas jet, the low-temperature (< −180 °C) gas media are sprayed into the cutting zone/grinding zone [38] for cooling [39]. Compared

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1 Introduction

with high-pressure gas and steam, low-temperature gas media have stronger cooling ability [40, 41]. Now, researchers are trying to use different kinds of gases as cooling media of machining, including argon, helium, CO2 and N2 [42]. In machining forms of turning, milling and grinding, researchers all have investigated cooling lubrication effect of low-temperature cooling through many experiments [43]. According to experimental results, low-temperature cooling technology contributed better workpiece surface quality, longer service of cutters and better cooling lubrication effect than dry grinding/cutting [44]. Nevertheless, the machining process of low-temperature cooling technology is basically similar with that of flooding lubrication technology, without obvious economic advantages [45]. Besides, low-temperature cooling technology is still immature to be applied to grinding. In particular, further studies concerning antiwear and anti-friction mechanism, material removal mechanism and optimisation of technological system are still needed to apply low-temperature cooling technology to grinding of difficult-to-process materials [46]. Besides, the use and storage of media like liquid nitrogen and CO2 may increase the costs. The most dangerous thing is that it may cause asphyxia of operators once N2 or CO2 concentration in air is too high. This proposes higher requirements on preventive measures for the use of low-temperature cooling technology. As a result, the further applications of low-temperature cooling lubrication are limited [47, 48].

1.1.4 MQL Grinding The minimum quantity lubrication (MQL) technology between the flooding grinding and dry grinding is to use the grinding fluid to the minimum extent under the premise of satisfying cooling and lubrication performances [49]. Specifically, two-phase flows are formed by mixing minimum quantity of lubricating fluid into the high-pressure gas. The lubricating fluid and high-pressure airflow (4.0–6.5 bar) are mixed and atomized, and then enter into the high-temperature grinding zone [50]. The high-pressure airflow serves for cooling and debris removal. MQL grinding fluid forms a lubricating oil film on the grinding wheel-workpiece interface to provide lubrication effect [51]. MQL grinding inherits the advantages of dry grinding and flooding grinding and the lubrication effect has extremely small differences from that of flooding grinding [52]. Grinding fluid usually uses vegetable oil with excellent biodegradability as the base oil [53]. In the traditional flooding cooling lubrication, the flow rate of grinding fluid is 60 L/h per width of grinding wheel, but it decreases to 30–100 ml/h (1/ 1000) [54] in MQL. Therefore, MQL grinding improves the working environment and decreases pollution to natural environment significantly. It is a high-efficiency and low-carbon processing technology. However, some study [55] has demonstrated that the cooling performances of high-pressure airflow in MQL are too limited to meet the heat exchange requirement under the environment with a high grinding zone temperature. The processing quality of workpieces and service life of grinding wheel

1.1 Introduction

7

still in MQL grinding have some gaps with those in traditional flooding grinding. The MQL grinding still has to be further developed [56].

1.1.5 Nanofluids MQL Grinding Nanofluids Minimum Quantity Lubrication (NMQL) is a new high-efficiency, lowconsumption, clean, low-carbon precise grinding mode to solve bottlenecks of MQL applications [57]. Specifically, a certain proportion of nanoparticles are mixed fully into MQL fluid to prepare nanofluids which are atomized through the compressed gas and then sprayed to the grinding zone through the nozzle. The grinding method that nanoparticles participate in heat transfer enhancement [58] not only inherits all advantages of MQL grinding, but also improves the heat exchange capability of traditional MQL grinding significantly. Due to the excellent anti-wear and antifriction properties, nanoparticles can improve the lubrication performances of the grinding wheel-debris interface and grinding wheel-workpiece interface [59], thus enabling to improve the machining precision and surface quality, especially surface integrity of workpieces greatly. Meanwhile, the working environment is improved. As a result, NMQL is expected to be a green sustainable grinding method with high performances in resource saving, environmental protection and energy utilization [60].

1.1.6 Thermodynamic Action Laws in NMQL Grinding Grinding force/heat mainly comes from elastoplastic deformation, debris production and frictional behaviors of workpieces under the action of grains. The value of grinding force/heat is related with grinding telecontrol parameters, grains and properties of workpieces. Grinding force/heat is the most important parameter in the grinding process and can influence workpiece surface quality, service life of grinding wheel, power consumption and grinding stability directly. Hence, grinding force/heat is usually used to analyse and diagnosis of grinding conditions. The formation mechanism, control methods and precise prediction of grinding force/heat are always the top research priorities in the field of grinding. The requirements on grinding performances are promoted to new heights as a response to the increasing requirements on performances of new material workpieces (especially high-temperature alloys, Ti alloys and carbon fibre) for aerospace, rail transportation and other application fields. Grinding force/heat control also becomes a technological challenge. Several new techniques to improve grinding performances and decrease grinding force have been tried by scholars, such as changing structures of grinding wheel (e.g. grooving grinding wheel and engineering grinding wheel), improving grinding parameters (e.g. creep feed grinding, high-speed/ ultrahigh-speed grinding and microgrinding), and different cooling lubrication modes (dry grinding,

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1 Introduction

flooding lubrication, low-temperature cold air lubrication, solid lubrication, MQL and NMQL). Based on the fundamental perspective of anti-wear and anti-friction on the grinding wheel-workpiece interface and grinding wheel-chip interface, NMQL controls the grinding force and improves grinding performances more effectively, without changing the original cutting efficiency. Therefore, NMQL is one of the most effective modes. Nanofluids are carried by the compressed gas and sprayed as fine mist drops from the nozzle. Nanoparticles which are suspending in grinding fluid and have a size of 1–100 nm are easier to enter into the grinding wheel-workpiece interface due to the small size effect and high surface energy. With the great potentials of nanoparticles in increasing heat conduction and convective heat transform as well as improvement of anti-friction and lubrication performances, nanofluids increase the heat exchange capacity and decrease wearing of the grinding wheel. Therefore, NMQL not only lowers the grinding force and grinding zone temperature, but also improves grinding performances and workpiece surface quality.

1.1.7 Measurement Methods of Thermal Parameters in NMQL Grinding For NMQL grinding, researchers are focusing on experimental studies of grinding forces under different technological parameters, optimization of grinding force/heat control parameters of typical workpiece materials as well as theoretical modelling and numerical simulation of grinding force/heat. In plane grinding experiments, threeway grinding force dynamometer is often applied to measure and record normal force, tangential force and axial force. The piezoelectric transducer of the dynamometer transforms force signals into electrical signals and then amplified by the charge amplifier. Electrical signals are then collected by the data acquisition unit at a certain sampling frequency and input into the “grinding force dynamic test system” for filtering. Finally, image files and data files of grinding force are gained (Fig. 1.3) [60].

1. nozzle, 2. grinding wheel, 3. workpiece, 4. measuring cell, 5. workbench, 6. data acquisition system, 7. Computer, 8. axial force, 9. tangential force, 10. normal force.

Fig. 1.3 Measurement method of grinding force [60]

1.1 Introduction

9

Grinding temperature is a generic term of workpiece temperature rise caused by grinding heats during machining. From the perspective of grinding heat effect, each grinding abrasive under working can be viewed as a point heat source which generates heats continuously. During grinding, the temperature on workpiece surface near the contact arc of grinding wheel rises, which is the result of the comprehensive actions of dispersed point heat sources in the contact arc [61]. To deepen studies on grinding temperature, it is further divided into temperature of different parts according to requirements in engineering studies, including overall average temperature of workpiece, workpiece surface temperature, grinding zone temperature of the grinding wheel, grinding point temperature of grains, etc. The measurement methods of grinding temperature in previous studies in the recent decades are summarized in Table 1.1 [62]. Chinese and foreign scholars have carried out a lot experiments and studies to get relatively accurate grinding temperature. The measurements methods of grinding temperature are generally divided into two types: direct contact temperature measurement methods and non-contact temperature measurement methods (Fig. 1.4). 1. Direct contact temperature measurement methods—coating temperature measurement method Coating temperature measurement method is to clip a piece of high-temperature coating material between two separated workpieces and then determines temperature by observing changes of the coating materials after grinding. This method is advantageous for applicability to all workpiece materials, no need of grooves or holes on workpiece, and no damage of workpiece integrity. It gets one isotherm from one experiment rather than temperature of one point, and it is applicable to measure materials with relatively high temperature [65]. This method also has obvious disadvantages: a series of complicated operations are needed after grinding to measure temperature, such as observing coating changes under a microscope, deducing phase changes, and so on. Considering the great gradient of grinding temperature and short grinding time, it is very difficult for the coating method to get accurate grinding temperature and cannot test temperature changes in the grinding process [76]. 2. Direct contact temperature measurement methods—thermocouple temperature measurement method In practical applications, the traditional thermocouple thermometry is the most common measurement method of grinding temperature and it is the only method that can measure grinding zone temperature so far. Thermocouple thermometry generally drills milling grooves or holes on workpieces, in which wire or foil of thermocouple is clipped or buried. The thermocouple wire is separated from the ontology by insulating materials. It is turned on and off by using epoxy resin bonding. Thermocouple nodes are formed by grinding heats produced during grinding. Due to the thermo-electric effect, the thermocouple will output thermoelectric potentials which are processed by the amplification and acquisition systems to get the temperature signals [89]. Thermocouple temperature measurement method transforms grinding temperature signals into electromotive force signals by using a thermocouple, then amplifies

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1 Introduction

Table 1.1 Common test methods of grinding temperature Types

Significance

Measurement methods

Overall average temperature of workpiece

The increasing overall average temperature of workpiece influences the size and shape precisions of parts

1. Artificial thermocouple tests the ground surface temperature 2. Artificial thermocouples are buried to test temperature inside the workpiece 3. Thermocolor tests temperature distribution on side surface of workpiece

Workpiece surface temperature

The two-dimensional temperature distribution of workpiece surface along the cutting depth and feeding direction influences the affected layer, cracks and residual stress of part surface

1. Measurement method of drilling holes and burying semi-artificial thermocouples 2. Measurement method of drilling holes and burying artificial thermocouples 3. Infrared measurement method of drilling holes and burying optical fibre

Grinding zone temperature of Temperatures on the contact grinding wheel arc surface between grinding wheel and workpiece are directly related with surface burns and cracks of parts

1. Measurement method of block specimens clipping wire 2. Measurement method of two grinding wheels clipping a piece of foil 3. Infrared measurement method

Grinding point temperature of The average temperature at the 1. Measurement method of grains contact point between cutting natural thermocouple edge of grains and workpiece composed of grinding influences wearing and wheel and workpiece breakage of grains, as well as 2. Measurement method of block specimens clipping chemical reaction between wires grains and workpiece materials

the electromotive force signals, inputs into a computer through digital-to-analog conversion, and finally gets the measured grinding temperature through a special software analysis. Since the workpiece speed is very high during high-speed and high-efficiency grinding, the action time of heat source on the thermocouple is very short. It is impossible for the thermocouple to reach the temperature at thermal balance due to its thermal inertia. At this moment, it is necessary to have a dynamic calibration of thermocouple [90]. Thermocouple temperature measurement method can be divided into two major types, namely, the open-top method and clip-type method. The later one can be further divided into artificial type and semi-artificial type [90].

1.1 Introduction

11

Fig. 1.4 Measurement method of grinding temperature

The basic principle of the open-top method is shown in Fig. 1.5. One or several stepped holes (for several temperature measurement of the same workpiece) are drilled on the workpiece, in which the prepared thermocouple is put and fixed. During grinding, the distance between the hole and top surface is changing. Therefore, thermoelectric potentials output by each grinding process reflect temperatures at different depths under the grinding surface. Nevertheless, it measures the temperatures after being transmitted by the workpiece material and the insulation layer since the thermocouple is put below the contact surface. Since the thermal properties of the insulation layer are often ignored, some errors are produced. Besides, there’s a great and nonlinear gradient of temperature near the grinding surface and grinding temperature can only be deduced from measurement results, thus influencing measurement accuracy of temperature [61]. The clip-type method generally drills a milling groove or hole on the workpiece, in which foil or wire of the thermocouple is clipped or buried. Due to plastic deformation and relatively high grinding temperature during cutting, the workpiece and thermocouple wire form an overlap joint at top or are welded into a thermocouple node after grinding, outputting thermoelectric potentials. Such thermoelectric potentials are then processed by amplification and acquisition systems to get the temperature signals (Fig. 1.6). The open-top method and clip-type method have a common structural defect. They both destroy the integrity of workpieces, which lead to different practical heat transfer from heat transfer of physical components, thus influencing authenticity of

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1 Introduction

1. grinding wheel, 2. fixture, 3. workpiece, 4. thermocouple, 5. charge-amplifier, 6. D/A, 7. computer.

Fig. 1.5 Schematic illustration of open-top approach

1. nozzle, 2. MQL fluid, 3. grinding wheel, 4. workpiece, 5. thermocouple, 6. grinding depth, 7. pre-machined slots, 8. 10μm thick mica

Fig. 1.6 Clip-type thermocouple [60]

the measured temperature [91]. Besides, the open-top method measures the temperature after being transmitted by the workpiece material and the insulation layer since the thermocouple is put below the contact surface. Since the thermal properties of the insulation layer are often ignored, some errors are produced. Besides, there’s a great and nonlinear gradient of temperature near the grinding surface and grinding temperature can only be deduced from measurement results, thus influencing measurement accuracy of temperature [61]. The thermocouple node formed in the clip-type method always has some thickness. In other words, the damage of insulation layer always has some depth and it does not reflect the real surface temperature. Thermocouple temperature measurement methods also have some requirements on workpiece materials. For example, they are inapplicable to some brittle materials which are difficult for drilling. 3. Non-contact temperature measurement method Since temperature is composed of heat flows. Heat is a kind of energy and it is the function to form elementary particles of substances. Temperature expresses the disturbance degree of these particles. The greater disturbance leads to the greater

1.2 Research Significance

13

Fig. 1.7 Principle of infrared temperature measurement

fluctuation of the produced electromagnetic field, that is, the higher temperature and the greater energy emitted by radiation. This is the major basis of infrared temperature measurement. At present, there are four major infrared temperature measurement technologies, including infrared thermal imaging temperature measurement, infrared radiation temperature measurement, optical infrared temperature measurement and two-colour infrared temperature measurement. The basic principle of infrared temperature measurement is shown in Fig. 1.7. The exothermic target produces infrared radiation and the quantity of infrared radiation energy within its scope which is determined by the optical parts and positions of the thermometer is captured through an optical system [92]. The infrared energy focusing on the photoelectric detector is transformed into corresponding electrical signals which are then processed by the signal amplifier and signal processor. The loop is transformed into temperature value of the testing target after calibration by internal algorithms of instruments and target emissivity. The temperature value is displayed and output by special processing software.

1.2 Research Significance NMQL grinding technology provides a new idea to green grinding with high surface quality in aerospace, rail transportation and other fields. It has become one of the most important manufacturing technological schemes under the national development strategy based on green manufacturing. However, some problems about the origin of science still remain in term of thermodynamic action laws of the new MQL technology involving nanoparticles, heat transfer enhancement, anti-wear and antifriction in the grinding zone: (1) the internal relationship between thermal conductivity of nanoparticles and heat exchange capability of nanofluids under high-pressure and high-speed gas–liquid-solid jet conditions? (2) How do particles impact mutually and disturb the heat transfer mechanism under influences of carrying fluid and Brownian force? How to form convective enhanced heat transfer between the jet and high grinding zone temperature in an extremely short period? (3) The variation laws of heat/force boundaries of grinding zone in NMQL and the material removal mechanism under influences of technological parameters, velocity effect and size effect; (4) The dynamic temperature field prediction model and grinding force prediction model

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1 Introduction

on the grinding wheel-workpiece constrained interface; (5) the dynamic macroscopic capillary/microtexture network on the grinding wheel-workpiece wedged constrained interface, formation mechanism of dynamic microscopic capillaries and dynamic model of microdroplet transport. Solving above scientific problems of thermodynamic action laws has important scientific significance and application values to initiative parameter design, optimization and high surface quality for grinding schemes of new materials and difficult-to-process materials.

1.3 Research Status in Thermodynamic Action Laws During Grinding Now, many single-factor experimental studies on NMQL grinding of different workpiece materials have been reported to explore methods to decrease grinding force/heat and technological optimization scheme. Firstly, the feasibility of technologies was investigated through verification experiments under different working conditions. Subsequently, studies on parameter optimization, including base solution of nanofluids, nanoparticles, nanofluid concentration and jet parameters were carried out to find the technology optimization scheme. Furthermore, performance enhancement approaches of NMQL grinding, including ultrasonic assistance, electrostatic assistance and low-temperature coupling were explored. Chinese and foreign scholars have made considerable contributions and the research results are gradually increasing in quantity and attract extensive attention.

1.3.1 Research Status in China In early studies, Chinese scholars focused on applications of MQL technology in cutting process, which provided references to study NMQL grinding The research team led by Professors Ning He and Liang Li from Nanjing University of Aeronautics and Astronautics (NUAA) [93] constructed a MQL atomization model based on the atomization mechanism and constructed a simulation model for commercial MQL nozzle structure. They investigated influences of air supply pressure on atomization effect through a numerical simulation of atomization of MQL oil by using Fluent software, and also carried out an experimental verification. Results showed that grain size of oil mist decreased with the increase of air supply pressure and the built atomization model presented high degree of fitting with the test data in experiments. Zhao et al. [94] carried out a relatively systematic study. They measured and analysed oil mist concentration in the cutting field under MQL conditions based on the gravimetry and discussed influencing laws of MQL system parameters like lubricant consumption, air supply pressure, jet range, jet temperature and lubricating

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oil properties on oil mist concentrations of PM10 and PM2.5 in the cutting field. Results demonstrated that lubricant consumption is the primary factor influencing oil mist concentration in cutting field and the oil mist concentration increased significantly with the increase of lubricant consumption. With the increase of air supply pressure and the decrease of jet range, the oil mist concentration increased accordingly. The jet temperature influenced the atomization effect by influencing viscosity of lubricant. The viscosity of lubricant decreased under a low temperature, thus decreasing the oil mist concentration accordingly. Physical properties of lubricant, such as viscosity and flow point, could influence the atomization effect directly. The lubricant with a high viscosity has poor atomization effect, thus decreasing oil mist concentration. Under low-temperature MQL conditions, the lubricant with a high flow point has poor atomization effect, which also leads to the low oil mist concentration. The team led by Professor Songmei Yuan from Beijing University of Aeronautics and Astronautics (BUAA) carried out an experimental study on milling of highstrength steel by using hard alloy cutters [95]. According to comparison and analysis of test data, they found that low-temperature MQL cutting could inhibit production of sticking substances at blades and thereby prolong the service life of cutters. Given the same cutting parameters, low-temperature MQL technology could decrease the cutting force and thereby decreases power consumption by the machine shaft and production of cutting heats [96]. The low-temperature MQL cutting could get better surface quality than dry cutting. Professor Songmei Yuan further carried out an orthogonal experimental study on the nozzle direction of low-temperature MQL technology [41], in which the importance degrees of 3 parameters of nozzle direction (β, α and d) on cutting performances were discussed. The team led by Professor Ming Chen from Shanghai Jiaotong University (SJTU) [97] conducted an experimental study on MQL milling of Ti alloy, in which the wearing rate, wearing laws and wearing mechanism of cutters were explored. Results demonstrated that MQL had more significant cooling and lubrication effects than dry cutting, and it prolonged the service life of cutters significantly. Professor Xiangming Huang from Hunan University [98, 99] conducted a grindhardening test of 40 Cr steel by using MQL technology and investigated influences of lubrication cooling techniques (e.g. grinding fluid supply mode, MQL jet flow and air pressure) on depth of the grind-hardening layer, surface microhardness and surface roughness. He concluded that increasing MQL jet flow and air pressure were both conducive to increase surface hardness of the grind-hardening layer and decrease surface roughness. The team led by Changhe Li from Qingdao University of Technology carried out systematic studies on thermodynamic action laws in NMQL grinding 1. Verification studies under different working conditions For action laws of grinding force, Zhang [100] conducted an experimental study on NMQL grinding performances of nodular cast iron on the K-P36 CNC surface grinding machine. The grinding performances were evaluated by grinding force, G ratio, grinding temperature and surface roughness under four working conditions of

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dry grinding, flooding grinding, MQL grinding and NMQL grinding. Results demonstrated that NMQL grinding improved heat exchange capability and the grinding zone temperature decreased by 150 °C compared to that in dry grinding. The workpiece surface roughness (Ra ) was 1.2 µm in dry grinding and 0.58 µm in NMQL grinding, showing a significant improvement in workpiece surface quality. Under lubrication effect of nanoparticles, the grinding force in NMQL grinding decreased by 15 and 7% compared to those of dry grinding and traditional MQL grinding. G ratio of NMQL grinding was the highest (33) under all four working conditions and it was only 12 in dry grinding. The abrasion loss of grinding wheel decreased significantly and its service life was prolonged. For action laws of grinding heats, Zhang [101] conducted an experimental study on cooling performances of NMQL grinding and compared workpiece surface temperatures in flooding grinding, dry grinding, MQL grinding and NMQL grinding. He found that NMQL had relatively good cooling effect and it provides a new way for applications of MQL to grinding. Zhang et al. [102] investigated cooling lubrication performances of flooding type, dry grinding, MQL and NMQL. They constructed the corresponding heat source model and heat transfer model by analysing the grinding process and heat transfer mechanism. Besides, they carried out a finite element simulation of grinding temperature field to analyse influencing laws of different cooling lubricating conditions on the grinding temperature field. Moreover, a plane grinding experimental study under different cooling lubricating conditions was implemented. Research results verified the excellent cooling performances of nanofluids. Yang [19] constructed a micro-grinding model, a heat flux density model, a convective heat transfer coefficient model and a heat transfer model in workpieces, and also carried out experimental and theoretical studies on NMQL grinding of biological bone materials. Results provided references to the crossing applications of mechanical and biomedical engineering. She concluded that micro-grinding temperatures under dripping cooling, MQL and NMQL conditions decreased by 10.1, 29.3 and 37% compared to that in dry grinding (41.6 °C), respectively. 2. Studies on optimization of different nanofluid base solutions Zhang [60] evaluated the cooling lubrication performances of NMQL grinding of MoS2 by using vegetable oil as the base oil. In the experiment, liquid paraffin was used as the control group and grinding performances when using soybean oil, palm oil and rap oil as base oil of MQL were compared from perspectives of grinding force, specific grinding energy and grinding heats. According to research results, the vegetable oil-based MQL achieved the lower micro-friction coefficient than the mineral oil-based MQL and MQL grinding based on vegetable oil nanofluids achieved better lubrication performances than MQL grinding based on pure vegetable oil. With respect to grinding force and micro-friction coefficient, there’s an order that palm oil < rap oil < soybean oil. Properties of vegetable oils, such as categories of fatty acids, saturation degree, viscosity and surface tension, all had significant influences on cooling lubrication performances. Furthermore, Wang [103] explored grinding force action laws of different vegetable oils. With respect to grinding force parameters, there’s an order that corn

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oil < rap oil < soybean oil < sunflower oil < peanut oil < palm oil < castor oil. Relatively low friction coefficients (0.30 and 0.33) and specific grinding energy (73.47 and 78.85 J/mm3 ) were achieved under MQL based on castor oil and palm oil. The castor oil presents ultra-strong lubrication performances because it has high viscosity (530.89 cP under room temperature) and fatty acid molecules contain abundant polar groups of –OH. Nevertheless, Li [104] found in his study that the cooling performances of castor oil are limited due to the excessive viscosity. With references to previous research results, Guo [105] tried to mix six kinds of vegetable oils with castor oil to decrease viscosity and strengthen cooling performances while maintaining the polar groups –OH in fatty acid molecules of castor oil. According to an experimental study, viscosity values of all mixed vegetable oils were smaller than that of pure castor oil. The specific grinding forces of all mixed base oils were smaller than that of castor oil (Ft ' = 0.91 N/mm and Fn ' = 2.454 N/mm). The soybean oil-castor oil mixture gained the lowest specific grinding forces, which were decreased by 27.03 and 23.15% to Ft ' = 0.664 N/mm and Fn ' = 1.886 N/mm compared to those of pure castor oil, respectively. The castor oil/soybean oil mixing volume was further optimized and the optimal mechanical parameters were achieved when the volume ratio was 1:2 [106]. 3. Exploratory studies on applications of different types of nanoparticles Wang [107] prepared nanofluids by using six types of nanoparticles, including MoS2 , SiO2 , diamond, CNTs, Al2 O3 and ZrO2 . He carried out a NMQL grinding experiment of high-temperature Ni-based alloys. Results demonstrated that among six kinds of nanofluids, ZrO2 showed the poorest lubrication performances, followed by CNTs, ND, MoS2 , SiO2 and Al2 O3 successively. The lamellar and spherical Al2 O3 , MoS2 and SiO2 nanoparticles had better lubrication performances. The lowest scratching friction coefficient (0.348), specific scratching grinding energy (82.13 J/mm3 ) and surface roughness (Ra = 0.302 µm) were acquired under Al2 O3 nanofluids, accompanied with the highest G ratio (35.94). In other words, the best surface quality was achieved in Al2 O3 nanofluids NMQL grinding. Nevertheless, Li [108] also discussed cooling performances of above six types of nanoparticles and gained different laws. Specifically, the average heat transfer coefficient of the boundary layer formed by CNT nanofluids was the highest 1.3 × 104 W/(m K). CNT nanofluids had good heat exchange capability due to the large contact angle and small surface tension. Yang [20] studied the dynamic heat flux density in microgrinding process by using Al2 O3 nanofluids with different grain sizes. According to research results, the micro-grinding temperature under MQL conditions was 33.6 °C and temperatures using nanofluids (nanoparticle size: 30, 50, 70 and 90 nm) decreased by 21.4, 17.6, 16.1 and 8.3%, respectively. To address grinding-induced burns of difficult-to-process materials, single type of nanoparticles cannot overcome the technological bottleneck to meet the cooling and lubrication performances in the same time [109]. Yanbin Zhang proposed the MoS2 / CNTs mixed NMQL technology and disclosed the anti-wear mechanism, anti-friction mechanism and heat transfer enhancement mechanism under “physical synergistic

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effect” of the mixed nanoparticles. He improved lubrication and cooling performances simultaneously. Compared with pure nanoparticles, the mixed nanoparticles of MoS2 and CNTs gained the lower friction coefficient (μ), surface roughness (Ra) and RSm, which were corresponding to better lubrication performances. The minimum friction coefficient (μMix(2:1) = 0.25 µm) and the minimum roughness (RaMix(2:1) = 0.294 µm) were gained when the mixing ratio of MoS2 and CNTs was 2:1. With references to research conclusions of Zhang et al. [110] further explored the lubrication performances of Al2 O3 and SiC mixed nanoparticles and the best lubrication performances were acquired at Mix(2:1), manifested by μ = 0.28, specific grinding energy (U) = 60.68 J/mm3 and and Ra = 0.323 µm. These three parameters decreased by 6.7, 20.1 and 29.3% compared to those under the pure Al2 O3 nanoparticles which have better lubrication performances. 4. Exploratory studies on grinding performances under different nanofluid concentrations Nanofluid concentration is a major factor that influences physical properties of nanofluids, thus enabling to influence cooling and lubrication performances significantly. Zhang [111] prepared different concentrations of nanofluids with MoS2 , CNTs and their mixture for NMQL grinding experiment. The preparation of nanofluids used mass fraction (wt.%) as the unit. The mass fractions of nanoparticles in nanofluids were set 2, 4, 6, 8, 10 and 12%, respectively. Results demonstrated that with the increase of mass fraction of nanofluids, friction coefficients under all three NMQL grinding conditions decreased firstly and then increased. Due to different physical properties of three nanoparticles, the minimum friction coefficients and nanofluid concentrations at the minimum friction coefficient were different, which were μCNTs (6%) = 0.293, μMoS2 (8%) = 0.281 and μMix (8%) = 0.274, respectively. Such variation trend was mainly because the excellent lubrication performances of nanofluids were broken by “agglomeration phenomenon” of nanoparticles when the nanofluid concentration was higher than the optimal value. Wang [112] explored the influencing mechanism of Al2 O3 nanofluid concentration on mechanical parameters and found that force ratio and specific grinding energy decreased firstly and then increased with the increase of nanofluid concentration. The minimum force ratio and specific grinding energy were reached when the volume fraction was 1.5%, and they decreased by 24.3 and 34.1% compared to those in pure oil MQL. The optimal abrasion loss of grinding wheel was achieved at 2.5% and G ratio was increased by 34.2%. Nanoparticles began to agglomerate after the volume concentration of nanoparticles exceeds 2.0%. Subsequently, viscosity of nanofluids fluctuated up and down. Meanwhile, the contact angle of droplets reached the minimum (θ = 45.5°) when the nanofluid concentration was 2.0%, which was corresponding to the maximum wetting area and the optimal lubrication performances. Li [34] carried out experimental studies on NMQL grinding of Ni-based alloys under different concentrations and compared grinding force, grinding temperature and proportionality coefficient of energy transferred into workpiece. Experimental

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results of MQL cooling grinding were analysed and discussed from physical properties of nanofluids. Results showed that the minimum grinding temperature (108.9 °C) and the lowest proportionality coefficient of energy (42.7%) were achieved under 2% nanofluid grinding condition. Nanofluid concentration has significant influences on viscosity, surface tension and thermal conductivity, thus influencing the cooling performances. 5. Effects of NMQL jet flow parameters on lubrication performances Han [113] carried out an experimental study on MQL jet flow parameters during highspeed grinding. Results demonstrated that the position of nozzle was the primary influencing factor of high-speed MQL grinding results. Jia [114] investigated distribution characteristics of particulate matters during MQL grinding and discussed the relationships between jet flow parameters (diameter of nozzle outlet, liquid–air supply pressure, flow rate of grinding fluid and gas–liquid flow ratio) and droplet particle size. Besides, he analysed distribution laws of droplet particle size and constructed a mathematical model of quantity and volume distribution function of droplet particles. Furthermore, the influences of jet flow parameters on lubrication effects of high-temperature Ni-based alloy grinding were analysed. Three groups of plane grinding experiments were carried out by using different compressed air pressure, gas–liquid ratio and liquid flow rate. Specific tangential grinding force, friction coefficient, specific grinding energy and surface roughness after experiments were compared. Results showed that the optimal lubrication effect was achieved when the compressed air pressure was 0.5 MPa, gas–liquid ratio was 0.4 and liquid flow rate was 0.005 kg/s. 6. Innovative exploration of low-temperature cold air coupling NMQL grinding Liu [36] designed and built a low-temperature gas atomization NMQL experimental platform to study the enhanced heat exchange mechanism of low-temperature gas atomization NMQL. He also built the grinding heat generation model, heat transfer model and energy distribution model. The grinding experimental parameters were optimized through signal-to-noise ratio (SNR) analysis and grey relational analysis of grinding temperature and specific grinding energy. It was proved by an experiment that low-temperature gas atomization NMQL was a better cooling and lubrication mode. Zhang [115] discussed the heat exchange performances in the grinding zone of Ti alloy under cold air NMQL (CNMQL) condition and explored its influences on specific grinding energy. Moreover, a finite difference numerical simulation of the grinding zone temperature under different cold flow ratios of vortex tube and verification experiment was carried out. Results showed that the optimal cooling effect was achieved under CNMQL. Moreover, there’s good lubrication effect and excellent heat transfer capacity when the cold flow ratio was 0.35, accompanied with the lowest grinding zone temperature.

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Scholars from other Chinese teams also have explored thermodynamic action laws in NMQL grinding Professor Cong Mao from Changsha University of Science and Technology (CSUST) conducted theoretical analysis and experimental study about NMQL grinding and implemented a comparative experimental study on grinding of quenched steel (AISI52100) under four cooling lubrication modes of Al2 O3 nanofluids, dry grinding, flooding lubrication and pure water MQL [116–118]. Results showed that the grinding temperature, grinding force and surface roughness of water-based Al2 O3 nanofluids decreased significantly compared to those of pure water MQL grinding. Due to the high surface energy, nanoparticles could infiltrate to workpiece-grinding wheel interface and grinding wheel-chip interface, thus providing excellent lubrication and anti-friction effects. As a result, the ideal workpiece surface quality was achieved. Besides, he also investigated influences of jet flow parameters on NMQL grinding performances. In the experiment, influences of jetting angle, carrying gas pressure and jet distance (target distance) on grinding performances were analysed. Results showed that the ideal grinding performances were achieved when the nozzle was above the reflux of “gas barrier”. The grinding force, grinding temperature and surface roughness all decreased with the increase of carrying gas pressure and the decrease of jet distance. Huang et al. [119] studied grinding temperatures in dry grinding, MQL, NMQL and ultrasonic-assisted disperse NMQL. Results showed that nanofluids have better thermophysical properties after nanoparticles were added in and they could carry away heats produced during grinding quickly. Nevertheless, nanoparticles may agglomerate in the base solution if there’s no appropriate dispersion mechanism and thereby influence the heat transfer performances of nanofluids. Moreover, the ultrasonic-assisted vibration mechanism can solve nanoparticle agglomeration problem effectively. Therefore, the cooling effect of NMQL with nanofluid ultrasonic-assisted dispersion was better than that of NMQL. Yang et al. [120] carried out grinding tests of the hardened bearing steel GCr15 under different lubricating conditions (dry grinding, flooding grinding, lowtemperature cold air MQL grinding and low-temperature cold air NMQL grinding) and different grinding parameters. The applicability of low-temperature cold air NMQL technology under different grinding parameters was analysed by comparing specific grinding energy and grinding temperature. Results demonstrated that the flooding grinding showed the best cooling and lubrication performances under low grinding speed and low grinding depth, while NA-CMQL achieved the best lubrication and cooling performances under high grinding speed and high grinding depth.

1.3.2 Research Status in Foreign Countries Sadeghi [121] carried out an experimental study on dry grinding, flooding grinding and MQL grinding of AISI 4140 steel. MQL agent used synthetic oil and vegetable

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oil, respectively. Compared to dry grinding, vegetable oil-based MQL grinding decreased the tangential grinding force and normal grinding force detected by 52 and 43%, respectively. Compared to synthetic ester, the vegetable oil-based MQL grinding decreased tangential grinding force and normal grinding force by 37 and 50%, respectively. Sadeghi [18] further carried out a grinding experiment of Ti–6Al– 4V under the same conditions. Shen [50] carried out a grinding experiment of nodular cast iron and drew the same conclusions. Bobby et al. found that although grinding force in MQL grinding of SKD11 tool steel decreased significantly compared to that in flooding grinding, the workpiece surface roughness increased to some extent, which was mainly attributed to shear fracture as the material removal mode. Rabiei et al. [122] compared workpiece surface quality in MQL grinding of hard steel and soft steel and found that the surface smoothness of S305 and CK45 soft steels was poorer than those of 100Cr6 and HSS hard steels. Hence, there are still some technological bottlenecks against MQL application to grinding. Shen [123] prepared nanofluids with MoS2 nanoparticles (< 100 nm) and soybean oil and applied them to NMQL grinding of nodular cast iron. The grinding force and grinding force ratio decreased significantly, while the highest G ratio was achieved. Shen [124] investigated wearing of grinding wheel and tribological properties of nanofluids through flooding grinding, dry grinding, Al2 O3 NMQL grinding and diamond NMQL grinding. They found that a layer of dense and hard mortar was formed on the grinding wheel surface after NMQL grinding, which could improve the grinding performances. Kalita [125] carried out a NMQL grinding experiment by using soybean oil and paraffin oil as the base oil. According to analysis of grinding force, friction coefficient, specific grinding energy and G ratio, the cooling performances of adding nanoparticles in MQL media were better than those by adding micro-particles, and MoS2 nanoparticles had very good tribological properties. According to further studies, the grinding zone temperature in NMQL grinding with a nanoparticle mass fraction of 8% was 160 °C, which was lower compared to NMQL grinding under a nanoparticle mass fraction of 2%. Lee and Nam [126, 127] from Korea carried out an experimental study on nanofluid microgrinding of tool steels. They prepared nanofluids with a volume fraction of 2–4% by adding 30 nm diamond and Al2 O3 nanoparticles into base fluid of paraffin oil. According experimental results, grinding force under NMQL decreased compared to those under dry grinding and pure base fluid MQL, and the surface quality was improved obviously. Types, grain size and volume fraction of nanoparticles had crucial influences on grinding performances. Setti [128] from Germany carried out an experimental study on NMQL grinding of Ti-6Al-4V alloy steel on a surface grinding machine. In the experiment, volume fractions of Al2 O3 nanofluids were set 1 and 4%, and liquid supply pressure and flow rate were 1.5 bar and 18 ml/h, respectively. According to results, the grinding force decreased obviously and surface quality was improved significantly compared to flooding grinding and pure water MQL grinding.

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Francelin [129] from Brazil carried out an experimental study on MQL of CBN grinding AISI 4340 material under two flow rates of 30 and 120 ml/h. Results demonstrated that MQL technology could realize high workpiece quality and it could be applied to industrial production. Dambatta [130] from Malaysia made a NMQL grinding experiment of Si3 N4 ceramic material. The Taguchi experimental method was applied. In this experiment, grinding force, workpiece surface roughness, surface damages and grinding wheel wearing were measured by using workpiece feed velocity, rotational speed of grinding wheel, grinding depth and type of base oil as variables. Balan [131] from India conducted a CFD simulation study on MQL jet. Under different input conditions, the jet velocity and droplet diameter were acquired, thus recognizing the optimal air pressure and mass flow rate of base oil. Finally, the ideal results (low grinding force and surface roughness) were acquired from MQL grinding of super-alloy (Inconel 751).

1.4 Research Status on Theoretical Modelling of NMQL Grinding Force Grinding force modelling has been a research hotspot of grinding theory. At present, researchers have basically reached a consensus on theoretical research idea. The research emphases are divided into three parts: kinematics of a single grain and material removal mechanism, mechanical model of a single grain, and geometry and kinematical modelling of ordinary grinding wheel. Each part involves scientific difficulties that challenge the model precision. Now, breakthroughs of grinding force modelling researches under dry grinding, especially NMQL grinding, are needed urgently. The research idea and scientific difficulties of grinding force modelling are shown in Fig. 1.8.

1.4.1 Kinematics of a Single Grain and Material Removal Mechanism For material removal mechanism, the grinding force is significantly higher than cutting force due to the negative rake cutting and random distribution of grains. In studies on grinding, Badger et al. [132] proposed two grinding force models. One is the two-dimensional plane strain slip-line field theory based on Challen and Oxley. The other is the three-dimensional ribbed micro-protrusion wearing model based on

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Fig. 1.8 Main contents and key difficulties of grinding force modelling

Williams and Xie. Both models simulate the contact between grains and workpiece as a rigid plastic contract. The mechanical behaviors are determined by vortex angle of grains and friction coefficient between micro-protrusion and materials. According to a test verification of grinding force, it is found that the second model has a high precision [133–136]. With considerations to influences of impact effect of the grinding contact zone on the whole plane grinding process, Xiu et al. [137] divided the contact zone into an impact zone and a cutting zone. An impact load model of a single grain and the grain quantity model of impact were constructed by analysing changes in impact loads produced by grains onto the workpiece in the impact zone. Based on above studies, it has reached a consensus to hypothesize the contact between grains and workpiece as rigid-plastic contact during grinding force modelling. The constructive modelling of material removal is the key to guarantee model precision. In particular, break limit and yield limit of materials may change during high-speed/ ultra-high-speed grinding due to thermal softening effect and strain rate strengthening effect. With considerations to the high heat generation during grinding, the Johnson–cook thermoviscoplasticity constructive model is the most applicable. Bikash et al. [138] constructed a turning force prediction model under MQL conditions and adopted the Johnson–cook constitutive model. For a specific material, coefficient in the model can be acquired through split Hopkinson pressure bar (SHPB) experiment. Nevertheless, SHPB can realize limited strain rate and it is impossible to acquire constitutive model parameters of material removal strain rate at the 109 order of magnitude during high-speed/ultra-high-speed grinding. As a result, the high-speed/ultra-high-speed grinding force modelling becomes a bottleneck and it is a research key in NMQL grinding force modelling in future.

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1.4.2 Mechanical Model of a Single Grain For geometric model of grains, grains have considerable influences on workpiece surface quality as the major part of grinding wheel participating in cutting. Lee et al. [126] summarized existing shapes of grains into four types, namely, conical, spherical, round-table and rectangular pyramid shapes. Li [139] carried out a statistical analysis on grains of different shapes and simplified grains into hexahedronal, pyramids, ellipsoidal, cylindrical and prismatic shapes. During grinding force modelling, scholars usually apply conoid grain model as the research object. For composition of grinding force, the grinding principle [1] divides the grinding force into several parts according to different contact states between grains and workpiece. In the grinding process, the elastic/plastic deformation stage between grinding wheel and workpiece, the debris forming stage and scratching stage all may produce grinding forces. Since previous studies have different emphases, the grinding force composition in the constructed models varies accordingly. According to the relationship between plane wearing area of grinding wheel and grinding force as well as other relevant principles, Malkin et al. [140] believed that the cutting deformation force of materials and scratching force in cutting form the grinding force together. Based on the study of Malkin, Li et al. [141] divided the grinding force into chip deformation force and frictional force. Unfortunately, above studies all view frictional force as the frictional force between wearing plane of grinding wheel and the workpiece. Durgumahanti et al. [142] divided frictional force into the extrusion force of cutting edge arc of grains, the frictional force between the wearing plane of grains and workpiece, as well as the frictional force between the bonding agent of grinding wheel and workpiece. However, this frictional force model ignored practical distribution of grains. In fact, grains have friction and extrusion effects with workpiece and debris during cutting and ploughing process, which also shall be covered into the frictional force. For friction component modelling, material removal mechanism is the basis for cutting force modelling and ploughing force modelling. These models are usually constructed according to yield limit and break limit of materials, such as plastic deformation and breakage. Nevertheless, friction component model is one of keys in NMQL grinding force modelling. Some study has pointed out that friction component accounts for more than 85% of total grinding force. Therefore, modelling precision of frictional force is very critical to prediction accuracy of the grinding force model. In the calculation formula of frictional force, friction coefficient (μ) is related with lubricating conditions. In previous studies, scholars have acquired empirical value of friction coefficient through the inversion method, thus establishing the semi-empirical prediction model of grinding force. Since this method does not fundamentally consider tribological properties of grain-workpiece interfaces, the grinding force model has very limited application ranges and it is only applicable to dry grinding. Bikash [138] constructed the MQL turning model and performed a scratching experiment on the turning machine to get friction coefficient. In the experiment, the WC-6Co pen with some radian was used as the cutter and slides

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on the workpiece surface, with friction coefficient measured. Moreover, scratching speed, MQL flow rate and MQL jet pressure were changed, thus getting multiple groups of friction coefficients. Through further fitting, the fitting empirical formula of friction coefficient was acquired. After this formula was brought into the turning force model, the mean variations of cutting force and axial force were 6.53 and 8.3%, respectively. Yanbin Zhang firstly proposed the theoretical calculation formula of tribology on the grain-workpiece interface [57]. Under NMQL conditions, there are direct contact state (point A), boundary oil film lubrication state (points B) and furrow effect state (points S) on the grain-workpiece interface, which is attributed to the irregular continuous peak-valley forms on the workpiece surface. Since grinding force has the same lubrication mechanism in three stages, the frictional forces in these three stages are established as the same frictional force model. The frictional force at point A comes from the plastic flowing pressure of metals and it is determined by shear strength of workpiece surface and plastic flowing pressure of metals. The frictional force at point B comes from the flowing pressure of the lubricating oil film and it is determined by shear strength of the lubricating film and pressure in the lubricating film. Nevertheless, distribution of frictional force is randomly dynamic and material deformation force is also influenced by speed and temperature. Hence, the model has not been verified yet and it needs further theoretical and experimental studies.

1.4.3 Geometry and Kinematical Modelling of Ordinary Grinding Wheel Grinding force of ordinary grinding wheel is the vector sum of interference force of a single grain which participates in material interference in the cutting zone. After the calculation formula of the interference force of a single grain is established, the grinding force can be predicted based on the ordinary grinding wheel model, dynamic effective grain distribution and cutting depth model. For the ordinary grinding wheel, grains distribute on the grinding wheel surface randomly, generally in normal distribution. Wang [143] established a grain distribution model of ordinary grinding wheel through normal distribution of grain size and positional vibration method of grains. If the centre coordinates and radius of the grains on ordinary grinding wheel are (x g , yg , zg ) and Rg , the mathematical model of grain distribution can be expressed by the N × 4 matrix. The cutting depth of valid grains decides their cutting state. Hence, cutting depth model of valid grains is another core problem [144]. In previous studies, researchers described the protrusion height of grains by establishing a probability model. For the grinding wheel with random distribution of grains, this approach can reproduce distribution of grains highly, thus solving the modelling problem of ordinary grinding wheel well. Hecker et al. [145] and Lang et al. [146] constructed the grinding force

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models hypothesized that chip thickness of grains presented Rayleigh probability density distribution. The only parameter of the function was determined based on properties of workpiece materials, dynamic conditions, processing dynamic effect and microstructure of grinding wheel. There’s a problem that this model hypothesizes all grains in contact with workpiece provide cutting action, without distinguishing cutting, ploughing and scratching grains. Zhang [147] constructed the grain size probability model of grains based on normal distribution, solved probabilities of cutting, ploughing and scratching grains at a fixed moment, and distinguished grains in three grinding processes. Nevertheless, the above model still has some disadvantages. On one hand, the protrusion heights and positions of grains in the grinding wheel matrix are random, but researchers only consider the protrusion height. On the other hand, although probabilities of different states of grains are gained through a probability model, cutting force of grains at each state is calculated from the average cutting depth, which has great deviation from practical grinding condition. Moreover, the cutting grains and ploughing grains are distinguished by the empirical judgment method proposed by the grinding theory [1] in the probability model: “cutting behaviors occur when the cut-in overlapping ratio between grains and workpiece material reaches 5% of radius of grains”. Obviously, the empirical judgment method has some defects since critical values vary among different workpiece materials.

1.5 Research Status on Theoretical Modelling of NMQL Grinding Heats 1.5.1 Definition of Grinding Temperature Field In view of universal temperature field problems, heats (Q) at a point in the space are generated instantly. Influenced by the transferred heats, temperatures at other nearby points change accordingly and are varying with both time and space. Temperature field is defined as the generic term of temperature distribution at different points in the space at a moment [148]. Generally speaking, temperature field is the function of space and time: T = f (x, y, z, t)

(1.1)

Equation (1.1) expresses the three-dimensional unsteady-state temperature field in which temperature of an object changes at all directions (x, y, z) and a fixed time. Many years ago, Chinese scholars have carried out theoretical studies on grinding temperature. In 1960s, Professor Jiyao Bei from Shanghai Jiaotong University (SJTU) [149] and Hou et al. from Harbin Institute of Technology (HIT) [150] studied grinding temperature. Meanwhile, Professor Guangqi Cai [151] and Professor Hang Gao [95] from the Northeastern University (NEU) constructed heat source models

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of billet polishing and intermittent grinding, respectively. Professor Tan Jin [89] studied the heat conduction mechanism of high-efficiency deep grinding systematically, constructed temperature field models under the inclined mobile heat source by using the triangular and uniformly distributed heat source model, and analysed grinding temperature of workpiece through three-dimensional and two-dimensional finite elements. Guo [152] and Li [153] et al. from Hunan University constructed an arc heat source model in studies of high-efficiency deep grinding, in which heat source distribution in the grinding zone was viewed as the combined action of countless mobile linear heat sources on the contact arc between grinding wheel and workpiece. Among existing heat source models, this arc heat source model is the one approaching to practical grinding of grinding wheel the mostly.

1.5.2 Solving Method of Grinding Temperature Field At present, the grinding zone temperature field is mainly solved by the analytical methods based on mobile heat source theory (laplace transformation method, integral transformation method and separation of variables method) and numerical methods based on discrete mathematics (finite difference method and finite element method) [154, 155]. The analytical methods get solution to the functional expression based on the mathematical analysis model of temperature field. During calculation of temperature field, there are explicit logical reasoning and physical concepts. The final solution can clearly express influencing laws of grinding zone factors on temperature distribution and heat conduction process. However, it is relatively difficult or impossible for analytical methods to get solutions upon any changes in grinding zone conditions. Instead, the original problems can only be simplified. For these reasons, researchers have to make a lot of hypotheses during the use of analytical methods, such as simplifying heat conduction state on the heat conductor surface, simplifying part shapes, and simplifying heat source distribution states on workpiece surface. These simplification processes all may affect the solving accuracy. Numerical methods are based on discrete mathematics and view computer as a tool. Although they have not strict theoretical basis like analytical methods, they are extremely applicable to solve problems in practical grinding temperature field [156]. 1. Solving the grinding temperature field based on analytical methods Based on heat transfer theory and law of conservation of energy, analytical methods solve the temperature rise function according to boundary conditions in practical grinding, thus getting temperatures at each nodes on workpiece surface and inside. With respect to advantages, the analytical methods not only can get functional relations related with temperature distribution, but also can analyse different influencing factors related with temperature field and their influencing laws on temperature field distribution. So far, researchers have constructed theoretical models of grinding heats based on the mobile heat source theory proposed by Jaeger [157] in 1942. The main idea is to use the heat source temperature field superposition method. In other words,

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the grinding interface is viewed as the non-point source composed of countless linear heat sources and a linear heat source is viewed as the combination of countless. The linear heat source of each microcell is simplified as the combined action of point heat sources. Therefore, the basis of the heat source temperature field superposition method is the solution of this temperature field at any moment after the instantaneous point heat source in the infinite large object emits some heats instantly. Workpiece moves at the same speed of the workbench when it moves. When passing through the grinding wheel, a banding heat source is formed under the interaction between the workpiece and grinding wheel. This banding heat source has the same moving speed with workpiece. The working surface temperature rises when the banding heat source passes through the workpiece surface. This action is called as the thermal interaction in the grinding process. Therefore, the grinding contact interface is viewed as the non-point heat source during calculation of temperature rise on the workpiece surface. Next, the non-point heat source is viewed as the combination of countless banding heat sources whose moving speed along the x-axis is equal to the moving speed (vw ) of the workpiece. Any one of banding heat sources is chosen, with a width of dx i . By calculating temperature rise produced by this banding heat source and integration, it can deduce the temperature rise at M point under actions of the whole non-point heat source. Many researchers have calculated grinding temperature field accurately by using analytical methods. Such heat source temperature field superposition method successfully deduces the theoretical solution of temperature field on the grinding interface under ordinary continuous grinding. 2. Solving the grinding temperature field based on finite difference method To solve the grinding temperature field, the analytical methods are considerably complicated even to solve the simple heat conduction problem. Moreover, grinding is more complicated than other machining modes. There are a lot of nonlinear coupling relations in the grinding process due to the complicated input parameters of grinding temperature field, irregularity of grain distribution, uncertainty of grain states (ploughing, scratching and cutting), cooling media participating in convective heat exchange of the grinding zone, and influences of surrounding airflow field of grinding wheel on temperature. Changes of any input parameters may influence deduction of subsequent expressions. As a result, analytical methods are more complicated and difficult to solve the temperature field. In this case, the finite element method based on numerical method is an effective way to solve heat conduction problems. It can calculate the grinding temperature field conveniently as long as determining the boundary conditions and initial conditions. It is a method which is extensively applied by researchers at present. Nevertheless, the finite element method has made a lot of hypotheses on grinding temperature field and boundary conditions and only the built-in specific module of specific software can be used. There’s a great error between the calculated grinding temperature and the practical temperature. The finite element method based on numerical method is another effective way to calculate grinding temperature field between the analytical methods and finite element methods. It implements the theoretical modelling to boundary conditions (e.g. heat

1.5 Research Status on Theoretical Modelling of NMQL Grinding Heats

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flow density, heat distribution proportion and convective heat exchange coefficient) of temperature field according to practical grinding conditions, and finally calculates the temperature field accurately. The temperature field is calculated by using the finite difference method. The object is divided into finite grid cells. The difference equation is gained by transforming the differential equation and the temperatures at microcell nodes of each grid can be calculated after numerical calculation. The basic principle of this method is to replace differential quotient by the finite difference quotient, thus transforming the original differential equation into a difference equation [158, 159].

1.5.3 Heat Source Distribution Model In the field of machining, many researchers have explored heat source distribution models during grinding by using ordinary grinding wheel, and have acquired relatively mature theory. It can be seen from Fig. 1.9 that during grinding with ordinary grinding wheel, a single grain exerts interferences to workpiece materials, which leads to plastic deformation of materials or cutting effects of materials, thus producing heats. Therefore, grains participating in the grinding process all can be viewed as a point heat source. A single grain which interacting with workpiece materials disperses on the grinding wheel surface. Therefore, workpiece surface temperature rises as a result to the combined action of these point heat sources in the contact area of grinding wheel and workpiece. However, heat conduction on workpiece surface may lead to uniform distribution of heat sources at these discrete points to some extents. As a result, the dispersed point heat sources in the grinding zone are often replaced by banding heat sources in continuous distribution during analysis of temperature field on workpiece surface, thus realizing the goal of model simplification. So far, heat source models established by scholars mainly include the large-depth heat source model (parabolic heat source distribution model) based on slow feeding grinding and high-efficiency deep grinding, the small-depth heat source model based on ordinary reciprocal grinding, and other discontinuous and continuous grinding heat source models. In small-depth continuous grinding temperature field analysis, the models are divided into triangular and rectangular (uniform distribution) heat source models. 1. Rectangular heat source distribution model During theoretical calculation of grinding temperature field, Jaeger viewed mobile heat sources as rectangular uniform distributed heat sources [157], as shown in Fig. 1.10a. A banding heat source was set, which had a width of 2l (2l = lc ) and moved along x-axis on the semi-infinite body at the speed of vw . 2. Triangular heat source distribution model Based on conclusions of Jaeger, Bei et al. [149] all gained the theoretical calculation formula of temperature field in the grinding contact arc zone according to the

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Fig. 1.9 Schematic diagram of surface temperature in grinding zone and grinding point temperature of grains [160]

Fig. 1.10 Schematic diagram of heat source distribution model

uniform distributed and triangular heat source model (Fig. 1.10b). During grinding, the debris in the high end of contact arc between grinding wheel and workpiece are the maximum, while debris thickness at the low end of contact arc decreases to zero. Therefore, it is impossible to have uniform distribution of heat source strength in the processing region. Hence, the triangularly distributed heat source strength model in the contact arc zone is often applied to analyse plane grinding heats. 3. Parabolic heat source distribution model The heat flux density transferred into the workpiece is related with thickness of undeformed chip in the grinding zone which is not in triangular or uniform distribution. Hence, heat flux density transferred into the workpiece changes when debris thickness increases from 0 to the maximum. Suppose heat flux density transferred into the workpiece distributes along the heat source surface in the parabolic pattern, as shown in Fig. 1.10c.

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1.5.4 Thermal Partition Coefficient Model in the Grinding Zone There’s an important problem during construction of temperature field model in the grinding zone. It has to determine the proportion of grinding heats transferred into samples during processing. In other words, it has to determine the thermal partition coefficient (Rw ). In the following text, five theoretical models of thermal partition coefficients which have been reported are introduced one by one. 1. Rated thermal partition coefficient model of grain points Outwater [161] pointed out that grinding heats consisted three parts: (1) wearing plane of grains and action surface of workpiece, as shown in Surface AB in Fig. 1.11. (2) Shearing surface of debris, as shown in Surface BC in Fig. 1.11. (3) Action surface of grains and debris, as shown in Surface BD in Fig. 1.11. Heats generated during plastic deformation (ploughing and material cutting) of materials caused by grains are transferred into grains and workpiece through these three surfaces. Based on the Outwater model, Hahn [162] improved the heat distribution model. He ignored cutting force on the shearing surface, and hypothesized that the workpiece surface was smooth and grains slide on the smooth workpiece surface, that is, the “grain scratching hypothesis” model. In this model, it hypothesized that grinding heats were generated on the grinding interface, that is, wearing plane of grains. Some grinding heats flew into the workpiece and other flew into the grains. On this basis, Hahn simplified grains which moved along the workpiece surface at the rate of vs into cones. Since the thermal conductivity of grains was higher than that of grinding fluid, Hahn hypothesized that grinding fluid didn’t carry away heats transferred into grains and all heats were transferred into grains. Besides, temperatures along the radius were equivalent. Based on the model of Rowe, Cong Mao [160] recalculated the proportion of heats transferred into the workpiece by considering changes of thermophysical properties (thermal conductivity, density and specific heat capacity) of materials under different grinding temperatures.

Fig. 1.11 Diagram of grinding heat generation and transfer [165]

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2. Thermal partition coefficient model of grinding wheel Ramanath [163] constructed a thermal partition coefficient model during plane dry grinding. In this model, debris carried away extremely few heats when grinding depth was relatively small. Hence, the heat source model during grinding was hypothesized into a uniform distributed heat source which moved between two static surfaces (cutting surface of grains and workpiece surface). Moreover, he hypothesized that the surface average temperatures of workpiece and grinding wheel in the grinding contact interface were equal. 3. Thermal partition coefficient model of grain-grinding fluid complex Lavine [164] hypothesized that grinding wheel was the complex of grinding fluid and grains, and its properties were determined by properties of grinding wheel and grinding fluid together. Specifically, grinding fluid was viewed as a part on the grinding wheel surface and it was not the convective heat exchange media. Therefore, it was unnecessary to determine coefficient of convective heat exchange. The heat flux between the complex and workpiece might be transferred into the workpiece, and rest were transferred into the complex. The velocity of the former banded heat flux was the same with the feed velocity of workpiece and it moved on the workpiece surface. The velocity of later banded heat flux was consistent with the linear velocity (vs ) of grinding wheel and it moved on the complex surface. Based on the calculation formula of linear specific grinding temperature proposed by Jeager, the liquid film area on the grinding wheel surface under wet grinding was Ar /An ≈ 1. 4. Thermal partition coefficient model of the grinding wheel/workpiece system Hadad [165] constructed a thermal partition coefficient model of the grinding wheel/ workpiece system (Fig. 1.12). In this model, the total heats in the grinding zone were divided into two parts: heats transferred into debris and heats transferred into the grinding wheel/workpiece system. Furthermore, heats of grinding wheel/workpiece system were the heats transferred into the workpiece and grinding wheel. Specifically, workpiece included the base and grinding fluid. 5. Thermal partition coefficient model considering convective heat exchange in the grinding zone The thermal partition coefficient model considering convective heat exchange in the grinding zone which was proposed by Rowe is generally applied to situations under high-efficiency deep grinding. This model is a theoretical mathematical model suggesting that total energy in the grinding zone was transferred into grinding wheel, debris, grinding fluid and workpiece materials during high-efficiency deep grinding. Moreover, feasibility of this model has been verified by abundant experimental results. In this model, the heat flux density into workpiece, grinding wheel, grinding fluids and debris is related with parameters like the maximum contact temperature (T max ), boiling point of grinding fluid (T b ) and melting point of workpiece (T m ). The proportion of heats into workpiece was calculated by calculating heat transfer coefficient of workpiece material, grinding wheel, grinding fluid and debris.

1.6 Description and Explanation of Research Problems

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Fig. 1.12 Thermal partition coefficient model based on grinding wheel/workpiece system

1.6 Description and Explanation of Research Problems (1) Challenges related with enhanced convective heat transfer mechanism during NMQL grinding and temperature field model: what is the international relationship between thermal conductivity of nanoparticles and nanojet heat transfer capacity? What is the scientific essence of convective heat transfer when nanoparticles impact on the micro/nano interface of carrying fluid media? How do the size effect of nanoparticles, surface effect and interface coupling effect as well as interaction of Van Der Waals force, electrostatic force and Brownie force on nanoparticles promote the enhanced heat transfer? (2) Enhanced material removal mechanism and grinding force model during NMQL grinding: What are influences of lubrication effect of the high-speed, hightemperature and high-pressure interface on material removal mechanism? What are judgment references of ploughing and cutting grains under different workpiece materials and different lubricating conditions? How do dynamic active grains distribute in the grinding zone and how to construct the cutting depth model? What are the material removal mechanical behaviors in the first and second deformation zones under influences of “velocity effect” during NMQL grinding? What is the influencing mechanism of NMQL on heat/force boundaries in the cutting zone > What are influencing mechanisms of lubrication effect and velocity effect on material constitutions? (3) Formation mechanism of dynamic macroscopic capillary/microtexture network and dynamic microscopic capillary on the grinding wheel/workpiece wedged constraint interface: how are holes on grinding wheel surface, micro-bulge, hard

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material points on workpiece surface, interface features of microcracks, capillaries and capillary network formed under wheel/workpiece wedged constraint space boundary conditions? What are distribution laws of capillary size and microtexture network? What are influencing laws of interface material deformation features during formation of capillaries and interface wearing process on infiltration of micro-droplets? What are quantitative relations of critical infiltration conditions of micro-droplet dynamic capillaries with physical properties of nanofluids and jet parameters according to energy equation? (4) The permeation and transportation mechanism of nanofluids in micro-droplet capillaries and adsorption film formation mechanism under high-speed, hightemperature and high-pressure boundary conditions: what are quantitative relations among size distribution of micro-droplets, surface tension of microdroplets, nanofluid viscosity and infiltration efficiency according to multiphase flow kinematics and kinetic equations? How to construct the migration dynamic model in capillaries of gas–liquid-solid flows? How to establish the interface frictional force equation under formation of capillaries? What are changes of physicochemical properties of nanofluids under nanoparticle-base oil coupling effect? How do thermal traction, shearing traction and negative pressure traction influence migration efficiency and film formation effect under dynamic high-temperature and high-speed boundary conditions?

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152. Mao C, Zhou FJ, Hu YL et al. Tribological behavior of cBN-WC-10Co composites for dry reciprocating sliding wear [J].Ceramics international, 2019, 45(5): 6447–6458. 153. Alves L, Ruzzi R, Silva R. Performance Evaluation of the Minimum Quantity of Lubricant Technique With Auxiliary Cleaning of the Grinding Wheel in Cylindrical Grinding of N2711 Steel[J]. Journal of Manufacturing Science and Engineering-Transactions of The Asme, 2019, 139 (12). 154. Kawamura S, Iwao Y, Nishiguchi S. Studies on the fundamental of grinding burn-surface temperature in process of oxidation[J]. Journal of Japan Society of Precision Engineering, 1979, 45 (1): 83–88. 155. Yao C F, Wang T, Xiao W, et al. Experimental study on grinding force and grinding temperature of Aermet 100 steel in surface grinding[J]. Journal Of Materials Processing Technology, 2014, 214(11): 2191–2199. 156. Feng W, Yao B, Yu X J, et al.Simulation of grinding process for cemented carbide based on an integrated process-machine model[J]. International Journal of Advanced Manufacturing Technology, 2017, 89(1–4): 265–272. 157. Jin T, Yi J, Lin P. Temperature distributions in form grinding of involute gears[J]. International Journal of Advanced Manufacturing Technology, 2017, 88(9–12): 2609–2620. 158. Wu S H, Kazerounian K, Gan Z X, et al. A material removal model for robotic belt grinding process[J]. Machining Science and Technology, 2014, 18(1): 15–30. 159. Hadad M, Beigi M. A novel approach to improve environmentally friendly machining processes using ultrasonic nozzle-minimum quantity lubrication system[J]. International Journal of Advanced Manufacturing Technology, 2021, 114(3–4): 741–756. 160. Mao C. The research on the temperature field and thermal damage in the surface grinding[D]. Changsha: Hunan University, 2008. 161. Outwater J Q, Shaw M C. Surface Temperature in Grinding[J]. ASME, 1952, 12 (1): 73–78. 162. Hahn R S. On the nature of the grinding process[C]. Proceedings of the 3rdMachine Tool Design and Research Conference, 1962. 163. Ramanath S, Shaw M C. Abrasive grain temperature at the beginning of a cut in fine grinding[J]. ASME Journal of Engineering for Industry, 1988, 110 (1): 15–18. 164. Lavine A S. A Simple Model for Convective Cooling During the Grinding Process[J]. Journal of Engineering for Industry, 1988, 110 (1): 1–6. 165. Hadad M, Sadeghi B. Thermal analysis of minimum quantity lubrication-MQL grinding process[J]. International Journal of Machine Tools & Manufacture, 2012, 63: 1–15.

Chapter 2

Analysis of Grinding Mechanics and Improved Predictive Force Model Based on Material-Removal and Plastic-Stacking Mechanisms

2.1 Introduction The author has analysed the cooling and lubrication mechanism of the grinding zone and tribological characteristics under nano NMQL; disclosed physicochemical properties of different vegetable oils, molecular structure of mixed nanoparticles and physical synergistic effect as well as influencing mechanism of physical properties of nanofluids with different concentrations on cooling and lubrication performances; investigated the influencing mechanism of physical properties of nanofluids (viscosity and surface tension) and molecular structure of vegetable oils on the lubricating film formation mechanism, enhanced heat transfer mechanism of nanofluids and micro-droplet infiltration mechanism in the grinding wheel/workpiece wedged space; discussed the surface damage mechanism that nanoparticles within the grinding zone participate in through a new method of surface morphological autocorrelation analysis. Moreover, he has optimized the grinding technologies for 45 steel and difficult-to-process material of high-temperature Ni-based alloy GH4169 and gained the optimal parameters. Nevertheless, some origin problems still remain in grinding, especially in NMQL grinding involving nanofluids, such as the material removal mechanism of workpiece and mechanical behaviors under interference of grains. Existing grinding force models ignore influences of lubricating conditions. Existing grinding force models cannot distinguish the state of grains clearly and haven’t calculated the grinding force based on stress state of a single grain. To address these problems, this study explored the material removal mechanism under low-speed quasi-static conditions and took the initiative to construct a new model of grinding force under different working conditions based on material fracture removal and plastic-stacking principle. Corresponding to the cutting stage and ploughing stage, the model divides dynamic active grains into cutting grains and ploughing grains. Grains have different cutting efficiencies in different stages. Considering influences of lubricating conditions on frictional force, a friction and wearing experiment between the workpiece material and grinding wheel material was carried out and friction coefficients under © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_2

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different lubricating conditions were calculated and brought into the grinding force model. Furthermore, an ordinary grinding wheel model was constructed to simulate the number of dynamic active grains and corresponding depth in the grinding zone. Next, stages of dynamic active grains were distinguished by cutting efficiency, thus enabling to calculate grinding force of a single grain according to its state. Finally, this grinding force was integrated with frictional force to get the total grinding force which was verified through a grinding experiment.

2.2 Grinding Force Model of a Single Grain During grinding, a single grain with large cutting depth experiences scratching stage, ploughing stage and cutting stage successively. At a fixed moment, stages of grains in the grinding zone can be judged according to cutting depth. Hence, they can be further named into scratching grains, ploughing grains and cutting grains. From the perspective of workpiece material removal and plastic-stacking mechanism, cutting grains, ploughing grains and scratching grains overcome break limit, yield limit and elastic limit of workpiece materials, respectively [1]. Scratching grains, ploughing grains and cutting grains have different interaction mechanisms with the workpiece. Scratching grains overcome elastic deformation. Plough abrasives overcome yield strength of materials to induce plastic deformation. Cutting grains overcome breaking strength of materials to form cutting behaviors. During contact between a single grain and workpiece material, the conical grain exerts a thrust perpendicular to the contact surface onto the workpiece through the conical surface which contacts with the workpiece. This thrust can be decomposed into a tangential force, a normal force and an axial force along the grinding feed direction. Due to the symmetrical form of grains, the axial force is approximately 0. Therefore, stress distribution on the grain-workpiece contact surface can be calculated according to metal deformation and stress conditions of grains at different stages. On this basis, the tangential force and normal force on a single grain can be calculated. Among grains under three states, the cutting grains have complicated stress conditions. In this section, key attention is paid to the stress distribution on the cutting grain-workpiece surface. As a major part of grinding wheel participating in cutting, grains have significant influences on surface quality of the processing workpiece. Lee et al. [2] summarized current grain shapes into four types, namely, conical, spherical, round-table and pyramidical (Fig. 2.1). In this study, diamond grains were applied. According to SEM observation, grains were conical with a cone angle of 120°. In the following analysis, the conical grain model was chosen as the research object. In this section, the interference mechanism of a single grain will be discussed in Sect. 2.2.1 and the grinding force models of cutting grains, ploughing grains and frictional force will be constructed in Sects. 2.2.2, 2.2.3 and 2.2.4, respectively.

2.2 Grinding Force Model of a Single Grain

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Fig. 2.1 Grain shapes

2.2.1 Grains/Workpiece Interference Mechanism and Debris Thickness During cutting stage of grains, only undeformed workpiece material is removed, while workpiece materials with plastic deformation stack as plastic flow at two sides of the furrow. Hence, the material removal mechanism of a single grain shall give full considerations to material deformation removal and plastic-stacking theory. It can be seen from Fig. 2.2 that after grains cut into the workpiece, the cutting depth of grains (ag ) increases gradually from 0 to the maximum thickness of undeformed chip (agmax ), and then decreases gradually until cutting out of the workpiece [3]. Grains experience the ploughing and cutting stages successively and the critical depth (agc ) is the critical value of state shift. When cutting depth of grains is smaller than agc , grains are in the ploughing state. When cutting depth of grains is higher than agc , grains are in the cutting state. In this study, agc is acquired from the scratching experiment of a single grain. 1. Plastic-stacking mechanism (1) When ag ≤ agc , grains are in the ploughing state (Fig. 2.3a). Due to the small cutting depth of grains, material strain in the interference process between grains and materials is relatively small and it doesn’t reach the break limit of the material. Hence, materials are pushed to two sides of the furrow, forming plastic swelling. (2) When ag ≥ agc , grains are in the cutting state (Fig. 2.3b). Under this state, there’s material fracture removal and plastic-stacking simultaneously. Chen and Rowe [4] also discovered in studies that there’s material removal in the cutting stage and some debris flow to two sides of the furrow through plastic deformation, forming plastic swelling. At this moment, workpiece materials at two sides of grains have relatively small strain which is far beyond the break limit. Hence, such workpiece materials are squeezed to two sides of the furrow. There are enough strains in material deformation of the cutting zone of grains and workpiece materials are discharged as debris after reaching the break limit. There’s a boundary line between two zones and stress on the materials above the boundary line is equal to the break limit.

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Fig. 2.2 Cutting depth of a single grain

Therefore, the grain-workpiece contact zone is divided into the cutting zone (0 − α1 ) and plastic deformation zone (α1 − π/2) in this study. The positional relationship between plastic deformation and critical angle of material removal (α1 ) is shown in Fig. 2.4. The value of α1 is related with mechanical performances of workpiece materials. For brittle materials, there’s hardly plastic deformation in the grinding process, thus resulting in the absence of a plastic deformation zone. For plastic materials, workpiece materials may develop elastoplastic deformation in the cutting process of grains, thus having an elastoplastic deformation zone. The size of this zone is determined by yield limit and break limit of the workpiece material. Du et al. [5] introduced in the cutting efficiency (β) to quantify the plastic-stacking degree of materials in the grain cutting process. It is defined as the ratio of removed material volume in the total formed furrow volume on the furrow morphology after grain cutting. Combining with Fig. 2.4, the relationship between α1 and β is: √ α1 = arccos( β)

(2.1)

It is important to note that both ploughing grains and cutting grains conform to the plastic-stacking theory. B approaches to 0 in the ploughing stage and approaches to 1 in the cutting stage. Therefore, cutting efficiency can be used as the judgment references whether grains are in the cutting stage or ploughing stage. Compared

2.2 Grinding Force Model of a Single Grain

(a) ploughing grains

(b) cutting grains Fig. 2.3 Interference actions of grains in surface grinding

Fig. 2.4 Plastic-stacking mechanism

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to previous grinding force model which uses empirical judgment method, “cutting behaviors occur when the cut-in overlapping ratio between grains and workpiece materials reaches 5% of grain radius”. The judgment method based on cutting efficiency can improve accuracy of the grinding force model significantly to different materials. 2. Material fracture removal mechanism The fracture removal effect of materials is an important theory of grain cutting stage. Due to complexity of the grinding process, there are diversified grinding mechanisms. Setti et al. [6] studied the debris forming mechanism by observing debris morphology and found that debris shapes under different grinding conditions differed significantly. In early studies of grinding mechanism, Doyle et al. [7, 8] observed debris and found that microstructure of debris was very similar with cutting and irregular debris shapes were related with shapes and cutting depth of grains. Debris shapes mainly could be divided into three types: banding shape, nodular shape and spherical shape. Spherical debris experienced an extremely fast melting and solidification stage. Abundant grinding heats were generated in the grinding process to soften materials and debris developed plastic flow among shear layers to form nodular shapes. In this study, debris were gained through a grinding experiment (V s = 20 m/ s, V w = 2 m/min and ap = 15 μm) of 440C workpiece and observed. The debris forming mechanism was further determined through morphology of debris. The SEM images of debris are shown in Fig. 2.5. It can be seen from Fig. 2.5 that debris in the experiment is mainly in banding form with smooth internal surface, rough external surface and large radius of curvature. Specifically, the rake face of grains contacts with the smooth surface of debris (internal surface). Debris in grinding has two differences from chips in cutting process:

Fig. 2.5 SEM of grinding debris and cards model

2.2 Grinding Force Model of a Single Grain

49

(1) The curvature of debris is relatively small and some debris even is presented as approximately straight lines. (2) The rear surface of debris is bamboo-shaped, but the rear surface of chip is relatively smooth. Such differences are attributed to differences in grain cutting mechanism and cutting process. Piispanen [9] constructed a “cards model” for the cutting zone. Suppose the removed materials in the first deformation zone in cutting is an extremely thin plane. As the cutting process continuous, chips form the ideal cards stacking layer, accompanied with slippage of among different layers during cutting. This cards model is applied to study debris forming mechanism. The observed phenomenon can be explained reasonably: (1) The cutting layers of workpiece experience “cards slippage”, thus forming debris. Due to the negative rake angle of grains, there’s plastic-stacking to bamboo shapes on the rear surface of debris in the “cards layer”. Due to the positive rake angle, the debris forming angle is relatively small during cutting. The front and rear surfaces of chips are relatively smooth. (2) Different from cutting mechanism, direction of cards layers changes greatly, which not only causes plastic deformation, but also eliminates deformation internal stress. Hence, debris has smaller curvature than chips. (3) It can be deduced from the debris forming mechanism that plastic deformation occurs in the debris forming process. Due to isotropism of materials, debrisgrain contact surfaces shall be in uniform distribution along the normal direction of the grain surface. 3. Stress distribution in the grain-workpiece interference zone Determining the grain stress distribution is a key part in grinding force modelling. According to the plastic-stacking and material removal mechanism, the strain distribution of grain-workpiece material interference is shown in Fig. 2.6. Suppose the material is isotropic and it is perpendicular to the grain surface in the deformation flowing process. Therefore, the stresses spread outward through the centre of a circle. For cutting grins, grains are divided into two symmetric parts along the movement direction, which have the same stress conditions. Based on material removal and plastic-stacking principle, stress distributions along circumferential directions of grains and normal direction of grain-workpiece contact surface shall have the following characteristics: (1) 0° ~ 90°: due to isotropism of the workpiece material, circumferential stress along the contact surface shall change continuously, without sudden changes of stress. (2) α 1 ~ 90° (cutting zone): in the cutting zone, grain-debris contact surfaces shall present a uniform distribution trend along the normal direction. Meanwhile,

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Fig. 2.6 Schematic diagram of the grain stress state

the sum of stresses (δ 0 ) provided by grains shall meet the material fracture condition of debris separation boundaries and stress along the debris fracture direction shall be higher than the break limit (δ b ) of materials. Additionally, it can be deduced to cards theory that stresses provided by grains also shall trigger plastic deformation of debris. (3) 0° ~ α 1 (plastic zone): with the increase of α, the workpiece material transits from elastic deformation to plastic deformation and the material breaks at the critical angle (α 1 ). Therefore, stress (δ 1 ) presents a linear growth trend. In the high-speed grain cutting process, the material rebounds at 0° by a low speed after elastic deformation. Hence, the stress shall be 0. 4. Solving β(αg) based on the scratch tests of a single grain Although stress distributions in the ploughing and cutting stages of grains have been concluded in above analysis, the boundary between these two stages still has to be further solved. Based on an experimental study of a single grain, Chen and Opoz [10] found that the cutting efficiency of grains increased with the increase of cutting depth. Hence, it is theoretically possible to distinguish ploughing and cutting stages through variations of cutting efficiency with cutting depth. As a result, scratch tests of a single grain were carried out in this study, in which the workpiece material used stainless steel 440C (Ra = 0.04–0.05 μm). The physical properties of stainless steel 440C are listed in Table 2.1. The three-dimensional morphology of furrow in scratch tests is shown in Fig. 2.7. The morphology of furrow surface is shown in Fig. 2.7a. The 2D surface profile data of furrows on a straight line perpendicular to the furrows was measured with a roughness measuring instrument TIME3220. The measurement results are shown Table 2.1 Elemental composition of 440C material Elements

C

Si

S

Cu

Mn

Mo

Cr

P

Ni

Components/ (%)

0.95

1.00

Margin

0.3

1.00

0.75

16–18

0.035

0.60

2.2 Grinding Force Model of a Single Grain

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Fig. 2.7 Result of scratch tests

in Fig. 2.7b. In the 2D surface profile of each curve, the furrow depth and plasticstacking rate were measured, forming a database related with furrow depth and plastic-stacking rate. This database was used to solve the variation law of plasticstacking rate with furrow depth. The 3D surface profile data was built through the 2D surface profile and data fitting was implemented by using MATLAB to realize the goal of reconstruct the furrow surface profile (Fig. 2.7c). It can be seen from Fig. 2.7 that with the continuous increase of furrow depth, there’s always plastic-stacking phenomenon. This proved the above analysis on ploughing and cutting mechanisms of grains. It indeed had the elastoplastic deformation zone and cutting zone simultaneously during grain cutting. According to further observation of surface morphology, the plastic-stacking height declined gradually with the continuous increase of furrow depth. Each of the measured 2D surface profile data was processed by MATLAB and the furrow depth as well as the corresponding cutting efficiency. The calculation principle is shown in Fig. 2.7b. The cross section of plastic-stacking part of the furrow surface morphology and cross section of removed workpiece material were calculated by programming. Furthermore, the calculation formula of cutting efficiency was: the ratio between the removed material volume and the total formed furrow volume on the furrow morphology after grain cutting: β = 1 − (S1 + S3 )/S2 . The variation laws of cutting efficiency (β) with furrow depth (ag ) are shown in Fig. 2.8. On this basis, the database of different furrow depth and corresponding cutting efficiency was built

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Fig. 2.8 Variation laws of cutting efficiency (β)

and the expression of variations of cutting efficiency with furrow depth was solved through data fitting. Fitting results are shown in Fig. 2.8. According to the data dot matrix of changes of β with ag , the cutting efficiency presented an S-shaped growth trend with the increase of furrow depth. According to previous analysis on grain cutting mechanism, it had plastic-stacking phenomena through grain cutting and the variation trend also had the same trend with the data dot matrix which was gained in tests. However, experimental data range was the furrow depth within 0 − 4.5 μm. It is also the same important to predict the variation trend with furrow depth higher than 4.5 μm. When the furrow depth was higher than 4.5 μm, the variation trend shall be a linear trend with slope approaching to a constant. Hence, cutting efficiency shall present an S-shaped growth curve with changes of furrow depth and it is a constant when the furrow depth further increases. Data fitting was conducted to get a specific variation function curve. R2 reached 0.9729 in Gaussian fitting. Combining with fitting curves, the goodness of fit reached the optimal value in multiple functions. Nevertheless, the variation trend of Gaussian fitting after x = 3.8 μm disagreed with the essential variation laws of cutting efficiency. This problem was solved by piecewise functions. The function of variation laws after fitting is shown as follows. The constants of the fitting formula are listed in Table 2.2 (95% confidence bounds). ⎧ a −b a −b a −b6 (−( gc 1 )2 ) (−( gc 2 )2 ) (−( gc )2 ) ⎪ 1 2 6 ⎪ + a2 · e + · · · + a6 · e , ⎨ a1 · e β(ag ) = 0 ≤ x ≤ 3.8/μm ⎪ ⎪ −b.ag ⎩ k · e(−a·e ) , x > 3.8/μm

(2.2)

2.2 Grinding Force Model of a Single Grain

53

In Fig. 2.8, the grinding zone can be divided into three parts according to curvature of the cutting efficiency curve, including ploughing stage, transition stage and cutting stage. By observing the variation laws of the cutting efficiency function, (1) Ploughing phenomenon occurred at 0.023 μm. In other words, 0–0.023 μm was the scratching stage. The proportion of scratching stage accounted for a lower proportion compared to research results of Hahn [11]. Since Hahn chose to measure macroscopic properties of grinding force distinguishing and randomness of grain distribution on the grinding wheel, the furrow experimental results were reasonable. (2) In 3 regions in Fig. 2.8, there are obvious differences in slope variation trends of curves and the cutting efficiency in ploughing stage presented a slow rising trend. The traditional grinding theory stated that “no debris is produced during ploughing and there’s only plastic deformation of the workpiece material”. The research conclusions were not contradictory with the grinding theory. The manifestation that numerical value of cutting efficiency was higher than 0 in the ploughing stage may not indicate material removal to form chips. The decreased materials in ploughing stage might be attributed to compressed material volume and partial material adhesion onto grains caused by ploughing behaviors. (3) Different from the traditional grinding theory, the cutting efficiency curve increased sharply after finishing the ploughing stage and entered into the transition stage. Transition from the ploughing stage to the cutting stage is a progressive process, without obvious transform values. In the transition stage, cutting efficiency increased dramatically, then increased slowly, and finally tended to be stable. The cutting efficiency tended to be a constant gradually after entering into the cutting stage. The cutting depth range in different grain stages and force equations are shown in Table 2.3. Table 2.2 Parameters of β(ag) (95% confidence bounds) Parameters

Values

Parameters

Values

Parameters

Values

a1

− 6.351 × e11

b1

71.85

c1

12.85

a2

0.02612

b2

2.732

c2

0.1701

a3

0.7112

b3

2.319

c3

1.517

a4

2.051

b4

5.66

c4

2.302

a5

0.06955

b5

1.881

c5

0.1619

a6

0.3025

b6

1.444

c6

0.2253

k

0.9215

a

5.21

b

2.004

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2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

Table 2.3 Grain stages and force equations Cutting depth ag

Grain stages

Force equations

0–1.18 μm

Ploughing stage

Ploughing force equations: 5.15, 5.15

1.18–2.85 μm

Transition stage

Cutting force equations: 5.13, 5.14

2.84 μm

Cutting stage

2.2.2 Cutting Force Models 1. Cutting force models in the cutting zone (α1 ~ π/2) Let δ 0 be the stress exerted by grains onto the workpiece in the cutting zone. According to the conservation of energy, some energy produced with movement of grains was used for plastic deformation (F 01 , E 01 , δ 01 ) of the workpiece material and the rest was used for material fracture and debris forming (F 02 , E 02 , δ 02 ). Due to isotropism of workpiece materials, the plastic deformation limit of materials was equal to the yield limit (δ s ). Therefore, the plastic deformation stress in the cutting zone was δ 01 = δ s . It can be seen from Fig. 2.9 that the calculation formula of integral unit (d s ) that: ds =

ag2 · tan θ 2 · cos θ

· dα

(2.3)

The plastic deformation force in the cutting zone was the function of ag . The expressions of tangential/normal forces were:

Fig. 2.9 Calculation principle of grain cutting force calculation principle

2.2 Grinding Force Model of a Single Grain

55

π

  Ftc(01) ag =

2

δs · ag2 · tan θ · cos α · dα

(2.4)

α1 π

  Fnc(01) ag =

2

δs · ag2 · tan2 θ · dα α1

=

π 2

 − α1 · δs · ag2 · tan2 θ

(2.5)

where δ s is the yield limit of the workpiece material. ag is the cutting depth of grains. 2θ is the vertex angle of grains. α1 is the critical angle of plastic-stacking. F tc(01) (ag ) is the plastic deformation force in the tangential cutting zone and F n(01) is the plastic deformation force in the normal cutting zone. It can be seen from Fig. 2.9 that the area of material breaking into debris at a fixed moment shall be Am and it has to overcome the break limit (δ b ) of materials to realize material breakage and finish cutting. Hence, the relationship between material removal stress (δ 02 ) and material removal force (F tc(02) (ag )) in the cutting zone is: π

  Ftc(02) ag =

2

δ02 · ag2 · tan θ · cos α · dα = δb · Am

(2.6)

α1

Based on the above equation, the stress (δ 02 ) can be calculated: π · tan θ · δb 2 · (1 − sin α1 )

δ02 =

(2.7)

The material removal force in the normal cutting zone can be calculated according to δ 02 : π

2 Fnc(02) (ag ) =

δ02 · ag2 · tan2 θ · dα a1

  π · π2 − α1 · δb · ag2 · tan3 θ = 2 · (1 − sin α1 )

(2.8)

To sum up, the stress (δ 0 ) of the cutting zone shall be: δ0 = δ01 + δ02 = δs +

π · tan θ · δb 2 · (1 − sin α1 )

(2.9)

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2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

2. Force models in the plastic deformation zone (0 ~ α1 ) With the increase of angles (0 ~ α1 ), the stress (δ 1 ) in the elastoplastic zone presented a linear growth from 0 to δ 0 . Hence, the function between δ 1 and α can be expressed as:

δs π · δb · tan θ ·α (2.10) δl (α) = + α1 α1 · (1 − sin α1 ) Furthermore, the grain cutting force in the elastoplastic zone can be calculated: α1 Ftc(1) (ag ) =

δ1 (α) · ag2 · tan θ · cos α · dα

(2.11)

0

α1 Fnc(1) (ag ) =

δ1 (α) · ag2 · tan2 θ · dα

(2.12)

0

3. Grinding force models of cutting grains By combining force equations in the cutting zone and elastoplastic zone, the calculation formula of cutting force can be gained: Ftc (ag ) = Ftc(1) (ag ) + Ftc(01) (ag ) + Ftc(02) (ag ) a1 = δ1 (α) · ag2 · tan θ · cos α · dα 0 π

2

δs · ag2 · tan θ · cos α · dα + δb · Am

+

(2.13)

a1

Fnc (ag ) = Fnc(1) (ag ) + Fnc(01) (ag ) + Fnc(02) (ag ) ⎡α ⎤   1 

π π · π2 − α1 · δb · tan θ + − α1 · δs ⎦ = ⎣ δ1 (α) · dα + 2 · (1 − sin α1 ) 2 0

· αg2 · tan2 θ

(2.14)

In above equations, the plastic-stacking critical angle (α1 ) is a function of ag and the function relationship could be gained from the following furrow tests. In the equations, other parameters are known parameters related with workpiece material

2.2 Grinding Force Model of a Single Grain

57

properties. Hence, the equation of cutting forces is a function of the grain cutting depth (ag ) and the specific numerical values can be calculated by bringing in ag .

2.2.3 Ploughing Force Models The essence of ploughing stage lies in the plastic deformation of materials under the action of ploughing forces, while plastic deformation limit of materials is called as the yield limit. Due to isotropism of materials, plastic deformation forces on grain surfaces are all perpendicular to the surface and have equal numerical values. As a result, the ploughing force of a single grain can be calculated as: π

2 Ft p (ag ) =

δs · ag2 · tan θ · cos α · dα

(2.15)

0

π Fnp (αg ) =

δz · αg2 · tan2 θ · dα =

π · δs · αg2 · tan2 θ 2

(2.16)

0

where other parameters are known parameters related with workpiece material properties. Hence, the equation of ploughing forces is a function of the grain cutting depth (ag ) and the specific numerical values can be calculated by bringing in ag .

2.2.4 Frictional Force Models In previous studies, scholars generally believe that frictional force is caused by scratching between top of the surfaced grains and workpiece materials. In fact, frictional force also shall include the frictional force between rake face of grains and debris as well as the frictional force between grain sides and side walls of furrows. 1. Calculation of the frictional forces on rake face and side of grains During grinding, grains plough and cut the workpiece materials to form plasticstacking and debris. In the ploughing stage, there are only plastic-stacking phenomena, but in the cutting stage, there’s both plastic-stacking and debris forming. These require grains to apply some stresses on the workpiece. Hence, frictional forces between grains and workpiece are generated. The value of such frictional forces is determined by not only stresses exerted by grains onto the workpiece in ploughing and cutting stages, but also lubrication between grains and the workpiece. At a fixed moment, debris moves to the grinding wheel in relative to grains. The frictional force on debris is parallel to the grain-workpiece interface and points to the workpiece. In plastic-stacking, grains squeeze and transport material flows outward, while the

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2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

Fig. 2.10 Frictional force on rake face and sides of grains

workpiece material moves toward the grinding wheel in relative to grains. Frictional force on the plastic deformation materials is parallel to the grain-workpiece interface and points to the workpiece. The frictional forces between grains and the workpiece are shown in Fig. 2.10. The frictional forces of ploughing grains and cutting grains are different due to their different contact stresses. (1) Frictional force equation of ploughing grains The calculation formula of frictional force F pf (ag ) between the ploughing grains and the workpiece is: π

π

2 F p f (ag ) = 2 ·

2 μ · δs · ds =

μ · δs · dg2 ·

0

0

tan θ · dα cos θ

(2.17)

where μ is the friction coefficient between the friction pair of workpiece materials and grains. On this basis, the frictional force is decomposed into a tangential component and a normal component: π

2 Ft p f (ag ) = F p f (ag ) · sin θ =

μ · δs · ag2 · tan2 θ · dα

(2.18)

0 π

2 Fnp f (ag ) = F p f (ag ) · cos θ =

μ · δs · ag2 · tan θ · dα 0

(2.19)

2.2 Grinding Force Model of a Single Grain

59

(B) Frictional force equation of cutting grains The calculation formula of frictional force F cf (ag ) between the cutting grains and the workpiece is: ⎛ π ⎞ 2 a1 ⎜ ⎟ Fc f (ag ) = 2 · ⎝ μ · δ0 · ds + μ · δ1 · ds ⎠ a1



0

π 2

μ · δ0 ·

=

α1

tan θ · da + · cos θ

ag2

a1

μ · δ1 · ag2 · 0

tan θ · da cos θ

(2.20)

Hence, the frictional force is decomposed into a tangential component and a normal component: π

2 Ftc f (ag ) = Fc f (ag ) · sin θ =

μ · δ0 · ag2 · α1

α1 +

μ · δ1 · ag2 · 0

tan θ · da cos θ

tan θ · da cos θ

(2.21)

π

2 Fnc f (ag ) = Fc f (ag ) · cos θ =

μ · δ0 · ag2 · tan θ · da α1

α1 +

μ · δ1 · ag2 · tan θ · da

(2.22)

0

In frictional force equations of cutting grains and ploughing grains with the workpiece, α1 is a function of ag and such functional relationship will be calculated in the following furrow tests. Friction coefficient (μ) is related with lubricating conditions. The value of μ is calculated from tribological tests under different working conditions. In above equations, other parameters are known parameters related with workpiece material properties. Hence, the equation of frictional forces between grains and the workpiece is a function of the grain cutting depth (ag ) and the specific numerical values can be calculated by bringing in ag . 2. Tribological forces of grains In previous studies, Durgumahanti et al. [16] calculated tribological forces of grains through the following equations: f n = Nd · Sw · p

(2.23)

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2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

f t = μ · Nd · Sw · p

(2.24)

where S w is the area of top wearing zone of grains and p is the mean contact pressure between grains and the workpiece. The cutting trajectories of grains are simulated by a parabola. Then, the deviation (Δ) of the cutting path radius (Rc ) of the grain i within the radius of grinding wheel is [12]: Δ=

1 2 − D Rc

(2.25)

4 · Vw Vs · de

(2.26)

Δ=±

where d e is the equivalent diameter of grinding wheel and there’s d e ≈ D for plane grinding. It can be seen from the study of Malkin [12] that p presents a linear rising trend with the increase of Δ. p = P0 · Δ =

4 · P0 · Vw Vs · D

(2.27)

p changes with grinding parameters. P0 is a constant that can be gained from experiments. Equations (2.26) and (2.27) are brought into Eqs. (2.23) and (2.24), so that the normal and tangential frictional forces can be expressed as: f n = Nd · Sw · p = f t = μ · Nd · Sw · p =

4 · K 1 · Nd · Vw 4 · P0 · Sw · Nd · Vw = Vs · D Vs · D

4 · μ · K 1 · Nd · Vw 4 · μ · P0 · δ · Nd · Vw = Vs · D Vx · D K 1 = P0 · Sw

(2.28) (2.29) (2.30)

In the tribological force equations of grains, μ is related with lubricating conditions and its value can be gained from tribological tests under different working conditions. K 1 is a physical variable related with wearing loss of grains on the grinding wheel and it can be calculated from grinding tests. Other parameters in the equation are known parameters. 3. Calculation of friction coefficient based on tribological tests It is difficult to calculate friction components accurately by determining friction coefficient through either single-grain grinding tests or overall grinding tests. Moreover, such calculation methods have some limitations. Researchers only focus on friction component under dry grinding. If lubricating conditions are involved, the calculation precision of friction coefficient further declines due to the complicated tribological

2.2 Grinding Force Model of a Single Grain

61

properties. Hence, friction coefficient was solved by using the rotating tribological tests and it was brought into frictional force equations. In tribological tests, the workpiece material 440C and corundum grinding wheel disk were used as two friction pairs. In tribological tests, dry grinding, pouring grinding, MQL grinding and NMQL grinding were simulated and the corresponding friction coefficients between the grinding wheel and the workpiece were measured. Experimental setup is shown in Fig. 2.11. Parameters of the grinding wheel disk are listed in Table 2.4. The parameters of tribological tests are presented in Table 2.5. Based on test results, friction coefficients under dry grinding, pouring grinding, MQL grinding and NMQL grinding are 0.607, 0.446, 0.505 and 0.417 when grinding parameters are set V s = 20 m/s, V w = 2 m/min and ap = 15 μm, respectively (Fig. 2.12).

Fig. 2.11 Experimental setup of tribological tests

Table 2.4 Parameters of corundum grinding wheel disk Model

Size

Grain size

Hardness

Binder

WA80H12V

Φ50 × Φ2 × 4

80 mesh

Moderate

Ceramics

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2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

Table 2.5 Parameters of Tribological tests Conditions

Values

Test temperature (°C)

25 ± 5

Test time (s)

1200

Loads (N)

10

Frequency (Hz)

2

Steel ball material

440C

Steel ball diameter (mm)

9.5

Steel ball hardness (HRC)

58–60

Fig. 2.12 Results of tribological tests

2.3 Ordinary Grinding Wheel Models and Dynamic Active Grains The mechanical equations of cutting grains and ploughing grains have been established in the above section. In this section, the calculation formulas of dynamic active grains in the grinding zone and their cutting depth will be established. An ordinary grinding wheel model will be established in Sect. 2.1. The matrix of static active grains in the grinding zone will be gained according to grinding process in Sect. 2.2. Finally, the position matrix of dynamic active grains and their cutting depth matrix will be acquired in Sect. 2.3.

2.3 Ordinary Grinding Wheel Models and Dynamic Active Grains

63

2.3.1 Protrusion Height of Grains in the Grinding Zone Grains distribute randomly and uneven on the grinding wheel surface. Zhang [13] supposed that grain size distribution in grinding wheel conforms to a normal distribution. Then, the mean diameter (d mean ) of grains is: dmean =

dmax + dmin 2

(2.31)

where d max is the maximum grain size and d min is the minimum grain size. According to characteristics of normal distribution function, the standard deviation (σ ) of grain size distribution can be gained [14]: σ =

dmax − dmin 6

(2.32)

According to the probability density formula of normal distribution function, the distribution function of grain size (d) can be gained: φ(d) = √

1 2π · σ

· e[−

(d−dmean )2 2σ 2

]

(2.33)

For a fixed model of grinding wheel, volume content (V g ) of grains in the grinding wheel can be calculated according to the structure number (S o ): Vg = 2 · (31 − S0 )

(2.34)

Grains in the grinding wheel are in uniform distribution. On this basis, the theoretical grain interval (L r ) can be calculated: / L r = dmean ·

 π −1 4Vg

(2.35)

Based on L r , b and L g , the grain numbers along circumferential and axial directions of the grinding wheel (N x and N y ) can be calculated: Nx =

Lg dmean + L r

(2.36)

Ny =

b dmean + L r

(2.37)

Therefore, the total grain number (N) of the grinding wheel is: N = Nx · N y

(2.38)

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2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

Based on the probability distribution function of grain size and N, a model matrix (G(d)) with a total grain number of N can be generated by MATLAB program. ⎡

d11 d12 ⎢ d21 d22 ⎢ G(d) = ⎢ . .. ⎣ .. . d Nx 1 d Nx 1

⎤ · · · d1N y · · · d2N y ⎥ ⎥ .. ⎥ .. . . ⎦ · · · d Nx N y

(2.39)

Grain positions along the protrusion height direction of the grinding wheel base are random. Sheng Wang from Qingdao University of Technology [15] simulated the grain positions along the protrusion height direction by using the “grain vibration method” when establishing the grinding wheel model. He believed that grains observe uniform distribution on the grinding wheel surface. According to a further study, the standard deviation of cross-section area of the 80# grinding wheel decreased to the minimum and tended to be stable when the oscillation number exceeded 800. The iterative equation of axial vibration of grains is: z gkn = z gk0 + δ · z gk0 + δ · z gk1 + · · · δ · z gkn

(2.40)

where k is number of grains, n is the number of vibration times, z gk0 is the initial Z-axis coordinate of grains, z gkn is the ultimate Z-axis coordinate of grains, and δz gk1 is a random number that meets the uniform distribution in the interval of [− L r , L r ]. Therefore, z gk0 was set 0 and n was 800 during grinding force modelling in this study. The axial position array of grains was generated: ⎡

z 11 z 12 ⎢ G(d) ⎢ z 21 z 22 + G(z g ) = ⎢ . G(z) = .. ⎣ .. 2 . z Nx1 z Nx1

· · · z 1N y · · · z 2N y . .. . .. · · · z Nx N y

⎤ ⎥ ⎥ ⎥ ⎦

(2.41)

2.3.2 Static Active Grains It can be seen from Fig. 2.13 that grains within the grinding arc zone can be divided into several state: uncontacted, scratching, ploughing and cutting. All three states of grains cause the workpiece deformation. These three states are different from cut-in depth of grains and they are determined by protrusion heights of grains under a fixed cutting depth. In practical production, the grinding wheel is required to arrive at the workpiece surface when looking for the relative zero point with the cutter. Given a cutting depth (ap ), the highest protruding grains were used as the benchmark and the protrusion height of grains which interfere with the workpiece in G(z) shall be within

2.3 Ordinary Grinding Wheel Models and Dynamic Active Grains

65

Fig. 2.13 Static and dynamic active grains in grinding zone

the interval of [zmax − ap , zmax ]. On this basis, static active grain matrix G(c) can be screened from G(z). furthermore, the cutting depth matrix G(ap ) of each grain in the static active grain array can be calculated: G(ad ) = G(c) − z max + α p

(2.42)

2.3.3 Dynamic Active Grains and Cutting Depth Due to different protrusion heights of grains during grinding process, not all static active grains may participate in the cutting process. Whether a grain interfere with the workpiece is determined by the difference between its distance to the previous grain and the protrusion height. Besides, the dynamic active grain number in the grinding zone and the corresponding cutting depth may change with grinding parameters. In Fig. 2.14, the static active grain 2 has no interference with the workpiece. Whether there’s interference between static active grains and the workpiece is determined by its distance to the previous dynamic active grain and its own protrusion height. For a single grain, it can be known from the grinding theory that the maximum undeformed chip thickness of two successive cutting grains can be calculated through the geometrical relationship: ag max

Vw =2·λ· · Vs

/

ap D

(2.43)

where agmax is the maximum undeformed chip thickness of grains and λ is the distance between two successive cutting grains.

66

2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

Fig. 2.14 Maximum undeformed chip thickness of dynamic active grains

For an engineering grinding wheel, distance between grains is equal to protrusion height and all grains in the grinding zone may participate in the grinding process. The value of λ is the mean distance between grains (L r + d). For an ordinary grinding wheel, the value of λ is the distance between active grains. With further considerations to different protrusion heights of dynamic active grains, it can deduce the maximum undeformed chip thickness of the nth grain: ag man(n)

Vw = 2 · λ(n∼n−1) · · Vs

/

ap + (a p(n) − a p(n−1) ) D

(2.44)

where agmax(n) is the maximum undeformed chip thickness of the nth dynamic active grain. λ(n~n−1) is the distance between the nth and (n − 1)th dynamic active grains. ap(n) is the protrusion height of the nth dynamic active grain and ap(n−1) is the protrusion height of the (n − 1)th dynamic active grain. Additionally, scholars defined the mean cutting depth of grains as agmean = 0.5agmax [16]. As a result, the dynamic active grain number (N d ) and corresponding cutting depth (ag ) can be gained through simulation and the dynamic active grain array G(ag ) can be generated. In the above text, N d and ag change with grinding parameters. To investigate influencing laws of grinding parameters on dynamic active grains in the grinding zone, the above models were applied for simulation. It was found in the simulation that circumferential velocity and feed velocity of grinding wheel had very

2.3 Ordinary Grinding Wheel Models and Dynamic Active Grains

67

small influences on dynamic active grains. On contrary, grinding depth influenced dynamic active grain number and maximum undeformed chip thickness significantly. It can be seen from Fig. 2.15 that with the increase of grinding depth, dynamic active grain number and maximum undeformed chip thickness both increased continuously.

Fig. 2.15 Dynamic active grains and ag in grinding zone

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2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

2.4 Grinding Force Models of Ordinary Grinding Wheel and Prediction 2.4.1 Construction of Grinding Force Models The process of grinding force predictive program is shown in Fig. 2.16. It can be divided into following steps: ➀ input grinding wheel parameters and grinding process parameters (Table 2.6) to get N d and ag . dynamic active grains are divided into cutting grains (N c ) and ploughing grains (N p ) according to cutting depth. ➁ input physical property parameters of the workpiece and forces are calculated through equations: cutting forces (Eqs. 2.13 and 2.14), ploughing forces (Eqs. 2.15 and 2.16), and frictional forces (Eqs. 2.18, 2.19, 2.21, 2.22, 2.28 and 2.29). The grinding force model of ordinary grinding wheel can be expressed as: Ft =

Nc  

p       Ftc agn + Ftc f (agn ) + Ft p (agm ) + Ft p f (agm ) + f t

N

1

Fn =

Nc   1

(2.45)

1



Fnc (agn ) − Fnc f (agn ) +

Nc  

 Fnp (agm ) − Fnp f (agn ) + f n

(2.46)

1

where F t is the tangential grinding force; F n is the normal grinding force; agn is the cutting depth of the nth cutting grain, 1 ≦ n ≦ N c ; agm is the cutting depth of the mth ploughing grain, 1 ≦ m ≦ N p , N c + N p = N d ; F tc (agn ) is the tangential cutting force of the nth cutting grain; F nc (agn ) is the normal cutting force of the nth cutting grain; F tp (agm ) denotes the tangential ploughing force of the mth ploughing grain; F np (agm ) denotes the normal ploughing force the mth ploughing grain; F tcf (agn ) is the tangential frictional force between the nth cutting grain and the workpiece; F ncf (agn ) refers to the normal frictional force between the nth cutting grain and the workpiece; F tpf (agm ) is the tangential frictional force between the mth ploughing grain and the workpiece; F npf (agm ) refers to the normal frictional force between the mth ploughing grain and the workpiece; f t denotes the tangential tribological force of grains and f n is the normal tribological force of grains.

2.4.2 Prediction of Grinding Force In the simulation, white corundum grinding wheel (WA80H12V) was applied and its parameters were: dimension: 300 mm × 50 mm × 76.2 mm; grain size: 80#; maximum linear velocity: 35 m/s. The stainless steel 440C was applied as the workpiece. In the model, there’s only one unknown parameter K 1 (a physical variable of grain wearing state) and it could be solved by a group of measured grinding forces.

2.5 Experimental Verification of Grinding Forces

69

Fig. 2.16 Process of grinding force predictive program

The grinding parameters were V s = 20 m/s, V w = 2 m/min, ap = 15 μm and K 1 = 18.36. Simulation results are shown in Fig. 2.17.

2.5 Experimental Verification of Grinding Forces 2.5.1 Experimental Setup Grinding forces under different workpiece parameters (V w , V s and ap ) were measured by single-factor tests. Furthermore, single-factor tests were carried out under dry grinding, pouring grinding, MQL and NMQL conditions. In these tests, MoS2 nanoparticles and palm oil were used to prepare nanofluids with a mass fraction of 4wt.% for the NMQL grinding test.

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2 Analysis of Grinding Mechanics and Improved Predictive Force Model …

Table 2.6 Input parameters Type

Parameters

Values

Grinding wheel parameter

Grinding wheel diameter D (mm)

300

Vertex angle of grains θ (°)

120

Grain size of grinding wheel (#)

80

Structure number of the grinding wheel

12

Maximum grain size d max (mm)

0.202

Minimum grain size d min (mm)

0.158

Circumferential velocity of the grinding wheel V s (m/s)

10–30

Feed velocity V w (m/min)

0.5–3.0

Grinding depth ap (mm)

0.01–0.04

Grinding width b (mm)

50

Yield stress δ s (MPa)

225

Breaking stress δ b (MPa)

540

Friction coefficient

Dry grinding (0.607)

Grinding parameters

Workpiece material

2.5.2 Comparative Analysis Between Predicted Values and Test Results The predicted values and test results of grinding forces under different working conditions are shown in Fig. 2.17. It can be seen from Fig. 2.17 that the predicted values of grinding force agree highly with test results. The mean deviation between the predicted results and test results is 4.19% for normal grinding force, and it is 4.31% for the tangential grinding force. A group of grinding condition was chosen for analysis (dry grinding, V s = 20 m/s, V w = 2 m/min, ap = 15 μm). The tangential frictional force accounted for 89.17% of the total grinding force and the normal frictional force accounted for 90.71% of the total grinding force. The rest was the sum of cutting force and ploughing force. Given the fixed grinding parameters, the proportion of tangential and normal frictional forces in total grinding force under MQL grinding decreased to 86.52 and 89.43%, respectively.

2.5.3 Variation Trend Analysis of Grinding Force With the increase of ap , the dynamic active grain number in the grinding zone and the corresponding cutting depth all increased, thus resulting in a rising trend of cutting force, ploughing force and frictional force. With the increase of rotational speed (V s ) of the grinding wheel, N c and cutting depth changed slightly, but the frictional force decreased significantly. As the feed velocity of workpiece (V w ) increased, N c and

2.5 Experimental Verification of Grinding Forces

71

(a) Different cutting depths ap (μm) under different lubricating conditions

(b) Different feed velocities Vw (m/min) Fig. 2.17 Predicted values and test results of grinding force

cutting depth changed slightly, but the frictional force increased significantly, thus increasing the total grinding force. Under different cooling and lubricating conditions, frictional force changed with friction coefficient. The minimum friction coefficient (0.42) and the minimum grinding forces (F n = 65.06 N, F t = 28.48 N) were achieved under NMQL grinding of stainless steel 440C. With the changes of friction coefficient, the tangential frictional force showed the higher variation rate than the normal one.

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(c) Different circumferential velocities of grinding wheel Vs (m/s)

(d) Different friction coefficients

Fig. 2.17 (continued)

References

73

2.6 Summary To address problems of existing grinding force models, such as the ambiguity of grain states and absent calculation of grinding force based on stress state of a single grain, this chapter carries out a theoretical study on material removal mechanism and mechanical behaviors in the grinding zone under low-speed quasi-static grinding conditions. Moreover, a grinding force prediction model is constructed. The specific research contents are introduced as follows: (1) The material removal mechanism of grinding zone is studied. During interference of grains and workpiece material, there’s material fracture removal effect and plastic-stacking effect simultaneously. The relationship between cutting depth of grains (ap ) and cutting efficiency of grains (β) is disclosed through a single grain scratching test. Moreover, grains are divided into cutting grains and ploughing grains accurately through the relation function. (2) The first grinding force model based on plastic-stacking and material fracture removal mechanism is put forward. Theoretical equations of cutting forces, ploughing forces and frictional forces are established, which can predict grinding force of a single grain with different cutting depth accurately. (3) The calculation models of dynamic active grain number and cutting depth in the grinding zone of workpiece are constructed. Grinding force modelling simulation is performed with considerations to stress state of each grain. The proposed method can reproduce the grain cutting state in the grinding zone better than existing popular methods based on mean cutting depth of grains. (4) Tribological tests of the workpiece and grinding wheel are conducted, through which friction coefficients under different lubricating conditions are acquired. They are brought into the grinding force prediction model to characterize different lubricating conditions. The minimum friction coefficient is achieved under NMQL grinding due to the excellent cooling and lubrication performances. (5) The predicted grinding force is verified by grinding tests. Results show that the predicted values of grinding force agree highly with test results. The mean deviation between the predicted values and test results is 4.19% for the normal grinding force and it is 4.31% for the tangential grinding force.

References 1. Cao J, Wu Y, Li J, et al. A grinding force model for ultrasonic assisted internal grinding (UAIG) of SiC ceramics[J]. International Journal of Advanced Manufacturing Technology, 2015, 81(5–8): 875–885. 2. Lee P H, Nam J S, Li C, et al. Review: Dimensional accuracy in additive manufacturing processes[C]. Proceedings of the Asme 9th International Manufacturing Science and Engineering Conference, 2014.

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3. Zhou M, Zheng W. A model for grinding forces prediction in ultrasonic vibration assisted grinding of SiCp/Al composites[J]. International Journal of Advanced Manufacturing Technology, 2016, 87(9–12): 1–14. 4. Mingzheng Liu, Changhe Li, Yanbin Zhang, Min Yang, Teng Gao, Xin Cui, Xiaoming Wang, Haonan Li, Zafar Said, Runze Li and Shubham Sharma, Analysis of grain tribology and improved grinding temperature model based on discrete heat source, Tribology International, (2022). https://doi.org/10.1016/j.triboint.2022.108196. 5. Du H, Rui Y, Wang Y, et al. MATLAB-based simulation method of surface’s three-dimensional model in grinding process [J]. Modern Manufacturing Engineering, 2009(2): 48–51. 6. Setti D, Sinha M K, Ghosh S, et al. Performance evaluation of Ti–6Al–4V grinding using chip formation and coefficient of friction under the influence of nanofluids[J]. International Journal of Machine Tools & Manufacture, 2015, 88(88): 237–248. 7. Zhang, Y., Li, C., Jia, D., Zhang, D., & Zhang, X. (2015). Experimental evaluation of the lubrication performance of MoS2/CNT nanofluid for minimal quantity lubrication in Ni-based alloy grinding. International Journal of Machine Tools and Manufacture, 99, 19–33. 8. Zhang, Y., Li, C., Jia, D., Zhang, D., & Zhang, X. (2015). Experimental evaluation of MoS2 nanoparticles in jet MQL grinding with different types of vegetable oil as base oil. Journal of Cleaner Production, 87, 930–940. 9. Wang, Y., Li, C., Zhang, Y., Yang, M., Li, B., Jia, D., Hou, Y., & Mao, C. (2016). Experimental evaluation of the lubrication properties of the wheel/workpiece interface in minimum quantity lubrication (MQL) grinding using different types of vegetable oils. Journal of Cleaner Production, 127, 487–499. 10. Chen X, Öpöz TT. Effect of different parameters on grinding efficiency and its monitoring by acoustic emission[J]. 2016, 4(1): 190–208. 11. Zhang, Y., Li, C., Ji, H., Yang, X., Yang, M., Jia, D., Zhang, X., Li, R., & Wang, J. (2017). Analysis of grinding mechanics and improved predictive force model based on material-removal and plastic-stacking mechanisms. International Journal of Machine Tools and Manufacture, 122, 81–97. 12. S. Malkin, Theory and application of machining with abrasives, Grinding Technology, Ellis Horwood Limited (1989). 13. Zhang J, Li H, Zhang M, et al. Study on force modeling considering size effect in ultrasonicassisted micro-end grinding of silica glass and Al2O3, ceramic[J]. International Journal of Advanced Manufacturing Technology, 2016: 1–20. 14. Wang S, Li C, Zhang D, et al. Modeling the operation of a common grinding wheel with nanoparticle jet flow minimal quantity lubrication[J]. International Journal of Advanced Manufacturing Technology, 2014, 74(5–8): 835–850. 15. Singh V, Sharma, M. Light intensity measurements of colloidal stability of Fe3O4 particles in aqueous suspensions for biomedical applications [J]. Magnetohydrodynamics, 2014, 49(3–4): 582–585. 16. Patnaik Durgumahanti US, Vijayender Singh, Venkateswara Rao P. A new model for grinding force prediction and analysis. International Journal of Machine Tools and Manufacture, 2010, 50(3): 231-240. 10.1016/j.ijmachtools.2009.12.004

Chapter 3

Velocity Effect and Material Removal Mechanical Behaviors Under Different Lubricating Conditions

3.1 Introduction The author has disclosed the cooling and lubrication mechanisms as well as interface tribological properties in the grinding zones under low-speed MQL and NMQL grinding processes, and concluded the optimal technological parameters for hightemperature Ni-based alloy GH4169 and 45 steel workpiece material. Furthermore, the author has constructed grinding mechanical models based on plastic mechanics theory under low-speed grinding and different lubricating conditions, which realized accurate prediction of grinding forces under MQL and NMQL conditions. With the development of grinding theory and technologies, high-speed and ultrahigh-speed grinding technologies show greater advantages [1]. The extremely strain rate under a higher cutting speed of grains changes material removal mechanism and decreases the specific grinding energy. Nevertheless, tribological properties of the grain-chip interface and grain-workpiece workpiece under high speed change accordingly. Moreover, material removal mechanical behaviors are different from the general plastic mechanics theory under low-speed grinding conditions. In the grinding process, there are multiple grains in the grinding zone that make reciprocating cutting of the workpiece material, thus forming fresh surfaces. As a result, grinding is different from cutting. On one hand, the negative rake cutting properties of grains change the material removal mechanism, which also incur a higher specific grinding energy and also generate abundant grinding heats. On the other hand, the positional relations of grains and changes in grinding parameters have great influences on interference curve between grains and the workpiece material, bringing high complexity and randomness of the grinding process. Therefore, studying cutting mechanism of a single grain is the most fundamental method to study the grinding mechanism [2] and also an important basis to get a deep understanding the cooling lubrication mechanism of grinding zone and material removal mechanical behaviors [3]. Therefore, this chapter is to study changes in output parameters of high-speed MQL and NMQL grinding, thus disclosing the influencing trends of material removal © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_3

75

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mechanism in the grinding zone, interface cooling lubrication mechanism and interface tribological properties and relevant parameters. On this basis, the material removal mechanical behaviors under high strain rate can be further understood.

3.2 Material Removal Mechanical Behaviors of High-Speed Grinding Under Different Lubricating Conditions 3.2.1 Grain-Workpiece Interference Geometric Model Grain-workpiece interference model is the basis to study cutting behaviors of grains. Chips and furrows are products after interference between grains and workpiece. In previous studies, scholars simplified the 3D model of debris gained from cutting of grain model with a vertex angle of θ into a fusiform structure with a triangular section. In fact, such modelling method ignores influences of cutting behaviors of the previous dynamic active grain on 3D model of the current debris. In the grinding process of ordinary grinding wheel, it is difficult to construct the 3D model of debris with considerations to grain morphology since two adjacent dynamic active grains have different shape features. Moreover it is impossible to simulate grinding process of the ordinary grinding wheel at a high reduction degree. Since the single-grain grinding wheel only has one grain participating in the cutting, the same debris can be gained in each cutting under fixed grinding parameters. Hence, a 3D model of debris with considerations to morphology of grains will be constructed in the following text. 1. Morphology of debris The free surface of debris gained from a single grain is the fresh surface formed after the last grain cutting. After materials are removed from the rake face of grains, a smooth surface is formed on debris and a fresh surface is formed on the workpiece. It can be seen from Fig. 3.1 that the removed materials (morphology before debris removal) by a single grain under constant technological parameters are “cymbiform”. It can be seen from Fig. 3.1 that the interference between a single grain and workpiece material can be described as: (1) Grains enter into the scratching/ploughing stages after cutting in from the entry point and the grain-workpiece interference cross-section area along the movement direction increases gradually from 0. Under this circumstance, no chips are formed. The grain-workpiece interference material flows toward two sides of the furrow and develops plastic deformation, thus forming plastic uplifts. Grains only bear the ploughing force generated by plastic deformation of materials. (2) Grains enter into the cutting stage after the cutting point and the grain-workpiece interference cross-section area along the movement direction increases gradually. It can be seen from Fig. 3.2b that the grain cutting thickness increases

3.2 Material Removal Mechanical Behaviors of High-Speed Grinding …

77

Fig. 3.1 3D model of debris

gradually as they cutting forward until reaching the maximum (maximum undeformed chip thickness agmax ) at the D-D interface. Under this circumstance, there’s plastic-stacking and material removal simultaneously and grains bear forces generated by material plastic deformation and material fracture removal. During grain cutting process, the grain cutting thickness changes and the cross section shapes and area of debris along the movement direction of grains also change. It can be seen from Fig. 3.2 that profiles at four section positions A, B, C and D are shown in Fig. 3.2c–f. Although the grain cutting thickness from point A to point D increases and reaches the maximum undeformed chip thickness at point D, the cross section at point D is not the maximum. Besides, deformation mechanism of each unit material in cross section is different, thus making different contribution rates to

(a) Top view of debris

(c)A—A

(d)B—B

(b) Section view E-E of debris

(e)C—C

Fig. 3.2 3D model of debris and cross sections at different cutting depths

(f)D—D

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grinding force. Therefore, 3D model of grain-workpiece interference materials shall be constructed firstly to study mechanical behaviors when grains cut the workpiece materials. 2. Thickness of debris In the high-speed grinding experiment of a single grain, the chips formed in each process have constant shapes under the constant grinding parameters and the chip thickness at the position of maximum thickness is called as the maximum undeformed chip thickness (agmax ). In previous studies, researchers calculated forces on formation of debris as a value which is proportion to agmax . Such research method ignores not only morphological changes of debris in the dynamic formation process, but also influences of grain cutting thickness and cross section area changes of interfering materials on grinding force. In Fig. 3.2, the grain cutting thickness increases firstly and then decreases from cut-in workpiece to cut-out workpiece of grains, reaching the maximum (agmax ) at point B. A calculation formula of grain cutting thickness (ag ) is established by using the swing angle of grains (ψ) as the independent variable. In Fig. 3.3, the ag function is discussed in two parts of A-B and B-C since the grain cutting thickness presents different variation trends before and after point B.

Fig. 3.3 Cutting depths and swing angle of a single grain

3.2 Material Removal Mechanical Behaviors of High-Speed Grinding …

79

(1) In Stage A-B, the interval of ψ is [0, ψ 1 ]. According to the geometry, it can get: ψ1 = arcos

D − 2ap D − 2ag max

(3.1)

When grains cut to point B, the cutting thickness of debris is the maximum undeformed chip thickness. For single-grain cutting, the interval of grains (λ) is equal to the circumference (π D) of the grinding wheel disk and it can be expressed as: ag max = 2 · π ·

Vw √ · ap D Vs

(3.2)

When grains cut to ψ (0 ≤ ψ ≤ ψ 1 ), the geometric relationship between the vertical distance from grains to the entry point (ap ) and ψ can be expressed as: ap (ψ) =

D (1 − cos ψ) 2

(3.3)

In Eq. (3.3), the vertical distance from grains to the entry point (ap (ψ)) is brought into Eq. (3.2) to replace ap , thus calculating the grain cutting depth at ψ 1 . Hence, the grain cutting depth can be expressed as: ag (ψ) = π · D ·

Vw √ · 2(1 − cos ψ) Vs

(3.4)

(2) In Stage B-C, the interval of ψ is [ψ 1 , ψ 2 ]. According to the geometry, it can get: ψ2 = ar cos

D − 2a p D

(3.5)

The coordinate system of cutting points of a single grain is established. The grinding path AC is the swinging line formed by combination of horizontal movement and circumferential rotational movement of grains. Given cutting parameters of a single grain, the variations of the equation of locus of cutting points with swing angle of grains can be expressed as: 

x= y=

D w (sin ψ + ψν ) 2 νs D (1 − cos ψ) 2

(3.6)

When grains cut to ψ 1 (ψ 1 ≤ ψ ≤ ψ 2 ), it can get according to geometric relationship:

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ag (ψ) =

ap − D2 (1 − cos ψ) ap − y(ψ) = cos ψ cos ψ

(3.7)

Based on the above analysis, the final cutting thickness equation of grains can be expressed as:

ag (ψ) =

⎧ ⎪ ⎨π · D ·

Vw Vs

·

√

2(1 − cos ψ), 0 ≤ ψ ≤ ψ1 (3.8)

⎪ ⎩ ap − D2 (1−cos ψ) ,

ψ1 ≤ ψ ≤ ψ2

cos ψ

3. Cross section shape and area of debris The cross section of debris is shown in Fig. 3.4. According to the geometric relationship between cutting path of grains and cross section height of debris (h), the calculation formula of h can be gained: h(ψ) =

ap −

D (1 2

− cos ψ) cos ψ

(3.9)

In Stage A-B, the cross section of debris is V-shaped and its height (h) decreases gradually with the increase of ψ. The V-shaped cross section area of debris (S v ) can be expressed as: Sv = h(ψ)2 · tan

θ θ θ − (h(ψ) − ag (ψ))2 · tan = ag (ψ) · tan · (2h(ψ) − ag (ψ)) 2 2 2 (3.10)

Fig. 3.4 The cross section shape of debris at different swing angles

3.2 Material Removal Mechanical Behaviors of High-Speed Grinding …

81

In Stage B-C, the cross section of debris is triangular and its height (h = ag ) decreases gradually with the increase of ψ. The triangular cross section area of debris (S t ) can be expressed as: St = h(ψ)2 · tan

θ 2

(3.11)

Hence, the calculation formula of cross section area of debris (S) is:  S(ψ) =

ag (ψ) · tan θ2 · (2h(ψ) − ag (ψ)), 0 ≤ ψ ≤ ψ1 h(ψ)2 · tan θ2 , ψ1 ≤ ψ ≤ ψ2

(3.12)

The curves of cutting depth function (ag (ψ)), cross section area function of debris (S(ψ)) and the primary grinding force waveform under V s = 100 m/s, V w = 0.01 m/ s and ap = 50 μm are shown in Fig. 3.5. With the increase of ψ, the debris length increases continuously and ag (ψ) presents approximately linear variation trend. It reaches the maximum (agmax ) at point B (ψ = ψ 1 ) and then decreases to zero. S(ψ) presents the quadratic functional variation trend and it reaches the maximum at A (d (S(ψ)) = 0) and then decreases gradually to 0. Obviously, the thickness at the maximum cross section area of grains (point A) is not the maximum undeformed chip thickness. The point A is closer to the middle point of debris. It can be seen from the grinding force signal in single-grain measurement that the maximum grinding force also occurs near the middle point in one grain cutting process. Therefore, it is more reasonable to describe grinding process and grinding force of a single grain by using the equation of cross section area of debris as the independent variable. 4. Correction model of cross section area of debris The calculation formula of cross section area of debris is based on the hypothesis that grains are cones with a vortex angle of θ, but it ignores microstructure of rake face of grains and the rounded characteristics of the vertex angle. Besides, the practical interference curve of grains in practical cutting often has some differences to the theoretical interference curve. Therefore, the calculation formula of cross section area of debris in the previous section is applicable to prediction of workpiece surface morphology and grinding force modelling in the grinding process using ordinary grinding wheels. Under such working conditions, many grains have uneven morphologies and different cutting states. At present, theoretical formula is the most effective simulation way. However, grain morphology and furrow morphology are captured through technological means in single-grain grinding, which provides conditions for correction of the theoretical formula of cross section area of debris. Based on model correction, the grinding performances can be predicted and grinding parameters can be analysed. Grinding performance parameters like grinding force and scratch morphology can be predicted by observing grain morphology and establish the mathematical model of grain boundaries to replace the conical grain model. In Fig. 3.6, the shape information of diamond grains were observed under a scanning electron microscope

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Fig. 3.5 Diagrams of the cutting depth function, cross section area function of debris and grinding force signal

(SEM) and a coordinate system was established. The 2D mathematical model (g(x)) of a single grain was constructed according to rake face views of grains: g(x) = a0 + a1 coswx + b1 sinwx + · · · + a4 cos4wx + b4 sin4wx

(3.13)

Constant values under 95% confidence level are listed in Table 3.1 Given the grinding parameters, the cross section shapes of debris at ψ (0 ≤ ψ ≤ ψ 1 ) are shown in Fig. 3.7. The upper boundary of this cross section is g1 (x) = g(x)-h(ψ) + ag (ψ), and the lower boundary is g2 (x) = g(x)-h(ψ). Let g1 (x) = 0 and g2 (x) = 0. Then, the functions of x-coordinates of points A, B, C and D about ψ are gained: X A (ψ), X B (ψ), X C (ψ), and X D (ψ). Therefore, the cross section area of

Fig. 3.6 The cross section area function of debris based on grain boundary model

3.2 Material Removal Mechanical Behaviors of High-Speed Grinding …

83

Table 3.1 Fitted values of parameters and confidence interval Parameters

Numerical values

Confidence interval

Parameters

Numerical values

a0

166.1

(44, 288.2)

w

a1

−152.1

(−271.8, − 32.41)

b1

−58.23

0.005433

Confidence interval (0.002743, 0.008123) (−106.3, − 10.2)

a2

−6.915

(−14.87, 1.04)

b2

27.63

(−9.265, 64.53)

a3

−0.5167

(−5.108, 4.074)

b3

−8.489

(−23.95, 6.968)

a4

−6.535

(−13.51, 0.4424)

b4

1.545

(−12.93, 16.02)

debris in the interval of 0 ≤ ψ ≤ ψ 1 is: X A (ψ) X C (ψ) S(ψ) = g2 (x)d x − g1 (x)d x X B (ψ) X D (ψ)

(3.14)

Similarly, the cross section area of debris in the interval of ψ 1 ≤ ψ ≤ ψ 2 is: X A (ψ) S(ψ) = g2 (x)d x X B (ψ)

(3.15)

In the same way, the calculation formula of cross section area of debris is solved by observing furrow morphology and measure the furrow boundary matrix under a single-grain grinding to replace the conical grain model, thus enabling to reproduce the grain cutting process. An accurate evaluation can be realized by combining

Fig. 3.7 The cross section area function of debris based on furrow model

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the measured grinding performance parameters. In Fig. 3.7, 3D shape information of furrows was measured by a 3D morphometer and a coordinate system was established. The morphology matrix (C(x)) of furrow boundaries was gained. Given the grinding parameters, the cross section shapes of debris at ψ (0 ≤ ψ ≤ ψ 1 ) are shown in Fig. 3.7. The upper boundary of this cross section is C 1 (x) = C(x) + ag (ψ), and the lower boundary is C(x). Let C (x) = h and C 1 (x) = h. Then, the functions of x-coordinates of points A, B, C and D about ψ are gained: X A (ψ), X B (ψ), X C (ψ) and X D (ψ). Therefore, the cross section area of debris in the interval of 0 ≤ ψ ≤ ψ 1 is: X A (ψ) X C (ψ) (3.16) S(ψ) = (C(x) + h)d x − (C1 (x) + h)d x X B (ψ) X D (ψ) Similarly, the cross section area of debris in the interval of ψ 1 ≤ ψ ≤ ψ 2 is: X A (ψ) S(ψ) = (C(x) + h)d x X B (ψ)

(3.17)

3.2.2 Mechanical Action Mechanism and Material Strain Rate in the Cutting Zone 1. Material deformation mechanism and mechanical behaviors in the cutting zone The material deformation mechanism in the single-grain grinding zone is shown in Fig. 3.8. The material deformation mechanism in the cutting zone during grinding is the same with that during cutting. there’s the first deformation zone and the second deformation zone simultaneously. Professor Wenfeng Ding from NUAA [4] simulated high-speed single-grain cutting of high-temperature Ni-based alloy workpiece and also observed the above phenomena. Different from the cutting process, the negative rake cutting of the grain led to different mechanical action mechanisms between the grain and debris. The equations of rake angle (ϕ), frictional angle (β f ) and strain rate changed accordingly. Moreover, influencing trends of grinding parameters and lubricating conditions on material removal mechanism were also different. Stress analysis of materials in the single-grain grinding zone is shown in Fig. 3.9. Material stresses and deformation mechanism can be described as follows: ➀ In the first deformation zone, stress analysis at point A is shown in Fig. 3.9a. The resultant force of the frictional force (F f ) and extruding force (F n ) is F r . According to the theory of mechanics of materials, the included angle between the material fracture chipping direction (direction of shear zone F s ) and F r is π/

3.2 Material Removal Mechanical Behaviors of High-Speed Grinding …

Zone II deformation

Vc Fn

Vd

Fs C

grit

Ff

D Fr Fs Fr

workpiece

85

Ff A Fn

Zone 1 deformation

Fig. 3.8 Material deformation mechanism in the cutting zone

(a) Stress analysis in the first deformation zone

(b) Stress analysis in the second deformation zone

Fig. 3.9 Stress analysis of the workpiece material in cutting zone

4, and the shear angle (ϕ) is on the horizontal line. Under this circumstance, F f points upward along the grain-chip interface and it facilitates material fracture chipping. Hence, the equation of ϕ can be calculated according to geometric relations of several angles: ϕ1 =

π + β f − γ0 4

(3.18)

The thickness and length ratio of debris in grain cutting is about 1/100 [5]. Therefore, the negative rake angle at grain cutting is γ 0 ≈ θ /2 and the frictional angle is β f = arctan(μ), where μ is the friction coefficient between rake surface of the grain and chips. The equations of γ 0 and β are brought into Eq. (3.18) and it can get: ϕ1 =

π θ + arctan μ − 4 2

(3.19)

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3 Velocity Effect and Material Removal Mechanical Behaviors Under …

➁ In the second deformation zone, stress analysis at point C is shown in 3.9b. The resultant force of the frictional force (F f ) and extruding force (F n ) is F r . According to the theory of mechanics of materials, the included angle between the material fracture chipping direction (direction of shear zone F s ) and F r is π/ 4, and the shear angle (ϕ) is below the horizontal line. Under this circumstance, F f points downward along the grain-chip interface and it hinders debris flowing. From the perspective of kinematics, the initial movement velocity on the graindebris interface is relatively low due to the frictional force, but the velocity on the free surface of debris is relatively high. Under high-speed cutting, an instantaneous velocity gap between the grain-debris interface and free face of the debris is generated due to the high strain rate of debris, thus generating a shear zone. As a result, the second deformation zone is formed. Hence, the equation of ϕ can be calculated according to geometric relations of several angles: φ2 = β f + γ0 −

θ π π = arctan μ + − 4 2 4

(3.20)

2. Strain rate in the cutting zone and its influencing factors For high-speed grinding, change of strain rate is a major factor that influences the material removal mechanism. The strain rate in the cutting process reaches as high as 104 –105 s−1 . The strain rate of removed materials is as high as 107 –108 s−1 under low-speed grinding (V s ≤ 30 m/s), which is attributed to the negative rake angle of grains. On this basis, it is speculated that the strain rate under high-speed grinding is 1 or 2 orders of magnitudes higher than that under low-speed grinding. In high-speed grinding process, the strain hardening effect and the strain rate strengthening effect caused by strain rate of material deformation have significant influences on material removal mechanism. Professor Tan Jin[183, 184] established the equations of shearing strain and strain rate in the shear zone of grains: γ = γ˙ =

cos( θ2 )

(3.21)

2λ1 v cos( θ2 ) sin φ

(3.22)

sin ϕ cos(ϕ + θ2 ) agmax cos(φ + θ2 )

where ϕ is the shear angle, θ is the vortex angle of grains, and λ1 is the mean length– width ratio (λ1 = 6 ~ 12) of the shear zone. v refers to the cutting speed of grains and there’s v ≈ V s during the single-grain grinding. Furthermore, equations of strain rate of debris in two deformation zones can be gained by bringing Eqs. (3.1),(3.19) and (3.20) into the Eq. (3.22): .

γ1 =

λνs2 cos( θ2 ) sin( π4 + arctan μ − θ2 ) √ π νw a p D cos( π4 + arctan μ)

(3.23)

3.2 Material Removal Mechanical Behaviors of High-Speed Grinding …

87

λνs2 cos( θ2 ) sin(arctan μ + θ2 − π4 ) √ π νw a p D cos(arctan μ + θ − π4 )

(3.24)

.

γ2 = −

According to Eq. (3.23), grinding parameters (V s , V w , ap ), grain shape (θ ) and lubrication characteristics of grind-debris interface (μ) are factors that influence strain rate of workpiece material deformation in the single-grain cutting process. In the following text, key attention is paid to analyse the influencing trends of V s , V w and μ on shear rate since V s /V w = 1 × 104 and the grain shapes are constant in this study. It can be seen from Fig. 3.10a that given the same other parameters, strain rates (γ˙ ) of the first and second shear zones presents a linear growth trend when V s increases from 30 to 120 m/s (accompanied with some growths of ϕ), which show higher growth rates than strain rates of the first and second deformation zones. In Fig. 3.10b, as μ increases (representing the lubricating conditions), the strain rate of the first deformation zone presents an increasing trend in the manner of quadratic function. This is because frictional force in the first deformation zone provides gains to material removal and strain rate increases with the increase of frictional force, which is more beneficial for debris forming. In the second deformation zone, as μ increases (representing the lubricating conditions), the strain rate of the second deformation zone presents a decreasing trend in the manner of quadratic function. Frictional force in the second deformation zone hinders outflow of debris and debris change to flow along grain surface rather than flow toward grains, thus decreasing the strain rate gradually. In Fig. 3.10c, the strain rate presents a linear reduction trend with the increase of grinding depth. Since this study focuses on velocity effect and lubrication effect in high-speed grinding, the influencing trends of grinding speed and friction coefficient on strain rate are taken into account. The variation trends of strain rates of the first and second deformation zones with grinding speed and friction coefficient are shown in Fig. 3.10d.

3.2.3 Debris and Furrow Forming Mechanisms The debris and furrow formation under high-speed grinding is a process of plastic deformation and fracture removal of workpiece materials through interference with grains. This process is often accompanied with strain hardening effect, strain rate strengthening effect and thermal softening effect. 1. Debris forming mechanism and influencing factors Morphology of debris is the comprehensive manifestation of several phenomena. Impact dynamics describe the material deformation behaviors under high speed as an adiabatic shear process. Adiabatic shear effect refers to the constitutive instability (thermal viscoplastic instability) of materials under impact loads. There’s extremely high strain rate in the shear zone of material removal under the impact loads and the shear zone is an insulated environment in an extremely short period. At this

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(a) Effects of Vs (m/s) on strain rate

(c) Effects of Vw (μm) on strain rate

(b) Effects of μ on strain rate

(d) Two-factor analysis

Fig. 3.10 Strain rate under different grinding parameters and friction coefficients

moment, the a lot of inelastic energy in the material deformation process is transformed into grinding heats, thus increasing material temperature in the shear zone dramatically and thereby decreasing material hardness (softening). At the moment, the softening effect is stronger than the strain hardening effect and strain rate strengthening effect, and a shear zone is formed, accompanied with material instability. Therefore, the debris formation process under grain cutting is a dynamic stress-heat coupling process under a high strain rate. For metallic materials, material removal process is attributed to plastic deformation of materials after the increase of strain. In previous studies, scholars have carried out abundant dynamic material tensile tests [6] which have proved the strain hardening and strain rate strengthening phenomena. It can be seen from Fig. 3.11 that material removal process with changes of strain rate can be divided into following three types according to the stress–strain curve. ➀ In Fig. 3.12, under quasi-static condition (γ˙ = 10–3 s−1 ): deformation stress of materials increases significantly with the increase of strain, indicating that

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89

Fig. 3.11 Stress–strain curve under “velocity effect”

the workpiece material has obvious strain hardening effect. Debris is formed when the stress increases to the break limit of the materials (σ b1 ) and the free face of debris presents periodic uplifts (bamboo-shaped), which are caused by compressional deformation during debris formation. However, the strain rate of material deformation is relatively low due to the low velocity, without forming obvious shear zone. ➁ In Fig. 3.13, under high strain rate (γ˙ = 103 s-1), it hypothesizes the shear zone of debris as an isothermal environment. The strain hardening stage of material deformation stress is significantly higher than that under the quasi-static condition. This phenomenon is called as the “strain rate strengthening effect” of material plastic deformation. The deformation resistance of materials is improved under the strain rate strengthening effect. Under this circumstance, since grains have strong impact effects on materials, the workpiece materials form shear layers under the high strain rate condition, thus forming debris. The break limit stress among shear layers is the material break limit (σb2) under the high strain rate condition. Obvious periodic shear-slip layers are formed on the free face of debris. Fig. 3.12 Debris forming mechanism under quasi static condition

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Fig. 3.13 Debris forming mechanism under high strain-isothermal condition

At the moment, the distance of shear-slip layers under high strain condition is significantly higher than that under quasi-static condition. Moreover, the higher velocity brings the higher strain rate and also the higher distance of shear-slip layers. It even may cause complete breakage and separation of shear layers due to the cliff-type fracture process. ➂ In Fig. 3.14, temperature rising on the grain-debris interface is considered under high strain rate condition (γ˙ = 103 s−1 ): in this case, the plastic deformation process of materials is the comprehensive results of strain rate strengthening effect and thermal softening effect, that is, the adiabatic shearing process. As shown in Fig. 3.11, the stress–strain curve under adiabatic shearing is between those under quasi-static condition (Curve 1) and high strain-isothermal condition (Curve 2). This can be explained as follows. Due to strain rate strengthening effect, materials are softened by the mass grinding heats, thus decreasing its deformation resistance. Moreover, more and more heats transferred into the shear zone with the increase of strain rate and the thermal softening effect is intensified. The break limits of materials under three boundary conditions are σ b2 > σ b3 > σ b1 . There’s material fracture and plastic flowing of materials after thermal softening simultaneously in the shear layers of debris. Therefore, studying strain rate effect and thermal softening effect under different grinding parameters and lubricating conditions and constructing an evaluation model Fig. 3.14 Debris forming mechanism under high strain condition

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91

are key problems to study material removal mechanism under high-speed grinding conditions. 3. Furrow forming mechanism and influencing factors In previous studies, the plastic-stacking effect under low-speed grinding conditions has been discussed and the influencing trends of cutting depth on cutting efficiency under quasi-static conditions have been explored. According to results of this experiment, the plastic-stacking effect still exists in high-speed grinding. The plastic-stacking effect of grains along the top view of grain cutting is shown in Fig. 3.15. Professors Opoz and Chen [7] carried out a single-grain cutting test and theoretical simulation and found that the plastic-stacking phenomenon weakens with the increase of grain cutting speed. However, the material deformation mechanism under the plastic-stacking effect was not given in this study. Considering the axial symmetrical relationship between two sides of debris, only the stress deformation of materials at the right edge of grains was analysed. Suppose material form fracture debris at point A (α = α 1 ). As shown in Fig. 3.16, it can be seen from mechanical relations of materials, the theoretical shear deformation zone between the removed and remained materials shall have the same direction with movement of grains during forward grain cutting. The resultant force of F f and F n is F r and the included angle between F s and F r is π/4. The resultant force is decomposed

Scratches threedimensional topography

Abrasive

Plastic stacking

Plastic stacking

Grit

Axonometric drawing Chip formation area Plastic stacking

Shape the stacking area

Altitude map

Fig. 3.15 Plastic-stacking mechanism and 3D morphology of furrow

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Shear deformation zone Chip formation area

Plastic accumulation zone

Grit

Fig. 3.16 Deformation mechanism and stress analysis of workpiece material at the grain edge

into F y which is parallel to the movement of grains and F x which is perpendicular direction. In the following text, the deformation mechanism of material removal is analysed.: (1) Suppose grinding parameters are constant. With the increase of the angle α, the included angle (ϕ) between the directions of practical material fracture force (F s ) and the theoretical shear deformation zone decreases continuously. Meanwhile, F y which is for material removal increases gradually. After α increases toα 1 (ϕ = 0), the value of F y matches with the ultimate stress for material fracture, thus forming chips. In the interval ofα[0,α 1 ], F y is lower than the ultimate stress for material fracture and materials flow to two sides of the furrow in the plasticstacking form. In other words, the negative rake (γ 0 ) of grain cutting decreases gradually with the increase of α. As a result, grains are sharper and materials are easier to break. This explains the plastic-stacking formation well. (2) The influencing trend of grinding speed on plastic-stacking at point B is discussed. The material removal process at point B can be simplified as the cutting process by the cutter with a negative rake angle γ 0 . With the increase of grinding speed, the strain rate of removed material at point B presents a rising trend. According to the strain rate strengthening effect, the fracture stress and strain of materials are positively related with deformation strain rate of materials. According to the theory of metal processing [8, 9], the ductility of metallic removed materials is related with the intensity relationship between strain rate strengthening effect and thermal softening effect when the strain rate increases:

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93

➀ Influences of temperature rise on the grinding zone are ignored. In other words, it supposes that the grinding temperature is constant. The material hardness increases with the increase of strain rate, thus decreasing ductility of removed workpiece materials. For three stages for grains to remove workpiece materials, velocity leads to weakening ploughing effect, which has been proved by some scholars [10]. Similarly, for the plastic-stacking phenomena at two sides of the furrow, the proportion of protrusion heights also declines with the reduction of ductility. This implies that the cutting efficiency increases. ➁ The thermal softening effect of temperature rise on grinding zone is considered. The ductility of material removal is related with the intensity relationship between strain rate strengthening effect and thermal softening effect. When the strain rate strengthening effect is stronger than the thermal softening effect, the proportion of uplifts at two sides of the furrow will decrease; On contrary, when the thermal softening effect is stronger than the strain rate strengthening effect, the proportion of uplifts at two sides of the furrow will increase. The material plasticity indexes under this working condition are shown in Fig. 3.17a.

Fig. 3.17 Influence of different lubricating conditions on the velocity effect of material removal

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(3) Different lubricating conditions during material removal may change the intensity relationship between strain rate strengthening effect and thermal softening effect. The thermal softening effect will be intensified under lubricating conditions with a high friction coefficient and a poor heat exchange capability. On contrary, it may produce few frictional heats and the cooling lubricating media may take away more grinding heats under the lubricating conditions with a low friction coefficient and good heat exchange capability, thus decreasing the influencing weight of softening effect. The principle is shown in Fig. 3.17b.

3.3 Experimental Method of Single-Grain High-Speed Grinding 3.3.1 Building of the Experimental Platform 1. Experimental platform for high-speed precision grinding with single-grain/ ordinary grinding wheels To meet high-speed grinding experimental conditions, the team has built a “experimental platform for high-speed precision grinding with single-grain/ordinary grinding wheels”. This platform mainly realizes measurement and analysis of singlegrain grinding forces, debris collection, scratch morphology observation and analysis. The major parameters of the high-speed precision grinder are: maximum output power of spindle = 5.5KW, maximum rotational speed = 18000r/min (using the 200 mm (diameter) grinding wheel with the maximum linear speed of 180 m/s), moving accuracy of the workbench along X/Y direction = 1 μm, and moving accuracy of the workbench along Z = 0.1 μm. The platform is shown in Fig. 3.18. 2. Single-grain grinding wheel The design and manufacturing of single-grain grinding wheel is the key of the whole experimental platform. The grinding wheel disk and the clamping are made of 45 steel. The diamond is embedded at top of the ladder spindle. The protrusion height of grains is about 550 μm and the vortex angle of grains is 122°, as shown in Fig. 3.19. In the assembling process, the diamond ladder spindle is installed in the ladder hole of the clamping to realize positioning. Meanwhile, the cylinder is clamped tightly at rear end of the ladder hole by using socket head cap screw with full threads. The clamping with a diamond grain is installed in the square groove of the grinding wheel disk. The circumferential positioning is performed at the square groove with the same width of the clamping by depending on the nominal dimension of circumferential width and radial position of clamping is realized by using two hexagon fit bolts. In the high-speed revolution of grinding wheel, the centrifugal force of the clamping is undertaken by the hexagon fit bolts, while the tangential grinding force generated by cutting action is undertaken by the side surface of square groove. Meanwhile, a clamping without diamond grain is installed at the axial symmetric position of the

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Fig. 3.18 Experimental platform of single-grain grinding

(a) Side surface of diamond

(b) Front view of diamond

Fig. 3.19 Surface morphology of single diamond grain

clamping with a diamond grain for the purpose of balance weight. During design and manufacturing of single-grain grinding wheel, the safe speed of rotation shall meet the minimum 200 m/s. After finishing the assembly, the high-speed dynamic balance debugging is authorized to Qingdao Sisha Taiyi Ultra-hard Grinding Co., Ltd. The devise is shown in Fig. 3.20. 3. Grinding force acquisition system In high-speed grinding experiment, YDM-III99 dynamometer based on piezoelectric quartz 3D force sensor was applied as the force measuring unit. The inherent

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Fig. 3.20 Clamping of single diamond grain

frequencies along the X and Y directions are over 5 kHz, and the inherent frequencies along the Z direction are higher than 25 kHz. The force signals are output by the dynamometer and then accessed into the electrical signal acquisition module through the charge amplifier (Linghua ADLINK USB-1902). The collection frequencies of the acquisition module can reach 80 kHz for each channel of X, Y and Z. The final force signal images are input into the “grinding force dynamic acquisition system” and output the images. In this experiment, the maximum grinding linear speed reached 120 m/s and the frequency of force signals generated after interference between single grain and workpiece material was lower than 200 Hz. The applied grinding force measurement system can collect force signals under high-speed grinding conditions. The grinding force acquisition system is shown in Fig. 3.21.

3.3.2 Discussion of Previous Single-Grain Experimental Methods Debris gained by material removal based on single-grain cutting is wedge-shaped. In the process from cut-in to cut-out of workpieces, the cutting depth of grains increases firstly and then decreases and the maximum undeformed chip thickness is at the maximum cutting depth. Therefore, the material removal mechanism changes with the cutting depth. The debris formation is divided into three stages with the increase of cutting depth, namely, scratching stage, ploughing stage and debris forming stage. The single-grain high-speed cutting test is to reproduce the grain cutting behaviors

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Fig. 3.21 Grinding force measurement method in the single-grain cutting test

during grinding wheel cutting. Nowadays, scholars have designed multiple experimental methods of single-grain cutting in accordance to objectives and grinding parameters. The most basic methods can be summarized as following three types: equal-thickness cutting, spindle cutting and triangular cutting (Fig. 3.22). (1) Equal-thickness cutting. Such experimental methods have realized that the grain cutting thickness is fixed and the cut-in depth of grains is the feeds of grinding wheel along the cutting depth. Since these methods have constant grinding parameters, each grain cutting process has the same cutting path and the same chip shape theoretically. Ohbuchi [11] firstly carried out an experimental study on equal-thickness cutting approaches. Turning is one of the most common equal-thickness cutting approaches. In the experiment, the workpiece material was processed into cylinders that were installed in the lathe, while the grain was

(a) Equal-thickness cutting

(b) Spindle cutting

Fig. 3.22 Experimental methods of single-grain cutting

(c) Triangular cutting

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installed as the lathe tool. Alternatively, the workpiece material was processed into disks that were installed at the spindle of the grinder, while the grain was installed at the workbench of the grinder. (2) Spindle cutting. Chips generated in spindle cutting look like shuttles, sharp at two ends and thick in the middle. F. Klocke [12], a German scholar, fixed the single grain on the grinding wheel disk to make spindle cutting test of the horizontal workpiece. Opoz and Chen [7], English scholars, also carried out a singlegrain experimental study of influences of cutting depth on plastic-stacking rate by using the same method. The principle is shown in Fig. 3.23a. Professor Hui Huang [13] from the Huaqiao University carried out an experimental study on spindle cutting of Ta12W material with diamond. In the doctoral dissertation, Professor Tan Jin from Hunan University [14] described a spindle single-grain cutting test, in which the single grain was fixed in the workbench of grinder and the arc workpiece was clamped in the grinding wheel disk. The principle is shown in Fig. 3.23b. Such method has a shortage that the grain may cut the scratch which was formed after one revolution of the workpiece for the second time and even for many times. In particular, such characteristic doesn’t conform to the real grain cutting behaviors completely under high-speed cutting. (3) Triangular cutting. In triangular cutting, the single grain cuts into the workpiece from a certain angle gradually to observe grinding phenomenon with the increase of cutting depth [15]. Such method is very difficult to be used in experiment since it has very high requirements on setting precision of the workpiece clamping angle. It is often used by scholars in simulation. The above three test methods have both advantages and disadvantages. PhD Zhenzhen Chen from NUAA [16] combined the equal-thickness cutting test and spindle cutting test (named as “one-step method”, Fig. 3.24), and brazed the diamond grain onto the grinding wheel disk to cut the horizontally feeding workpiece at a certain cutting depth. The chip shapes in this method agreed with those in real grinding.

(a) Spindle cutting test (the grain rotates)

Fig. 3.23 Experimental methods of spindle cutting

(b) Spindle cutting test (the workpiece rotates)

3.3 Experimental Method of Single-Grain High-Speed Grinding

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Fig. 3.24 One-step method

Moreover, it avoids repeated grinding caused by excessive rational speed of the grinding wheel. PhD Lin Tian from NUAA [17] proposed the “two-step method” based on the “one-step method” (Fig. 3.25). Step 1: “Initial scratching”. The centre of grinding wheel moves in relative to the workpiece along the direction with an angle of θ to the x-axis. The grain cuts the workpiece surface to form the initial furrow. Step 2: the centre of grinding wheel moves along the x-axis only and the grain cuts the workpiece surface to form secondary furrow. Debris formed in the interference zone of twice grain cutting furrows is wedge-shaped and its size increases gradually with the increase of cutting depth. Such method realizes observation of scratching, ploughing and debris forming stages. It is also the best method to study size effect so far.

3.3.3 Experimental Methods of Single-Grain High-Speed Grinding Under Different Lubricating Conditions The experiment is to discuss influencing mechanism of velocity effect and lubricating effect on mechanical behaviors and tribological characteristics of grain cutting materials under single-grain high-speed MQL and NMQL grinding conditions. The cutting efficiency, grinding force, debris morphology and furrow morphology were observed by changing grain cutting speed and lubricating conditions. Hence, the “one-step method” was enough to meet experimental requirements. 1. Experimental scheme The speed parameter with a fixed velocity ratio of V s /V w = 104 was chosen. Moreover, the feed depth of grains was fixed at ap = 50 μm. These can assure to form debris with the same thickness by the single grain under different speeds. The grinding parameters are listed in Table 3.2.

100

3 Velocity Effect and Material Removal Mechanical Behaviors Under … O2 vs

O1

z

x

O

vf

O3

O2

vf O3 vs

O1

O1 θ

θ

θ

y vw

O3

O2

(a) Step 1

O3

(b) Step 2

O2

(c) Final superposition effect

Fig. 3.25 Two-step method

Table 3.2 Experimental scheme V s (m/s) Vw

(10−4

m/s)

30

40

50

60

70

80

90

100

110

120

30

40

50

60

70

80

90

100

110

120

Dry grinding

D-1

D-2

D-3

D-4

D-5

D-6

D-7

D-8

D-9

D-10

MQL

M-1

M-2

M-3

M-4

M-5

M-6

M-7

M-8

M-9

M-10

NMQL

N-1

N-2

N-3

N-4

N-5

N-6

N-7

N-8

N-9

N-10

2. Preparation of samples The workpiece surface in the experiment was pre-processed according to following steps: firstly, the experimental surface of the workpiece was ground to reach a surface roughness (Ra) lower than 0.3 μm. Next, the workpiece surface was polished to remove furrows after grinding, which can increase Ra to Ra = 0.04–0.05 μm. 3. Mass fraction of nanofluids Nanofluids with a mass fraction of 8% were prepared by using MoS2 /CNTs mixed nanoparticles and palm oil, which were used as the grinding fluid in the experiment.

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3.4 Experimental Results and Discussions During high-speed MQL/NMQL grinding, grinding force, debris, single-grain furrow and other experimental parameters changed with speed of the grinding wheel and lubricating conditions. Combining with experimental results, the velocity effect and lubrication effect under high-speed grinding were analysed.

3.4.1 Debris Morphology and Material Removal Mechanism 1. Effects of grinding speeds on debris morphology The comparison of debris between ordinary grinding and single-grain cutting under dry grinding condition when the rotational speed of the grinding wheel is 30 m/s is shown in Fig. 3.26. The debris morphology in single-grain cutting is highly similar with that in ordinary grinding. This proves that single-grain cutting test reproduces the material removal process in actual grinding well. The chip morphologies formed during dry condition under different linear velocities of grains are presented in Fig. 3.27. Clearly, chips under different cutting speeds of the grain have similar features: the grain-debris contact interface (hereinafter referred as the “cutting face”) is relatively smooth and the free face of debris presents “lamellar” structures with some arrangement laws. According to characteristics of debris, adiabatic shear occurs during material deformation removal due to the extremely high strain rate of materials. The adiabatic shear phenomenon means that under the impact loads, the removed material has extremely high deformation strain rate and plastic deformation occurs, accompanied with generation of abundant heats in a short period. When the thermal conductivity of workpiece material is very low (for example, the thermal conductivity of high-temperature Ni-based alloy GH4169 is about 14.7 W/m·k), a thermal insulation environment is formed in debris materials and a lot of heats concentrate in

Fig. 3.26 Comparison of debris between single-grain cutting and ordinary grinding experiments

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Fig. 3.27 Debris morphology at different cutting speeds

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103

the shear slip zone of debris, which leads to local high temperature and strengthens softening, thus causing shearing instability. Under the same grinding parameters, the workpiece material with high thermal conductivity (for instance, thermal conductivity of Aluminium alloy is about 121–151 W/m·k) has no shear slip phenomenon. Compared to cutting, grinding leads to a higher strain rate and more violent friction on the cutter-chip interface due to the negative rake cutting, thus making it easier to develop adiabatic shearing. In Fig. 3.27, adiabatic shear occurs on free face of debris when the rotational speed of the grinding wheel increases from 40 to 120 m/s. Hence, the adiabatic shear takes the dominant role in material removal mechanism of high-temperature Nibased alloys within this speed range. Moreover, the slipping distance of the adiabatic shear layer increases with the increase of rotational speed of the grinding wheel. This is because the strain rate of debris material is increased significantly with the increase of rotational speed of the grinding wheel, thus intensifying the adiabatic shear and making the shear layer of debris sliding by a further distance. Additionally, the distribution of zigzag shear layers under the adiabatic shear effect has obvious periodicity. In the cutting theory, the concentrated shear frequency is used for a quantitative description of forming characteristics of zigzag chips. The equation of shear layer forming frequency ( f ) is: f =

1 v = T Lc

(3.25)

where v is the flowing velocity of chips. For single-grain cutting, v = V s . L c is the pitch of chips. Based on above equations, intervals of shear layers in SEM images of debris under each speed were measured by the following method (Fig. 3.28). (1) The debris morphology images area read by MATLAB software and transformed into a pixel point matrix. Coordinates of pixel points at points P3 and P4 are captured by using point mapping function and the real length ratio (Δl) of each pixel point is calculated: Δl =

L X4 − X3

(3.26)

where L is the scale length (μm). X 3 and X 4 are x-coordinate values of P3 and P4 . (2) Coordinates of pixel points at the starting point P1 and terminal point P2 of the debris shear layer are captured by using the point mapping function. The interval (L c ) of debris shear layers can be expressed as: L c = Δl ·

√

(X 2 − X 1 )2 + (Y2 − Y1 )2

(3.27)

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Fig. 3.28 Calculation method of shear frequency

where X 1 and Y 1 are x-axis and y-axis coordinates of point P1 . X 2 and Y 2 are x-axis and y-axis coordinates of point P2 . Ten groups of adjacent shear layers were chosen from SEM images of debris under each speed and intervals of shear layers were measured. The mean values were calculated and then the concentrated shear frequency was calculated. The shear frequencies under different grinding speeds are presented in Fig. 3.29. In Fig. 3.29, intervals (L c ) of debris shear layers and concentrated shear frequency both presented rising trends with the increase of grinding speed. When the grinding speed is 120 m/s, L c reaches 4.14 μm and the concentrated shear frequency reaches 29.01 MHz, which are increased by 60.47% and 149.42% compared to those at 30 m/ s, respectively. On one hand, the increase of L c is attributed to the sharp increase of grinding strain rate and there’s stronger trend of slipping forward under the impact effect of the grain. On the other hand, the tribological action between the grain and debris is intensified and the strain rate of materials increases significantly with the increase of cutting speed, thus generating abundant grinding heats. The adiabatic shear phenomenon of debris is further intensified, thus strengthening the “thermal softening effect” of debris materials. His decreases constraint against the longer sliding distance of shear layers.

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Abrasive chip spacing

Centralized shear frequency

Abrasive chip spacing Centralized shear frequency

Abrasive cutting speed Fig. 3.29 Shear frequency under different cutting speeds

Besides, the concentrated shear frequency also increases significantly as a response to the sharp growth of strain rate and great enhancement of “thermal softening effect”, indicating that the adiabatic shear phenomenon becomes more and more prominent with the increase of cutting speed. Under such effect, the unit block area of debris shear layers decreases and the critical deformation energy of adiabatic shear declines, which are conducive to decrease the unit grinding force and specific grinding energy. 2. Effects of lubricating conditions on debris morphology Debris morphologies under different lubricating conditions are shown in Fig. 3.30. When the grinding speed is 40 m/s, the debris shapes under three working conditions are similar, showing as successive banded chips. This is because given the low speed, materials have a low strain rate and the thermal softening effect of the grinding zone is relatively weak. At 80 m/s, obvious shear zones are observed on free faces of debris under three working conditions. This reflects that materials experience adiabatic shear in the shaping process under a high speed. Differently, L c under dry grinding is the lowest, followed by those under MQL grinding and NMQL grinding successively. Material fracture even occurs under NMQL grinding. On one hand, the lubrication effects are strengthened gradually from dry grinding to MQL grinding and then to NMQL grinding, while friction coefficients decrease successively. As a result, the strain rate of the first deformation zone under the same speed increases gradually, accompanied with gradual growth of shear slip distance. On the other hand, the strengthening lubrication effect decreases the yields of frictional heats, and the strengthening cooling effect increases the heats discharged from the shear zone. As a result, the thermal softening effect during chip formation

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Fig. 3.30 Debris morphologies at different lubricating conditions

under NMQL grinding is weaker than that under dry grinding and slippage of the debris shear layers is mainly dominated by material fracture, accompanied with plastic flows. Consequently, interval of debris shear layers is greater and even debris fracture occurs. The above laws are further intensified at 120 m/s. Banded chips are still formed under dry grinding due to the thermal softening effect. Debris fracture also occurs under MQL grinding due to the excessive intervals of shear layers. The debris fracture is further intensified under NMQL grinding. Based on above analysis, lubricating conditions have significant influences on debris forming mechanism. The cooling and lubrication performances under dry grinding, MQL grinding and NMQL grinding have been verified. Due to the excellent tribological characteristics and enhanced heat transfer ability of nanofluids, NMQL provides the best cooling and lubrication effects of the grinding zone. In single-grain cutting test, furrow morphologies under dry grinding, MQL grinding and NMQL grinding were measured (Fig. 3.31). Under dry grinding, the furrow surface had debris adhesion and adhesion layer formed by secondary rolling after material peeling, which proved the poor cooling and lubrication performances under dry grinding. There were only microscopic furrows in the furrow morphology under MQL grinding, and partial adhesions were discovered at furrow edges. This proved that the cooling

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107

Fig. 3.31 Furrow morphologies at different lubricating conditions

and lubrication performances were improved to some extent under MQL grinding. The optimal workpiece surface was achieved under NMQL grinding, indicating the optimal cooling and lubrication performances of NMQL.

3.4.2 Plastic-Stacking Phenomenon and Influencing Factors The author explained the plastic-stacking phenomenon of furrows formed by singlegrain cutting and quantized the degree of plastic-stacking phenomenon by using cutting efficiency. The higher cutting efficiency represents the lighter plastic-stacking phenomenon of furrows. Obviously, the higher cutting efficiency brings the higher grinding efficiency and the higher workpiece surface quality. In experiments in this chapter, furrow morphology formed by debris was measured. The 3D furrow morphology images and 2D morphology images under different working conditions

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Fig. 3.32 Furrow morphology

were gained. Furthermore, cutting efficiency of the 2D morphology images was estimated. The 3D morphology images and 2D morphology images of typical furrows are shown in Fig. 3.32. 1. Effects of grinding speed and lubricating conditions on plastic-stacking The variation trends of cutting efficiency of the grain with grinding speed under dry grinding, MQL grinding, and NMQL grinding are shown in Fig. 3.33 (furrow depth: 5 μm). With the increase of grinding speed, cutting efficiency of dry grinding fluctuated within 0.73–0.79 and it was generally stable. This is because that strain rate strengthening effect and thermal softening effect always keep a balance and offset mutually under dry grinding. The fluctuation amplitude (0.06) of cutting efficiency is 7.9% of the mean (0.758), indicating the mild variation. The cutting efficiency values under MQL grinding and NMQL grinding increased slowly. Since the influencing weight of thermal softening effect decreases due to the excellent heat transfer capability of nanofluids, the cutting efficiency increases as a response to the strain rate strengthening effect. Compared to MQL, NMQL has better cooling and lubrication performances, thus increasing the cutting efficiency more. 2. Plastic-stacking under different cutting depths The variation trends of cutting efficiency of grains with cutting depth under dry grinding, MQL and NMQL are shown in Fig. 3.34. With the increase of grinding depth, cutting efficiency of furrows presents a rising trend and it fluctuates stably after reaching a value. This is because as cutting

3.4 Experimental Results and Discussions

109

Fig. 3.33 Cutting efficiency under different working conditions

depth increases gradually, the grain experience ploughing stage and cutting stage successively during interference with the workpiece material. Moreover, the cutting efficiency increases continuously until reaching the mean at the inflection point. However, the positions of reaching the inflection point of cutting efficiency are different under different working conditions. Under dry grinding. the cutting efficiency keeps stable when the cutting depth is 10 μm. The curve variation trend under MQL grinding is the same with that under dry grinding except that the stable cutting efficiency is achieved at about 9 μm. Under NMQL grinding, cutting efficiency reaches stable at about 3 μm. This is because temperature of the cutting zone is lowered due to the excellent cooling and lubrication performances of NMQL, the thermal softening effect of the removed materials is weakened, and deformation of the removed materials is mainly manifested as material fracture. These might decrease the critical cutting depth for the formation of debris, thus entering into the cutting stage earlier.

3.4.3 Effects of Lubricating Conditions and “Velocity Effect” on Unit Grinding Force 1. Calculation method of unit grinding force In the experiment, grinding force signals in the grain cutting process were collected and the original grinding force signals are shown in Fig. 3.35. Different from grinding force signals in ordinary grinding, the grinding force signals in single-grain cutting were pulse signals with some frequency and frequency of these pulse signals were

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Fig. 3.34 Effect of cutting depth on cutting efficiency

negatively related with grinding speed. At the maximum pulse signal of each section, there’s the grinding force where the cross section area of debris reaches the maximum. According to variation trends of signal images of normal force and tangential force, the maximum pulse signal of grinding force increases firstly and then decreases as the grinding process continues. According to the variation trend, the grinding force signals can be divided into three stage: the cut-in zone, stable grinding and cut-out zone. In the single-grain cutting test, there’s flatness error on the workpiece surface due to the heterogeneity of the workpiece material, thus resulting in fluctuation of maximum grinding force signal within a certain range after reaching the given cutting depth. Calculating the mean of all pulse signal maximums only will surely have a great error with the real test results. Therefore, a new grinding force data acquisition

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111

Fig. 3.35 Signal image of cutting force of a single grain

and review method was applied in this study to eliminate experimental errors caused by above factors. The calculation method is shown in Fig. 3.36. (1) The 2D morphology of the furrow section which has some distance with the entry point was measured by a 2D mophometer. With the increase of measuring distance, the cutting depth of furrows increases gradually. A total 10 groups of data were measured at an equal interval within the whole length of furrows. (2) The cross section area correction model of debris was applied and a coordinate system was established according to 2D morphology. Meanwhile, the morphology matrix (C(x)) of the furrow interface was solved. The equation

Fig. 3.36 Calculation method of unit grinding force

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of cross section area of debris (S(ψ)) under this working condition was established by combining grinding parameters and the maximum cross section area of debris at dS(ψ) = 0 was further analysed. (3) The pulse signals in the force signal image which were corresponding to the 2D morphological grinding distance of furrows were positioned. Two signal pulses were chosen at the left and right of the positioning pulse signals and the maximum grinding forces of 5 pulse signals were measured. The mean was calculated and its ratio with the maximum cross section area of debris was the specific grinding force. 2. Experimental results of unit grinding force As shown in Fig. 3.37, the unit grinding force has different variation trends under different working conditions. With the increase of grinding speed, the unit grinding force under dry grinding is generally constant and numerical value fluctuates around 0.1N/μm2 . PhD Lin Tian from NUAA [18] also found this law. They believed that since the increase of fracture stress caused by strain rate strengthening effect offsets with the reduction of fracture stress caused by thermal softening effect in the adiabatic shear phenomenon, the unit grinding force generally remains stable. The variation trend of fracture stress is also presented in Fig. 3.37. Generally, there’s a rising trend of unit grinding force under MQL with the increase of grinding speed. It is 0.15 N/μm2 at 30 m/s, which is 59% lower compared to that (0.37 N/μm2 ) in dry grinding under the same grinding speed. This is because frictional force decreases because of the lubrication performances of MQL, thus decreasing the unit grinding force. When the grinding speed increases to 70 m/s, the unit grinding force enters into the threshold range of dry grinding force and it is kept

Fig. 3.37 Unit grinding force under different working conditions

3.5 Summary

113

stable in the range of 0.1N/μm2 . This indicates that MQL has some cooling and lubrication performances before 70 m/s and carries away abundant grinding heats, thus decreasing the influencing weight of thermal softening effect. As a result, the material fracture stress under the strain rate strengthening effect increases continuously. The unit grinding force in NMQL generally keeps a slow rising trend with the increase of grinding speed. It values 0.07 m/s at 30 m/s, which is 81 and 53% lower than those in dry grinding and MQL, respectively. This is because friction coefficient of the grinding zone decreases due to the excellent lubrication characteristics of nanoparticles. In the speed range of 120 m/s, the influencing weight of thermal softening effect is always lower than that of strain rate strengthening effect due to the excellent heat exchange performances of nanofluids. Based on analysis of strain rate strengthening effect, thermal softening effect under NMQL grinding is weaker than that under MQL grinding due to the better cooling performances, thus resulting in the higher fracture stress. Unit grinding force is the sum of material removal force and frictional force. Due to the better lubrication performance, the frictional force in NMQL grinding decreases significantly compared to that in MQL grinding, thus resulting in the lower unit grinding force.

3.5 Summary A theoretical study and experimental verification of material removal mechanism during high-speed dry grinding, MQL grinding and NMQL grinding are carried out. Some major conclusions can be drawn: (1) Single-grain/workpiece interference models and 3D models of debris under high-speed grinding conditions are constructed. The variation trend of grainworkpiece interference cross section under different grinding parameters is disclosed and a calculation formula of cross section area is established. The maximum cross section of the grain and the maximum undeformed chip thickness occur at different positions, which are closer to the middle point of the debris length. Furthermore, the corrected equation of grain-workpiece interference cross section area (S(ψ)) is established according to grain morphology and furrow morphology. This equation can reproduce and predict the material removal process by the grain more accurately. (2) The workpiece material deformation mechanism and mechanical behaviors in the grain cutting zone are disclosed. The calculation formulas of strain rates of the first and second deformation zones are established. The influencing laws of grinding speed (V s ), grinding depth (V w ) and friction coefficient (μ) on the strain rate are investigated. The influencing mechanisms of velocity effect and lubrication effect on material removal mechanism are disclosed. Given the same other parameters, strain rates (γ˙ ) of the first and second shear zones present a

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3 Velocity Effect and Material Removal Mechanical Behaviors Under …

linear increasing trend when V s increases from 30 to 120 m/s (accompanied with some increase of ϕ). (3) The debris forming mechanism and plastic-stacking mechanism under the collaborative influence of strain hardening effect, strain rate strengthening effect and thermal softening effect are investigated. Moreover, influencing trends of technological parameters on adiabatic shear phenomenon and furrow plastic-stacking phenomenon are studied. (4) A high-speed grinding experimental platform is built for single-grain cutting tests under different working conditions. The above theories are verified by test results of debris morphology, furrow morphology and grinding force. Results prove that the intensity relationship between strain rate strengthening effect and thermal softening effect varies with lubricating conditions in the material removal process, thus changing the material removal mechanism. Compared to other lubricating conditions, NMQL brings the higher cutting efficiency (with a maximum of 94%) and the lower unit grinding force (81 and 53% lower than those in dry grinding and MQL grinding).

References 1. Chen J, Li B. Fast numerical calculation of the offset linear canonical transform [J]. Journal of the optical society of America A-optics image science and vision, 2023, 40(3): 427–442. 2. Zhang T, Jiang F, Yan L, et al. Research on the stress and material flow with single particlesimulations and experiments [J]. Journal of Materials Engineering & Performance, 2017(5–6). 3. Yang M, Li C, Zhang Y, et al. Maximum undeformed equivalent chip thickness for ductilebrittle transition of zirconia ceramics under different lubrication conditions [J]. International Journal of Machine Tools & Manufacture, 2017, 122. 4. Ding W, Dai J, Zhang L, et al. An investigation on the chip formation and forces in the grinding of Inconel718 alloy using the single-grain method [J]. Issues in Mental Health Nursing, 2014, 28(1): 1–2. 5. Li CH. Grinding theory and key technology of nanofluid minimal quantity lubrication [M]. Science Press, 2017. 6. Peng K L, Lu P, Lin F H, et al. Convective cooling and heat partitioning to grinding chips in high speed grinding of a nickel based superalloy. Journal of Mechanical Science and Technology, 2021, 35(6):2755–2767. 7. Öpöz T T, Yasar H, Ekmekci N et al. Particle migration and surface modification on Ti6Al4V in SiC powder mixed electrical discharge machining [J]. Journal of Machine Manufacturing processes, 2018, 31:744–758. 8. Li CH, Zhang YB, Yang M. Grinding Thermodynamic Mechanism of Nanofluid Minimal Quantity Lubrication [M]. Science Press, 2019. 9. Liu P Z, Zou W J, Peng J, et al. Investigating the Effect of Grinding Time on High-Speed Grinding of Rails by a Passive Grinding Test Machine [J]. Micromachines, 2022, 13(12):2118. 10. LIU M Z, LI C H, ZHANG Y B, et al. Analysis of grinding mechanics and improved grinding force model based on randomized grain geometric characteristics [J]. Chinese Journal of Aeronautics, 2022, (1–34). 11. Zhang, Y., Li, C., Ji, H., Yang, X., Yang, M., Jia, D., Zhang, X., Li, R., & Wang, J. (2017). Analysis of grinding mechanics and improved predictive force model based on material-removal and plastic-stacking mechanisms [J]. International Journal of Machine Tools and Manufacture, 122, 81–97.

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12. Klocke F, Wirtz C, Mueller S, et al. Analysis of the material behavior of cemented carbides (WC-Co) in grinding by single grain cutting tests [J]. Procedia CIRP, 2016, 46:209–213. 13. Chen B, Luo L, Li S S, et al. Grinding marks suppression strategy based on adjusting grinding traces distribution [J]. Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture, 2022. 14. Mingzheng Liu, Changhe Li, Yanbin Zhang, Min Yang, Teng Gao, Xin Cui, Xiaoming Wang, Haonan Li, Zafar Said, Runze Li and Shubham Sharma, Analysis of grain tribology and improved grinding temperature model based on discrete heat source [J]. Tribology International, 2022. 15. Liang Y K, Deng B W, Zhang H D, et al. Research on the grinding characteristics of lignite based on grinding kinetics [J]. International Journal of Coal Preparation and Utilization, 2022. 16. Tian L, Fu Y, Yang L, et al. Investigations of the “Speed Effect” on critical thickness of chip formation and grinding force in high speed and ultra-high speed grinding of superalloy [J]. Journal of Mechanical Engineering (in Chinese), 2013, 49(9): 169–177. 17. Tian L. Fundamental research on the high speed grinding with regular abrasive distribution wheel [D]. Nanjing University of Aeronautics and Astronautics, 2013.

Chapter 4

Probability Density Distribution of Size and Convective Heat Transfer Mechanism of Nanofluid Droplets

4.1 Introduction As everyone knows, the thermal conductivity of solid materials is several orders of magnitudes higher than that of fluids under room temperature. For example, the thermal conductivity of copper is 700 times higher than that of water and the thermal conductivity of carbon nanotube is 5000 times higher than that of water [1]. It can be speculated that adding solid particles into fluid can increase the thermal conductivity to some extent. In 1995, Choi [2] from Argonne National Laboratory of America proposed the concept of “nanofluids” for the first time: nanofluid refers to the uniform suspension formed after mixing of liquid and appropriate amount of non-metal or metal nanoparticles through some steps. After nanoparticles are added in, the thermal conductivity and thermodynamic properties of the base fluid are improved significantly. The small-size effect of nanoparticles brings different thermophysical properties, structural characteristics, flow characteristics and energy transfer characteristics of nanofluids from traditional pure liquid and solid–liquid mixtures. Spray cooling is to atomize liquid in some way, spray it onto the object surface, and thereby cool the object effectively [3]. There are two common atomization modes. One is to atomize liquid through the atomizing nozzle based on high-pressure gas, that is, gas-assisted atomizing spray. The other is to atomize liquid based on a pressure pump, that is, pressure atomizing spray. Spray cooling has become a research hotspot in the field of cooling recently due to its advantages, such as low cost, strong controllability, safety and pollution-free, uniform cooling, large adjustable range of cooling ability, etc. Nanofluid technology and spray cooling technology are both developed to solve the heat dissipation problem of high heat flux. The nanofluids spray cooling technology which combines the nanofluid technology and spray cooling technology and uses nanofluids as the cooling medium in spray cooling has attract extensive attention of researchers. It has been widely applied to spacecraft thermal control, hightemperature superconductor cooling, thermal control in thin film deposition, cooling of high-intensity laser mirror, heat dissipation of high-power electronic components, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_4

117

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4 Probability Density Distribution of Size and Convective Heat Transfer …

cooling of machining, etc. [4]. In the machining field, nanofluids spray cooling and lubrication has achieved completely mature application to gear machining (e.g. gear shaping, gear milling, gear hobbing and gear shaving) as well as hole milling, turning and tapping of difficult-to-process materials. Moreover, it has been used successfully in rail traffic, aerospace, precision manufacturing of high-end parts, and other industries [5]. The convective heat transfer coefficient (h) covers all influencing factors related with convective heat transfer and it is the most direct parameter that characterizes the heat transfer ability of cooling medium [6]. In the spray cooling technology, there are diversified factors that may influence heat transfer performances of the spray medium, which have coupling effect. As a result, the heat transfer mechanism is very complicated. So far, there’s no method or theory to calculate the convective heat transfer coefficient of spray cooling. Spray droplet distribution is the most direct influencing parameter of spray cooling performance. In this chapter, spray mechanism and spray characteristics are studied. Density probability density statistical analyses and calculations of the spray droplets are carried out. On this basis, a mathematical model of convective heat transfer coefficient under the nanofluids spray cooling conditions is constructed.

4.2 Research Status on Convective Heat Transfer Mechanism of Nanofluids Spray Cooling Due to the excellent performances of nanofluids spray cooling, many teams engaging in machining have carried out basic theoretical studies around the whole world.

4.2.1 Research Status of Heat Transfer Mechanism of Nanofluids in the Grinding Zone The team led by Professor Cong Mao from Changsha University of Science and Technology (CSUST) has studied the boiling heat transfer mechanism in nanofluids spray grinding deeply. Zhou [7] carried out theoretical studies on thermal conductivity, specific heat capacity, viscosity and density of nanofluids prepared with Al2 O3 nanoparticles and deionized water, and discussed the relevant influencing factors of spray droplet size and speed. According to the variation laws of boiling heat transfer characteristics of nanofluids with temperature distribution on the grinding surface, a theoretical model of heat transfer coefficient of nanofluids spray cooling was constructed. Heat input and allocation in the grinding zone were analysed and calculated. The temperature distribution and variation laws under NMQL grinding, pure water MQL grinding and dry grinding were compared, which proved the good heat transfer performances of NMQL. Mao [8, 9] discussed influences of nozzle

4.2 Research Status on Convective Heat Transfer Mechanism of Nanofluids …

119

size, liquid performances, gas–liquid pressure and gas–liquid mass ratio on speed and diameter of spray droplets. Since droplets showed different heat transfer characteristics in zones with different grinding temperatures, the heat transfer area of grinding was divided into four zones, namely, steady film boiling zone, transition boiling zone, nucleate boiling zone and non-boiling zone. On this basis, a theoretical model of heat transfer coefficient in the grinding zone under spray cooling condition was built. Mao [10] carried out an experimental study on pouring grinding, dry grinding, pure oil spray grinding and oil–water spray grinding and found that grinding temperature and thickness of the influencing layer under oil–water spray grinding were lower compared to those under the pure oil spray grinding. The team led by Professor Changhe Li from Qingdao University of Technology explored the heat transfer mechanism of nanofluids spray grinding deeply. Liu [11] analysed the components and preparation process of nanofluids, measured thermal conductivity of nanofluids, implemented a finite element simulation of ceramic grinding under the nanofluid spray lubrication and cooling condition, and calculated heat allocation in the grinding zone. According to experimental and simulation results, thermal conductivity of nanofluids was better than other traditional single fluid medium and the nanofluids could transfer heats out from the grinding arc zone effectively, thus preventing structural changes due to influences of high grinding temperature on material structure. Zhang [12] investigated cooling and lubrication performances under NMQL, MQL, pouring grinding and dry grinding conditions, and constructed a heat source model and a mathematical model of heat distribution coefficient in workpiece under NMQL condition by analysing convective heat transfer on grinding interfaces. Besides, he analysed temperature rise trend after grinding heats were transferred into the workpiece through simulation results. He concluded that the heat transfer effect of MoS2 and CNTs was good and it improved with the increase of volume concentration of nanoparticles. Li [13] prepared nanofluids by using several kinds of vegetable oils (corn oil, castor oil, soybean oil, peanut oil, palm oil, colza oil and sunflower oil) and nanoparticles (Al2 O3 , diamond, MoS2 , CNTs, ZrO2 and SiO2 ) for MQL grinding tests of high-temperature Ni-based alloy, and analysed influences of physical properties of nanofluids (contact angle, thermal conductivity and viscosity) on heat transfer mechanism. According to simulation and experiment, the 2% (vol.%) nanofluids had the optimal cooling and lubrication effect. Liu [14] suggested to replacing the roomtemperature high-pressure gas in conventional nanofluid spray cooling lubrication by the high-speed low-temperature gas, thus further improving the enhanced heat transfer ability of nanofluids spray cooling. The low-temperature gas atomization NMQL supply system and nozzle device were innovated theoretically and the structure was improved. The enhanced heat transfer mechanism under low-temperature gas atomisation nanofluids spray cooling and lubrication condition was investigated, and a boiling heat transfer coefficient model was constructed. On this basis, a temperature field model was built. The accuracy of the constructed models was verified by a comparative analysis between experimental temperature and simulation temperature. Zhang [15] discussed influences of cold current ratio of vortex tube on heat

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4 Probability Density Distribution of Size and Convective Heat Transfer …

transfer mechanism in cold air NMQL grinding. He analysed the cooling and lubrication mechanism of grinding zone under different cold current ratios of vortex tube from perspectives of surface tension and contact angle of nanofluids, specific grinding energy, atomization and boiling heat transfer effect of the grinding zone, and viscosity of nanofluids, thus concluding the optimal cold current ratio. In foreign countries, some experimental studies and preliminary theoretical analysis on heat transfer mechanism in the grinding zone under NMQL condition have been reported. Lee [16] et al. studied nanofluids spray microgrinding and constructed microscale grinding heat source model and heat flux model based on the computational fluid dynamics (CFD). They estimated temperature on workpiece subsurface by the response surface methodology (RSM) by inputting the initial temperature of workpiece and grinding heat flux. Results showed that nanofluids spray can lower temperature of workpiece subsurface significantly compared to spray microgrinding.

4.2.2 Research Status of Convective Heat Transfer Coefficient in Spray Cooling For quantitative characterization of heat transfer performances of cooling media, most researchers apply convective heat transfer coefficient to characterize the ability of cooling medium to carry away heats from the grinding zone. Sienski [17] summarized heat transfer coefficient ranges of several typical heat transfer methods (Fig. 4.1). The spray cooling technology which uses water as the cooling medium has the higher heat transfer coefficient than other cooling modes. Moreover, it gains better surface temperature uniformity and needs lower mass flow of cooling fluid. Therefore, it has greater advantages. For the application of spray cooling in grinding, Zhou [7] and Shen [18] have calculated convective heat transfer coefficient. Hongfu Zhou applied the jet parameters: gas supply rate = 20 m3 /h, gas pressure = 0.5 Mpa, and flow rate of cooling fluid = 5 mL/min. The cooling medium used the 5 vol.% nanofluids prepared with Al2 O3 nanoparticles and deionized water. The nozzle diameter was 1.2 mm, the spray target distance was 30 mm, the grinding surface dimension of the workpiece was 8 × 4 mm, and the radial distribution range of spray droplets was 8 mm. Hence, spray droplets can cover the grinding surface completely. The calculation results are shown Fig. 4.2. (1) In the non-boiling zone (grinding zone temperature T < 105 °C), heat transfer coefficient is 0.01 W/mm2 K. (2) In the nucleate boiling zone (105 °C < T < 148 °C), the value of heat transfer coefficient increases with the increase of T and it reaches the maximum (0.052 W/ mm2 K) at the critical point. (3) In the transit boiling zone (148 °C < T < 320 °C), heat transfer coefficient decreases with the increase of T.

4.2 Research Status on Convective Heat Transfer Mechanism of Nanofluids …

Fig. 4.1 Heat transfer coefficient ranges for several typical heat transfer methods [17] Fig. 4.2 Variation trend of heat transfer coefficient of cooling medium with grinding zone temperature [7]

121

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4 Probability Density Distribution of Size and Convective Heat Transfer …

(4) In the steady film boiling zone (T > 320 °C), the heat transfer curve is approximately a horizontal straight with the increase of T. Since heat transfer coefficient is equal to heat transfer volume/temperature gap, heat transfer coefficient of the steady film boiling zone presents a decreasing trend and it decreases to 0.006 W/mm2 K at 320 °C. Based on above analysis, the relationship between heat transfer coefficient and grinding zone temperature under spray cooling condition can be gained (Fig. 4.2). In the non-boiling zone, heat transfer coefficient is kept constant with the increase of grinding zone temperature. It is positively related with grinding temperature the nucleate boiling zone and reaching the maximum at critical heat flux. However, it decreases with the increase of grinding temperature in the transit boiling zone and steady film boiling zone. The heat transfer coefficient decreases more in the transit boiling zone and tends to be gentle in the steady film boiling zone. Shen [18] studied temperature field in the grinding zone under NMQL condition deeply (Fig. 4.3). The convective heat transfer area of workpiece-cooling medium was divided into front edge, contact zone and rear edge of grinding wheel/workpiece. The convective heat transfer coefficient of the grinding zone was estimated according to Eq. (4.1). Results are shown in Table 4.1   ⎧ lc h2 − h1 ⎪ ⎪ h x + + = h (x) contact 1 ⎪ ⎪ lc 2 ⎨ h1 + h2 ⎪ h = ⎪ ⎪ contact 2 ⎪ ⎩ h trailing = h 1

Fig. 4.3 Convective heat transfer area of workpiece/cooling medium [18]

(4.1)

4.3 Mathematical Model of Convective Heat Transfer Coefficient Under …

123

Table 4.1 Convective heat transfer coefficient values in different heat transfer areas [18] Cooling mode

Flow rate (mL/min) Convective heat transfer coefficient h (W/mm2 K)

MQL (soybean oil)

5

Pouring grinding (5 vol.% Cimtech 500 grinding fluid)

5400

h2

Contact zone

Rear edge

0.039

0.025

0.01

0.74

0.42

0.095

where l c is the contact arc length between the grinding wheel and workpiece in the grinding zone. h1 and h2 are intermediate variables of convective heat transfer coefficient. Based on literature review, researchers around the world have carried out macroscopic studies on nanofluids spray grinding temperature field by adjusting jet parameters (e.g. nozzle angle, nozzle distance, gas–liquid ratio and volume fraction of nanoparticles). However, none of them have explored convective heat transfer mechanism of grinding zone from microscopic perspectives, such as nanofluids spray droplet size distribution, heat transfer characteristics of single nanofluid droplets. To disclose the enhanced heat transfer mechanism of nanofluids droplet particle swarm in grinding zone, a quantitative characterization of nanofluids spray cooling performances was performed. It is urgent to construct a mathematical model of convective heat transfer coefficient under the nanofluids spray cooling condition.

4.3 Mathematical Model of Convective Heat Transfer Coefficient Under Nanofluids Spray Cooling 4.3.1 Nanofluids Atomization Mechanism and Probability Density Distribution of Droplet Size Spray cooling is to atomize the cooling medium through the atomization nozzle by using high-pressure gas (gas assisted atomization) or depending on pressure pump (pressure atomization spray) and then spray mist droplets onto the object surface to cool it effectively. Viscosity of liquid can increase stability of existing liquid shape. Moreover, liquid has surface tension which force liquid to form balls. When external forces like aerodynamic force, pressure and electrostatic force are applied onto the liquid, they may interact with viscosity force and surface tension to trigger disturbing phenomenon on liquid surface. When the action intensity of external forces increases to the collaborative intensity of viscosity force and surface tension, the liquid is atomized, producing atomization phenomenon [19]. In the atomization process of cooling medium, the size distribution of the sprayed droplets is an important index to evaluate atomization quality and mist characteristics.

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The droplet size distribution pattern formed by a specific nozzle is mainly determined by physical properties of cooling medium, pressure of the high-pressure gas and physical properties of gases surrounding the atomization zone at the spraying outlet. Moreover, size distribution of spray droplets is a major factor that influences gas– liquid and liquid–solid mass transfer and heat transfer [20]. When the cooling medium is atomized into small droplets at the nozzle outlet, the surface tension of liquid hinders the breakage and deformation of liquid, and makes droplets of a specific volume to keep the minimum surface area. In other words, surface tension makes droplets to keep ball shapes. Droplet size is the optimal size parameter to describe spherical droplets and it is concentrated within a certain interval. An accurate and reliable theoretical model is needed to describe size distribution of spray droplet. As the most intuitive method in statistics, columnar histogram is widely applied to probability statistical analysis of random events. The discrete probability distribution of droplets with different sizes is shown in Fig. 4.4. The yaxis refers to the percentage of droplets in the ΔD size range in total droplet, that is, the probability density distribution function of spray droplet size (P(D)). The x-axis refers to the size of spray droplet (D) and it is divided at an equal interval (ΔD): N 

P(Di ) = 1

(4.2)

i=1

When variations of droplet size approaches to 0 (ΔD → 0) infinitely: P(D) = lim

ΔD→0

˜ P(D) ΔD

(4.3)

In this way, Fig. 4.4 is transformed into Fig. 4.5 which refers to the continuous probability distribution curve of spray droplet size [21]. P(D) of spray droplet size has to meet following conditions: Fig. 4.4 The discrete probability distribution of droplet size

4.3 Mathematical Model of Convective Heat Transfer Coefficient Under …

125

Fig. 4.5 The continuous probability distribution of droplet size

D P(D)dD = 0

lim

D→0

(4.4)

0

∞ P(D)dD = 0

lim

D→∞

(4.5)

D

P(D) ≥ 0

(4.6)

P(D)dD = 1

(4.7)

∞ 0

According to P(D) of spray droplet size, the droplet density with a fixed size is N t and its distribution function can be gained: N (D) = Nt P(D)

(4.8)

The m-order moment equation of spray droplet size can be gained from Eq. (2.8): ∞ mm =

D m N (D)dD

(4.9)

o

The universal expression (Djm ) of average droplet size can be gained from Eq. (2.9) [21]:

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4 Probability Density Distribution of Size and Convective Heat Transfer …

∞ Djm =

 o∞ o

D j N (D)dD D m N (D)dD

1/( j−m)



mj = mm

1/( j−m) (4.10)

where d10 is the mean droplet size when j = 1 and m = 0. d32 is the Sauter mean size when j = 3 and m = 2. The physical meaning of Sauter mean size refers to the ratio of mean droplet volume produced by atomization and mean droplet area. Researchers often replace the original droplet group by the droplet group with a size of d 32 which has the same total volume and surface area with the original droplet group. The general expression of d 32 is [22]:

0.5 −0.259 ρa Δpd01.5 d32 = 3.07 d0 σt0.5 μ

(4.11)

where σ t is the surface tension coefficient of droplets. M is the dynamic viscosity of spray medium. ρ a is the density of medium in the nozzle outlet environment. Δp is the pressure gap between inside and outside of the nozzle. d 0 is the diameter of nozzle.

4.3.2 Effects of Airflow Field Around Micro-abrasive Tool on Droplet Distribution Pattern Air has viscosity. Due to the high-speed revolving of micro-abrasive tools during micro-grinding, the tools drive surface air to make relative movements with a certain speed and pressure under the action of tool surface-air friction and centrifugal force, thus forming a gas barrier layer around the tools. On the high-speed revolving tool surface, there are generally four types of rotating airflows, including internal flow, permeable flow, radial flow and circulation flow. For micro-abrasive tools with a metal base, there’s only radial flow and circulation flow, but no permeable flow and internal flow due to the absent air holes on the metal base (Fig. 2.6). Radial flow is formed by the centrifugal force of tool revolving and interaction between the abrasive tool surface and surrounding air. It has small influences on cooling liquid supply. The circulation flow is the airflow which rotates around the circumferential direction of the abrasive tool and it may hinder supply of the grinding fluid [23] (Fig. 4.6). A simulation analysis on the airflow field distribution characteristics around the micro-abrasive tool was carried out to further determine the nozzle position. The spherical head diameter and rotational speed of the micro-abrasive tool were set r = 1 mm and ω = 60,000 r/min, respectively. The airflow field around the microabrasive tool is shown in Fig. 4.7. The comprehensive airflow of the circulation airflow and radial flow can be further divided into inflow, return flow and gas barrier layer. The outer layer is the gas barrier layer that keeps cooling liquid out of the grinding zone. Hence, it shall avoid to set the jet position out of the gas barrier layer. Inflow is beneficial to carry cooling medium to the micro-grinding zone. The return

4.3 Mathematical Model of Convective Heat Transfer Coefficient Under …

127

Fig. 4.6 Diagram of gas barrier layer on the abrasive tool surface

flow carries some cooling medium out of the grinding zone and hinders the entrance of cooling medium to the micro-grinding zone. Hence, injection of cooling medium shall avoid its contact with the return flow [24]. Based on above analysis, the optimal injection angle and distance of the cutting fluid are shown in Fig. 4.7. According to measurement, when the nozzle axis has an angle (8–29°) and some distance (0.45–0.75 mm) with the sample surface, the airflow field can carry the cooling medium, while the return flow has the weakest effect in hindering cooling medium. As a result, the cooling medium is easier to enter into the cutting zone. At this moment, the airflow speed is 1.2 m/s and it is far lower than the spray high-pressure gas speed (30–50 m/s). Therefore, influences of

Fig. 4.7 Airflow field around micro-abrasive tool

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4 Probability Density Distribution of Size and Convective Heat Transfer …

airflow field around the micro-abrasive tool will be ignored in the following analysis of spray boundaries and probability density of spray droplet size.

4.3.3 Theoretical Models of Spray Boundary Some typical spray boundary experiments are shown in Fig. 4.8. Silk et al. [25] studied heat transfer performances of spray cooling by using PF5060 as the cooling medium, 2 × 2 array as the nozzle and 1 cm2 square copper surface as the heat source surface under the premise of constant height (17 mm) and different spray angles (β = 45°, 30°, 15° and 0°). Results showed that when the spray angle is 30°, the critical heat flux (CHF) of the system reached the maximum. Hsieh [26] studied influences of spray angles on heat transfer effect of square heat source when a solid nozzle with water as the cooling medium (nozzle diameter = 0.38 mm and 0.21 mm; spray angle = 60° and 80°) was used in the inclined spraying. He concluded that the best heat transfer performances of the system were achieved when the spray angle was about 30°. Li et al. [27] investigated influences of spray angle (60°, 50°, 40°, 20°, 0°) on heat flux in spray cooling by using PF5060 as the medium (2 l.8 mL/min, 26 °C) under the constant height (14 mm) from the single pressure rotating nozzle (spray cone angle = 35° ± 3°) to the heat source surface. They found that when β was 0°–40°, the heat transfer performances of the system were hardly influenced. With the increase of β, the critical heat flux of heat transfer of spray cooling increased slightly, while the heat transfer performances of the system dropped sharply when β exceeded 40°. Mudawar et al. [22] demonstrated that the critical heat flux reached the maximum at the internal connection between heat source boundary and spray boundary. On this basis, they studied influencing factors of heat transfer performances of the spray cooling system. According to different spray height (H), spray angle (β) and spray cone angle (α), the spray boundary formed after nanofluids droplet groups are sprayed from the

Fig. 4.8 Several typical spray experiments

4.3 Mathematical Model of Convective Heat Transfer Coefficient Under …

129

Fig. 4.9 Schematic diagram of circular spray boundary

nozzle and impact onto the heat source surface can be divided into the closed circular type, the closed elliptic and the open parabolic type [20, 28]. These three types of spray boundaries will be analysed one by one in the following text. (1) When β = π2 , the nozzle sprays onto the heat source surface perpendicularly. Obviously, the spray boundary is a closed circle (Fig. 4.9). Such circular spray boundary is expressed as: x 2 + y 2 = H 2 tan2

α 2

(4.12)

(2) When 0 < π2 − β < π2 − α2 , the spray boundary is a closed ellipse (Fig. 4.10), with a long axisαof  2ll and ashort axis of 2l s . The intermediate variable C C = 2 sin β + 2 sin β − α2 is introduced in. Such elliptic spray boundary is expressed as: (x − x0 )2 (y − y0 )2 + =1 ls2 ll2

(4.13)

/ 1 where ll = H 2C sin β; ls = H C1 sin β2 . (3) When β = α2 , the spray boundary is not closed, but a parabola (Fig. 4.11). Let F be the focal distance of the parabola. It can be seen from Fig. 4.11 that:

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4 Probability Density Distribution of Size and Convective Heat Transfer …



β x0 = H tan α − 2

(4.14)

According to definition of a parabola, the parabolic spray boundary can be expressed as: y 2 = F(x − x0 ) Fig. 4.10 Schematic diagram of elliptic spray boundary

Fig. 4.11 Sketch of parabolic spray boundary

(4.15)

4.3 Mathematical Model of Convective Heat Transfer Coefficient Under …

 where F = H tan

β 2

− tan2

β 2

131

 tan α .

4.3.4 Probability Density Statistics of Size of Droplets with Effective Heat Transfer In Sect. 4.3.2, the coverage area of droplet groups reaches the maximum under elliptic spray boundary. The total droplet number (N t ) is: Nt =

Qf Vd32 f

(4.16)

where Qf is the liquid supply flow of the spray device. F is the liquid supply frequency of MQL device. V d32 is the volume of droplets with a size of d 32 . Suppose droplets fall onto the bone surface uniformly. Then, the droplet number in the grinding zone is: Nz = Nt · sg /Se

(4.17)

where sg is the grinding interval area and S e is the area of elliptic spray boundary. Levy et al. [29] found that for solid conical spray, the droplet size of χ 2 -distribution sampling conforms to practical situation better. Therefore, the initial droplet size is described by using χ 2 -distribution: P(D) =

1 6D

4

D3e

−D/

D

(4.18)

where W/(m 2 .k) is the determined degree of freedom (D = d32 /3) and the probability of the corresponding χ 2 -distribution reaches the maximum. The possible effect after droplets impact on the heat source surface is determined by size, incidence velocity and angle of droplets as well as roughness and temperature of heat source surface. To describe such effect, Weber criterion number [30] (We number) and Laplace number (La number) were introduced in to control results after impacts of droplets onto the heat source surface. We =

ρ f Dv2 σ

(4.19)

La =

ρ f Dσ μ2

(4.20)

where ρ f is the density of spray cooling medium and v is the velocity component of droplets perpendicular to the heat source surface.

132

4 Probability Density Distribution of Size and Convective Heat Transfer …

Zhou [7] has calculated velocity of spray droplets thoroughly. According to the Bernoulli’s equation, the relation among the velocity of droplets sprayed from the nozzle, pressure of high-pressure gas (pa ) and flow of the grinding fluid (Qf ) is:

v0 =

[ | | √

pa − p0 ρf

+

16Q 2f π 2 d02

1 + ξr

(4.21)

where ξ r is the drag coefficient and p0 is atmospheric pressure. Obviously, the gravity of droplets is significantly lower than the surrounding air drag before they impact onto the micro-grinding zone. Hence, the gravity of droplets can be ignored and only influences of surrounding air viscous drag on droplets have to be considered. According to the aerodynamics principle, the drag of surrounding air against the droplets can be known [31]: FD =

CD Sf γa · (va − vl ) · |va − vl | 2ga

(4.22)

where va is the surrounding air velocity, γ a is air weight, S f is the windward surface area of droplet, vl the droplet velocity, and C D is the air drag coefficient. Since flow velocity of air surrounding the droplets is far lower than the velocity of high-speed droplets, the surrounding air is viewed as approximately static. Therefore, Eq. (4.22) can be expressed as: FD = −

CD Sf γa vl2 2ga

(4.23)

Therefore, the velocity of droplets at any moments before impacting onto the sample and abrasive tool can be expressed as: vl =

1+

/

2v0 2CD Sf γa v0 t mga

+1

(4.24)

It can be seen from Sect. 4.3.2 that the drag effect of airflow field generated by high-speed rotation of the micro-abrasive tool on the cooling medium could be ignored by adjusting nozzle angle and height. The distance between nozzle outlet and grinding zone is very small (0.45–0.75 mm in this study), it is extremely short for droplets to arrive at the grinding zone from the nozzle outlet. Hence, the velocity when droplets impact onto the sample surface and micro-abrasive tool can be viewed as the velocity at the nozzle outlet. In Fig. 4.12, three behaviors of rebounding, spreading and splash occur successively with the increase of We number of incidence droplets. When the initial droplet energy is low, the droplets are rebounded. When droplets impact onto the heat source surface at a high energy, coronary droplet splash is formed and droplets fly away

4.3 Mathematical Model of Convective Heat Transfer Coefficient Under …

133

Fig. 4.12 Probability distribution of spray droplets

from the coronary edges, breaking into many small droplets. Droplets under these two conditions cannot participate in heat transfer effectively. Effective heat transfer of the heat source surface only occurs when droplets spread. In other words, there’s effective heat transfer of the heat source surface only when droplets impact onto the surface and spread into liquid film along the surface [32]. The critical We number of spreading droplet is: 2.0 × 104 × La−0.2 ≤ We ≤ 2.0 × 104 × La−1.4

(4.25)

Based on Eq. (4.25), the range of size (D) of droplets which can spread or make effective heat transfer can be calculated Dmin ≤ D ≤ Dmax , as shown in Fig. 4.12. Therefore, the proportion of droplets making effective heat transfer is: Dmax P= Dmin

1 6D

4

D 3 e−D/D dD

(4.26)

The droplet number of effective heat transfer is: Ne = Nz · P(D)

(4.27)

134

4 Probability Density Distribution of Size and Convective Heat Transfer …

4.3.5 Convective Heat Transfer Coefficient Model of Nanofluids Spray Cooling In Sect. 4.3.4, the spray mechanism and probability density distribution pattern of nanofluids spray droplet size have been disclosed. The droplet size distribution has extremely important influences on gas–liquid mass transfer and heat transfer process. In this section, the idea to construct a convective heat transfer coefficient model under nanofluids spray cooling condition in the micro-grinding zone is to integrate the three-phase flow of nanoparticles which are sprayed by the nozzle onto the heat source surface, base fluid and high-pressure gas into a two-phase flow of nanofluids and high-pressure gas. For nanofluids, a probability statistical analysis of droplets with effective heat transfer in the grinding zone is carried out by using the mathematical statistical method in Sect. 4.3.4. Meanwhile, heat transfer coefficient of single nanofluid droplet is calculated, thus getting the heat transfer coefficient of nanofluids. The sum of the heat transfer coefficient of nanofluids and heat transfer coefficient of high-pressure gas jet is the convective heat transfer coefficient under nanofluids spray cooling condition. For a single nanofluid droplet, the heat transfer coefficient (hs ) meets [7]: ⎧ J = cf m d (ΔT ) ⎪ ⎪ ⎨ qs hs = ⎪ ΔT ⎪ ⎩ J = q s A ' ts

(4.28)

where J is the heat transfer volume of single droplet; cf is the specific heat capacity of the droplet; ΔT is the heat transfer temperature difference; qs is the heat transfer flux of single droplet; th is the heat transfer time; md is the mass of the droplet; A' is the spreading area of the droplet. For A' , ⎧ ' 2 ⎪ ⎪ A = π · rsurf , ⎪ ⎪ ⎪ gc · D ⎪ ⎨ rsurf = [ | π ⎪ gc = 3 | ⎪ |   ⎪ ⎪ √ ⎪ ⎪ 3π tan1θc cos1 θc − 1 1 + ⎩

1 1 3 tan2 θc



1 cos θc

−1

2 

(4.29)

where r surf is the spreading radius of droplet; gc is the constant related with the contact angle; θ c is the contact angle. Based on calculation of effective droplet number in the grinding zone in Sect. 4.3.4, the heat transfer coefficient of all droplets with effective heat transfer is: Dmax 1 h n = Nz hs D 3 e−D/D d D 4 6D Dmin

(4.30)

4.4 Conclusions

135

The convective heat transfer coefficient (ha ) of the high-pressure gas jet and heat source surface is: ha = ka Nu/b

(4.31)

where Nu is Nusselt number (Nu) and its relations with Reynolds number (Re) and Prandtl number (Pr) are: ⎧ 1/2 1/3 ⎪ ⎨ Nu = 0.906Re Pr (4.32) Re = va ρa d0 /μa ⎪ ⎩ Pr = μa ca /λa where k a is the thermal conductivity of air; μa is the dynamic viscosity of gas; ca is the constant pressure specific heat of air. The comprehensive convective heat transfer coefficient of nanofluids spray cooling is: h = hn + ha

(4.33)

According to Eqs. (4.16)–(4.33), given the fixed spray angle and nozzle height, the convective heat transfer coefficient of nanofluids spray cooling is determined by jet parameters (spray cone angle, liquid supply flow and liquid supply frequency), spreading characteristic parameters of droplets (surface tension, density, viscosity, contact angle and incidence velocity) and pressure of compressed air. Meanwhile, the number of droplets with effective heat transfer influences heat transfer performances of cooling medium directly. In the spray cooling process, the higher number of droplets with effective heat transfer is accompanied with the lower Dmin , the higher Dmax , and the better enhancement of heat transfer performances. The variation trends of Dmin and Dmax with viscosity, surface tension, density and velocity of cooling liquid are shown in Fig. 4.13. Clearly, Dmin is positively related with viscosity and surface tension, but negatively related with density and droplet velocity. Dmax is positively related with viscosity, but negatively related with surface tension, density and velocity. Take the 2 vol. % SiO2 nanofluids for example. The input and output parameters of the model are listed in Tables 4.2 and 4.3. According to calculation, the convective heat transfer coefficient of 2 vol. % SiO2 nanofluids is 4.19 × 10–2 W/mm2 ·K.

4.4 Conclusions Based on the nanofluid atomizing mechanism, the distribution characteristics of spray droplet size are analysed. A probability density distribution model of spray droplet size based on surface tension, viscosity, density and incidence velocity of cooling

136

4 Probability Density Distribution of Size and Convective Heat Transfer …

Fig. 4.13 Variation trend of minimum and maximum spreading droplet size with viscosity, surface tension, density and velocity Table 4.2 Input parameters for the calculation of spray convective heat transfer coefficient of SiO2 -saline nanofluids Input parameters

Values

Input parameters

Values

Nozzle diameter

d 0 = 1 mm

Spray cone angle

α = 21°

In–out pressure gap of the nozzle

Δp = 0.54 MPa

Fluid density

ρ = 1.053 g/cm3

Dynamic viscosity of fluid

μ = 2.17 mPa s

Surface tension of fluid

σ t = 48.58 N/mm

Liquid supply flow

Q' = 50 mL/h

Specific heat capacity of fluid

c = 4018 J/kg °C

Spray angle

β = 18°

Contact angle of droplets

θ = 83.86°

Nozzle height

H = 0.6 mm

Gas velocity

va = 34.5 m/s

4.4 Conclusions

137

Table 4.3 Output parameters for the calculation of spray convective heat transfer coefficient of SiO2 -saline nanofluids Output parameters

Values

Sauter mean diameter

d 32 = 21.2 μm

Total droplet number

N t = 1.69 × 108

Droplet number in the grinding zone

N z = 583 361

Determined degree of freedom

D = 7.06 μm

Minimum size of spreading droplets

Dmin = 29.35 μm

Maximum size of spreading droplets

Dmax = 162.4 μm

Proportion of droplets with effective heat transfer

P = 0.7362

Heat transfer coefficient of all droplets with effective heat transfer hn = 4.18 × 10–2 W/mm2 K Natural convective heat transfer coefficient

ha = 7.5 × 10–5 W/mm2 K

Comprehensive heat transfer coefficient

h = 4.19 × 10–2 W/mm2 K

medium is constructed. The influencing laws of thermodynamic properties of cooling medium and nanofluids parameters on droplet number with effective heat transfer in the grinding zone are disclosed. On this basis, a convective heat transfer coefficient model of nanofluids spray cooling is constructed. Some conclusions can be drawn: (1) According to different spray height, spray angle and spray cone angle, the spray boundary formed after nanofluids droplet groups are sprayed from the nozzle and impact onto the heat source surface can be divided into the closed circular type, the closed elliptic and the open parabolic type. The coverage area of droplet groups reaches the maximum under the closed elliptic spray boundary. (2) Three behaviors of rebounding, spreading and splash occur successively with the increase of We number of incidence droplets. When the initial droplet energy is low, the droplets are rebounded. When droplets impact onto the heat source surface at a high energy, coronary droplet splash is formed and droplets fly away from the coronary edges, breaking into many small droplets. Droplets under these two conditions cannot participate in heat transfer effectively. Effective heat transfer of the heat source surface only occurs when droplets spread. In other words, there’s effective heat transfer of the heat source surface only when droplets impact onto the surface and spread into liquid film along the surface. (3) Given the fixed nozzle angle and height as well as liquid supply flow and liquid supply frequency, the number of droplets with effective heat transfer is a function of surface tension, viscosity, density and incidence angle of cooling liquid. In the spray cooling process, the higher number of droplets with effective heat transfer is accompanied with the lower Dmin , the higher Dmax , and the better enhancement of heat transfer performances. Specifically, Dmin is positively related with viscosity and surface tension, but negatively related with density and droplet velocity. Dmax is positively related with viscosity, but negatively related with surface tension, density and velocity.

138

4 Probability Density Distribution of Size and Convective Heat Transfer …

(4) Given the fixed spray angle and nozzle height, convective heat transfer coefficient of nanofluids spray cooling is determined by jet parameters (spray cone angle, liquid supply flow and liquid supply frequency), spreading characteristic parameters of droplets (surface tension, density, viscosity, contact angle and incidence velocity) and pressure of compressed air.

References 1. Li, B., Li, C., Zhang, Y., Wang, Y., Jia, D., & Yang, M. (2016). Grinding temperature and energy ratio coefficient in MQL grinding of high-temperature nickel-base alloy by using different vegetable oils as base oil. Chinese Journal of Aeronautics, 29(4), 1084–1095. 2. Choi S U S, Eastman J A. Enhancing thermal conductivity of fluids with nanoparticles[R]. Argonne National Lab., IL (United States), 1995. 3. Zhang, J., Li, C., Zhang, Y., Yang, M., Jia, D., Liu, G., Hou, Y., Li, R., Zhang, N., Wu, Q., & Cao, H. (2018). Experimental assessment of an environmentally friendly grinding process using nanofluid minimum quantity lubrication with cryogenic air. Journal of cleaner production, 193, 236–248. 4. GailDuursma, KhellilSefiane, AidenKennedy. Experimental Studies of Nanofluid Droplets in Spray Cooling[J]. Heat Transfer Engineering, 2009, 30 (13): 1108–1120 5. Yanbin Zhang, Hao Nan Li, Changhe Li, Chuanzhen Huang, Hafiz Muhammad Ali, Xuefeng Xu, Cong Mao, Wenfeng Ding, Xin Cui, Min Yang, Tianbiao Yu, Muhammad Jamil, Munish Kumar Gupta, Dongzhou Jia, Zafar Said (2021). Nano-enhanced biolubricant in sustainable manufacturing: From processability to mechanisms. Friction. 10(6): 803–841. 6. X. Cui, C.H. Li, W.F. Ding, Y. Chen, C. Mao, X.F. Xu, B. Liu, D.Z. Wang, H.N. Li, Y.B. Zhang, Z. Said, S. Debnath, M. Jamil, H. Muhammad Ali, S. Sharma, Minimum quantity lubrication machining of aeronautical materials using carbon group nanolubricant: from mechanisms to application, Chinese Journal of Aeronautics, 2022, 35(11):85–112. doi: https://doi.org/10.1016/ j.cja.2021.08.011. 7. Zhou H. Research on temperature filed of surface grinding applied nanofluid for minimum quantity lubricant[D]. Changsha: Changsha University of Science & Technology, 2013. 8. Mao C, Zou H, Huang Y, et al. Analysis of heat transfer coefficient on workpiece surface during minimum quantity lubricant grinding[J]. International Journal of Advanced Manufacturing Technology, 2013, 66 (1–4): 363–370. 9. Mao C, Zou H, Huang X, et al. The influence of spraying parameters on grinding performance for nanofluid minimum quantity lubrication[J]. International Journal of Advanced Manufacturing Technology, 2013, 64 (9–12): 1791–1799. 10. Mao C, Tang X, Zou H, et al. Experimental investigation of surface quality for minimum quantity oil-water lubrication grinding[J]. International Journal of Advanced Manufacturing Technology, 2012, 59 (1–4): 93–100. 11. Liu Zhanrui. Grinding of the Surface Integrity in Lubrication and the Evaluation theory by Nanofluids jet the Research of Heat Transfer, Qingdao university of technology, China, 2010. 12. Zhang D. The mechanism of convective heat transfer and experimental investigation in grinding nickel-base superalloy by nanoparticle jet MQL[D]. Qingdao: Qingdao University of Technology, 2014. 13. Li, B., Li, C., Zhang, Y., Wang, Y., Jia, D., Yang, M., Zhang, N., Qu, Q., Han, Z., & Sun, K. (2017). Heat transfer performance of MQL grinding with different nanofluids for Ni-based alloys using vegetable oil. Journal of Cleaner Production, 154, 1–11.

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Chapter 5

Design and Experimental Evaluation of Convective Heat Transfer Coefficient Test System in Nanofluids Spray Cooling

5.1 Introduction Currently, researchers usually measure convective heat transfer coefficient (h) of nanofluids through the in-pipe transient measurement method. The principle is introduced as follows. A hot water source is applied to form periodic changes of temperature of the testing fluid and make the testing fluid flow through the testing cooper pipe at a low speed. Based on the propagation characteristics of periodically changing fluid temperature in the pipe, h is determined by calculating the amplitude ratio or phase angle difference between the testing fluid and temperature changes on the pipe wall [1]. Such measurement method is quick and accurate. It is applicable to measurement of convective heat transfer coefficient of cooling media for high-temperature superconductor cooling, high-intensity laser mirror cooling, heat dissipation of high-power electronic components, spacecraft thermal control, thermal control of thin film deposition, and so on. In the machining field, such in-pipe transient measurement method obviously disagrees with practical spray cooling conditions since Cooling media are carried by high-pressure gases to the high-temperature grinding zone as high-speed spray droplets. So far, there’s no appropriate measuring device of convective heat transfer coefficient under the spray cooling. Therefore, measurement of convective heat transfer coefficient under spray cooling is still a bottleneck at present. According to lumped parameter analysis, temperatures of heat transfer media in the system of thermal conductor differ slightly at the same moment when the Biot number of cooling media is far lower than 1. Hence, all media in the system can be viewed as a lumped system under the mean temperature and the temperature (T ) is only a function of time (t) [2]. On this basis, convective heat transfer coefficient can be gained simply by measuring the system temperature and time. In this chapter, a measurement system of convective heat transfer coefficient conforming to practical situation of spray cooling is designed and built [3]. The measuring errors of the system are analysed and calculated. A contrast experiment based on pure normal saline is carried out. Nanofluids are prepared by using 2 vol. % HA, SiO2 ,

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_5

141

142

5 Design and Experimental Evaluation of Convective Heat Transfer …

Fe2 O3 , Al2 O3 , CNTs and normal saline, respectively. Firstly, thermophysical properties (contact angle, density, thermal conductivity, viscosity, surface tension and specific heat capacity) of normal saline and the prepared nanofluids are measured and calculated. The built measurement system of convective heat transfer coefficient is used to measure convective heat transfer coefficients of normal saline and the prepared nanofluids. The measured convective heat transfer coefficients of the prepared nanofluids are compared with the convective heat transfer coefficient model results in Chap. 4 to analyse and calculate errors. The heat transfer mechanism of nanoparticles in nanofluids is analysed from nanoparticle-induced changes in base fluid structure and micro-motion of nanoparticles.

5.2 Research Status on Measuring Device of Convective Heat Transfer Coefficient Convective heat transfer coefficient is one of important characterization parameters when solving the heat conduction problem on surface with convective heat transfer. Direct measurement methods of convective heat transfer coefficient can be divided into steady-state method and transient method. The former one has a strict requirement on stability of the experimental environment for a long period, thus resulting in difficult control over the stability of the measurement system and great measuring errors. The later one has been extensively applied by researchers recently to measurement of convective heat transfer coefficient due to the short experimental period, small heat dissipation damages, small errors and easy operation. In the following text, transient measuring methods of convective heat transfer coefficient are summarized.

5.2.1 In-Pipe Transient Measurement of Convective Heat Transfer Coefficient The in-pipe transient measurement method of convective heat transfer coefficient is a method that researchers prefer to measure convective heat transfer coefficient of cooling media. The fluid temperature wave T f (t) measured in the experiment is unfolded to Fourier series by using the Fourier series analysis method. The equations of coefficients of the primary harmonic sine and cosine function terms are [1]: ⎧ 2π ⎪ ⎪ 1 ⎪ ⎪ us = Tf (t) sin ω' tdt ⎪ ⎪ ⎪ π ⎨ 0

⎪ 2π ⎪ ⎪ 1 ⎪ ⎪ uc = Tf (t) cos ω' tdt ⎪ ⎪ ⎩ π 0

(5.1)

5.2 Research Status on Measuring Device of Convective Heat Transfer …

143

Then, the primary harmonic can be expressed as:   θl = u f sin ω' t + ϕf

(5.2)

/ where the amplitude is u f = u 2s + u 2c . The phase angle is ϕf = arctan (uc/us). The period of primary harmonic is P = 2tp. The angular velocity is ω' = π/tp. If thermal-conduction resistance of pipe wall is ignored, the energy equation of pipe wall is: Cw dTw = h Fi (Tf − Tw ) − α0 Fo (Tw − Ta ) dt

(5.3)

The primary harmonic of periodically oscillating temperature of pipe wall is T w (t) = u0 sinω' t. then, the leading phase angle (ϕ f ) and amplitude (uf ) of fluid temperature are: 

⎧ C w ω' ⎪ ⎪ ϕ = arctan ⎪ ⎨ f h Fi + α0 F0 /

(5.4)

  ⎪ C w ω' 2 α0 F0 2 ⎪ ⎪ ⎩ μf = μ0 + 1+ h Fi h Fi As a result, h can be determined by the measured phase angle difference (ϕ f ) or the amplitude ratio (uf /u0 ). The in-pipe transient measuring device of convective heat transfer coefficient is shown in Fig. 5.1. In this experimental device, a piece of ϕ17 mm copper pipe with a length of 60 cm is applied. There’s some distance from fluid to the temperature measuring points on the outer wall surface of the pipe. Thermal insulation materials are set at outer of the pipe. Temperature measurement uses the nickel chromium (NiCr)-NiSi thermocouple and the rotating reversing valve is driven by a micromotor to assure that cold and hot fluid flows through the testing pipe alternatively, with controllable cold-hot alternation time. With the switchover of the rotating reversing valve, the cold and hot fluids flow through the testing pipe through the stable cold and hot water sources under the action a water pump, forming stable in-pipe flow with periodic temperature changes. The in-pipe transient measurement method of convective heat transfer coefficient is quick and accurate. The oscillation period of fluid temperature has some influences on test results.

144

5 Design and Experimental Evaluation of Convective Heat Transfer …

Fig. 5.1 Schematic diagram of in-pipe measuring device of convective heat transfer coefficient [1]

5.2.2 Measurement of Forced Convective Heat Transfer in a Narrow Annular Channel In published reports related with micro-heat transfer channels, researchers prefer rectangular channel or circular microtube as the research objects. The diameter of channels ranges from micrometers to hundreds of micrometers and length is dozens of millimetres. The circumferential size of a narrow annular channel is the same with that of ordinary channels and its circumferential feature size is the same with the feature size of microchannel. In Fig. 5.2, the experimental section of the measuring device for forced convective heat transfer in a narrow annular channel is assembled of three steel pipes, forming three channels of inner annular pipe, middle annular pipe and external annular pipe. To assure concentric positioning of the inner, middle and external annular pipes, a “Yshaped” point support structure is applied on the cross section of annular channels. The loop of the measuring device uses ultrafine glass wool wrap insulation and the working medium flow is measured by weighting method. Temperatures at inlet and outlet of the experimental section are measured by the copper-constantan sheathed thermocouple. The experimental section of the measuring device is installed vertically on the system loop which uses water as the working medium and consists of A and B loop systems. The high-temperature water from the boiler is divided into

5.2 Research Status on Measuring Device of Convective Heat Transfer …

145

Fig. 5.2 Schematic diagram of measuring device for forced convective heat transfer in narrow annular channel [4]

two branches which flow to the inner pipe and external annular pipe through the turbine flowmeter, then flow downward and finally return to the boiler through the circulating water pumps, thus forming a closed loop. The working pressure of Loop B is the atmospheric pressure. Driven by the pump head, the working media enter into the middle annular channel of heat transfer component, flow upward, and finally return to the water tank after participating in heat transfer [4].

5.2.3 Measurement of Convective Heat Transfer in Helical Grooved Tube with Inner Helical Teeth Tubular heat transfer device is a kind of widely used heat transfer equipment. Due to low cost and easy processing, light tube becomes the most common heat transfer pipe in tubular heat transfer device. Nevertheless, light tube has small heat transfer area, large volume, and poor heat transfer performances. Hence, the key to study heat transfer device is to decrease volume of light tube and improve its heat transfer performances. Based on exploration of helical grooved tube, researchers in the world have discovered that the helical grooved tube with inner helical teeth is superior to light tube in term of heat transfer performances. The enhanced heat transfer device in the helical grooved tube with inner helical teeth is shown in Fig. 5.3. It is composed of the heat transfer device, cooling water system and steam system. There’s steam out of the helical grooved tube with inner helical teeth and cooling medium inside it, generally water. The steam flow is controlled by a ball valve and steam from low-pressure oil burning boiler enters

146

5 Design and Experimental Evaluation of Convective Heat Transfer …

Fig. 5.3 Schematic diagram of convective heat transfer measurement device in the helical grooved tube with inner helical teeth [5]

into the heat exchanger through the steam header and it is cooled into condensed water in the experimental section. The condensed water is further discharged by the drain valve and flow into a tank. The mass of condensed water in the tank is weighted to evaluate the enhanced heat transfer performances in the helical grooved tube with inner helical teeth. For the enhanced heat transfer device in the helical grooved tube with inner helical teeth, the cooling medium flows at a low speed in the tube. Rotation and vortex are produced in fluids due to the convex shoulders in the tube, which further trigger rotation of the boundary layer and main current, thus thinning the bottom layer of the laminar flow in the fluid flowing boundary layer. Therefore, heat transfer coefficient of the inner tube surface is increased significantly [5]. To sum up, fluids flow in tubes (or grooved tubes) in all of existing measurement methods of convective heat transfer coefficient. They are designed by changing the fluid temperature or convective flow loop to measure the convective heat transfer coefficient. In the machining field, cooling media are carried by high-pressure gases to the high-temperature zone as high-speed spray droplets. Such in-pipe transient measurement method of convective heat transfer coefficient based on low-speed flow of fluid apparently disagrees with practical conditions. So far, there’s no appropriate measuring device of convective heat transfer coefficient under spray cooling mode. For this reason, a measuring device of convective heat transfer coefficient under spray cooling model will be designed and built in the following text. Moreover, it is used to measure convective heat transfer coefficients of pure normal saline and nanofluids.

5.3 Characterization of Thermophysical Properties of Nanofluids

147

5.3 Characterization of Thermophysical Properties of Nanofluids 5.3.1 Preparation of Medical Nanofluids In the bio-medical fields, HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs nanoparticles all have characteristics of non-toxic and good biocompatibility. They are common medical carriers in nanodrug sustained release system. Normal saline is a common kind of cooling medium in clinics at present since its osmotic pressure is basically equal to that of human blood plasma. Hence, HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs (mean diameter = 50 nm; mean length = 10–30 μm) nanoparticles are applied as nano solid additives and normal saline is used as base fluid to prepare HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs nanofluids. With excellent lubrication and non-toxicity, polyethylene glycol 400 (PEG400) is widely applied to lubrication of colonoscopy and gastroscopy. Its safety to human body has been proved clinically. Moreover, PEG400 has good dispersibility. Therefore, PEG400 was applied as the dispersing agent. According to test, the nanofluids with 2 vol. % nanoparticles and 0.2 vol. % dispersing agent have the best suspension stability. Therefore, nanofluids in this study are prepared by “two-step method”. In other words, 2 mL HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs nanoparticles and 0.2 mL PEG400 are added into 100 mL normal saline, assisted with 15 min of ultrasonic vibration.

5.3.2 Characterization of Thermophysical Properties of Nanofluids (1) Thermal conductivity of nanofluids [6] In 1881, Maxwell proposed the thermal conductivity theoretical model of liquid–solid mixture to calculate the suspending spherical solid particles.   kp + 2kf − ϕv kf − kp knf   = kf kp + 2kf + ϕv kf − kp

(5.5)

where k p is the thermal conductivity coefficient of discontinuous solid particle phase. k f is the thermal conductivity coefficient of base fluid. ϕ v is the volume fraction of solid particles. This theoretical model requires a low concentration of suspension liquid and spherical solid particles scattering randomly in the main media. The distance among particles is relatively large and the influences of particle interaction are ignored. In 1962, Hamilton and Crosser improved the Maxwell model with considerations to influences of particle surface shapes on thermal conductivity of two-phase mixtures. A thermal conductivity of the mixture was proposed:

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5 Design and Experimental Evaluation of Convective Heat Transfer …

  kp + (n − 1)kf − (n − 1)ϕv kf − kp knf   = kf kp + (n − 1)kf + ϕv kf − kp

(5.6)

where n is an empirical shape factor (n = 3/ψ, ψ refer to the sphericity of solid particles). Based on the Maxwell theoretical model, Choi and Yu et al. considered that adsorption of liquid phase on nanoparticle surface may become solid-like nanolayer and its thermal conductivity is higher than that of the dispersion liquid. Hence, it can increase effective volume fraction of nanoparticles. Suppose the thickness of solidlike nanolayer is hs-n and particle radius is r s . The effective volume of nanoparticles is:

 4 4 3 ' h s−n 3 3 ' φc = π(rs + h s−n ) n = πrs n 1 + = ϕv (1 + βs )3 3 3 rs

(5.7)

where the particle number in the unit volume is n'. β s is the ratio between nanolayer thickness and original particle radius. According to effective medium theory, the thermal conductivity (k pc ) of the formed composite particle is: kpc =

 2(1 − γr ) + (1 + βs )3 (1 + 2γr ) γr −(1 − γr ) + (1 + βs )3 (1 + 2γr )

kp

(5.8)

where γ r is the ratio between thermal conductivity of nanolayer and thermal conductivity of nanoparticles. (2) Density of nanofluids After nanoparticles scatter uniformly in liquid-phase medium, the overall density of nanofluids may change. If the thermodynamic properties of nanofluids meet existing theory, the density can be expressed as [7]: ρnf = (1 − ϕv ) · ρf + ϕv ρb

(5.9)

where ρ b is the density of nanoparticle block material and ρ f is the density of base fluid. (3) Specific heat capacity of nanofluids According to calculation conditions of nanofluids density, the specific heats of nanofluids are calculated according to the principle of addition. The calculation formula is [8]: cnf =

ϕv ρb cs + (1 − ϕv ) · ρf cf ρnf

(5.10)

5.3 Characterization of Thermophysical Properties of Nanofluids

149

where cs is the specific heat capacity of nanoparticle block material and cf is the specific heat capacity of base fluid. The thermal conductivity, density and specific heat capacity of normal saline (NS) and nanoparticle block materials are shown in Table 5.1. Except density, specific heat capacity and thermal conductivity, thermodynamic properties of nanofluids also include surface tension, contact angle and viscosity of nanofluids. Viscosity, contact angle and surface tension of nanofluids were measured by DV2TLV viscometer, JC2000CIB contact angle measuring apparatus and BZY201 surface tension meter (Fig. 5.4). Each parameter was measured by 5 groups and means were collected. The measured surface tension, contact angle and viscosity of NS and nanofluids as well as the calculated thermal conductivity, density and specific heat capacity are shown in Fig. 5.5. Clearly, adding nanoparticles influences thermodynamic parameters of base fluid significantly. Compared with NS, surface tension of nanofluids with HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs nanoparticles decreases by 25.87%, 32.48%, 29.79%, 36.46% and 34.79%, respectively; the contact angle decreases by 5.82%, 1.76%, 2.4%, 3.81% and 4.28%, respectively; the viscosity increases by 123.83%, 116.29%, 122.64%, 122.05% and121.45%, respectively; the thermal conductivity increases by 2.61%, 4.74%, 5.36%, 5.82% and 6.12%, respectively; the density Table 5.1 Thermophysical properties of nanoparticle block materials and base fluid Thermal conductivity (W/m K)

Density (g/cm3 )

Specific heat capacity (J/ (kg °C))

Base fluid

NS

0.66

1.03

4150

Nanoparticle block material

HA

2.16

3.61

732

SiO2

7.6

2.2

966

Fe2 O3

15

5.27

670

Al2 O3

40

3.7

882

CNTs

3000

1.3

692

Fig. 5.4 Measuring instruments of surface tension, contact angle and viscosity

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increases by 5.01%, 2.27%, 8.23%, 5.18% and 0.52%, respectively; the specific heat capacity decreases by 5.50%, 3.20%, 7.93%, 5.38% and 2.09%. In other words, nanoparticles have relatively greater influences on viscosity of base fluid, followed by surface tension. In the following text, the influencing mechanism of nanoparticles on thermophysical properties of base fluid is analysed. After adding in nanoparticles, the contact angle of base fluid decreases. This is because nanoparticles may gather on the liquid surface automatically. Single nanoparticle is often ignored due to small size and weight. However, the weight of single nanofluid droplets cannot be ignored. Each nanoparticle on the surface layer is influenced by gravity, these nanoparticles all

Fig. 5.5 Thermophysical properties of pure normal saline and nanofluids

5.3 Characterization of Thermophysical Properties of Nanofluids

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Fig. 5.6 Schematic diagram of solid–liquid-gas equilibrium of droplets

have a trend of moving downward in liquid, that is, the spreading trend as much as possible. As a result, the contact angle decreases. Moreover, contact angle reflects the size of surface tension. Given the smaller surface tension, molecules in droplets have smaller attraction to surface molecules and droplets have a trend of spreading on surface as much as possible, thus decreasing the contact angle. Additionally, The relationship between contact angle and surface tension can be gained from the Yong’s equation [9] (Fig. 5.6). The Yong’s equation describes the relations between surface tensions (γ sg , γ sl , γ lg ) of solid–gas, solid–liquid and liquid–gas interfaces and contact angle of solid surface (θ c ). This is also called the wetting equation: γlg cosθ = γsg − γsl

(5.11)

It can be seen from Eq. (5.11) and Fig. 5.6 that the contact angle between liquid and solid surface decreases when γ lg decreases. Compared with pure normal saline, viscosity of nanofluids increases. This is because there’s viscous force among particles due to interaction of nanoparticles, thus increasing the viscosity of nanofluids. It can be seen from Table 5.1 and Eqs. (5.5)– (5.10) that since solid particles have higher thermal conductivity and density than base fluid, the thermal conductivity and density of nanofluids increase. On contrary, the solid particles have lower specific heat capacity than base fluid, and the specific heat capacity of nanofluids after adding with nanoparticles decreases.

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5.4 Design and Building of the Measurement System for Convective Heat Transfer Coefficient Under Nanofluids Spray Cooling 5.4.1 Experimental Principle In the unsteady heat conduction process, there are tiny differences of temperatures at different points in the heat conductor system at the same moment when thermalconduction resistance (lt /k c , where lt is the feature size of heat conductor and it is 1/2 of the thickness; k c is the thermal conductivity of heat conductor) of the heat conductor is far lower than the convective thermal resistance (1/h) between the heat conductor and fluid, that is, Bi = hlt /k c < 0.1. All heat-conducting medium of the system can be viewed as a lumped system under the mean temperature. According to the lumped parameter system (LPS), the heat conduction problem of system is analysed. At this moment, T is simply a function of time (t): T = f(t) [2, 10]. Suppose the initial temperature of the heat conductor is T 0 . The energy equilibrium at the moment that heat conductor contacts with the fluid is: h As (T − Tf ) = −ρp Vp cp

dT dt

(5.12)

where cp is the specific heat capacity of the heat conductor; V p denotes the volume of heat conductor; ρ p is the density of a heat conductor; As is the area of heat conductor in contact with cooling medium. Excess temperature (T' = T − T f [11]) was introduced in. Then, there’s dT ' dt T ' (t = 0) = T0 − Tf = T0'

h As T ' = −ρp Vp cp

(5.13)

Bring it into the Eq. (5.12) and it can get: 

dT ' h As dt = − T' ρp Vp cp

(5.14)

Calculate integral of Eq. (5.14) and it can get:

ln

T' T0'



 h As = − t ρp Vp cp

(5.15)

In other words,  T − Tf ρp Vp cp h = − ln T0 − Tf As t

(5.16)

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153

Moreover, T' T − Tf − h As t = e ρp Vp cp ' = T0 T0 − Tf

(5.17)

A dimensional analysis of the index in Eq. (5.17) is carried out:  W  2  m 1 h As W 2 = =  mK   = kg Jkg ρp Vp cp J s m3 m3

(5.18)

K

  In other words, it has the same dimension with the time reciprocal 1t . ρ Vc Meanwhile, it can be known from Eq. (5.17) that when t = ph Aps p , there’s: T' T − Tf = e−1 ' = T0 T0 − Tf

(5.19) ρ V c

The Eq. (5.19) demonstrates that when the heat transfer time is t = ph Aps p , the excess temperature of objects has reached e−1 of the initial temperature. Therefore, convective heat transfer coefficient under the spray cooling condition can be gained by measuring temperature of the heat conductor at thermal steady state and the ρ V c temperature at t = ph Aps p .

5.4.2 Design and Building of the Measurement System According to Sect. 5.4.1, the measuring device of the convective heat transfer coefficient under nanofluids spray cooling condition is designed by using the lumped parameter method (LPM). Firstly, Biot number is pre-estimated. According to calculated results of Hongfu Zhou and Shen, the orders of magnitudes of convective heat transfer coefficient under spray cooling is 0.01 W/mm2 K. For heat conductor, thermal conductivity of diamond is the highest in solid materials, reaching 2000 W/(m K). Nevertheless, diamond has high costs and cannot be made into specific shapes and size. Diamond film synthesized artificially by chemical vapour deposition (CVD) lowers the production cost of diamond and quality of CVD diamond film is catching up with natural diamond gradually, and it is even superior to natural diamond in some aspects. As a result, diamond film is extensively applied to thermal deposition, optical, electrochemistry and biomedical fields. According to test, the thermal conductivity of 0.5 mm thick CVD diamond film reaches 1800 W/(m K). Therefore, the 0.5 mm thick CVD diamond film is used as the heat conductor. Under this circumstance, the Biot number is:

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Bi =

hlt 0.01 × 0.25 = = 1.39 × 10−3 < 0.1 kc 1 800 × 10−3

(5.20)

Hence, measuring the convective heat transfer coefficient under nanofluids spray cooling by using the 0.5 mm thick CVD diamond film as the heat conductor conforms to the measurement conditions of LPM. The built measurement system of convective heat transfer coefficient is shown in Fig. 5.7. It is composed of the spray feeding system, insulation box, nozzle, heating plate, heat conductor and thermocouple measurement system. The parameters of the spray feeding system are introduced as follows: flow rate Qf : 50 mL/h; pressure of compressed air: pa = 0.54 MPa; nozzle angle β = 18°, nozzle cone angle α = 21°, and nozzle height H = 12.27 mm. The power of the heating plate in the temperature rising stage is 5 W and the power in the stage of reaching and keeping the constant temperature is 2 W. The size of heating plate and CVD diamond film is 25 × 20 × 0.5 mm. They are connected by glue which can resist high temperature. There’s a thermocouple groove on the contact surface between heating plate and CVD diamond film. A hole with a diameter of 1 mm is drilled at the intersection of diagonals of the CVD diamond film. Thermocouple nodes are set at this hole to measure temperature of the CVD diamond film surface. Surfaces 1–5 of the insulation box are made of polymethyl methacrylate (or known as the acrylic plate) without thermal insulation effect. Hence, a vacuum insulated panel is set. There’s an insertion hole for the nozzle, a gas extraction hole and holes for power cord of the heating plate and thermocouple on Surface 6 of the insulation box and Surface 6 is made of polycarbonate (or known as sunshine plate). Therefore, it has good thermal insulation effect (0.08 W/(m K)), without a vacuum insulated panel. Air exhaust of the insulation box is needed before measurement to avoid heats on the heating plate to be transferred into air in the insulation box (heats transferred

Fig. 5.7 Measurement system for convective heat transfer coefficient of nanofluids spray cooling

5.4 Design and Building of the Measurement System for Convective Heat …

155

to nozzle and outlet of heating plate are ignored) and make them transferred only to the CVD diamond film. The air exhaust time can be calculated according to exhaust rate of the air pump and internal volume of the insulation box. Turn on the heating plate and it begins to work. Temperature curve tested by the h measurement system under normal saline spray cooling condition is presented in Fig. 5.8. Temperature firstly increases sharply to the universal evaluation standard of “thermal steady state” in engineering: the temperature gap of specimens in 1.7 h is no higher than 3 °C [12]. Clearly, the temperature difference measured in the experiment in 1.7 h is 1.66 °C. In other words, the system has reached thermal steady state. Under this circumstance, turn on the spray supply system and spray the atomised normal saline to the CVD diamond film surface. Temperature drops sharply. It has to note the following two points: (1) It can be seen from Fig. 5.8 that temperature do not increase any more at 0.17 h and the internal system of the insulation box begins to enter into the thermal steady state. To assure that the experimental time is not too long, the temperature on the CVD diamond film which is sprayed with cooling medium is measured after 0.17 h (about 10 min). (2) According to searching, the maximum bone grinding temperature can reach 70 °C, lower than the boiling point of water-based cooling medium. On this basis, the constant temperature of heating plate is set 80 ± 10 °C. Therefore, there’s no boiling heat transfer during heat transfer under mist and nanofluids spray cooling conditions.

Fig. 5.8 Test curve of convective heat transfer coefficient

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5.4.3 Measuring Errors of Experimental Device Measuring errors of the experimental system are analysed under the pure normal saline spray cooling condition in Fig. 5.8. The constant temperature of the heating plate is 83.04 °C and T f is 17.37 °C. Then, T 0 = 41.53 °C and t = 0.575 s. It can be seen from Eq. (5.16) that when ρ p and cp of heat conductor are fixed, the error of the h measurement system is caused by temperature accuracy (T, T f , T 0 ) of thermocouple measurement, time accuracy (t) and dimensional accuracy (V p , As ) of heat conductor [2]. (1) The temperature accuracy of thermocouple is ± 0.032 °C. The error caused by thermocouple is: ⎧ ρp Vp cp 1 ⎪ Δh T = − ΔT = − 2.07 × 10−5 W/mm2 K ⎪ ⎪ ⎪ A t T − T s f ⎪ ⎪ ⎨ ρp Vp cp 1 Δh T0 = − ΔT0 = − 3.78 × 10−7 W/mm2 K ⎪ As t (T − Tf )(T0 − Tf ) ⎪ ⎪ ⎪ ⎪ ρ Vc T − Tf ⎪ ⎩ Δh Tf = − p p p ΔTf = − 7.63 × 10−6 W/mm2 K As t (T − Tf )(T0 − Tf ) (5.21) (2) The measurement frequency of the thermocouple is 100 Hz. In other words, the response time is 0.01 s and the relevant error is:

Δh t = − ln

 T − Tf ρp Vp cp Δt = 2.81 × 10−4 W/mm2 K T0 − Tf As t 2

(5.22)

(3) The size accuracy of specimens is ± 0.05 mm and the relevant error is:  T − Tf ρp cp ΔL = 1.32 × 10−4 W/mm2 K Δh L = − ln T0 − Tf t

(5.23)

Influences of convective heat transfer coefficient on surface roughness of heat conductor are ignored. Moreover, it hypothesized errors caused by incomplete thermal insulation and thermal radiation. Based on the sum of above errors, the errors of the built measurement system can be calculated as 0.044 × 10–2 W/mm2 K.

5.5 Experimental Result Analysis and Discussions

157

5.5 Experimental Result Analysis and Discussions 5.5.1 Experimental Results Convective heat transfer coefficients of pure normal saline and 2 vol. % HA, SiO2, Fe2O3, Al2O3 and CNTs nanofluids were measured, respectively. Each group was measured by five times and means were collected. Results of the SiO2 nanofluid were analysed in this study (Fig. 5.9). Experimental data processing is introduced as ρ V c follows: it can be seen from Eq. (5.19), when the heat transfer time is t = ph Aps p , the −1 excess temperature of objects has reached e of the initial temperature. Figure 5.9 shows that the temperature (T0 ) when the insulation box reaches the thermal steady state is 78.75 °C and the temperature of nanofluids (Tf ) is 18.1 °C. Nanofluids are sprayed and temperature drops to T = e−1 (T0 −Tf ) + Tf (40.41 °C) at 0.22 s. It is calculated from the Eq. (5.16) that the convective heat transfer coefficient is 4.03 × 10–2 W/mm2 K. The calculated and measured convective heat transfer coefficients under pure normal saline and HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs nanofluids spray cooling conditions are shown in Fig. 5.10. Clearly, the measured convective heat transfer coefficients under HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs nanofluids spray cooling conditions are increased by 141.98%, 137.65%, 130.25%, 141.36% and 145.06% compared to that under pure normal saline spray cooling condition, respectively. Moreover, the calculated results and measured results agree well, showing a model error of 7.26%.

Fig. 5.9 Test curve of convective heat transfer coefficient of SiO2 nanofluids

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Fig. 5.10 Measured and calculated values of convective heat transfer coefficients of nanofluids

5.5.2 Analysis and Discussions Given the fixed spray angle and nozzle height, convective heat transfer coefficient of nanofluids spray cooling is determined by jet parameters, spreading characteristic parameters of droplets (surface tension, density, viscosity, contact angle and incidence velocity) and pressure of the compressed air. In the process of spray cooling, the higher number of droplets with effective heat transfer is accompanied with the lower Dmin , the higher Dmax , and the better improvement in heat transfer performances. Dmin and Dmax of pure normal saline and the prepared nanofluids were calculated from Eqs. (4.16)–(4.26) in Sect. 4.3.4. Results are shown in Fig. 5.11. Compared with normal saline, adding nanoparticles has no obvious influences on Dmin , but it has great influences on Dmax . When solid particle size enters into the nanoscale, the behaviors of solid nanoparticles are close to those of liquid molecules under the comprehensive action of quantum scale effect, surface effect and small-sized effect, showing different attributes with micron and millimeter particles. Many researchers have proved that adding some solid nanoparticles can improve heat transfer performances of cooling medium significantly and the growth rate exceeds the prediction results of classical theory [13, 14]. In the following text, the enhanced heat transfer mechanism of nanoparticles is analysed from micro-motion of nanoparticles and nanoparticle-induced changes in structure of base fluid.

5.5 Experimental Result Analysis and Discussions

159

Fig. 5.11 Dmin and Dmax of pure normal saline and nanofluids

(1) Nanoparticles change structure of base fluid The adsorption effect of liquid molecules on particle surface is the most direct influences of nanoparticles on base fluid. This refers to the liquid adsorption layer formed on nanoparticle surface. Many researchers have reported effects of liquid adsorption layer on nanoparticle surface in improving enhanced heat transfer performances of nanofluids. They believe that liquid adsorption layer on nanoparticle surface is an important mechanism of enhanced heat transfer of nanofluids [15–17]. The liquid adsorption layer on nanoparticle surface means that liquid molecules near nanoparticles are adsorbed onto the nanoparticle surfaces directly. Since the action force of nanoparticles on liquid molecules is stronger than interaction force among liquid molecules, the adsorbed liquid molecules are influenced by uniform distribution of solid molecules, while liquid molecules in the adsorption layer are in ordered arrangement similar with solid molecules rather than scattering randomly like free liquid molecules. The thermal conductivity of solid is higher than those of liquid and gas because molecular arrangement in solids is more regular than those in liquid and gas. As shown in Fig. 5.12, arrangement of liquid molecules in the adsorption layer is more regular compared to arrangement of liquid molecules which are far away from nanoparticles. Hence, thermal conductivity of nanofluids which are formed by adding nanoparticles into base fluid is higher compared to that of base fluid, but lower than that of nanoparticle block material. Besides, liquid molecules adsorbed on nanoparticle surface are influenced by nanoparticles all the time and move with nanoparticles rather than keeping far away from nanoparticles. Moreover, thermal resistance against heat transfer between the base fluid and solid particles is decreased significantly due to the existence of the absorption layer with a thermal conductivity between those of nanoparticle block material and base fluid. This is conducive to heat dissipation in nanofluids.

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Fig. 5.12 Schematic diagram of liquid adsorption layer on the nanoparticle surface

Fluid molecular Adsorbed Molecular Nanoparticle

(2) Micro-motion of nanoparticles in base fluid Due to the small-size effect of nanoparticles, nanoparticles make heat dissipation, irregular walking (dispersion), Brownian diffusion and other micro-motion as a response to micro-forces (e.g. Brownian force and Van Der Waals force). Due to micro-motion of nanoparticles, micro-convective phenomena are produced between particles and base fluid. This is conducive to enhance energy transfer process between nanoparticles and base fluid. Moreover, energy carried by nanoparticles in base fluid migrates when they are walking irregularly [18]. As shown in Fig. 5.13, energy migration process brought by micro-motion of nanoparticles is introduced as follows. Nanoparticles which have the same temperature with the core temperature of liquid approach to the heat source surface and then become countless heat sources, leave the heat source quickly after heat transfer with the heat source surface to give way to subsequent nanoparticle heat sources, and finally return to the core area. Due to the large surface area, nanoparticles can transfer heats with core liquid quickly and then reach a thermal equilibrium. If nanoparticles stay on heat source surface for a shorter period, the internal heat exchange cycling speed of nanofluids is higher and the heat transfer intensity also increases. In this way, nanoparticles can become major medium for heat transfer at different regions in the nanofluids and heat transfer between nanofluids and heat source. Finally, there’s abundant heat transfer phenomena on the heat source surface to form temperature gradients. Meanwhile, nanoparticles make translational motion and rotational motion while they flow with nanofluids, which are attributed to the interaction between atoms and liquid molecules in nanoparticles and vibration of nanoparticle atoms (Fig. 5.14). Nanoparticles in different shapes produce significantly different resistance against motion. Since non-spherical particles have larger and effective hydraulic volume, they generate stronger resistance against base fluid and the nanofluids have the higher viscosity. Moreover, translational and rotational motions of nanoparticles may enhance micro-convective phenomenon between nanoparticles and fluids. The non-spherical nanoparticles have greater disturbance area to base fluid than spherical

5.5 Experimental Result Analysis and Discussions

161

Nanoparticle which moving to workpiece Droplet

Heat source surface

Temperature gradient

Fig. 5.13 Schematic diagram of energy migration due to micro-motion of nanoparticles

ones due to the higher rotational speed, which is more beneficial for convective heat transfer of nanofluids. Based on above analysis, microstructure of nanofluids, that is, fluids around any nanoparticle in the nanofluids, can be divided into three layers according to liquid adsorption layer on the nanoparticle surface as well as irregular walking and rotation of nanoparticles. Along the radial direction of nanoparticles, these three layers are liquid adsorption layer, rotational fluid layer and spherical finite space (Fig. 5.15) [19– 21]. The random rotational speed of nanoparticles in the base fluid is ωn . Due to strong adsorption force from solid atoms of nanoparticles, the liquid close to nanoparticle surfaces is adsorbed onto nanoparticle surfaces tightly, forming the first fluid layer out of nanoparticles––liquid adsorption layer. Since the adsorption layer moves with nanoparticles, it can be viewed as an effective component of nanoparticles. Hence, the rotational speed of the adsorption layer is the same with rotational speed of nanoparticles (ωn ). Out of the adsorption layer on the nanoparticle surface, base fluid molecules may rotate with nanoparticles under the action of viscosity force, thus forming the second layer––rotational fluid layer. The rotational speed of the rotational fluid layer is lower than ωn and it is set ωn '. In nanofluids, each rotating nanoparticle and the adsorption layer and rotational fluid layer on its surface are limited within a spherical zone with a radial range of Rn . It is the action range of another nanoparticle out of Rn . In other words, each nanoparticle has a spherical finite space.

Fig. 5.14 Schematic diagram of rotation motion of nanoparticles with different shapes

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Fig. 5.15 Schematic diagram of rotating fluid microelements in nanofluids [14]

Based on above analysis on fluid zone around a single nanoparticle in nanofluids, the internal microstructure of nanofluids can be viewed as the composition of rotational fluid microelements produced by micro-motion of countless nanoparticles. In Fig. 5.15, there are countless rotating nanoparticles in the nanofluids, which is different from the microstructure of single-phase fluid. These rotating nanoparticles are equivalent to make the nanofluids full of countless rotational fluid microelements. This is very beneficial for mixing of internal fluid micelles, thus further facilitating heat transfer and exchange of nanofluids. Besides, dynamic microstructure of nanofluids is analysed. Since nanoparticles are “crowded” in the base fluid significantly and make translational motion and rotational motion, there’s a very high probability of impact among nanoparticles and heat transfer channels will be built up directly among them [22]. It can be seen from Fig. 5.16 that heat diffusion of one nanoparticle can penetrate through the outer base fluid and heats can be transferred to the adjacent nanoparticles due to the small distance among nanoparticles. The micro-flow of nanofluids is more conducive to strengthen such effect. Hence, heat transfer mode and enhanced heat transfer performances in nanofluids may change fundamentally due to the existence of nanoparticles compared to that of single-phase cooling medium.

5.6 Summary

163

Rotating fluid layer Adsorbed layer Nanoparticle Spherical finite space

Heat

Fig. 5.16 Schematic diagram of heat transfer channels among nanoparticles [14]

5.6 Summary Research status on measurement methods of convective heat transfer coefficient is summarized. Thermophysical properties of medical nanofluids are calculated and measured. Based on the high-speed and high-pressure jet characteristics of nanofluids spray cooling, a measurement system of convective heat transfer coefficient which conforms to practical spray condition is designed and built based on LPM to measure convective heat transfer coefficients of pure normal saline and nanofluids spray cooling modes. The heat transfer enhancement mechanism of base fluid based on nanoparticles is analysed. Some major conclusions can be drawn: (1) In the measurement system of convective heat transfer coefficient based on LPM, the temperature (T) is only a function of time (t). The convective heat transfer coefficient under spray cooling condition can be gained by measuring temperature at thermal stable state of the heat conductor and the temperature at t = ρ p V p cp /hAs . (2) The errors of measurement system of convective heat transfer coefficient come from temperature measurement accuracy and measurement frequency of thermocouple as well as size accuracy of the heat conductor. According to calculation, the measurement error is 0.044 × 10–2 W/mm2 K. (3) Compared to pure normal saline, nanofluids with HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs nanoparticles have lower surface tension, contact angle and specific heat capacity, but higher viscosity, thermal conductivity and density. Nanoparticles influence viscosity of base fluid the mostly, followed by surface tension. (4) The measured convective heat transfer coefficients of HA, SiO2 , Fe2 O3 , Al2 O3 and CNTs nanofluids increase by 141.98%, 137.65%, 130.25%, 141.36% and145.06% than that of pure normal saline, respectively. This verifies the enhanced heat transfer ability of nanofluids. The theoretical calculated value of convective heat transfer coefficient agrees well with measured values, showing a model error of 7.26%.

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5 Design and Experimental Evaluation of Convective Heat Transfer …

(5) Compared to normal saline, adding nanoparticles has no regular influences on the minimum size of spreading droplets, but it influences the maximum size of spreading droplets greatly. (6) Solid nanoparticles improve the enhanced heat transfer performances of base fluid through two mechanisms, including changing the structure of base fluid and micro-motion in base fluid. It is easy to form a liquid adsorption layer on the nanoparticle surface, which is conducive to lower thermal resistance of the interface for heat transfer between particles and free liquid. Due to the small-size effect, nanoparticles walk irregularly in base fluid. This is easy to strengthen micro-convective phenomenon between nanoparticles and fluid and it is in favour of convective heat transfer of nanofluids.

References 1. Wang, Y., Li, C., Zhang, Y., Yang, M., Li, B., Dong, L., & Wang, J. (2018). Processing characteristics of vegetable oil-based nanofluid MQL for grinding different workpiece materials. International Journal of Precision Engineering and Manufacturing-Green Technology, 5(2), 327-339. 2. Yang W C, Zhou Y, Zhang J, Liu H, et al. Role of radiative and convective heat transfer during heating of an ingot product in a tubular furnace: experiment and simulation. Journal of Iron and Steel Research International, 2022, 29:(12):1978–1985. 3. Wang L, Liu Q S. Transient Heat Transfer Characteristics of Twisted Structure Heated by Exponential Heat Flux (vol 9, 771900, 2021). Frontiers in Energy Research, 2022, 10:2. 4. Wan Z P, Hu X S, Wang X W, et al. Experimental study on the boiling/condensation heat transfer performance of a finned tube with a hydrophilic/hydrophobic surface. Applied Thermal Engineering, 2023, 229:12. 5. Uddin M, Gurgenci H, Klimenko A, et al. Heat transfer analysis of supercritical CO2 in a High-Speed turbine rotor shaft cooling passage. Thermal Science and Engineering Progress, 2022, 39:10. 6. Shen Z J, Min J C. Non-equilibrium thermodynamic analysis of coupled heat and moisture transfer across a membrane. Chinese Journal of Chemical Engineering, 2022, 44:497-506. 7. X. Cui, C.H. Li, W.F. Ding, Y. Chen, C. Mao, X.F. Xu, B. Liu, D.Z. Wang, H.N. Li, Y.B. Zhang, Z. Said, S. Debnath, M. Jamil, H. Muhammad Ali, S. Sharma, Minimum quantity lubrication machining of aeronautical materials using carbon group nanolubricant: from mechanisms to application, Chinese Journal of Aeronautics, 2022, 35(11):85.112. 8. Lushchik V G, Makarova M S, Reshmin A I. Double-Pipe Heat Exchanger with Diffuser Channels. High Temperature, 2022, 60(SUPPL 2):S215.S222. 9. Kiseev V M, Sazhin O V. Heat Transfer Enhancement in Two-Phase Systems with Capillary Pumps. Technical Physics, 2022, 67(2):136-145. 10. Solnechnyi E M, Cheremushkina L A. Dynamic Properties of a One-Dimensional Heat Transfer System with a Moving Heat Source. Autom Remote Control, 2022, 83(8):1172-1179. 11. Wang L, Cheng Q L, Sun W, et al. Study on the Exergy Transfer Characteristics of the Heat Transfer Process of the Tube Heating Furnace. Journal of Thermal Science and Engineering Applications ,2023, 15(4):13. 12. Xu B W, Lia J W, Lu N X, et al. Experimental study on heat transfer characteristics of hightemperature heat pipe. Thermal Science 26(6):5227–5237. 13. Zhang M, Sun B. Improved Heat-Transfer Correlation for Transcritical Methane Based on a Velocity Profile Correction Term. Journal of Thermal Science and Engineering Applications, 2023, 14(4):9.

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14. Ali M R, Al-Khaled K, Hussain M, et al. Effect of design parameters on passive control of heat transfer enhancement phenomenon in heat exchangers-A brief review. Case Studies in Thermal Engineering, 2023, 43:19. 15. Mingzheng Liu, Changhe Li, Yanbin Zhang, Min Yang, Teng Gao, Xin Cui, Xiaoming Wang, Haonan Li, Zafar Said, Runze Li and Shubham Sharma, Analysis of grain tribology and improved grinding temperature model based on discrete heat source, Tribology International, (2022). https://doi.org/10.1016/j.triboint.2022.108196. 16. Min Yang, Changhe Li, Yanbin Zhang, Yaogang Wang, Benkai Li, Dongzhou Jia, Yali Hou, Runze Li. Research on microscale skull grinding temperature field under different cooling conditions. Applied Thermal Engineering, 2017, 126: 525.537. 17. Li L, Zhang Y, Ma H, et al. An investigation of molecular layering at the liquid-solid interface in nanofluids by molecular dynamics simulation[J]. Physics Letters A, 2008, 372 (25): 4541-4544. 18. Yang, M., Li, C., Zhang, Y., Jia, D., Li, R., Hou, Y., & Cao, H. (2019). Effect of friction coefficient on chip thickness models in ductile-regime grinding of zirconia ceramics. The International Journal of Advanced Manufacturing Technology, 102(5), 2617-2632. 19. Du X C, Li W T, Zhang X R, et al. Experimental Research on the Flow and Heat Transfer Characteristics of Subcritical and Supercritical Water in the Vertical Upward Smooth and Rifled Tubes. Energies, 2023, 15(21):22. 20. He R D, Wang Z M, Dong F. Influence of heat-transfer surface morphology on boiling-heattransfer performance. Heat and Mass Transfer, 2022, 58(8):1303-1318. 21. Min Yang, Changhe Li, Zafar Said, Yanbin Zhang, Runze Li, Sujan Debnath, Hafiz Muhammad Ali, Teng Gao, Yunze Long. Semiempirical heat flux model of hard-brittle bone material in ductile microgrinding, Journal of Manufacturing Processes, 2021, 71: 501-514. 22. Yang, M., Li, C., Luo, L., Li, R., & Long, Y. (2021). Predictive model of convective heat transfer coefficient in bone micro-grinding using nanofluid aerosol cooling. International Communications in Heat and Mass Transfer, 125, 105317.

Chapter 6

Research on Microscale Skull Grinding Temperature Field Under Different Cooling Conditions

6.1 Introduction Currently, the analytical method based on the theory of moving heat source is often applied to study and solve grinding temperature field. Based on the mathematical model, the final results of this method are analytical solutions expressed in functions and they can reflect influencing laws of different factors on temperature distribution and heat conduction as well as their quantitative relations. Nevertheless, the original problem has to be simplified and some hypotheses have to be made when the analysis object is relatively complicated. For example, to simply the workpiece shape and the heat transfer state on the heat conductor surface, it hypothesizes that the heat source distributes and moves uniformly on the workpiece surface at a certain law [1]. Such simplification and hypothesis may influence the solving accuracy to some extent. Nevertheless, the analysis process of such approximate analytic method is relatively intuitive and easy to be solved, and it is still the most extensive analytical method to solve theoretical grinding temperature. Moreover, it has solved and predicted heat conduction process in different grinding processes successively [2]. Everyone knows that the temperature field is composed of heat dissipation and heat generation (Fig. 6.1), which can be expressed by convective heat transfer coefficient (h) and heat flux density (qw ). In heat dissipation, a theoretical model of h under nanofluids spray cooling condition has been established in Chap. 4. In heat generation, it has to determine heat flux density under different material removal modes (plastic shear removal, powder removal and brittle fracture removal) in order to solve micro-grinding temperature field of bio-bone since the material removal modes and grinding-induced heat generation are different. Existing heat flux density models are all established based on plastic material grinding. For plastic materials, there’s only plastic shear removal. However, biobone is a typical kind of hard and brittle material. It can be known from Chap. 4 that hard and brittle bone materials include plastic removal, powder removal and brittle fracture removal. As everyone knows, heat generation in the grinding process varies with material removal modes. Therefore, the heat flux density model of hard and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_6

167

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Fig. 6.1 Overall research map for the dynamic model of temperature field in bio-bone microgrinding with nanofluids spray cooling

brittle bone materials has to be established for different material removal modes to solve the micro-grinding temperature field of bones. Additionally, most researchers got the constant heat flux density by calculating the mean of tangential force based on test of grinding force in studies of grinding temperature field. However, it can be seen by measuring temperature at different points on bone surface that microgrinding temperature of bones changes with time. Hence, it conforms to practical situation to get dynamic heat flux density by real-time collection of grinding force signals according to variation trends of grinding force and then calculate loads. In this chapter, the solving methods of grinding temperature field are summarized firstly. The basic principle of finite difference method and methods which use finite element technique to solve grinding temperature field are discussed. The constant heat flux density model in grinding of metal materials with ordinary wheel is summarized. The energy generation and consumption form in micro-grinding process of bone materials are discussed according to different material removal modes of hard and brittle bone materials. The dynamic heat flux density models of bone materials

6.2 Definition of Grinding Temperature Field

169

under plastic shear removal and powder removal are established. Moreover, the heat allocation coefficient models in the grinding zones are summarized. Based on the convective heat transfer coefficient models, a micro-grinding heat allocation coefficient model of nanofluids spray cooling is constructed. Finally, the thermal damage domain of bones under dry grinding is analyzed by the finite element method.

6.2 Definition of Grinding Temperature Field Firstly, heats (Q) at a point in the space are generated immediately from the perspective of ordinary temperature field. Influenced by the heats transferred in, temperatures at other near points change accordingly and they are changing with time and space. The temperature field is defined as the generic term of temperature distribution at different points in the space at a certain moment [3]. Generally speaking, temperature field is the function of space and time. T = f (x, y, z, t )

(6.1)

Equation (6.1) expresses the three-dimensional unsteady-state temperature field that temperature of objects change along x, y, z and at different time nodes. In this study, the temperature field is divided into three types: (1) Temperature field is divided into steady-state temperature field and transient temperature field according to whether temperature changes with time. As shown in Eq. (6.1), if temperature field doesn’t change with time: ∂∂tT = 0, it is a steady-state temperature field; otherwise, it is a transient temperature field. Since movable heat source is applied, temperature at specific points of bone surface changes with time. Therefore, the temperature field in this study is a transient one. (2) Temperature field is divided into temperature field in cut-in zone, temperature in steady-state zone and temperature field in cut-out zone according to length of the grinding tool-sample contact arc. In Fig. 6.2, the length of the grinding too-sample contact arc is lc when the effective cutting part of the grinding tool is completely within the length of sample material, and the temperature field is the temperature field in steady-state zone. In the beginning of grinding process, the length of the grinding tool-sample contact arc increases gradually, but it hasn’t reached lc . At this moment, the grinding tool/sample material enters into the cut-in stage, and the temperature field is the temperature field in cut-in zone. When the grinding tool begins to move out of the sample length, the length of contact arc decreases gradually to 0. At this moment, the grinding tool cuts out of the sample material and the temperature field is the temperature field in cut-out zone. Temperature field in cut-in zone, temperature in steady-state zone and temperature field in cut-out zone will be analyzed thoroughly in Sect. 7.5. (3) Temperature field is divided into constant temperature field and dynamic temperature field according to whether sample temperature below the moving heat source in the steady-state zone changes with time. Previous researchers got the

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Fig. 6.2 Schematic diagram of grinding tool-bone contact states

constant heat flux density by calculating the mean of tangential force. The temperature field which is calculated by loading a constant heat flux density is a constant temperature field. Nevertheless, it is found by measuring temperatures at different points on sample surface that temperature of sample surface changes all the time. Therefore, it shall get the dynamic heat flux density for loading according to realtime collected grinding force signals and the calculated temperature field based on the dynamic heat flux density is a dynamic temperature field. The dynamic temperature field of hard and brittle bio-bone materials will be analyzed thoroughly in Sect. 6.6. Many years ago, Chinese scholars have begun to carry out theoretical studies on grinding temperature. In 1960s, Professor Jiyao Bei from Shanghai Jiaotong University [4] and Zhenbing Hou et al. from Harbin Institute of Technology studied grinding temperature. Moreover, Professor Guangqi Cai and Professor Hang Gao from Northeastern University [5] constructed the heat source models of billet polishing and interrupted grinding, respectively. Professor Tan Jin [6] studied the heat conduction mechanism of high-efficiency deep grinding systematically. He constructed the temperature field model under the inclined moving heat source by using the triangle and uniform distribution heat source model, and analyzed grinding temperature of workpieces by using three-dimensional and two-dimensional finite elements. Li Guo [7] and Bo Li [8] et al. from Hunan University constructed arc heat source models in studies on high-efficiency deep grinding, which viewed heat source distribution in the grinding zone as the collaborative effect of countless moving linear heat sources on the wheel-workpiece contact arc. It is the heat source model which is the closest to the practical grinding wheel.

6.3 Solving Method of Grinding Temperature Field Nowadays, solving methods of temperature field in the grinding zone mainly include the analytical methods based on moving heat source theory (Laplace transformation method, integral transform method and separation variable method) and numerical method based on discrete mathematics (finite element method and finite element method) [9, 10]. The analytical method gets solution expressed by functional forms

6.3 Solving Method of Grinding Temperature Field

171

based on the mathematical analysis model of temperature field. During calculation of temperature field, the logic reasoning and physical concept are explicit and the final solution can express influencing laws of factors in the grinding zone on temperature distribution and heat conduction clearly. The analytical method is difficult or impossible to solve upon any slight changes of working conditions in the grinding zone, and it only has to simplify the original problem. Based on these reasons, researchers have to make a lot of hypotheses for the use of analytical method, such as simplification of heat transfer state on conductor surface, simplification of part shapes and simplification of distribution state of heat sources on workpiece surface. The solving accuracy might be affected by these simplifications. Numerical method views computer as tools based on the discrete mathematics. Although it has no strict theoretical basis for analytical method, it is extremely applicable to solving problems in practical grinding temperature field [11, 12].

6.3.1 Solving Grinding Temperature Field Based on Analytical Method The analytical method is based on heat transfer theory and law of conservation of energy. The temperature rise function is solved based on various boundary conditions in real grinding processing, thus getting temperature at each not on the workpiece surface and inside the workpiece. The analytical method has an advantage that it not only can get the functional relation related with temperature distribution, but also can analyze different influencing factors and their influencing laws on temperature field. Now, researchers have established the grinding thermal theory model based on the moving heat source theory proposed by Jaeger [1] in 1942. The main idea is to use the superposition method of temperature field of heat source. In other words, the grinding interface is viewed as a non-point heat source composed of countless linear heat sources and the linear heat sources are viewed as the combination of countless microunit linear heat sources. Each micro-unit linear heat source is simplified into the collaborative effect of point heat sources. Hence, the basis of superposition method of heat-sourced temperature field is the solution to the temperature field at any moment when the transient point heat source in the infinite large object emits some heats instantly. It can be seen from Fig. 6.3 that it hypothesizes a point heat source locates in the infinite objects and at the origin of coordinates. In the initial moment (t = 0 s, T = 0 °C), the heats (Q) are emitted instantly from the point heat source at the origin of the coordinates and then stop emitting heats immediately. According to the heat transfer theory, the temperature rise at point M(x, y, z) at any position of the coordinate system is [13]: T =

R2 Q e− 4αt t 3/2 cρ(4π αt )

(6.2)

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y

Fig. 6.3 Schematic diagram of instantaneous point heat source

M (x, y, z)

z

x

where c is the specific heat of heat-conducting medium. Q is the instantaneous heat generation of point heat sources. α t is the thermal diffusion coefficient of heat-conducting medium. P is the density of heat-conducting medium. t refers to any moment after instantaneous heat emission of the heat source. R is the distance between point M and the origin of the coordinate system. When the workbench moves, the workpiece also moves at the same speed. When it passes through the grinding wheel, a belt heat source is formed under the interaction between workpiece and grinding wheel. The moving speed of this belt heat source is the same with that of workpiece. When it passes through the workpiece surface, it causes temperature rise on the workpiece surface. This effect is called the thermal effect in the grinding process. Hence, the grinding contact interface is viewed as a non-point heat source to calculate the temperature rise on workpiece surface and then the non-point heat source is viewed as the combination of countless belt heat sources. The moving speed of these belt heat sources along the x-axis is the moving speed (vw ) of workpiece. Any one of belt heat source is chosen and its width is dx i . Influenced by this belt heat source, the temperature rise at point M (x, 0, z) in the x–z plane is [13]: dT =

    / vw qw (xi )d xi (x − xi )vw K0 exp − (x − xi )2 + z 2 π kw 2αt 2αt

(6.3)

Through integration of Eq. (6.3), it can deduce the calculation formula of temperature rise at point M under the action of the whole non-point heat source: qw T (x, z) = π kw

l

    / vw (x − xi )vw 2 2 K0 exp − (x − xi ) + z s(xi )dxi 2αt 2αt

(6.4)

0

where qw is the heat flux density into the workpiece. k w is the heat conductivity coefficient of workpiece. vw is the moving speed of linear heat source (equal to the speed of workpiece). T is temperature at any point M (x, 0, z). K 0 (u' ) is the modified class-B zero Bessel function.

6.3 Solving Method of Grinding Temperature Field

173

Many researchers have calculated the grinding temperature field accurately by using the above analytical method. This type of superposition method of heat source temperature fields proposed the theoretical solution to the temperature field of grinding interface under ordinary continuous grinding relatively successfully.

6.3.2 Solving Grinding Temperature Field Based on Finite Difference Method For solving the grinding temperature field, it is quite complicated to use the analytical method even though solving a simple heat conduction problem. Grinding process is more complicated than other processing modes. The complicated input parameters of grinding temperature field, irregular abrasive distribution, uncertainty of grinding states (ploughing, sliding and cutting) of abrasives, cooling medium participating in convective heat transfer in the grinding zone and effects of airflow field surrounding grinding wheel all can influence temperature. There are a lot of nonlinear coupling relations in the grinding process and changes of any an input parameter may influence follow-up deduction of various expression formulas, thus increasing complexity and difficulty in solving temperature field based on analytical method. Under such circumstance, the finite element method based on numerical method is a very effective method to solve the heat conduction problem. It can calculate grinding temperature field conveniently and quickly as long as determining boundary conditions and initial conditions. It is an extensively used method by researchers at present. Nevertheless, the finite element method has proposed a lot of hypotheses to grinding temperature field and boundary conditions, and it can only use inbuilt module of specific software. The calculated grinding temperature has large errors with actual temperature. The finite difference method based on numerical value method is an effective method to calculate grinding temperature field between analytical method and finite element method. Theoretical modeling of boundary conditions (heat flux density, heat distribution proportion and convective heat transfer coefficient) of temperature field is carried out according to actual grinding conditions. Finally, the temperature field is calculated accurately. At present, there are few reports of calculating the grinding temperature field based on finite difference method. In the following text, the finite element method will be introduced thoroughly. (1) Basic principle of finite difference method The object is divided into finite grid cells and the difference equation is gained through the transformed differential equation. Temperature at micro-cell nodes of each grid is gained after numerical calculation. It can be seen from Fig. 6.4 that under the 2D heat conduction problem, the object is divided into rectangular grids along the x and y directions at the intervals of Δx and Δy. The node is defined as the intersection point of each grid lines and p(i, j) expresses the position of each node, where i refers to the sequence number of nodes along x and j is the sequence number

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6 Research on Microscale Skull Grinding Temperature Field Under … y i, j+1 ( j+1)Δy Δy ( j-1)Δy

i, j+1 i-1, j i, j

i+1, j

i-1, j

i, j

i+1, j

i, j-1 i, j-1 x

(a) Grid unit

(b) Grid nodes

Fig. 6.4 Schematic diagram of mesh lines and mesh nodes in finite difference method

of nodes along y. The intersection points between object boundaries and grids are defined as boundary nodes. The basic principle of the finite difference method is to replace the differential quotient by finite difference quotient, thus changing the original differential equation into a difference equation [3, 14]. (2) Establishment of differential equation of heat conduction In problems of grinding heat conduction, Fourier’s law is the most basic heat conduction equation. In other words, heats passing through the microelement isothermal surface dA at the finite time interval (dt) is dQ and it is proportional to temperature gradient ∂∂nT , but it has opposite direction with the temperature gradient. dQ = −kw

∂T dAdt ∂n

(6.5)

For heat flux density: qx = −kw

∂T ∂x

(6.6)

where qx is the heat flux density along the x direction. ∂∂Tx is the temperature gradient along the x direction. The differential equation of heat conduction can be gained through the Fourier’s law and law of conservation of energy. Suppose there’s no internal heat source in the objects. Based on above hypotheses, microelements dV = dxdydz are divided from the object for heat conduction. It can be seen from Fig. 6.5 that three sides of this microelement are parallel to x, y and z axes. The heat balance of microelements is analyzed. It can be seen from the law of conservation of energy, the net heats transferred in and out of the microelements in the time dt shall be equal to the growth of energy in microelements: The net heats transferred in and out of the microelements (I) = growth of energy in the microelement (II) [3]

6.3 Solving Method of Grinding Temperature Field

175

Fig. 6.5 Schematic diagram of thermal conductivity microelement

In the following text, I and II will be calculated, respectively. The energy balance of microelements in Fig. 6.5 is analyzed. The net heats transferred in and out of the microelements can be gained from net heats transferred in and out of the microelements along x, y and z. The heats transferred in along x-axis through the x surface in the time dt: dQ x = qx dydzdt

(6.7)

The heats output from the x + dx surface are: dQ x+dx = qx+dx dydzdt

(6.8)

x where qx+dx = qx + ∂q d x. ∂x Therefore, the net heats transferred in and out of microelements along x-axis in the time dt are:

dQ x − dQ x + dx = −

∂qx dxdydzdt ∂x

(6.9)

Similarly, the net heats transferred in and out of microelements in this period along y-axis and z-axis are dQ y − dQ y + dy = −

∂qy dxdydzdt ∂y

(6.10)

dQ z − dQ z + dz = −

∂qz dxdydzdt ∂z

(6.11)

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The net heats transferred in and out of microelements along x, y and z directions are summed:   ∂qy ∂qz ∂qx + + dxdydzdt (6.12) I=− ∂x ∂y ∂z According to Fourier’s law, in the Eq. (6.12), there’s: ⎧ ∂T ⎪ ⎪ qx = −kx ⎪ ⎪ ∂x ⎪ ⎪ ⎨ ∂T qy = −ky ⎪ ∂y ⎪ ⎪ ⎪ ⎪ ∂T ⎪ ⎩ qz = −k z ∂z

(6.13)

Bring it into the Eq. (6.12) and it can get:       ∂ ∂ ∂T ∂T ∂T ∂ kx + ky + kz dxdydzdt I= ∂x ∂x ∂y ∂y ∂z ∂z 

(6.14)

In dt, the growth of energy in microelements is: I I = ρc

∂T dxdydzdt ∂t

(6.15)

Based on Eqs. (6.14) and (6.15), it can get: ρc

      ∂ ∂ ∂ ∂T ∂T ∂T ∂T = kx + ky + kz ∂t ∂x ∂x ∂y ∂y ∂z ∂z

(6.16)

The Eq. (6.16) can be simplified as:  2  ∂ T ∂T ∂2T ∂2T = αt + + ∂t ∂x2 ∂ y2 ∂z 2

(6.17)

(3) Conversion of differential equation into a difference equation The workpiece is hypothesized as a rectangular plane and it is decomposed into plane grid structures through discretization. Equal length of space interval Δx = Δz = Δl is chosen and two groups of parallel lines with equal interval are made for subdivision of the rectangle samples. The parallel line equation is [14]:

x = xi = iΔl, i = 0, 1, . . . , M, MΔl = lw z = z j = jΔl, j = 0, 1, . . . , N , N Δl = bw

(6.18)

6.4 Boundary Conditions

177

where x i and zj are coordinate of the ith transverse line along the x direction and the coordinate of the jth vertical line along the z direction which form the difference grid. l w and bw are length and height of workpiece, respectively. M and N are natural number, respectively. After subdivision, the grid region of difference calculation is gained (Fig. 6.4). A difference equation set based on the second-order difference quotient is set up: ⎧ 2 ∂ T T (i + 1, j ) + T (i − 1, j ) − 2T (i, j ) ⎪ ⎪ (i, j ) = + O(Δl 2 ) ⎪ ⎪ 2 ∂ x Δl 2 ⎪ ⎪ ⎨ 2 ∂ T T (i, j + 1) + T (i, j − 1) − 2T (i, j ) (i, j ) = + O(Δl 2 ) 2 2 ⎪ ∂z Δl ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ∂ T (i, j ) = Tt+Δt (i, j ) − Tt (i, j ) + O(Δt) ∂t Δt

(6.19)

The difference equation of nodes in internal grids can be gained: Δt{kx · [T (i, j + 1) + T (i, j − 1)] + kz · [T (i + 1, j) + T (i − 1, j )]} ρw cw Δl 2   2Δt (kx + kz ) Tt (i, j ) + 1− (6.20) ρw cw Δl 2

Tt+Δt (i, j ) =

6.4 Boundary Conditions Heat transfer means heats transfer from a system to another system and it mainly contains three major forms of convection, heat conduction and radiation. In grinding, the grinding wheel-workpiece contact interface is cooled by grinding fluid. Hence, grinding fluid which flows on this interface may transfer heats on the sample surface. Heat convection is the major heat transfer form. Grinding fluid contacts with the sample surface and makes some heats on workpiece surface carried away by the cooling liquid through heat convection. The rest heats are kept at the sample base and transferred into the sample. Therefore, heat transfer performances of cooling liquid or strengthened cooling liquid can strengthen cooling effect of the processing region. Given the temperature of external medium and heat convection coefficient of external medium (Fig. 6.6), the heats on the grinding interface are input by grinding effect of the tool and carried away by external cooling medium. By analyzing a node on workpiece surface, the instantaneous heats generated by the grinding tool transfer to this node. Meanwhile, cooling medium on the workpiece surface and adjacent nodes (i – 1, 1), (i + 1, 1), (i, 2) all contact with this node (i, 1). Hence, heats at this node may be transferred to the cooling medium through convective transfer and make heat conduction to the adjacent nodes. Finally, the grinding tool-workpiece interface will reach a stable temperature [15].

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Fig. 6.6 Schematic diagram of heat conduction model and convective heat transfer in grinding interface

The thermal balance analysis of heat conduction in temperature field is to solve differential equation. The complete description of heat conduction process includes univalued conditions and differential equation of heat conduction. The univalued conditions cover time conditions, physical conditions, geometric conditions and boundary conditions. Boundary conditions are characteristics that interpret heat transfer process on boundaries of the object. In other words, boundary conditions are condition for interaction between inverse heat transfer process and surrounding environment. Hence, it has to set initial conditions (temperature at t = 0) and boundary condition (preset temperature in the boundary area or input or output heat flux density) in the temperature field. Based on heat transfer theory, the thermodynamic conditions are usually divided into the following three types [3].

6.4.1 Type-I Boundary Conditions This type of boundary condition is the forced convective boundary condition and it means the temperature value at the boundary surface of a given object at any moment. It is also called as Dirichlet condition: T |sf = Tw

(6.21)

6.4 Boundary Conditions

179

where T w is the temperature set at the boundary surface sf . if the boundary temperature is kept constant, T w is a fixed value. If the boundary temperature changes with time, T is a functional expression related with time.

6.4.2 Type-II Boundary Conditions This type of boundary conditions means the normal heat flux density of object boundary surface at any moment and it is also called Neumann conditions. The relation between temperature gradient and heat flux density is gained through Fourier’s law and it is equal to normal variation rate of temperature at the boundary sf at any moment.

∂ T

Qw = (6.22)

∂n sf k where Qw is the heats through the boundary surface (sf ). Qw = 0 for heat insulation boundary, and Qw is a fixed value when the boundary heat conduction is constant. Qw is a function of time when it changes with time. The differential equation at type-II boundary is:       ∂ ∂ ∂ ∂T ∂T ∂T kx · + ky · + kz · = Qw ∂x ∂x ∂y ∂y ∂z ∂z

(6.23)

6.4.3 Type-III Boundary Conditions This type of boundary conditions refer to heat convection between boundary interface and surrounding medium, and it is also called Robin condition. It can be seen from Newton’s Law of Cooling that the temperature between boundary layer of samples and the cooling heat transfer medium is the heat convection: h(T |z=0 − T0 ) − k

∂T |z=0 = qw ∂z

(6.24)

where qw is the convective heat flow of the cooling heat transfer medium and workpiece boundary surface (sf ). h is the convective heat transfer coefficient of cooling heat transfer medium and sample boundary. The differential equation at type-III boundary is:       ∂ ∂ ∂ ∂T ∂T ∂T kx · + ky · + kz · = h( T |sf − Tf ) ∂x ∂x ∂y ∂y ∂z ∂z

(6.25)

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According to interpretation of Type-III boundary conditions, the Type-III boundary conditions can describe micro-grinding temperature field of bones under nanofluids spray cooling conditions accurately. Therefore, the Type-III boundary conditions were applied to solve the grinding temperature field of bones. In Chap. 4, a theoretical model of convective heat transfer coefficient of nanofluids spray cooling is constructed and calculated. A theoretical analysis of dynamic heat flux density of hard and brittle bone material will be carried out in the following text.

6.5 Constant Heat Source Distribution Model in Grinding of Metal Materials with Ordinary Wheel In the machining field, many researchers have explored the heat source distribution model of grinding with ordinary wheel and concluded relatively mature theories. In Fig. 6.7, a single-grain intervenes with the workpiece material in grinding with ordinary wheel to induce plastic deformation of materials or cut the materials, thus generating heats. Hence, all grains participating in the grinding process can be viewed as point heat sources. The single-grain interfering with the workpiece material presents a discrete distribution on the grinding wheel surface. Due to the collaborative effect of these point heat sources in the grinding wheel-workpiece contact zone, the temperature on the workpiece surface increases during grinding. Nevertheless, heat conduction on the workpiece surface can contribute to a uniform distribution of these discrete point heat sources to some extent. Therefore, it often replaces the discrete point heat sources with belt heat sources in continuous distribution in the grinding zone to analyze temperature field of workpiece surface, thus realizing the goal of model simplification. Such simplification has following reasons [2]: (1) in grinding with ordinary granularity wheel, there’s at least one grain on the wheel surface per square millimeter is causing plastic deformation (ploughing) of the material or participating in cutting removal of materials. When the circular velocity of the grinding wheel is relatively high (20–50 m/s in ordinary grinding), the working grain density in the grinding zone is relatively high, which is equivalent to a continuous heat source. (2) In grinding process, the most protruding grain and binding agent on the grinding wheel surface both bear a strong normal force, thus increasing elastic deformation volume of the grinding wheel. The grains at deep positions begin to contact and act on the workpiece surface materials, and the number of grains which contact with the workpiece also increases significantly. Moreover, some grains on workpiece surface only make sliding friction, thus causing scratching and ploughing effect. Nevertheless, there are still a lot of heats generated under such effect. From the perspective of heat source opinion, grinding heats are generated under the collaborative action of friction heats in the ploughing stage and cutting heats in the chip formation stage. Therefore, the continuous heat source close to actual conditions is chosen to analyze temperature field in grinding process.

6.5 Constant Heat Source Distribution Model in Grinding of Metal …

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Fig. 6.7 Surface temperature in grinding zone and grinding point temperature of grains [2]

So far, the heat source models which are constructed by scholars mainly include large-depth heat source models based on slow feeding grinding and high-efficiency deep grinding, small-depth heat source models based on ordinary reciprocal grinding and other discontinuous and continuous grinding heat source models. Heat source models are divided into triangular and rectangular (uniform distribution) heat source models in analysis of small-depth continuous grinding temperature field.

6.5.1 Rectangular Heat Source Distribution Model In theoretical calculation of grinding temperature field, Jaeger views the moving heat source as a uniform distribution heat source [1], as shown in Fig. 6.8a. A belt heat source is set, with a width of 2 l (2 l = lc ). it moves along x on the semi-infinite body at the speed of vw . Temperatures at different points on the workpiece surface can be inferred from the rectangular heat source model: 2qtotal Rw αt T (x, z) = πkw vw

X+L '

 1/2 ' e−u K 0 Z 2 + u '2 du

(6.26)

X −L '

where qtotal is the total heat flux density. Rw is the proportion of heats transferred into the workpiece. X denotes the dimensionless distance to the heat source center. L' refers to the dimensionless Peclet number. Z expresses the dimensionless distance to the workpiece surface. The dimensionless X, Z and L' are defined as follows:

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Fig. 6.8 Schematic diagram of heat source distribution model

⎧ ' ⎪ ⎨ L = vwlc /4αt X = vw x/2αt ⎪ ⎩ Z = vw z/2αt

(6.27)

6.5.2 Triangular Heat Source Distribution Model Based on the conclusion of Jaeger, Takazawa K¯oya and Kawamura Miku [13, 16], and Jiyao Bei et al. [17] gained the theoretical calculation formulas of temperature field in the grinding contact arc zone from the uniform distribution and triangle heat source models (Fig. 6.8b). In grinding process, the chip thickness at the high end in

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the grinding wheel-workpiece contact arc zone is the maximum, but it decreases to zero at the low end. Hence, it is impossible to have uniform distribution of the heat source intensity in the processing zone. Hence, if often chooses heat source intensity model in triangular distribution in the contact arc zone to analyze plane grinding heats. Based on the triangular heat source model, it can calculate temperature rise at any point in the semi-infinite large heat conductor: 2qtotal Rw αt T (x, z) = πkw vw

  1/2 ' u' 2  X e−u 1 + ' − ' K 0 Z 2 + u '2 du L L

X+L '

X −L '

(6.28)

6.5.3 Parabolic Heat Source Distribution Model Heat flux density transferred into the workpiece is related with thickness of undeformed chips in the grinding zone. The later one is not in triangular or uniform distribution state. Hence, the heat flux density transferred into the workpiece changes when the chip thickness increases from 0 to the maximum. Suppose the heat flux density transferred into the workpiece distributes along the heat source surface and presents a parabolic pattern [2], as shown in Fig. 6.8c. The functional expression of heat flux density on the heat source surface is: q(x) = ax 2

(6.29)

where a is a coefficient of heat flux in parabolic distribution. Since the total heat source intensity transferred into the workpiece is the same not matter which heat source models are chosen, the total heat source intensity of the parabolic heat source model and uniform distributed heat source model is always equivalent. Through integration of heat flux in Eq. (6.29), it can get: lc ax 2 dx = lc q0

(6.30)

0

where q0 is the mean heat flux density transferred into the workpiece. Through integration of Eq. (6.30), the coefficient of heat flux density in parabolic distribution can be gained: a=

3q0 lc2

(6.31)

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Equation (6.31) is brought into Eq. (6.29) and the heat flux density function along the contact arc zone is calculated: qw =

3q0 2 x lc2

(6.32)

The temperature rise at a point caused by a linear heat source with a width of dx’ is calculated according to the instantaneous linear heat source: dT (x, z) =

2 w t)+z qw dx ' dt − (x−x ' +v 4αt t e 2πkw t

(6.33)

The temperature rise which is calculated at any point in the semi-infinite large conductor deduced by the parabolic linear heat source model is: 3qw Rw αt T (x, z) = 2π kw vw L '2

X+L '

 2  1/2 ' e−u X + L ' − u ' K 0 Z 2 + u '2 du

(6.34)

X −L '

6.5.4 Comprehensive Heat Source Distribution Model In the grinding process of plastic metal materials, there three stages between grains and workpiece, including scratching stage, ploughing stage and cutting stage. In the scratching stage, grains begin to contact with and act on the workpiece surface material, without cutting effect. There’s only scratching on the workpiece surface and the workpiece only develops elastic deformation which is recovered immediately, without grinding debris. In the ploughing stage, the grinding force of materials is higher than the plastic deformation at yield limit with the increase of cutting depth. When the grinding edge of grains presses in the workpiece surface, the workpiece material in front of the grinding edge is pushed to the front end and two sides of grains, thus resulting in uplifts of workpiece surface. In this stage, grains only make ploughing effect, without cutting effect. In the cutting stage, the grinding edge of grains pushes materials to reach the critical grinding depth and the uplift materials slides out of the front of grinding edge, forming grinding debris. Materials with plastic deformation pile up at two sides of grains, thus forming furrow banks and grinding debris is formed. In the cutting stage, there’s obvious cutting effect and material removal rate is relatively high. Meanwhile, some grains are still make scratching and ploughing effects to workpiece materials. Zhang [18] and Lei Zhang [19] analyzed that if grains make scratching and ploughing effects on the workpiece, the heat source distribution model is in a rectangular distribution and the generated heat flux intensities are almost equivalent along the contact length, in which the tribological action takes the dominant role. When

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grains make cutting behaviors on the workpiece, the normal force and tangential force increase gradually with the increase of cutting depth of grains into the material. Accordingly, the generated heat flux density also increases continuously. This is the triangular heat source distribution model. In the whole grinding process, grains on the grinding wheel surface have different protruding heights, so some grains may provide scratching effects at the same position at a moment, and cut the workpiece material. Therefore, it is insufficient to solve the grinding temperature by using triangular or rectangular heat source distribution only. The collaborative effects of scratching, ploughing and cutting of grains also shall be included. Lei Zhang [19] established a comprehensive model of heat source distribution with considerations to comprehensive action of scratching, ploughing and cutting of grains to the workpiece in the grinding process (Fig. 6.9). The grains at the bottom of the grinding wheel and entry point of materials are used as the origin of coordinates (O). A rectangular coordinate system is established by using s(x)-axis as the vertical direction and the grinding heat source distribution is divided into two parts. One is the rectangular heat source distribution which is produced by scratching and ploughing effect of grains to the workpiece materials. The heat flux intensity is ξ q0 and the length of rectangular heat source is ar . The other is the triangular heat source distribution. Due to material cutting effect by grains, the peak of triangular heat flux density is uq0 and the distance to O is bt . The grinding arc length is l c . In Fig. 6.9, the vertical coordinate s(x) is the shape functional equation of the comprehensive model of heat source distribution in grinding [18]. The heat flux density of this comprehensive model of heat source distribution can only be expressed by the product of s(x) and the mean heat flux density (q0 ). Fig. 6.9 Comprehensive model of heat source distribution [19]

vs Grinding wheel

s(x)

uq0 ξq0

Workpiece

O ar vw

x bt lc

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Fig. 6.10 Schematic diagram of different heat source distribution models

s(x) =

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

0 ξ

ξ (bt −x)+u(x−ar ) bt −ar u(x−lc ) bt −lc

0

x ∈ (−∞, 0) x ∈ (0, ar ) x ∈ (ar , bt ) x ∈ (bt , lc ) x ∈ (lc , +∞)

(6.35)

In Eq. (6.35), values of ar and ξ are related with sharpness of grinding wheel and lubrication performances of grinding fluid. The value of bt is related with grinding mode (down grinding and up grinding). lc is a function of grinding depth and the diameter of grinding wheel. It can be seen from Fig. 6.9 and Eq. (6.35) that if ar and bt are all equal to l c and ξ = u = lc , there’s serious wearing loss of the grinding wheel. The grains are relatively blunt and they make scratching and ploughing effects to the workpiece materials. As shown in Fig. 6.10a, the comprehensive model of heat source distribution is transformed into a rectangular heat source distribution. If ar = 0, bt = l c , ξ = 0 and u = 2, the grains are relatively sharp and they mainly cut the workpiece materials, as shown in Fig. 6.10b. If the front material removal of the grinding wheel-workpiece contact arc is relatively small, the amount of generated heats is relatively low and the heat flux density is small. In the rear end of the contact arc, the cutting depth of grains into the workpiece material is large, resulting in the high volume of material removal, high generated heats and high heat flux density. The comprehensive model of heat source distribution is transformed into a right triangular heat source distribution model. If ar = 0, bt = l c /2, ξ = 0 and u = 2 (Fig. 6.10c), grains show strong cutting effect in the middle of the contact arc. The heat flux density is high and the comprehensive model of heat source distribution is transformed into a isosceles triangular heat source distribution model. If bt = l c (Fig. 6.10d), the comprehensive model of heat source distribution is transformed into a heat source distribution where the front end of the grinding wheelworkpiece contact arc zone is rectangular, and the rear end is triangular. This is called

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187

the rectangular triangular heat source distribution model. Therefore, ar and ξ are relatively small when the scratching and ploughing effects of grains are relatively small; otherwise, they are high. Suppose ar is proportional to ξ: ξ = ar /lc

(6.36)

Since the total grinding heat flows are equivalent, it can get: ⎧ (lc − ar )uq0 ⎪ ⎨ l c · ξ q0 + = l c · q0 2 a ⎪ ⎩ξ = r lc

(6.37)

It can be known from Eq. (6.37) that: u =ξ +2

(6.38)

When ar = 0 and bt = l c (Fig. 6.10e), the comprehensive model of heat source distribution is transformed into a gradient heat source distribution model. Since grains have non-equivalent protruding heights in grinding, there are scratching, ploughing and cutting effects of grains on the workpiece material. Therefore, the gradient heat source distribution is divided into superposition of rectangular and triangular heat source distribution. In the front end of grinding wheel-workpiece contact zone, grains cut in the workpiece materials for a small depth and the generated heats are relatively small. Hence, the heat flux density is relatively small. On contrary, heat flux density is relatively high at the rear end of grinding wheel-workpiece contact zone. According to equivalent total heat sources, the relationship between ξ and u can be inferred: lc q0 · (ξ + u) = l c q0 2

(6.39)

It can be seen from Eq. (6.39) that: ξ +u =2

(6.40)

6.6 Dynamic Heat Flux Model of Ductility Domain Removal of Hard and Brittle Bio-Bone Materials It hypothesizes that energy is all transformed into heat energy except that the grinding power is used to generate new material surfaces. The energy generation and consumption forms in different micro-grinding behaviors of hard and brittle bone materials are shown in Fig. 6.11.

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Fig. 6.11 Energy generation and consumption form in micro-grinding of bio-bone material

(1) When hu < hmin , materials only suffer scratches and ploughing, without material removal. No new surfaces are generated and the grinding power is only used for heat generation. (2) When hmin < hu < hc (hc is the critical thickness of undeformed chips for hard and brittle materials to develop cracks), materials produce scratching, ploughing and plastic shear chipping. The consumption of grinding power is composed of scratching energy, ploughing energy and plastic shear chipping energy. Among them, the plastic shear chipping energy is used to generate new material surfaces, while scratching energy and ploughing energy are completely transformed into thermal energy. (3) When hc < hu < hd-b , materials develop scratching, ploughing, shear chipping and powder removal chipping effects. The consumption of grinding power consists of scratching energy, ploughing energy, plastic shear chipping energy and powder removal chipping energy. Specifically, the plastic shear chipping energy and powder removal chipping energy are used to generate new surfaces, while the scratching energy and ploughing energy are completely transformed into thermal energy. For hc , the critical normal loads to generate median cracks can be gained according to fracture toughness and Vickers hardness of bone materials: Fn = 855

4 K IC Hv3

(6.41)

Therefore, the thickness of undeformed chips when the hard and brittle material begins to generate cracks can be determined according to the normal force.

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189

Based on previous studies, plastic removal and brittle removal modes of materials are corresponding to different energy consumptions. Moreover, the plastic deformation of materials (E p ) and energy (E f ) which has to be consumed for brittle fracture are irreversible [20]. Solve E p and E f . Then, the total grinding energy is subtracted by E p and E f , thus enabling to get total heats (Qd ) produced in the hard and brittle bone ductility domain under different removal modes. Furthermore, the removal heat flux density of micro-grinding ductility domain of bone is acquired. For the total energy consumed in grinding, the grinding power is: W = Ft (sF ) · sF

(6.42)

where sF is the distance for action of F t . F t is the function of displacement (sF ). Then, the total grinding power is: l W =

Ft (sF )dsF

(6.43)

0

To get the micro-grinding heat source distribution model of hard and brittle bone materials with spherical mounted point, it has to calculate the number of effective cutting grains in the micro-grinding zone by using the spherical mounted point firstly. On this basis, the energy consumed for plastic and brittle fractures of materials is also calculated. Through geometric kinematics analysis of micro-grinding, the microgrinding heat source distribution model of hard and brittle bone materials by using spherical mounted point is acquired.

6.6.1 Statistics on Effective Grinding Abrasive Number of Spherical Head On the grinding tool surface, grains are distributed unevenly and randomly. Jianhua Zhang [21] hypothesized that grain size distribution of grains in the grinding wheel observes normal distribution. Hence, the mean diameter (d mean ) of grains is: dmean =

dmax + dmin 2

(6.44)

where d max refers to the maximum grain size and d min refers to the minimum grain size. According to the functional characteristics of normal distribution, the standard deviation (σ s ) of grain size distribution can be gained: σs =

dmax − dmin 6

(6.45)

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It can be inferred from the probability density formula of normal distribution function that the distribution function of grain size (d) is: P(d) = √

2

) − (d−dmean 2

1 2π · σs

·e

2σs

(6.46)

The number of grains per unit volume of grinding tool (N v ) and the number of grains per unit area (N s ) can be acquired from d mean and grain rate (ωr , the volume fraction of grains in the grinding tool): Nv =

1 π(dmean /2)3

ωr1/3

Ns = Nv2/3

(6.47) (6.48)

The surface area of effective cutting part of the spherical micro-grinding tool is shown in Fig. 6.12. Hence, there’s: Sc = πrap

(6.49)

The total number of grains in the grinding zone is: Ntotal = Sc · Ns

Fig. 6.12 Schematic diagram of effective cutting part of micro-grinding tool

(6.50)

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191

6.6.2 Energy Consumption for Plastic Shear Removal of Bone Material Bone materials develop plastic deformation in the ploughing stage and plastic shear removal stage. In the ploughing stage of bone materials, some grains make scratching effect on the material and the other grains make ploughing effect. In the cutting stage, some grains make scratching effect on the material, some grains make ploughing effect, and some grains make plastic shear removal effect of materials. The energy for plastic deformation of materials is [22]: E p = σp Vp−r

(6.51)

where σ p is the yield strength of materials and V p-r is the volume of material plastic deformation. In the following text, the volume of plastic material deformation under plastic shear removal mode has to be calculated thoroughly. The radius of cutting edge of grains has very important influences on the minimum thickness of chips. Therefore, grains are simplified into spheres in this study. When hu < hc , materials have scratching, ploughing and shear chipping effects. At a moment in micro-grinding of bone materials, suppose there are N s-p grains participating in scratching and N c grains participating in ploughing and plastic shear removal of materials. In N c grains, grain size can be divided into three conditions in the figure according to different cut-in states of grains to the bone material: (1) grain size is larger than thickness (hu ) of undeformed chips (d 1 > 2hu ); (2) grain size is equal to hu (d 2 = 2hu ); (3) grain size is smaller than hu (d 3 < 2hu ), as shown in Fig. 6.13. In Fig. 6.14, the rebounding thickness can be known from the critical debris formation state (geometric model of minimum chip thickness) of materials: ⎧ ts = L f sin ϕs ⎪ ⎪ ⎪ ⎪ ⎪ π ⎪ ⎪ ⎨ ϕs = + γn − βf 4 re − h u ⎪ ⎪ γn = arcsin ⎪ ⎪ ⎪ re ⎪ ⎪ ⎩t = h − t r u s

(6.52)

Therefore, material removal volumes by plastic deformation caused by grains with a size of d 1 (2hu < d 1 < d max ), d 2 (d 2 = 2hu ) and d 3 (2hmin < d 3 < 2hu ) are: ⎧ ⎪ ⎨ Vd1 = Sd1 · lc Vd2 = Sd2 · lc (6.53) ⎪ ⎩ Vd3 = Sd3 · lc

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Fig. 6.13 Material removal volume by grains

Fig. 6.14 Critical debris formation state of hard and brittle materials

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193

S d1 , S d2 and S d3 are cross-section areas of grains with different sizes (d 1 , d 2 and d 3 ) cutting into the materials. The probabilities of grains with different sizes (d 1 , d 2 and d 3 ) are: ⎧ dmax ⎪ )2 ⎪ 1 − (x−dmean ⎪ 2σs2 ⎪ P(d1 ) = ·e dx √ ⎪ ⎪ ⎪ 2π · σ ⎪ s ⎪ 2h u ⎪ ⎪ ⎪ ⎨ (d −d )2 1 − 2 mean 2σs2 P(d2 ) = √ ·e ⎪ 2π · σs ⎪ ⎪ ⎪ ⎪ 2h ⎪  u ⎪ )2 ⎪ 1 − (x−dmean ⎪ 2σs2 ⎪ P(d ) = · e dx √ ⎪ 3 ⎪ ⎩ 2π · σs

(6.54)

2hmin

For plastic shear removal, the total material removal volume caused by plastic deformation is: ⎛d max (d2 −dmean )2 (x−dmean )2 1 1 Vp−r = Ntotal lc ⎝ Sd1 · √ · e 2σs2 dx + Sd2 · √ · e 2σs2 2π · σs 2π · σs 2h u

2h u + 2h min

⎞ (x−dmean )2 1 Sd3 · √ · e 2σs2 dx ⎠ 2π · σs

(6.55)

The Eq. (6.55) is brought into the Eq. (6.51), so the energy consumed by grains to induce plastic shear removal of bone materials can be gained. Therefore, the heat generation volume of bone materials under plastic shear removal is: Q d = W − Ep

(6.56)

6.6.3 Energy Consumption for Removal of Bone Material Powder The energy consumed for brittle fracture of materials is [22]: E f = G Af

(6.57)

where Af is the surface area which is produced again by crack propagation. In the following text, the surface area which is newly produced under powder removal of bone material will be calculated thoroughly.

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When hc < hu < hd-b , materials have scratching, ploughing, shear chipping and powder removal chipping. Suppose there are N p grains are inducing powder removal of materials and the size of grains is d 4 (2hc < d 4 < d max ). Then, the proportion of grains with a diameter of d 4 is: dmax P(d4 ) =

√ 2hc

1 2π · σs

2

) − (x−dmean 2

·e

2σs

dx

(6.58)

Bifano [23] demonstrated that for a single-grain, surface which is generated by propagation and connection of middle cracks and lateral cracks can be expressed as two semi-cylindrical surfaces with a radius of C l and a height of lc formed by lateral cracks as well as the two planes formed by middle cracks (Fig. 6.15). Sf = 2(πCl + Cm ) · lc

(6.59)

It can be seen from Eqs. (6.58) and (6.59) that the surface area regenerated by crack propagation is: dmax )2 1 − (x−dmean 2σs2 Af = 2Ntotal lc (πCl + Cm ) √ ·e dx 2π · σs

(6.60)

2hc

Under powder removal mode, the volume of material removal by plastic deformation is:

Fig. 6.15 Surface area of materials newly formed by crack propagation

6.6 Dynamic Heat Flux Model of Ductility Domain Removal of Hard …

' Vp−r

195

⎛ 2h d−b  1 1 − (x−dmean ) = Ntotal lc ⎝ Sd1 · √ · e 2σs2 dx + Sd2 · √ ·e 2π · σs 2π · σs 2h u

(d2 − dmean )2 − + 2σs2

2h u

2h min

⎞ (x−dmean )2 1 Sd3 · √ · e 2σs2 dx ⎠ 2π · σs

(6.61)

The Eq. (6.60) is brought into Eq. (6.57), and the energy consumed by powder removal of bone materials by grains can be gained. Furthermore, heat generation under powder removal of hard and brittle bone materials is: Q d = W − Ep − Ef

(6.62)

6.6.4 Dynamic Heat Flux Model for Ductility Domain Removal of Hard and Brittle Bio-Bone Effects of motion parameters on contact state and deformation between grinding tool and samples during grinding are ignored. It can be seen from the grinding model in Fig. 6.16 that the contact arc length is: lc = r ' =

/ r 2 − (r − ap )2

(6.63)

It can be seen from Fig. 6.16a that the total grinding force of undeformed chips is decomposed into three mutually vertical components along x, y and z (F x , F y and F z ). In Fig. 6.16b, grains participating in grinding distribute on edges of shadow parts on the cross section (P) and the included angle between cutting force (F t ) per unit area and the x-axis is δ ' . The force (F y ' ) on the cross section along the y-axis is: Fy'

π/2 =

πr' · Ft cos δ ' dδ '

(6.64)

−π/2

It can be seen from Fig. 6.16c that through integration of each cross section, the total grinding force (F y ) along the y-axis is:  r π/2 √ Fy = π r2 - z2 · Ft cos δ ' dδ ' dz r - ap −π/2

(6.65)

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Fig. 6.16 Schematic diagram of cutting force for micro-grinding of bone materials

F y is the force along the y-axis which is measured by the measuring cell in the experiment. On this basis, the tangential force per unit area (F t ) can be calculated. the surface area (S c ) of grinding tool participating in grinding part is: √

r 2 −(r −ap )2

1 Sc = · 4 √ −



2πr dx

(6.66)

r 2 −(r −ap )2

Therefore, the micro-grinding force (acting force, F c ) is [24]: Fc = Ft · Sc

(6.67)

6.6 Dynamic Heat Flux Model of Ductility Domain Removal of Hard …

197

Fig. 6.17 Micro-grinding geometric model and temperature field model of bone materials

The mean heat flux density is:   q0 = Q d / Sp · t

(6.68)

where S p is the projection area of effective grinding part of micro-grinding on the x–y surface. According to the geometric model of nanofluids micro-grinding of bones in Fig. 6.17(a), the spherical micro-grinding tool moves on the bone sample surface at a rotating speed of ω and a feeding speed of vw . The nozzle also moves with the grinding tool at the speed of vw . According to the actual contact state between micro-grinding tool and materials and the morphology of undeformed chips, the grinding effect of micro-grinding on bone materials will generate a semi-circular curved surface heat source in Fig. 6.17b. For more intuitive expression of the temperature field, the 3D temperature fields in Fig. 6.17b are projected onto the bone sample surface (x–y surface) and side surfaces of bone samples (z-x surface), respectively. It can be seen from Fig. 6.18 that on the x–y surface, the heat source boundary presents a semi-circle with a radius of r ' according to the actual contact state between micro-grinding tools and materials. Moreover, heat flux densities at different points on the semi-circle heat source edges are equal, which are equal to q0 . According to the actual contact state between micro-grinding tools and materials, it can be known that heat sources present a circular distribution along OA on the z-x surface (Fig. 6.19). For the convenience of calculation, the micro-grinding circular heat sources are simplified into parabolic heat sources. On this heat source surface, the heat flux density is: qw = ax 2

(6.69)

Since the total heat source intensity is always equal no matter what is the distribution state of heat flux density into the material, the total heat source intensity in

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Fig. 6.18 Temperature field model on the x–y surface

Fig. 6.19 Temperature field model on the x–z surface

circular distribution along OA is equal to the total heat source intensity in uniform distribution along the same contact arc. Through integration of heat flux density in Fig. 6.19, it gains: lc /2 ax 2 dx = lc q0

(6.70)

−lc /2

The heat flux coefficient of circular heat source distribution can be gained from the Eq. (6.68): a=

12q0 lc2

(6.71)

6.7 Thermal Partition Coefficient Model in the Grinding Zone

199

The heat flux density along the contact arc OA can be gained by bringing it into the Eq. (6.69): qw =

12q0 2 x lc2

(6.72)

6.7 Thermal Partition Coefficient Model in the Grinding Zone There’s an important problem when establishing the temperature field model in the grinding zone. It has to determine the proportion of grinding heats transferred into samples during processing. In other words, it has to determine the thermal partition coefficient (Rw ). Under non-dry grinding conditions, it can be seen from Fig. 6.20 that the total heats generated in the grinding zone is [25]: qtotal =

Ft vs = qw + qg + qc + qf bg lc

(6.73)

where bg is the width of grinding wheel. qw is the heats remained on the sample surface. qg is the heats transferred into grains of grinding tools. qc is the heats carried away from grinding debris. qf is the heats transmitted from the cooling medium. Therefore, the thermal partition coefficients of workpiece and cooling medium are: Fig. 6.20 Heat distribution in grinding zone

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⎧ qw ⎪ ⎨ Rw = q total ⎪ R = qf ⎩ f qtotal

(6.74)

6.7.1 Rated Heat Supply Coefficient Model at Grinding Points Outwater [25] pointed out that the grinding heats during grinding process are composed of three parts: (1) the wearing plane of grains and acting plane of workpiece, AB surface in Fig. 6.21. (2) Shearing surface of grinding debris, BC surface in Fig. 6.21. (3) Acting surface of grains and grinding debris, BD surface in Fig. 6.21. Through these three surfaces, the heats generated by grains to cause plastic deformation of materials (ploughing and cutting of materials) are transferred into grains and the workpiece. Based on the Outwater model, Hahn [26] improved the heat distribution model. by ignoring the cutting force on the shear surface, he hypothesized that the workpiece surface is smooth and grains sliding on the smooth workpiece surface. This is known as the “grain sliding hypothesis” model. In this model, it hypothesized that grinding heats are generated on the grinding interface, that is, the wearing surface of grains. Some grinding heats flow into the workpiece and the other heats flow into grains. On this basis, Hahn simplified grains with a velocity of vs and moving along the workpiece into cones. Since the heat conductivity coefficient of grains is higher than that of grinding fluid, Hahn hypothesized that the grinding fluid didn’t carry away heats transferred into grains and these heats are all transferred into grains. Moreover, the temperatures along the radius direction are equal. Based on the above hypothesizes, the proportion of grinding heats transferred into workpiece is:

D

Chip C

Vs

Abrasive

Abrasive Shear plane Workpiece

A B Abrasive wear planes

(a) Grinding heat generating surface

Coolant

Coolant Workpiece qg

(b) Transfer of grinding heat

Fig. 6.21 Diagram of grinding heat generation and transfer [25]

6.7 Thermal Partition Coefficient Model in the Grinding Zone



kg

201

−1

Rw = 1 + / r0 · vs · (kρc)w

(6.75)

where the lower scripts g and w represent grains and workpiece, respectively. Based on the Hahn model, Rowe proposed the heat distribution ratio of grinding wheel-workpiece: Rws =

−1  0.974 kg qw = 1+ 0.5 0.5 qw + qg (kρc)0.5 w · r 0 · vs

(6.76)

where k g is the heat conductivity coefficient of grains and r 0 is the effective contact radius of grains on the grinding wheel. Based on the model of Rowe, Cong Mao [2] recalculated proportion of heat distribution into the workpiece by considering changes of thermal physical property parameters of workpiece materials (heat conductivity coefficient, density and specific heat capacity) under different grinding temperatures. ⎛ ⎞ a v −1  ρw cw Tmp √p w ap dw 0.974kg qw ⎠ Rw = = 1+ · ⎝1 − 0.5 0.5 qt √ Ft vs (kρc)0.5 w r 0 vs

(6.77)

ap dw bg

6.7.2 Thermal Partition Coefficient Model of Grinding Wheel Ramanath [27] established a thermal partition coefficient model during surface dry grinding. In this model, the grinding debris carries away extremely few heats when the grinding depth is relatively small. Hence, the heat source model during grinding is hypothesized into a uniform distributed heat source which moves in the middle between two static surfaces (cutting surface of grains and workpiece surface). Suppose the average surface temperatures on workpiece and grinding wheel in the grinding contact interface are equal, and it can get the expression of heat distribution ratio:   (kρc)g −1 Rw = 1 + (kρc)w

(6.78)

This model is a function related with geometric mean thermal characteristics and it simplifies the actual processing significantly. However, it is only applicable to estimate the heat distribution ratio since it doesn’t consider influences of parameters in processing.

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6.7.3 Thermal Partition Coefficient Model of Abrasive/ Grinding Fluid Complex Lavine [28] hypothesized that grinding wheel is a complex of grinding fluid and grains. The properties of this complex are determined by properties of grinding wheel and grinding fluid together. Specifically, the grinding fluid is viewed as a part on the grinding wheel surface rather than the convective heat transfer medium. It is unnecessary to determine convective heat transfer coefficient. The heats between the complex and workpiece will be transferred into workpiece and the rest will be transferred into the complex. The former belt heat flow is the same with feeding rate of workpiece and it moves on the workpiece surface. The later belt heat flow is consistent with the linear velocity (vs ) of grinding wheel, and it moves on the complex surface. Based on Jeager’s calculation formula of linear specific grinding temperature, the liquid film membrane of grinding wheel surface is Ar /An ≈1 under wet drying condition and the heat distribution ratio in the workpiece can be calculated: Rw =

Qw = Qw + Qg

1+



1

 (kρc)g vs Ar 0.5 (kρc)w vw An

+



(kρc)f vs (kρc)w vw

0.5

(6.79)

On this basis, Rowe [19] further studied and proposed the heat distribution ratio between grinding wheel and workpiece: ⎛ Rw−g = ⎝1 +

/

⎞−1 vs · (kρc)g ⎠ vw · (kρc)w

(6.80)

6.7.4 Thermal Partition Coefficient Model of Grinding Wheel/Workpiece System Hadad [29] established a thermal partition coefficient model in the grinding wheelworkpiece system and believed that the grinding heats generated by acting of grains on workpiece materials during grinding are composed of three parts: (1) heats generated by friction on the grain-workpiece wearing plane and grain-grinding debris interface; (2) heats generated by plastic deformation on the grain-workpiece shearing surface. It can be seen from Fig. 6.22 that it hypothesizes heats are transferred into grinding debris and grinding wheel-workpiece system instantaneously: qtotal = qc + qw−g

(6.81)

6.7 Thermal Partition Coefficient Model in the Grinding Zone

203

Fig. 6.22 Thermal partition coefficient model based on grinding wheel-workpiece system [29]

The heats transferred into the grinding wheel-workpiece system (qw-s ) are further transferred into workpiece and grinding wheel: qw−g = qw + qg

(6.82)

The heats transferred into the workpiece finally will flow into the workpiece and cooling medium: qw = qw−b + qf

(6.83)

6.7.5 Thermal Partition Coefficient Model Considering Convective Heat Transfer of Grinding Zone The thermal partition coefficient model proposed by Rowe and with considerations to convective heat transfer in the grinding zone is generally applied to high-efficiency deep grinding conditions. This model proposes that total energy in the grinding zone during high-efficiency deep grinding is transferred into the theoretical mathematical model of grinding wheel, grinding debris, grinding fluid and workpiece materials. Furthermore, many experimental results have verified feasibility of the model. The heat flux density transferred into workpiece, grinding wheel, grinding fluid and grinding debris is related with some parameters, such as maximum contact temperature (T max ), boiling point of grinding fluid (T b ), melting point of workpiece (T m ), etc. (T max ≤ T b ) [30]:

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⎧ qw = h w · Tmax ⎪ ⎪ ⎪ ⎨q = h · T g g max ⎪ q = h · T f f max ⎪ ⎪ ⎩ qc = h d · Tm

(6.84)

where hw , hg , hf and hd are heat transfer coefficients of workpiece materials, grinding wheel, grinding fluid and grinding debris, respectively. The heat distribution ratio into the workpiece can be gained: Rw = h w · Tmax /qtotal

(6.85)

To sum up, most researchers ignore outflow heat ratio from the cooling medium (Rf ) when calculating heat distribution in the grinding zone or calculate Rf by estimating hf , thus getting the heat distribution ratio into samples. Nevertheless, nanofluids are major media for heat outflow in the grinding zone during nanofluids spray cooling. Although the Rw model proposed by Rowe has considered convective heat transfer coefficient of cooling medium, it has to calculate Rw under the premise that temperature in the grinding zone is known. It cannot predict Rw before grinding process. According to definition of heat transfer coefficient, it refers to the transferred heats per unit area of materials in unit time. In grinding process, the thermal partition coefficient of workpiece characterizes the ratio of heats transferred into the workpiece material in total heats. Therefore, the thermal partition coefficients of materials, grains (Rg ), grinding debris (Rc ) and cooling medium (Rf ) characterize the abilities of heat transfer media to fight for heats in unit area of the grinding zone in unit time. Moreover, heat transfer coefficient (hd ) of grinding debris is related with melting point of sample material. The grinding temperature of bone materials cannot reach its melting point (T m ) and boiling point of cooling medium (T b ) even under the dry grinding conditions. On this basis, the thermal partition coefficient of workpiece is simplified into: Rw = 1 − Rg − Rc − Rf =

hw hw + hg + hd + hf

(6.86)

In nanofluids spray cooling, hf was calculated by using the convective heat transfer coefficient (h) model in Chap. 4. For hw , hg and hd [30]: ⎧  1/2 ⎪ 1/2 vw ⎪ ⎪ h = 0.75(kρc) w ⎪ w ⎪ lc ⎪ ⎪ ⎨  1/2 vs h g = 0.75(kρc)1/2 ⎪ g ⎪ lc ⎪ ⎪ ⎪ ⎪ vw ⎪ ⎩ h d = (ρcα)w lc

(6.87)

6.7 Thermal Partition Coefficient Model in the Grinding Zone

205

Hence, dynamic model of micro-grinding temperature field of bio-bone has been established completely under nanofluids spray cooling conditions. It can be seen from Fig. 6.23 that given the initial condition (T 0 ), the differential equation (Eq. 6.20) is solved by loading the boundary conditions (Eq. 6.24), thus getting the grinding temperature field of bones. Firstly, the thermal damage domain of bone micro-grinding under dry grinding conditions (convective heat transfer coefficient = 0) is analyzed. The experimental study on dynamic temperature field in bone micro-grinding under nanofluids spray cooling conditions will be carried out in the following text.

Fig. 6.23 Flow chart for solving dynamic temperature field of bio-bone micro-grinding under nanofluids spray cooling

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6.8 Thermal Damage Domain in Dry Grinding of Bio-Bone Suppose the heats transferred from the bone grinding zone constantly into bone samples under dry grinding conditions are 0.65 W and the contact arc length is set 1.4 mm [12]. The thermal damage domain under dry grinding of bio-bone is solved by using Eq. (6.2) and 50 °C was used as the threshold of irreversible thermal damage of bones. The thermal damage domains of bone grinding on x–y surface (feeding direction) and x–z surface (cutting depth direction) are shown in Figs. 6.24 and 6.25. Since no cooling measures have been applied, irreversible thermal damages will occur in the x–y surface within 1.45 mm × 0.63 mm to the grinding tool and the x–z surface where is 1.53 mm × 0.23 mm below the grinding tool.

Fig. 6.24 Thermal damage zone on x–y surface of bio-bone dry grinding

z (mm)

6.9 Summary

207

10

80

9

75

8 70

7 zz

6

xx

65

vw

5

60

4

55

3

50

2

45

1

40 1

2

3

4

5

6

7 8 9 1.53 mm

10

11

12

13

14 15 x (mm)

10

80

0.23 mm

z (mm)

ω

75 70 65 60 55 50

9

45 40 8

9 x (mm)

Fig. 6.25 Thermal damage zone on x–z surface of bio-bone dry grinding

6.9 Summary According to different removal modes of hard and brittle bone materials, the dynamic heat flux density model under plastic shear removal and powder removal of bone materials is established. Based on the convective heat transfer coefficient model, a thermal partition coefficient model of micro-grinding under nanofluids spray cooling is constructed. Moreover, the thermal damage zones of bone dry grinding are analyzed through finite difference method. Some conclusions can be drawn: 1. According to cut-in state of grains to plastic metal materials, the heat source distribution models of grinding with ordinary wheel mainly include triangular, rectangular and parabolic heat source distribution models and comprehensive heat source distribution model. 2. In micro-grinding of hard and brittle bones, when hu < hmin , materials only have scratching and ploughing, without material removal. There’s no new surface generation of materials, and grinding work is only used to produce heats. When

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hmin < hu < hc , the consumption of grinding work is composed of scratching energy, ploughing energy and plastic shear chipping energy. The plastic shear chipping energy is used to generate new material surfaces, while scratching energy and ploughing energy are completely transformed into heat energy. When hc < hu < hd-b , the consumption of grinding power is composed of scratching energy, ploughing energy, plastic shear chipping energy and powder removal chipping energy. Among them, the plastic shear chipping energy and powder removal chipping energy are used to produce new surfaces, while scratching energy and ploughing energy are all transformed into heats. 3. Thermal partition coefficients of workpiece materials, grains, grinding debris and cooling medium characterize abilities of heat transfer media (sample materials, grains, grinding debris and cooling medium) to fight for heats in unit area of the grinding zone in unit time. Therefore, thermal partition coefficient of sample materials can be expressed as function of heat transfer coefficients of various heat transfer media in micro-grinding zone. 4. The thermal damage zones of bone dry grinding are calculated by the finite difference method. Results showed that since no cooling measure is adopted, irreversible thermal damages will occur in the 1.45 mm × 0.63 mm zone along the feeding direction and the 1.53 mm × 0.23 mm zone along the cutting depth direction.

References 1. Zhang, Y., Li, C., Ji, H., Yang, X., Yang, M., Jia, D., Zhang, X., Li, R., & Wang, J Analysis of grinding mechanics and improved predictive force model based on material-removal and plastic-stacking mechanisms. International Journal of Machine Tools and Manufacture, 2017, 122, 81–97. 2. Smith S L, O’Neill H B, Isaksen K, et al. The changing thermal state of permafrost. Nature Reviews Earth & Environment, 2022, 3(1):10–23. 3. Ren X K, Huang X K, Gao K Y, et al. A review of recent advances in robotic belt grinding of superalloys. The International Journal of Advanced Manufacturing Technology, 2023, 127(3– 4):1447–1482. 4. Jia G S, Ma Z D, Xia Z H, et al. Influence of groundwater flow on the ground heat exchanger performance and ground temperature distributions: A comprehensive review of analytical, numerical and experimental studies. Geothermics, 2022, 100:28. 5. Cui X, Li C H, Zhang Y B, et al. Comparative assessment of force, temperature, and wheel wear in sustainable grinding aerospace alloy using biolubricant. Frontiers of Mechanical Engineering, 2023 18(1):33. 6. Jin T, He X, Wang Q R, et al. Development of high performance grinding processes to challenge physical limitations: Application prospects in aeronautical manufacture engineering. Aeronautical Manufacturing Technology, 2022, 65(9): 20–33. 7. Yang, M., Li, C., Zhang, Y., Jia, D., Zhang, X., Hou, Y., Li, R., & Wang, J. (2017). Maximum undeformed equivalent chip thickness for ductile-brittle transition of zirconia ceramics under different lubrication conditions. International Journal of Machine Tools and Manufacture, 122, 55–65.

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8. Yang, M., Li, C., Zhang, Y., Jia, D., Li, R., Hou, Y., Cao, H., & Wang, J. (2019). Predictive model for minimum chip thickness and size effect in single diamond grain grinding of zirconia ceramics under different lubricating conditions. Ceramics International, 45(12), 14908–14920. 9. Zhang, Y., Li, C., Jia, D., Li, B., Wang, Y., Yang, M., Hou, Y., & Zhang, X. (2016). Experimental study on the effect of nanoparticle concentration on the lubricating property of nanofluids for MQL grinding of Ni-based alloy. Journal of Materials Processing Technology, 232, 100–115. 10. Li H N, Axinte D. On a stochastically grain-discretised model for 2D/3D temperature mapping prediction in grinding. International Journal of Machine Tools & Manufacture, 2017, 116: 60–76. 11. Costa S, Pereira M, Ribeiro J, Soares D. Texturing Methods of Abrasive Grinding Wheels: A Systematic Review. Materials, 2022, 15(22):26. 12. Min Yang, Changhe Li, Yanbin Zhang, Yaogang Wang, Benkai Li, Dongzhou Jia, Yali Hou, Runze Li. Research on microscale skull grinding temperature field under different cooling conditions. Applied Thermal Engineering, 2017, 126: 525–537. 13. Wang, Y., Li, C., Zhang, Y., Yang, M., Li, B., Dong, L., & Wang, J. (2018). Processing characteristics of vegetable oil-based nanofluid MQL for grinding different workpiece materials. International Journal of Precision Engineering and Manufacturing-Green Technology, 5(2), 327–339. 14. Shen B. Minimum Quantity Lubrication Grinding Using Nanofluids. Michigan: The University of Michigan, 2008. 15. Zhang D K. The mechanism of convective heat transfer and experimental investigation in grinding neckel-base superalloy by nanoparticle jet MQL. Qingdao University of Technology, 2014. 16. Guo, S., Li, C., Zhang, Y., Wang, Y., Li, B., Yang, M., Zhang, X., & Liu, G. (2017). Experimental evaluation of the lubrication performance of mixtures of castor oil with other vegetable oils in MQL grinding of nickel-based alloy. Journal of Cleaner Production, 140, 1060–1076. 17. Yang, M., Li, C., Luo, L., Li, R., & Long, Y. (2021). Predictive model of convective heat transfer coefficient in bone micro-grinding using nanofluid aerosol cooling. International Communications in Heat and Mass Transfer, 125, 105317. 18. Zechen Zhang, Menghua Sui, Changhe Li, Zongming Zhou, Bo Liu, Yun Chen, Zafar Said, Sujan Debnath, Shubham Sharma,(2021), Residual stress of MoS2 nano-lubricant grinding cemented carbide. Int J Adv Manuf Tech. https://doi.org/10.1007/s00170-022-08660-z. 19. Zhang Lei. Experimental Study and Analysis of SinglePlane Grind-hardening Process, Shandong University, China. 2006. 20. Wu C, Li B, Yang J, et al. Prediction of grinding force for brittle materials considering coexisting of ductility and brittleness. The International Journal of Advanced Manufacturing Technology, 2016. 21. Zhang J H, Ge P Q, Zhang L. Research on the Grinding Force Based on the Probability Statistics. China Mechanical Engineering, 2007, 18 (20): 2399–2402. 22. Yanbin Zhang, Hao Nan Li, Changhe Li, Chuanzhen Huang, Hafiz Muhammad Ali, Xuefeng Xu, Cong Mao, Wenfeng Ding, Xin Cui, Min Yang, Tianbiao Yu, Muhammad Jamil, Munish Kumar Gupta, Dongzhou Jia, Zafar Said (2021). Nano-enhanced biolubricant in sustainable manufacturing: From processability to mechanisms. Friction. 10(6): 803–841. 23. X. Cui, C.H. Li, W.F. Ding, Y. Chen, C. Mao, X.F. Xu, B. Liu, D.Z. Wang, H.N. Li, Y.B. Zhang, Z. Said, S. Debnath, M. Jamil, H. Muhammad Ali, S. Sharma, Minimum quantity lubrication machining of aeronautical materials using carbon group nanolubricant: from mechanisms to application, Chinese Journal of Aeronautics, 2022, 35(11):85–112. 24. Yang M, Li C H, Zhang Y B, et al. Theoretical Analysis and Experimental Research on Temperature Field of Microscale Bone Grinding under Nanoparticle Jet Mist Cooling. Journal of Mechanical Engineering, 2018, 54 (18): 194–203. 25. Mingzheng Liu, Changhe Li, Yanbin Zhang, Qinglong An, Min Yang, Teng Gao, Cong Mao, Bo Liu, Huajun Cao, Xuefeng Xu, Zafar Said, Sujan Debnath, Muhammad Jamil, Hafz Muhammad Ali, Shubham Sharma. Cryogenic minimum quantity lubrication machining: From mechanism to application. Frontiers of Mechanical Engineering.2021,16(4):649–697.

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26. Xin Cui, Changhe Li, Min Yang, Mingzheng Liu, Teng Gao, Xiaoming Wang, Zafar Said, Shubham Sharma, Yanbin Zhang. Enhanced grindability and mechanism in the magnetic traction nanolubricant grinding of Ti-6Al-4V. Tribology International, 2023: 108603. https://doi. org/10.1016/j.triboint.2023.108603. 27. Teng Gao, Yanbin Zhang, Changhe Li, Yiqi Wang, Qinglong An, Bo Liu, Zafar Said, Shubham Sharma. Grindability of carbon fiber reinforced polymer using CNT biological lubricant. Scientific Reports. 2021, 11: 22535. 28. Li, B., Li, C., Zhang, Y., Wang, Y., Jia, D., Yang, M., Zhang, N., Qu, Q., Han, Z., & Sun, K. (2017). Heat transfer performance of MQL grinding with different nanofluids for Ni-based alloys using vegetable oil. Journal of Cleaner Production, 154, 1–11. 29. Stachurski W, Sawicki J, Januszewicz B, Rosik R. The Influence of the Depth of Grinding on the Condition of the Surface Layer of 20MnCr5 Steel Ground with the Minimum Quantity Lubrication (MQL) Method . MATERIALS, 2022, 15(4). 30. Yang, M., Li, C., Zhang, Y., Jia, D., Li, R., Hou, Y., & Cao, H. (2019). Effect of friction coefficient on chip thickness models in ductile-regime grinding of zirconia ceramics. The International Journal of Advanced Manufacturing Technology, 102(5), 2617–2632.

Chapter 7

Process Parameter Optimization and Experimental Evaluation for Nanofluid MQL in Grinding Ti-6Al-4V Based on Grey Relation Analysis

7.1 Introduction Titanium (Ti) alloy is a kind of typical plastic material and it has been extensively applied to aerospace industry in China and foreign countries due to the good heat resistance, corrosion resistance and high specific intensity. Nevertheless, there are some problems during Ti alloy grinding, such as high processing temperature, strong chemical active type in the grinding zone, and serious grinding surface pollution. Therefore, reasonable grinding parameters are premise to assure surface quality and grinding efficiency of Ti alloy. Jingxin Ren et al. [1] carried out a grinding experiment of Ti alloy by using different types of grinding wheel, grinding fluids with different oiliness and different grinding parameters. They found that during low-speed grinding of Ti alloy with CBN grinding wheel, the grinding depth shall be within the range of 0.01–0.02 mm, the feeding rate of workpiece shall be within 12–16 m/min, the speed of grinding wheel shall be no higher than 25 m/s, and the grinding wheel of ceramic binding agent has better grinding performances. Guo et al. [2] ground Ti–6Al–4 V by using Sic grinding wheel and studied the mechanical processing performances of the workpiece by analyzing the grinding force, specific grinding energy, surface residual stress and metallographic structure. Setti et al. [3] carried out NMQL grinding of Ti–6Al–4 V by using Al2 O3 and CuO nanofluids with different volume fractions and found that it could decrease tangential grinding force and grinding temperature better under Al2 O3 NMQL. Sadeghi et al. [4] applied MQL into grinding of Ti–6Al–4 V. In the experiment, different grinding parameters, different lubrication liquid and different jetting parameters of MQL were set. The final experimental results demonstrated that MQL could reach surface quality of traditional flood grinding, but the secondary material deposition phenomenon still remains unsolved. The synthesis lipid has better lubrication performances than vegetable oils. Although scholars have carried out a lot of grinding experiments and relevant analyses on Ti alloy, none of them have concluded the reasonable ranges of grinding parameters for the reference of actual process. Moreover, influencing degrees of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_7

211

212

7 Process Parameter Optimization and Experimental Evaluation …

factors of grinding parameters on indicators (grinding temperature (T ), grinding force (F t ), specific grinding energy (U) and surface roughness (Ra )) haven’t been analyzed yet. The main goal of this study is to set factors and levels reasonably by using orthogonal experimental design (L16 ), analyze stability of indicators by signalto-noise ratio (S/N), and conclude the optimal combination of about four parameters. Furthermore, two combinations of parameters which have the optimal comprehensive effects of T, F t , U and Ra are gained through grey correlation analysis. Finally, 3 groups of parameter combinations with relatively optimal surface quality are gained by analyzing surface profile supporting length ratio and surface morphology analysis under the optimized 6 groups of parameter combinations. Subsequently, experimental evaluation of the workpiece removal parameter (Λw ) and specific grinding energy (U) is carried out based on the assurance to workpiece surface quality. Finally, the optimal parameter combination of surface quality and processing efficiency is acquired, which lays theoretical foundations for further analysis on CNMQL conditions and also provides some references for practice of Ti alloy grinding.

7.2 Experimental Design 7.2.1 Experimental Equipments In the experiment, Ti alloy workpiece (Mode: Ti–6Al–4 V; size: 80 mm × 20 mm × 40 mm) was grounded by using a precise plane numerical control grinder (Mode: K-P36) and SiC ceramic binding agent grinding wheel (Mode: GC80K12V; Size: 300 mm × 20 mm × 76.2 mm). The nanofluids were transferred to the nozzle through the MQL device (Mode: KS-2106) and then atomized by the high-speed gases. Meanwhile, a three-way grinding force tester (Mode: YDM-III99) and thermocouple (Mode: MX100) were applied to measure data about grinding force and grinding temperature, respectively. After finishing the grinding, the workpiece was taken down to measure Ra and surface profile support ratio after grinding by using the surface contourgraph (Mode: TIME 3220). The microstructure and EDS of processed workpiece surface were analyzed by using the scanning electron microscope (Mode: S-3400N). The Experimental equipments is shown in Fig. 7.1. The schematic map of data measurement is shown in Fig. 7.2. The grinding parameters used in the experiment are listed in Table 7.1. To realize the controllable grinding process, the sharpness of grinding wheel in each experiment was consistent and grinding wheel was finished before experiment. The finishing parameters are listed in Table 7.1.

7.2 Experimental Design

213

Fig. 7.1 Experimental device setup

7.2.2 Experimental Materials The elemental composition of Ti alloy (Ti-6Al-4 V) workpiece is shown in Table 7.2. In the experiment, three different cooling lubrication liquid was applied. The flood grinding used Syntilo 9930 water-based grinding fluid. MQL chose KS-1008 synthesis lipid. NMQL chose the 2% (volume fraction) Al2 O3 nanofluid. Specifically, the Al2 O3 nanofluid was prepared by two-step method [5, 6]. The physical characteristics of Al2 O3 nanoparticles are shown in Table 7.3.

214

7 Process Parameter Optimization and Experimental Evaluation …

Fig. 7.2 Schematic diagram of experimental data measurement process Table 7.1 Grinding experimental parameters Grinding type

Plane grinding and up-grinding

Type of grinding wheel

SiC: GC80K12V

Lubrication mode

Dry grinding, flood grinding, MQL, NMQL

Flood flow rate

60L/h

MQL flow rate

50 ml/h

Linear speed of grinding wheel (vs )

15–24 m/s

Workpiece feeding speed (vw )

2– 8/min

Grinding depth (ap )

5–20 μm

MQL nozzle distance (d)

12 mm

MQL nozzle angle (α)

15°

MQL air pressure (P)

0.6 MPa

Total finishing depth (ad )

40 μm

Finishing velocity (vd )

300 mm/min

Table 7.2 Elemental composition of Ti-6Al-4 V Nominal components

Base

Alloy element wt/ %

Impurities < wt/%

Ti-6Al-4 V

Ti

Al

V

Fe

Si

C

N

H

O

5.5–6.8

7.5–4.5

0.3

0.1

0.1

0.05

0.15

0.01

7.3 Results and Discussion

215

Table 7.3 Physical properties of Al2 O3 nanoparticles Size nm

Crystal texture Melting point (°C)

Apparent density (g/ cm3 )

Thermal conductivity (W/m K)

Colors

Moh’s hardness

50

Hexagonal close packing

0.33

36

White

8.8–9.0

2050

Table 7.4 Factors and levels of grinding process parameters Factors

Levels 1

2

3

4

Cooling lubrication mode

Dry grinding (Dry)

Flood grinding (Flood)

MQL

NMQL

vs (m/s)

15

18

21

24

vw (m/min)

2

4

6

8

ap (μm)

5

10

15

20

7.2.3 Experimental Schemes An experimental exploration of grinding parameters of Ti alloy was carried out by using the orthogonal experimental design. In orthogonal experimental design, grinding parameters, or known as orthogonal experimental factors, included cooling lubrication mode, grinding wheel velocity, feeding speed of workpiece and grinding depth [7]. A four-factor and four-level L16 (44 ) orthogonal experiment was carried out. The experimental levels and parameters are shown in Table 7.4. Choosing grinding parameters reasonably is vital to grinding performances of Ti alloy. For reasonable arrangement of value range of different factor levels, these experimental parameters were all chosen according to preliminary optimization of Ding [8], Zhao [9], Setti [10] and Sahoo [11]. The orthogonal experiment is shown in Table 7.5.

7.3 Results and Discussion 7.3.1 Single-Index SNR Analysis The experiment is to optimize the grinding parameters to get better T, F t , U and Ra (relatively low values). Therefore, the small-the-better characteristics were used in the study. During S/N analysis, the calculation formula of the small-the-better characteristics is:   n 1  2 S/N = −10 log y (7.1) n i=1 i

216

7 Process Parameter Optimization and Experimental Evaluation …

Table 7.5 L16 Orthogonal experimental table Groups

Cooling lubrication mode

vs (m/s)

vw (m/min)

ap (μm)

1–1

Dry

15

2

10

1–2

18

4

15

1–3

21

6

20

1–4

24

8

5 20

1–5

15

4

1–6

Flood

18

2

5

1–7

21

8

10

24

6

15

15

6

5

1–10

18

8

20

1–11

21

2

15

1–12

24

4

10

15

8

15

1–14

18

6

10

1–15

21

4

5

1–16

24

2

20

1–8 1–9

1–13

MQL

NMQL

where yi is the acquired sample test data and n is the number of experimental data. The S/N values calculated by T, F t , U and Ra are shown in Table 7.6. The response table of S/N ratios of corresponding factors is shown in Table 7.7 1. Grinding temperature It can be seen from Fig. 7.3 that the highest S/N ratio is achieved in flood grinding, indicating that the flood cooling lubrication mode can decrease temperature in the grinding zone (T ) the most effectively. Compared with dry grinding and MQL grinding, NMQL can get the higher S/N ratio. Through macroscopic observation of workpiece surface morphology, no obvious grinding-induced burn damages were observed in 16 groups of experiments, indicating that the grinding parameters chosen preliminarily in this range were relatively reasonable. There’s no linear relationship between S/N ratios of the grinding wheel velocity (vs ) and grinding temperature (T ), because grinding heats come from consumption of grinding power. When vs is too low, it can be seen from Figs. 7.4 and 7.5 that the tangential grinding force (F t ) increases sharply, the specific grinding energy (U) reaches the maximum, and the energy consumption for unit workpiece material removal increases, thus resulting in the high temperature. Nevertheless, when vs is too high, there are many effective grains involved in unit time and thickness of the maximum undeformed chips decreases. In other words, grinding debris are cut finely and the changing performances of chips increase. Meanwhile, the number of grains participating in ploughing and scratching increase, thus intensifying the scratching and increasing grinding temperature accordingly.

7.3 Results and Discussion

217

Table 7.6 Experiment values and their corresponding S/N ratios (dB) of each factor Groups T (°C) F t (N)

U(J/mm3 ) Ra (μm) S/N ratio S/N ratio S/N ratio S/N ratio of T (db) of F t (db) of U (db) of Ra (db)

1–1

252

55.59

125.2

0.82

−48.03

−34.91

−41.96

1.72

1–2

321.3

96

86.49

0.82

−50.14

−39.65

−38.74

1.72

1–3

435

135.13

71.01

1.26

−52.79

−42.62

−37.03

−2

1–4

147.5

65.52

119.55

0.524

−47.14

−36.35

−41.46

5.62

1–5

134.1

150

84.46

0.576

−42.59

−47.52

−38.53

4.78

1–6

48.5

20.8

114.05

0.688

−37.75

−26.4

−41.06

7.248

1–7

145.8

94

74.1

0.657

−47.84

−39.46

−37.4

7.65

1–8

227.2

87.5

67.45

1.104

−46.99

−38.44

−36.51

−0.86

1–9

141.9

70.94

106.52

0.557

−47.04

−37.02

−40.55

5.08

1–10

228.5

215.75

72.89

1.346

−47.18

−46.68

−37.25

−2.584

1–11

272.1

44.64

97.29

0.628

−48.70

−37.01

−39.46

4.044

1–12

215.5

56.08

101.04

0.546

−46.67

−34.98

−40.1

5.25

1–13

187.3

227

85.2

1.044

−45.26

−47.12

−38.61

−0.38

1–14

181.8

90.54

81.57

0.553

−44.38

−39.14

−38.23

5.14

1–15

137.8

37.21

117.82

0.427

−42.58

−31.42

−41.4

7.39

1–16

381.9

46.72

87.71

0.683

−51.65

−37.4

−38.51

7.30

Similar with grinding temperature (T ), there’s no linear relationship between feeding speed (vw ) of workpiece and S/N ratio. Since temperature on workpiece surface is influenced by heat source intensity and acting time of heat source comprehensively, the heat source intensity increases gradually with the increase of vw , but the acting time decreases gradually with the accelerating movement of heat source. Increasing grinding depth (ap ) means that the thickness of undeformed chips of a single-grain increases gradually and the generated energy increases gradually, accompanied with a rise in grinding temperature. It can be seen from arrangement of response ranking of S/N ratio in Table 7.7 that ap has the maximum influences on T. It has to decrease ap firstly in order to lower T. The optimal parameters to lower T are: flood grinding, vs = 18 m/s, vw = 8 m/ min and ap = 5 μm. 2. Tangential grinding force In Fig. 7.4, flood grinding still has great advantageous in decreasing tangential grinding force (F t ). Compared with dry grinding and MQL, NMQL can get the higher S/N ratio. In other words, the lower F t is achieved. This means that after nanoparticles are added in the base liquid, the grinding force is decreased significantly due to the good anti-friction and anti-wearing effects of Al2 O3 nanoparticles. Increasing vs leads to a reduction in the maximum thickness of undeformed chips of a single-grain and an increase of S/N ratio of F t . In other words, F t is decreased.

218

7 Process Parameter Optimization and Experimental Evaluation …

Table 7.7 Response table for S/N ratios of each factor Factors

Cooling lubrication modes

vs (m/s)

vw (m/min)

ap (μm)

Grinding temperature (T ) 1

−48.52

−44.72

−45.52

−40.61

2

−41.63

−44.06

−45.47

−45.79

3

−46.40

−46.82

−46.99

−47.77

4

−46.16

−47.10

−44.71

−48.53

Delta

6.89

7.05

2.28

7.93

Ranking

2

3

4

1

Tangential grinding force (F t ) 1

−38.37

−40.64

−31.91

−32.78

2

−36.94

−37.96

−37.39

−37.12

3

−37.92

−36.62

−39.3

−39.55

4

−37.77

−35.78

−42.4

−41.55

Delta

0.883

1.261

0.351

0.656

Ranking

4

3

1

2

Specific grinding energy (U) 1

−39.82

−39.91

−40.24

−41.17

2

−38.41

−38.84

−39.7

−39.42

3

−39.32

−38.81

−38.1

−38.33

4

−39.18

−39.17

−38.7

−37.82

Delta

1.4

1.1

2.14

7.35

Ranking

3

4

2

1

Surface roughness (Ra ) 1

1.7634

2.8060

7.0811

5.3440

2

2.7073

1.8841

4.7907

7.9435

3

2.9497

7.2684

1.8404

0.8787

4

7.8686

7.3304

1.5768

0.8787

Delta

2.1053

1.4463

7.2139

4.4553

Ranking

3

4

2

1

With the increase of vw and ap , S/N ratio of F t decreases sharply. In other words, F t increases dramatically. It can be seen from ranking in Table 7.7 that vw is the primary influencing factor of F t . To decrease F t , the vw of the workpiece has to be decreased firstly. The optimal parameters to decrease F t are flood grinding, vs = 24 m/s, vw = 2 m/min and ap = 5 μm.

7.3 Results and Discussion

Fig. 7.3 Main effects plot of S/N ratio for T

Fig. 7.4 Main effects plot of S/N ratio for Ft

219

220

7 Process Parameter Optimization and Experimental Evaluation …

Fig. 7.5 Main effects plot of S/N ratio for U

3. Specific grinding energy In Fig. 7.5, the maximum S/N ratio is acquired in flood grinding. Compared to dry grinding and MQL, NMQL can get the higher S/N ratio. In other words, a smaller value of specific grinding energy (U) was acquired. U is related with F t , vs , vw and ap . Given the constant of rest three factors, the variation trend of U is consistent with that of F t . There’s no linear correlation between S/N ratios of vs and U. According to definition of specific grinding energy (Eq. 7.2), F t declines although vs increases. Combining with Fig. 7.4, the reduction rate of F t declines with the increase of vs , thus changing the overall trend of U. After increasing the feeding speed of workpieces, the material removal in unit time increases and the grinding efficiency increases and U decreases to some extent. However, the cutting force increases significantly when vw is too high, and S/N ratio of U decreases again. In other words, U increases. The proportion of ap increases with the increase of ap even though it is accompanied with a growth of F t . As a result, S/N ratio of U increases gradually. In other words, U decreases gradually and the grinding efficiency increases gradually. The calculation formula of specific grinding energy is: U=

P F · vs = Qw vw · a p · b

(7.2)

7.3 Results and Discussion

221

where U is specific grinding energy (J/mm3 ). P is the total energy consumed by grinding (J). Qw is the total volume of workpiece material removal (mm3 ). F t is the tangential grinding force (N). vs refers to speed of the grinding wheel (m/s). vw refers to the feeding speed of workpiece (mm/s). ap expresses the grinding depth of grinding wheel (mm). b is the width of workpiece (mm). According to ranking in Table 7.7, ap influences U the mostly, followed by vw . Give a low ap and vw , scratching and ploughing take the dominant role in chip formation and they have to consume relatively high energy, thus resulting in the high specific grinding energy [11]. The ap shall be increased firstly to decrease U and increase grinding efficiency. The optimal parameters to decrease U are flood grinding, vs = 18 m/s, vw = 6 m/min and ap = 20 μm. 4. Surface roughness (Ra) It can be seen from Fig. 7.6 that the highest S/N ratio is achieved under NMQL, thus getting the lowest Ra value. The lowest S/N ratio is achieved under dry grinding since there’s no cooling and lubrication medium. The S/N ratio under MQL is higher than that under flood grinding, indicating that the lubrication performances of synthesis lipid used in MQL are better than those of water-based grinding fluid used in flood grinding. S/N ratio of NMQL is higher compared to that of MQL, which is attributed to the good anti-friction and anti-wearing characteristics of Al2 O3 nanoparticles. The experimental factors are arranged reasonably and effectively in orthogonal experiment, thus decreasing the experimental error to the maximum extent. However, we can see that the minimum S/N ratio is achieved when vs is 18 m/s. This doesn’t

Fig. 7.6 Main effects plot of S/N ratio for Ra

222

7 Process Parameter Optimization and Experimental Evaluation …

mean that given the same other conditions, surface quality deteriorates when vs increases from 15 to 18 m/s. This is because experimental results are influenced by many factors together (cooling lubrication mode, vw and ap ) rather than influenced by a single factor. It can be seen from Table 7.7 that grinding wheel velocity has the smallest influences on Ra , because vs changes very small. According to the overall trend of S/N ratio that grinding wheel velocity influences Ra , S/N ratio is positively related with vs . However, such correlation doesn’t change obviously even though increasing vs can decrease Ra to some extent. This is because vs only changes within a small range. Different from grinding of ordinary materials, the thickness of undeformed chips of a single-grain during grinding of Ti-6Al-4 V increases with the increase of vw , thus increasing Ra accordingly. However, there’s material adhesion in the grinding process [12] S/N ratio of Ra increases firstly and then decreases with the increase of vw . When vw is too low (2 m/min), grinding debris accumulates in the grinding zone and cannot move out of the grinding zone timely. Grinding debris is easy to be melted onto workpiece and grinding wheel surface under high temperatures, thus resulting in the poor processed surface quality of workpiece and fast wearing of the grinding wheel. Same with the variation trends of grinding temperature and tangential grinding force, the S/N ratio of Ra presents a linear reduction trend with the increase of grinding thickness. It can be seen from ranking in Table 7.7 that ap is the primary influencing factor of Ra . The grinding surface quality has to be increased to lower the value of Ra . Firstly, it shall decrease ap . The optimal parameters to decrease Ra include NMQL grinding, vs = 24 m/s, vw = 4 m/min and ap = 5 μm.

7.3.2 Multi-Index Grey Correlation Analysis The following experimental data can be acquired through grey correlation analysis (Table 7.8). The comprehensive effect of indexes is better if the grey relational grade is higher. Next, the large-the-better characteristic of grey relational grade was analyzed (Eq. 7.3). The responses of the large-the-better characteristic of grey relational grade are shown in Table 7.9. The main effects plot of S/N ratio for grey relational grade is shown in Fig. 7.7. The formula of grey relational grade is:     mini min j xi0 − xi j  + ς maxi max j xi0 − xi j      εi j = x 0 − xi j  + ς maxi max j x 0 − xi j  i

(7.3)

i

εij is the grey relational grade of the ith index in the jth experiment. It can be seen from Fig. 7.7 that the S/N ratio for grey relational grade reaches the maximum under flood grinding, vs = 21 m/s, vw = 2 m/min and ap = 5 μm. Under this working condition, the comprehensive effect of T, F t , U and Ra reaches

7.3 Results and Discussion

223

Table 7.8 The calculated grey relational grade among S/N ratios of different indexes Groups T

Ft

S/N ratio

Grey S/N relational ratio grade

U

Ra

Grey S/N relational ratio grade

Grey S/N relational ratio grade

Grey relational Grey relational grade grade

1–1

−48.03 0.4

−34.91 0.55

−41.96 0.333

1.72 0.468

0.438

1–2

−50.14 0.637

−39.65 0.439

−38.74 0.55

4.15 0.468

0.456

1–3

−52.79 0.333

−42.62 0.39

−37.03 0.84

−1.03 0.347

0.477

1–4

−47.14 0.503

−36.35 0.51

−41.46 0.355

5.62 0.74

0.527

1–5

−42.59 0.519

−47.52 0.377

−38.53 0.574

5.58 0.656

0.532

1–6

−37.75 1

−26.4

−41.06 0.375

5.01 0.546

0.73

1–7

−47.84 0.486

−39.46 0.442

−37.4

7.65 0.571

0.563

1–8

−46.99 0.418

−38.44 0.463

−36.51 1

−0.86 0.377

0.564

1–9

−47.04 0.506

−37.02 0.494

−40.55 0.403

5.08 0.683

0.522

1–10

−47.18 0.415

−46.68 0.338

−37.25 0.786

−1.33 0.333

0.468

1–11

−48.70 0.389

−37.01 0.611

−39.46 0.48

5.29 0.595

0.519

1–12

−46.67 0.424

−34.98 0.547

−40.1

6.21 0.7

0.526

1–13

−45.26 0.452

−47.12 0.333

−38.61 0.565

0.59 0.393

0.435

1–14

−44.38 0.473

−39.14 0.449

−38.23 0.613

5.94 0.69

0.556

1–15

−42.58 0.519

−31.42 0.674

−41.4

7.39 1

0.638

1–16

−51.65 0.347

−37.4

−38.51 0.577

7.30 0.549

0.518

1

0.597

0.754

0.432

0.358

Table 7.9 Response table for S/N ratios of the grey relational grade Factors

Cooling and lubrication mode

vs (m/s)

vw (m/min)

ap (μm)

1

−6.498

−6.386

−5.333

−4.466

2

−4.544

−5.311

−5.452

−5.713

3

−5.884

−5.255

−5.537

−6.178

4

−5.489

−5.462

−6.093

−6.056

Delta

1.954

1.131

0.759

1.712

Ranking

1

3

4

2

an optimal value. The influencing degrees of different factors on grey relational grade are reflected in Table 7.9. Obviously, cooling and lubrication mode influences grey relational grade the mostly and vw presents the lowest influencing degree. In the grinding process, the comprehensive effects of flood lubrication mode on indexes still have a great advantage. The NQML is improved significantly compared to dry grinding and MQL grinding. Under the same working condition, NMQL can replace the flood grinding. It decreases costs for grinding fluid effectively and realizes green manufacturing.

224

7 Process Parameter Optimization and Experimental Evaluation …

Fig. 7.7 Main effects plot of S/N ratio for grey relational grade

7.4 Verification Experiment The optimal parameters that influence T, F t , U and Ra were concluded by analyzing the S/N ratio, which were corresponding to Test 2–1, Test 2–2, Test 2–3 and Test 2–4, respectively. Through grey correlation analysis, the optimal parameters for comprehensive effects of above indexes are Test 2–5 and Test 2–6. Specifically, Test 2–6 realizes a comparative experiment on effective replacement of grinding fluid under NMQL grinding. Test 1–15 compares parameter combinations in orthogonal experiments with minimum Ra , that is, relatively high surface quality. The specific experimental parameters are shown in Table 7.10. Table 7.10 Experimental design for verification Groups

Cooling and lubrication mode

vs (m/s)

vw (m/min)

ap (μm)

2–1

Flood

18

8

2–2

Flood

24

2

5

2–3

Flood

21

6

20

2–4

NMQL

24

4

5

2–5

Flood

21

2

5

2–6

NMQL

21

2

5

1–15

NMQL

21

4

5

5

7.4 Verification Experiment

225

7.4.1 Workpiece Surface Quality Analysis The profile supporting length ratio curves of 6 groups of verification experiments are shown in Fig. 7.8. The statistical table of surface running-in characteristics, wearing resistance and oil retention performances in different groups of experiments based on analysis of Fig. 7.8 is shown in Table 7.11. The surface morphologies in 6 groups of verification experiments are shown in Fig. 7.9. Obviously, there are lamellar adhesive substances on the workpiece surfaces in Group 2–2 and Group 2–6, thus causing surface “protrusion” and thereby deteriorating workpiece surface quality. According to EDX analysis of Group 2–2 and Group 2–6 IN Fig. 7.10, the element contents for surface “protrusion” are approximately equal to the element contents on workpiece surface. This proves that surface “protrusion” is workpiece materials rather than grains of grinding wheel or other impurities carried by lubricant. Surface “protrusions” are all sheets adhering onto the workpiece surface rather than the plastic deformation layer formed by ploughing

Fig. 7.8 Profile supporting length ratio curve tp (c) under different grinding parameters

Table 7.11 The mechanical properties under different grinding parameters Groups

Running-in characteristics

Supporting performances Rk (μm)

Mr1 -Mr2 (%)

Oil retention performances

2–1

Poor

1.98

81.5

优

2–2

Good

1.18

80.2

良

2–3

Poor

1.9

84.5

良

2–4

Excellent

0.93

81

优

2–5

Poor

1.5

54.5

良

2–6

Excellent

1.22

83

差

1–15

Good

1.6

79

差

226

7 Process Parameter Optimization and Experimental Evaluation …

Fig. 7.9 SEM morphology of workpiece under different grinding parameters

effect of grains. Hence, it can deduce that these surface “protrusions” are grinding debris of workpiece materials which cannot separate from the grinding zone effectively in the high-temperature grinding zone. Grinding debris is further adhered onto the workpiece surface under extrusion of the grinding wheel (Fig. 7.11). It can be seen from Fig. 7.8 that under different grinding conditions, Group 2–4 achieves the most ideal processing surface, with the minimum peak zone area and the best running-in characteristics. The core profile depth is Rk (2–4) = 0.93 μm and the profile supporting rate is Mr1 -Mr2 (2–4) = 81%. The supporting rate in the core area increases the most quickly. Group 2–4 shows the highest surface supporting performances. The valley area is relatively large, the oil retention performances of workpiece surface is relatively good, and the comprehensive surface quality is the best. Hence, it can be seen from the workpiece surface morphology in Fig. 7.9 that the surface texture is clearer and the overall distribution of micro-convex peaks on workpiece surface is more precise and relatively uniform, without obvious surface plastic layer. Hence, the workpiece shows the best surface morphology (Fig. 7.9 (2–4)). In Group 2–2, the peak area is relatively large, but the running-in characteristics are relatively good. There’s Rk (2–2) = 1.18 μm and Mr1 -Mr2 (2–2) = 80.2%, indicating the good surface supporting performances and good wearing resistance. Moreover, the valley area is relatively large and the oil retention performances on the

7.4 Verification Experiment

227

Fig. 7.10 EDX analysis scheme of group 2–2 and group 2–6

workpiece surface are relatively good. According to workpiece surface morphology in Fig. 7.9, there are some plastic deformation layers and adhesion of grinding debris on workpiece surface. This is because decreasing grinding force indicates that plastic deformation of workpiece materials is relieved and the surface furrows are relieved. However, the contact time between grinding wheel and workpiece base is relatively long due to the excessively low feeding speed of workpiece (vw = 2 m/min) and high grinding wheel velocity (vs = 24 m/s). Grinding debris cannot be removed from the grinding zone effectively, and melted again onto the workpiece surface under the extrusion of grinding wheel. Consequently, the workpiece surface quality declines to some extent (Fig. 7.9 (2–2)).

228

7 Process Parameter Optimization and Experimental Evaluation …

Fig. 7.11 Workpiece material removal mechanism under NMQL condition

Group 2–6 also achieved a relatively ideal processing surface. It has relatively small peak area and the best running-in characteristic. The core profile depth is Rk = 1.22 μm and the profile supporting rate is Mr1 -Mr2 (2–6) = 83%. The valley area is relatively small, the surface texture roughness is relatively low, and the oil retention performances are relatively poor. According to workpiece surface morphology in Fig. 7.9, the surface texture of Group 2–6 is relatively explicit, without obvious surface plastic layer. It shows relatively good surface morphology. However, Group 2–6 shows mild adhesion phenomenon of grinding debris (Fig. 7.9 (2–6)). The poorest processing surfaces of Group 2–1 and Group 2–3 are gained, manifested by large peak area and relatively poor running-in characteristics. The growth rate of supporting rate in the core zone is relatively slow. Even though the profile supporting ratio reaches Mr1 -Mr2 (2–1) = 81.5 and Mr1 -Mr2 (2–3) = 84.5%, the core profile depth reaches Rk (2–1) = 1.98 μm and Rk (2–3) = 1.9 μm and the supporting performances are still poor. Group 2–1 gets the largest valley area, indicating the highest surface roughness. It is disadvantageous to surface quality, but the oil retention performances are relatively good. According to workpiece surface morphology in Fig. 7.9, Group 2–1 and Group 2–3 have ambiguous surface texture and serious material deposition. Decreasing the grinding temperature (T ) implies reduction of vs , increases of vw and maximum thickness of undeformed chips of single-grain, and serious surface plastic layer (Fig. 7.9 (2–1)). Decreasing the specific grinding energy (U) means that that vs , vw and ap are all relatively large. Although U is decreased to some extent, ap is relatively large and vw is relatively high. Ti alloy material is easy to produce adiabatic shear phenomenon, serious plastic deformation, insufficient material removal and serious material adhesion of workpiece surface, thus resulting in the poorest overall surface quality of workpieces (Fig. 7.9 (2–3)). Specifically, Group 2–5 and Group 2–6 are a group of single-factor experiments and lubrication mode is the only one variable. The processing surface quality of Group

7.4 Verification Experiment

229

2–5 is relatively poor. The peak area is the largest, indicating the poor running-in characteristics. The valley area is relatively large, indicating the high surface roughness and good oil retention performances. The core profile depth is Rk (2–5) = 1.5 μm and Mr1 -Mr2 (2–5) = 84.5%, and the wearing resistance is relatively poor. According to comparison of Group 2–5 and Group 2–6, changing flood grinding into NMQL grinding can improve running-in characteristics and supporting performances of workpiece surfaces effectively when other grinding parameters are the same. Moreover, it can be seen intuitively from two groups of surface morphologies in Fig. 7.9 that surface texture of Group 2–5 is relatively ambiguous, showing obvious furrows and plastic deformation layers (Fig. 7.9 (2–5)). The surface texture of Group 2–6 is relatively explicit, without obvious surface plastic layers, showing good surface morphology (Fig. 7.9 (2–6)). This implies that NMQL grinding has better lubrication performances than flood grinding and it increases the grinding performances of Ti alloy. However, there’s mild grinding debris adhesion phenomenon since the grinding temperature of NMQL is relatively high and the cooling performance is poorer compared to that in flood grinding. Group 1–15 in orthogonal experimental groups was chosen for comparison and it was chosen as the experimental group with the minimum Ra , indicating the relatively good surface quality. Group 1–15 and Group 2–6 form the single-factor experiment and vw is the only variable. The peak area and valley area of Group 1–15 both are increased to some extent compared to Group 2–6. The core profile depth Rk = 1.6 μm and the profile supporting rate is Mr1 -Mr2 (1–15) = 79%. The surface wearing resistances are all poorer than Group 2–6. According to comparison of Ra (1–15) = 0.427 μm and Ra (2–6) = 0.496 μm, it can be seen that vw of Group 2–6 declines and the surface wearing resistance is improved to some extent, but its Ra increases to some extent. According to workpiece surface morphology in Fig. 7.9, the surface texture of Group 1–15 is relatively explicit, but the surface shows mild “furrows” and plastic deformation layer. However, “furrows” on the workpiece surface of Group 2–6 are relatively fine, but adhesion of some grinding debris occurs. It can infer that decreasing vw brings a decrease in thickness of undeformed chips of a singlegrain and decrease of energy carried by a single-grain, but increased surface texture performances of workpieces and surface wearing resistance. However, the contact time between grinding wheel and workpiece base during grinding process is relatively long since vw is excessively low. Grinding debris cannot be removed from the grinding zone by high-speed gases effectively and melted onto the workpiece surface again under high grinding temperature. There are increased surface “protrusions”, thus deteriorating surface quality. Furthermore, grinding debris under two groups of working conditions was extracted for analysis to prove this deduction, as shown in Fig. 7.12. Clearly, the grinding debris of Group 2–6 is relatively thin and long and its front surface is relatively smooth, indicating the debris has relatively small deformation force and good material removal performances. However, there are relatively serious crossing clusters among grinding debris, and such clustering grinding debris is easier to adhere onto the surface of grinding wheel to block pores on the grinding wheel, thus resulting in fast wearing of grinding wheel. Moreover, grinding debris adhered onto the grinding wheel will be adhered onto the workpiece surface when

230

7 Process Parameter Optimization and Experimental Evaluation …

Fig. 7.12 SEM images of grinding debris under different conditions

the grinding wheel further grinds the workpiece. Comparatively, the grinding debris of Group 2–6 is relatively wide and short, and its front surface is relatively rough. Moreover, some broken grinding debris occurs, indicating that the processed surface of workpiece is relatively poor. Hence, the material removal performances can be improved effectively controlling the reasonable vw .

7.4.2 Grinding Efficiency Analysis of Workpiece Material After analysis of the profile supporting length ratio curve (t p (c)) and microstructure of surface, it can conclude that Groups 2–2, 2–4 and 2–6 present relatively optimal surface qualities. At the pursuit of workpiece surface quality, vs is relatively high, while vw and ap are relatively low, thus decreasing workpiece material removal efficiency. During reasonable optimization of grinding parameters, it shall increase grinding efficiency under the guarantee of workpiece surface quality. In the experiment, the grinding efficiency of Ti Alloy workpiece under different working conditions is characterized by workpiece removal parameters and specific grinding energy. For better analysis of influencing laws of single factor on Λw and U, the Group 1–15 was chosen for comparison. The histograms of Λw and U of Groups 2–2, 2–4, 2–6 and 1–15 are shown in Fig. 7..7.13. It can be seen from Fig. 7.13 that Group 2–4 gained the maximum Λw value and relatively small U. It not only gains the best surface quality, but also acquires the optimal grinding efficiency of Ti alloy. According to comparison of Group 2–4 and Group 1–15, given the same other grinding parameters, the tangential grinding force (F t ) and normal grinding force (F n ) of Group 2–4 decrease to some extent by increasing vs to 24 m/s, and Λw increases accordingly. However, U increases to some extent due to the comprehensive influences of vs and F t .

7.5 Summary

231

Fig. 7.13 Histograms of material removal rate (Λw) and specific grinding energy (U) of workpiece under different grinding parameters

According to comparison of Group 2–6 and Group 1–15, given the same other grinding parameters, vw and grinding force of Group 2–6 decrease. Moreover, Λw value declines and U increases, thus resulting in a reduction of grinding efficiency.

7.5 Summary Through grinding performance analysis, S/N analysis and grey correlation analysis of Ti alloy, a statistical optimization was carried out to combination of grinding parameters in orthogonal experiments. Based on experimental analysis and evaluation of profile supporting length ratio, surface morphology, Λw and U under optimized groups of parameter combination, some major conclusions could be drawn: (1) According to S/N in orthogonal experiments, ap is the primary influencing factor of T, U and Ra . Decreasing ap can decrease values of T and Ra , but increase U accordingly, thus decreasing processing efficiency. vw influences F t the mostly. Decreasing vw can lower the grinding force significantly. However, grinding debris cannot be moved from the grinding zone timely and may be melted again onto workpiece surface when vw is too small, thus decreasing the workpiece surface quality. (2) According to grey correlation analysis, lubrication mode is the primary influencing factor of multiple indexes (grinding temperature, grinding force, specific grinding energy and surface roughness), followed by the grinding depth. Flood grinding still develops an important role in influences of indexes. However, influences of NMQL, a new environmental-friendly lubrication mode, on indexes are

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7 Process Parameter Optimization and Experimental Evaluation …

increased obviously compared to those of MQL grinding. According to singlefactor experimental comparison of Group 2–5 and Group 2–6, NMQL grinding gets better surface quality than flood grinding. (3) The optimized combination of grinding parameters is acquired through S/N analysis and grey correlation analysis. The optimized combination of grinding parameter is evaluated by using t p , Λw and U. The optimal surface quality and optimal workpiece material removal efficiency are achieved in NMQL grinding under vs = 24 m/s, vw = 4 m/min and ap = 5 μm. (4) Effects of different grinding factors on grinding surface quality of Ti alloy are verified by profile supporting length ratio curve, surface microstructure and EDX analysis. It can improve workpiece surface quality by using NMQL grinding under a relatively high vs and an appropriate vw . If vw is too low, there’s a long contact period between grinding wheel and workpiece base in the grinding process. Grinding debris cannot be separated from the grinding zone effectively and be melted onto the workpiece surface under the extrusion of grinding wheel, thus decreasing the workpiece surface quality.

References 1. Zhang, Y., Li, C., Jia, D., Zhang, D., & Zhang, X. (2015). Experimental evaluation of MoS2 nanoparticles in jet MQL grinding with different types of vegetable oil as base oil. Journal of Cleaner Production, 87, 930–940. 2. Cai KD, Zhao B, Wu BF, Ding WF, Zhao YJ, Zhu JH, Si WY, et al. Structure design and experimental study on ultrasonic vibration-assisted induction brazing cubic boron nitride abrasive tools [J]. International Journal of Advanced Manufacturing Technology, 2022, 123(3-4): 943–955. 3. Setti D, Sinha M K, Ghosh S, et al. Performance evaluation of Ti–6Al–4V grinding using chip formation and coefficient of friction under the influence of nanofluids[J]. International Journal of Machine Tools & Manufacture, 2015, 88(88):237–248. 4. Huang XM, Ren YH, Jiang W, et al. Investigation on grind-hardening annealed AISI5140 steel with minimal quantity lubrication [J]. International Journal of Advanced Manufacturing Technology, 2017, 89(1–4): 1069–1077. 5. Enomoto T, Satake U, Mao, X. New water-based fluids as alternatives to oil-based fluids in superfinishing processes [J]. Cirp Annals-Manufacturing Technology, 2020, 69(1): 297–300. 6. Li B, Li C, Wang Y, et al. Technological Investigation about Minimum Quantity Lubrication Grinding Metallic Material with Nanofluid[J]. Recent Patents on Materials Science, 2015, 8(3):208–224. 7. Kaynak Y, Gharibi A, Ozkutuk M. Experimental and numerical study of chip formation in orthogonal cutting of Ti-5553 alloy: the influence of cryogenic, MQL, and high pressure coolant supply[J]. International Journal of Advanced Manufacturing Technology, 2017(5):1–18. 8. Ding W, Zhao B, Xu J, et al. Grinding behavior and surface appearance of (TiC p+ TiB w)/Ti-6Al-4V titanium matrix composites[J]. Chinese Journal of Aeronautics, 2014, 27(5): 1334–1342. 9. Zhao B, Ding W F, Dai J B, et al. A comparison between conventional speed grinding and superhigh speed grinding of (TiCp + TiBw ) / Ti–6Al–4V composites using vitrified CBN wheel[J]. The International Journal of Advanced Manufacturing Technology, 2014, 72(1):69–75.

References

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10. Setti D, Sinha M K, Ghosh S, et al. An investigation into the application of Al2 O3 nanofluidbased minimum quantity lubrication technique for grinding of Ti-6Al-4V[J]. International Journal of Precision Technology, 2014, 4(3/4):268–279. 11. Zhang, Y., Li, C., Jia, D., Li, B., Wang, Y., Yang, M., Hou, Y., & Zhang, X. Experimental study on the effect of nanoparticle concentration on the lubricating property of nanofluids for MQL grinding of Ni-based alloy. Journal of Materials Processing Technology, 2016, 232, 100–115. 12. Li P T, Xu J, Zou H F, et al. The material removal mechanism and surface characteristics of Ti-6Al-4 V alloy processed by longitudinal-torsional ultrasonic-assisted grinding. International Journal of Advanced Manufacturing Technology, 2022, 119(11–12): 7889–7902.

Chapter 8

Temperature Field Model and Experimental Verification on Cryogenic Air Nanofluid Minimum Quantity Lubrication Grinding

8.1 Introduction NMQL has good lubrication effect, but insufficient heat transfer effect. Although CA can lower temperature of grinding zone effectively, the lubrication performance is unsatisfying due to the lack of lubrication medium. Since both two green processing techniques have their own advantages and disadvantages, cryogenic air nanofluids minimum quantity lubrication (CNMQL) is proposed by combining NMQL and CA technologies. In CNMQL, low-temperature cold air carries nanofluid lubricants for cooling and lubrication of the grinding zone. The cryogenic air has functions of chip removal and cooling. It improves processing performances of materials and strengthens heat transfer effect. The minimum quantity lubrication can decrease the frictional force between grinding wheel and workpiece, and decrease grinding heat production. The combination of cryogenic air and minimum quantity lubrication can realize good cooling and lubrication performances in the grinding zone. CNMQL not only improves processing quality and processing efficiency, but also avoids environmental pollution and damages to workers, and incurs a low technical cost. It meets the new philosophy of green manufacturing and sustainable development. Although Chinese and foreign scholars have carried out a lot of studies on CA and NMQL in the machining field, there are rare studies on heat transfer mechanism of grinding zone under CNMQL. Excessive grinding temperature is one of major factors that influence and restrict quality of processed parts and service life of the grinding wheel. Therefore, how to provide effective cooling of the grinding zone and thereby lower temperature of the grinding zone and control grinding burns is an important topic in grinding process. In this chapter, cooling performances of CNMQL are explored by using Ti alloy (Ti-6Al-4 V) which has excellent mechanical performances and is widely applied in aerospace field as the workpiece materials.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_8

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8 Temperature Field Model and Experimental Verification on Cryogenic …

8.2 Numerical Simulation of Grinding Temperature Field In actual grinding process, grinding temperature measured by existing temperature measurement technologies have some errors with practical situations since it has very complicated influencing factors. Calculation of temperature of grinding zone based on the pure theoretical formula has some disadvantages of complicated process and heavy calculation loads. With the development of computer technology and numerical simulation model, it has become an important mean to make numerical simulation of grinding temperature field based on computer. Hence, solving the temperature of grinding zone based on numerical analysis method is of important significance. For grinding temperature field, the major numerical analysis methods at present mainly include the following two types: finite element method (FEM) and finite difference method (FDM). It requires multiple parameter modifications and model rebuilding during temperature field analysis based on FEM, which results in the high difficulties and heavy workloads. Hence, the FDM was chosen for numerical simulation analysis of grinding temperature field. The core idea of FDM is to replace differential by difference and discretize a continuous region into a zone composed of finite grids, and solve the partial differential equation by establishing the finite difference equation set.

8.2.1 Mathematical Model of Grinding Temperature Field 1. Heat transfer model In the process of plane grinding, material removal of workpiece will consume plenty of heats which accumulate in the grinding zone. The grinding wheel which contacts with the workpiece and makes cutting behaviors is equal to a moving heat source. With the feeding of the workpiece, the heat source moves forward continuously. According to the First Law of Thermodynamics and Fourier’s law of heat transfer, the field variables T (x, y, z, t) at the transient temperature field all meet the following differential equation of balanced heat conduction [1]: kx

∂2T ∂2T ∂2T ∂T + k y 2 + k z 2 + ρw Q = ρw cw 2 ∂x ∂y ∂z ∂t

(8.1)

where T refers to temperature (°C); t is time (S); k x , k y and k z are heat conductivity coefficients of materials along X, Y and Z (W/[m2 K]); Q is the heat flux density (J/ [m2 K s]); ρ w is density of workpiece materials (kg/m3); cw is specific heat capacity of workpiece materials (J/[kg K]). The first three terms on the left of the equation represent internal temperature rise of workpiece materials caused by heat conduction. The last term on the left reflects temperature rise produced by heat source in the temperature field and there’s no internal heat source in the grinding process. In other words, this grinding temperature field model is an unsteady-state heat transfer model.

8.2 Numerical Simulation of Grinding Temperature Field

237

Fig. 8.1 Heat transfer model

Hence, ρ w Q is equal to zero. The first term on the right of the equation refers to the total energy consumed for temperature rise of the workpiece. The 3D heat transfer model of grinding temperature field is shown in Fig. 8.1. Heats transferred into the workpiece diffuse toward deep and peripherial areas of the workpiece by centering at the heat source. Since the heat source is uniform along the y direction, there’s no heat exchange along the y direction (axial direction of grinding wheel). The analysis on grinding temperature field can be simplified as 2D heat transfer. According to the First Law of thermodynamics and Fourier’s heat transfer laws, there’s no transient temperature field of internal heat source in 2D that meets the following differential equation of heat balance [2]: 

∂2T ∂2T + ∂x2 ∂ z2 k α= ρw cw

 =

1 ∂T α ∂t

(8.2)

where k is the heat conductivity coefficient of workpiece materials (W/[m2 K]); α is the thermal diffusion coefficient of materials (m2 /s); T refers to the transient temperature of materials (°C); t denotes time (S); ρw is the density of workpiece materials (kg/m3); cw is the specific heat capacity of workpiece materials (J/[kg K]). Grinding is a process that countless grains cut the workpiece materials randomly. In this experiment, the cutting depth is 15 μm. According to abundant studies of scholars, the temprature distribution data gained from the triangle moving heat source model conforms better to the cutting depth of this experiment than other heat source models. Hence, the triangle moving heat source model is applied in the following text.

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8 Temperature Field Model and Experimental Verification on Cryogenic …

Fig. 8.2 Plane uniform gridding structure

2. Establishment of difference equation The workpiece is simplified into a 2D rectangular plane and it is discretized into a plane uniform grinding structure by FDM: Δx = Δz = Δl, as shown in Fig. 8.2. Intersection points of grid lines are called as nodes and intersection points between grid lines and object boundaries are called as boundary nodes. Temperature at each node represent temperature of the grid unit that the node lies in. Take a node (i, j) in the workpiece for example. The adjacent nodes (I − 1, j), (i + 1, j), (i, j + 1) and (i, j − 1) all contact with node (i, 1). According to the First Law of thermodynamics, heats at the node (i, j) may be conducted to surrounding adjacent nodes. The heat conduction ends when the heat transfer reaches a balance. Finally, a stable temperature is achieved. Based on the principle of replacing differential quotient by difference quotient in FDM, difference discretization is performed to the partial differential equation and boundary conditions in the field domain simultaneously. A finite difference equation set is established based on the second-order difference quotient: ⎧ 2 ∂ T T (i + 1, j ) − 2T (i, j ) + T (i − 1, j ) ⎪ ⎪ + O(Δx 2 ) ⎪ 2 (i, j ) = ⎪ 2 ∂ x Δx ⎪ ⎪ ⎨ 2 ∂ T T (i, j + 1) − 2T (i, j ) + T (i, j − 1) + O(Δz 2 ) (i, j ) = 2 ⎪ ∂z Δz 2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ∂ T (i, j ) = Tt+Δt (i, j ) − Tt (i, j) + O(Δt) ∂t Δt

(8.3)

where T (i, j) refers to temperature at the node (i, j). T t (i, j) and T t+Δt (i, j) are temperatures at node (i, j) at t and t + Δt. Δt refers to increment of time. Then, O represents infinitesimal. The difference equation set is brought into the heat conduction equation under the 2D space state, thus enabling to express difference equations of different nodes in grids.

8.2 Numerical Simulation of Grinding Temperature Field

239

αΔt[T (i + 1, j ) + T (i − 1, j ) + T (i, j + 1) + T (i, j − 1)] Δl 2 2 Δl − 4αΔt + T (i, j ) (8.4) Δl 2

Tt+Δt (i, j ) =

3. Boundary Conditions of Temperature Field A node (i, 1) on the workpiece surface is chosen to analyze boundary conditions of the grinding zone. In Fig. 8.3, heat inputs on the grinding wheel-workpiece contact surface in the grinding process, heat transfer among different nodes, temperature rise at nodes as well as convective heat transfer among grinding surface of workpiece, cooling and grinding fluid and surrounding air all observe the law of conservation of energy: q(i−1,1)→(i,1) + q(i+1,1)→(i,1) + q(i,2)→(i,1) + q A = ρw Cw V0

 ∂T + G A Ti,1 − Ta ∂t (8.5)

where T i,1 refers to temperature at node (i, 1). T a is temperature of grinding fluid. V 0 expresses the volume of unit grid: V 0 = Δx·ΔZ·1 = Δl2 . G is the comprehensive heat transfer coefficient: G = [1/h] + ΔZ/(2 k)]−1 . A is the surface area of unit grid: A = Δx·1 = ΔZ·1 = Δl. The heat transfer between nodes (i-1,1) and (i,1) on workpiece surface during grinding can be expressed as:   Ti−1,1 − Ti,1 = k(Ti−1,1 − Ti,1 ) q(i−1,1)→(i,1) = k(Δz · 1) Δx

(8.6)

Similarly, the heat transfer between node (i + 1, 1) and node (i, 1) and heat transfer between node (i, 2) and node (i, 1) on the workpiece surface can be expressed as follows:

Fig. 8.3 Heat transfer state at node (i, 1)

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8 Temperature Field Model and Experimental Verification on Cryogenic …

q(i+1,1)→(i,1) = k(Ti+1,1 − Ti,1 )

(8.7)

q(i,2)→(i,1) = k(Ti,2 − Ti,1 )

(8.8)

The above three equations are brought into Eq. (8.5), and temperatures at node (i,1) after the experience time Δt is calculated: Δt {k · [T (i − 1, 1) + T (i + 1, 1) + T (i, 2)−3T (i, 1)] ρw Cw Δl 2 + [q − G(Tt − Ta )] · Δl} + T (i, 1) (8.9)

Tt+Δt (i, 1) =

Similarly, temperature rise at other boundary conditions also can be solved by heat equilibrium equation. Temperature of pure minimum quantity of lubricating gases is similar with room temperature and the initial temperature is Tt=0 = 20 °C. Under CNMQL conditions, the measured temperature is used as the initial temperature.

8.2.2 Determination of Simulation Parameters Component contents and boiling point of synthesis liquid used in the experiment are listed in Table 8.8. Since dearomatization accounts for the highest proportion and has the lowest boiling point, the boiling point of grinding nanofluids is approximately 105 °C. Based on Eqs. (8.10) and (8.11), it can calculate that ΔT s = 2.1 °C and ΔT min = 122 °C. 

  Ts 2σ 2σ Ts2 1+ lg 1 + lg(1 + ) B r ps B r ps



1/2

1/3 ρg' ς g(ρg − ρl ) 2/3 σ μl = 0.127 ' Kg ρl + ρg g(ρg − ρl ) g(ρg − ρl ) ΔTs =

ΔTmin

(8.10)

(8.11)

where ΔT s is the minimum degree of superheat produced by bubbles (°C). r is the radius of the concave meniscus (mm). σ is a surface tension (N/m). B is a constant, ps = 0.1Mpa. T s is the saturated temperature (°C). pl refers to density of liquid (kg/m3 ). pg denotes density of air (kg/m3 ). μl denotes dynamic viscosity of liquid (kg/m3 ). ΔT min refers to the minimum degree of superheat from film boiling heat transfer (°C). p' g refers to the density of gas film (kg/m3 ). K' g expresses the heat transfer coefficient of gas film (kJ/[m K s]). Z is the latent heat (kJ/kg). According to the constructed heat transfer coefficient model in the grinding zone and combining with temperatures of grinding zone under different cooling modes, nanofluid droplets which are sprayed onto the grinding zone under NMQL condition are in the transition boiling heat transfer stage during which heat transfer coefficients in the transition boiling phase and nucleate boiling phase presents a linear variation

8.2 Numerical Simulation of Grinding Temperature Field

241

trend. Hence, heat transfer coefficients under different cooling modes can be calculated through linear interpolation method. The heat transfer coefficients under NMQL are divided into four stages for solving. Parameters of gas and droplet under NMQL condition are listed in Table 8.1. When the surface temperature of workpiece is smaller than 107.1 °C, the heat transfer surface may not develop boiling heat transfer. The convective heat transfer of normal-temperature air and enhanced convective heat transfer of nanofluids are major heat transfer modes, and the later one takes the dominant role. The convective heat transfer coefficient (h' a ) of normal-temperature air can be calculated from Eq. (8.12) according to the convective heat transfer coefficient between gas and walls. The heat transfer coefficients at turning points of different stages can be gained through Eqs. (8.12)–(8.16). Details are shown in Table 8.2. Through an interpolation Table 8.1 Given parameters Given parameters Numerical value Given parameters

Numerical value

Length of workpiece a (m)

Saturated temperature of nanofluid T s (°C)

105

Feeding speed of 0.067 workpiece vw (m/ s)

Temperature at initial point of nucleate boiling T n1 (°C)

107.1

Width of grinding 20 debris b (mm)

Temperature at initial point of transition boiling T n2 (°C)

157.1

Atmospheric 0.11 pressure po (Mpa)

Temperature at initial point of film boiling T n3 (°C)

227

Internal pressure of nozzle pa (Mpa)

0.4

Spreading radius of single droplet r su (μm)

120

Nanofluid supply in unit time Q' (μm3 /s)

1.39 × 1010

Specific heat capacity of droplets cl (J/ (kg K))

1870

Included angle 15 between droplet jetting direction and the horizontal direction θ (°)

Latent heat of droplet vaporization hfa (J/kg)

384,300

Velocity of gas v (m/s)

Surface tension of droplet σ (N/m)

1.84 × 10–2

Nanofluid density 665 ρ l (kg/m3 )

Heat conductivity coefficient of steam λv (W/m K)

0.02624

Nanofluid temperature T l (°C)

25

Dynamic viscosity of steam μv (Pas)

0.018448

Contact angle θ n (°)

42.5

Mass thermal capacity of steam cv (J/ (kg K))

1004

0.08

340

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8 Temperature Field Model and Experimental Verification on Cryogenic …

calculation, it calculates hn = 3.74 × 10 4 W/m2 K when the workpiece surface temperature is 214.1 °C. The heat transfer coefficients are shown in Fig. 8.4. When the pure compressed air or low-temperature cold air medium has enhanced convective heat transfer with workpiece surface, the convective heat transfer coefficient (ha ) of air and wall is: Table 8.2 Calculation results Given parameters

Values

Given parameters

Values

2.14 × 106

Non-boiling heat transfer coefficient hn1 (W/m2 K)

3.8 × 104

Single-droplet diameter d 0 (μm)

160

Maximum heat transfer coefficient hn2 (W/m2 K)

8.2 × 104

Number of droplets N l

7800

Heat transfer coefficient at initial point of the film boiling heat transfer hn3 (W/ m2 K)

2.92 × 104

Convective heat transfer coefficient of normal-temperature air h' a (W/m2 K)

278

Actual heat transfer coefficient under NMQL hn (W/m2 K)

3.74 × 104

Vertical velocity of droplet impacting onto the heat transfer surface vn (m/s)

10.8

Single-droplet volume V l

(μm3 )

Fig. 8.4 Effects of grinding surface temperature on the boiling heat transfer under NMQL condition

8.2 Numerical Simulation of Grinding Temperature Field

⎧ / h a = λa N μ l ⎪ ⎪ ⎪ ⎪ ⎨ N u = 0.906 Re1/2 Pr1/3 / ⎪ Re = v ' aρa l μa ⎪ ⎪ ⎪ / ⎩ Pr = μa ca λa

243

(8.12)

where λa is the thermal conductivity of air (W/[m2 K]). Nu is the Nusser number. l refers to the heat transfer width of the grinding zone (mm). Re is the Reynolds number. Pr refers to Prandtl number. v' a is the velocity of gas. ρ a denotes density of gas (kg/m3 ). μa is dynamic viscosity of gas (cP). ca refers to the constant pressure specific heat capacity of air (J/[kg K]). Nanofluid lubricant is sprayed onto the grinding zone through a minimum quantity lubricating device. The nanofluids sprayed in unit time can be discretized into Nl droplets with a volume of Vl [3]: ⎧ 3 rsur ⎪ f ⎪

V = ⎪ l

 2  ⎪ ⎪ ⎪ π 1 1 1 1 1 ⎪ 1 + − 1 − 1 ⎪ 2 tgθn cos θn 3 tg 2 θn cos θn ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ π d03 Vl = 6 ⎪ ⎪ ⎪ ' ⎪ ·t Q ⎪ ⎪ = N ⎪ l ⎪ Vl ⎪ ⎪ ⎪ ⎪ ⎪ ⎩t = a vw

(8.13)

where Q' refers to nanofluid supply in grinding time (μm3 /s). r surf is the spreading radius of a single droplet (μm). N l refers to number of droplets. t denotes the total time of grinding process (s). a denotes length of the workpiece (μm). vw is the feeding speed of workpiece (μm/s). V l refers to the volume of a single droplet (μm3 ). d 0 refers to the spherical radius of a single droplet (μm) and θ n is the contact angle (°). According Yang’s study on non-boiling heat transfer coefficient in the grinding zone, hn1 is expressed as [4]: h n1 =

Nl cl ρl Vl + h a' 2 πrsur · t f

(8.14)

where N l is the number of droplets, cl is the specific heat capacity of droplet (J/[kg K]). ρ l is the density of nanofluid (kg/m3 ). V l refers to volume of a single droplet (μm). r surf is the spreading radius of a single droplet (μm). T s is the saturated temperature (K). h' a refers to the convective heat transfer coefficient of normal-temperature air (W/[m2 K]). The heat transfer coefficient reaches the maximum (hn2 ) at the end point of nucleate boiling heat transfer, that is, the point of critical heat flux density. It reaches the minimum (hn3 ) at the end of transition boiling heat transfer, that is, the initial

244

8 Temperature Field Model and Experimental Verification on Cryogenic …

point of film boiling heat transfer. The value of hn2 is [1]: h n2 =

[h f a + cl (Ts − Tl )]Q ' ρl + h a' 2 πrsur f (Tn2 − Tl )

(8.15)

where q' a is the convective heat transfer volume of normal-temperature air. N l is the number of evaporated droplets. cl is the specific heat capacity of droplets (J/(kg K)). hfa is the latent heat of vaporization. T s is the saturated temperature (K). T n2 is the temperature at the initial point of the transition boiling heat transfer (K). T l refers to the nanofluid temperature (K). The value of hn3 is [1]: √ ⎧ 0.08 ln(W e/35+1) −90 ' B 1.5 ⎪ Q ρ [h + c (T − T )] · [0.027e + 0.21kd Be W e+1 ] N l l fa l s l ⎪ ⎪ h n3 = + h a' ⎪ ⎪ ⎪ b · lc · (Tn3 − Tl ) ⎪ ⎪ ⎪ ⎪ ρl d0 vn2 ⎪ ⎪ ⎪ W e = ⎪ ⎪ ⎪ ⎪ / σ ⎪ '2 ⎪ pa − p0 ⎪ + 16Q ⎨ ρl π 2 d02 vn = · cos θ 1+ε ⎪ ⎪ ⎪ ⎪ cv (Tne − Ts ) ⎪ ⎪ ⎪ ⎪B = ⎪ h fa ⎪ ⎪ / ⎪ ⎪ ⎪ lc = a p · ds ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ k d = λv cv μv (8.16)

where pa is internal pressure of the nozzle (Pa). po is the atmospheric pressure (Pa). vl refers to the droplet jetting speed along the nozzle direction (m/s). vn is the vertical velocity of droplets impacting onto the heat transfer surface (m/s). b is the width of grinding zone (mm). lc refers to the length of the contact arc (mm). λv is heat conductivity coefficient (W/[m K]) of steam. μv is the dynamic viscosity of steam (cP). cv is the mass heat capacity of steam (J/[kg K]). θ is the included angle between the droplet jetting direction and the horizontal direction (°). σ is the surface tension (N/m). Similarly, heat transfer coefficients at turning points in different heat transfer stages under CNMQL are calculated by using the same calculation method. Next, the actual heat transfer coefficient in these stages are calculated through interpolation method. The calculated heat transfer coefficients under three working conditions are listed in Table 8.3. The heat flux density and proportional coefficient of energy are calculated by Eqs. (8.17) and (8.18). The heat flux density in the workpiece is:

8.2 Numerical Simulation of Grinding Temperature Field

245

Table 8.3 Temperature and heat transfer coefficient of grinding zone under different conditions Cooling modes

Temperature T(°C)

Heat transfer coefficients h (W/m2 K)

NMQL

214.1

3.74 × 104

CA

197.5

221

CNMQL

155.9

4.38 × 104

qw =

qw vs Ft vs Ft = ·R= / ·R qtotal blc b ds a p

(8.17)

where qw is the heat flux density in the workpiece (J/[m2 K s]). qtotal is the total heat flux density (J/[m2 K s]). F t is tangential grinding force. vs is the linear velocity of grinding wheel (m/s). lc refers to the contact arc length of workpiece and grinding wheel. b refers to grinding width (mm). Ds is the equivalent diameter of grinding wheel (mm). ap is the grinding depth (μm). The proportional coefficient (R) of energy transferred into the workpiece is [5]: 1/2

R=

kw vw

θ 1/2 1/4 1/4 max

qtotal βαw a p ds

(8.18)

where β is a constant. α w is the thermal diffusivity of workpiece (m2 /s). θ max is the maximum temperature rise (°C).

8.2.3 Numerical Simulation Results A simulation analysis of temperature field in the grinding zone of grinding wheel and workpiece under three cooling modes was carried out based on the Matlab simulation platform. The overall changes of heat source in the grinding zone from cut-in to cut-out under NMQL are shown in Fig. 8.5. The simulation images of grinding temperature changes at one point on the workpiece under different cooling conditions with time are shown in Fig. 8.6. It can be seen from Figs. 8.5 and 8.6 that the grinding temperature in the grinding wheel-workpiece contact area is the highest (red region), and the workpiece temperature declines gradually after the heat sources passes by. Temperature rise mainly concentrates at the heat source point and the region that the heat source just passes by. Due to low heat conductivity coefficient of Ti alloy, temperature of the unprocessed surface is always close to the environmental temperature before the grinding wheel grinds to the grinding point, without showing obvious temperature changes [6, 7]. When the grinding wheel grinds to the grinding point, the workpiece surface temperature increases dramatically, but the temperature declines slowly after the grinding wheel leaves the point until reaching the environmental temperature finally. According to analysis, the simulation results conforms to the variation trend of grinding temperature in the actual grinding process.

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8 Temperature Field Model and Experimental Verification on Cryogenic …

Fig. 8.5 Simulation phase diagram of grinding surface temperature field under NMQL condition

Fig. 8.6 Simulation curves of grinding surface temperature field under different conditions

8.3 Experimental Verification

247

8.3 Experimental Verification 8.3.1 Experimental Equipments Experimental equipments: a precise numerical control (NC) surface grinder is used and its parameters are shown in Table 8.4. A GC80K12V SiC grinding wheel (300 mm × 20 mm × 76.2 mm) is applied. The nanofluid lubricant is transformed to the grinding zone by a nozzle through the KS-2106 minimum quantity lubrication supply device for cooling and lubrication. VC62015G vortex tube is used as the low-temperature cold air supply device. The YDM-III99 three-way grinding dynamometer is applied for real-time recording and measurement of threeway grinding forces. The MX100 thermocouple is used for online recording and data measurement of grinding temperature. Experimental equipments are shown in Fig. 8.7. The measurement of grinding force and grinding temperature is shown in Fig. 8.8. Table 8.4 Parameters of K-P36 grinder Grinder performances

Parameters

Power of the principal axis (KW)

4.5

Maximum speed of revolution of principal axis (r/min)

4800

Size of worktable (m)

0.95 × 1

Maximum transverse feeding speed (m/min)

30

Maximum longitudinal feeding speed (m/min)

4

Fig. 8.7 Experimental equipments. (1) delivery pipeline, (2) oil storage cup, (3) Lubricants, (4) pressure regulator, (5) intake valve, (6) pressure control valve, (7) plunger pump, (8) grinding wheel, (9) Workpiece, (10) Dynamometer, (11) Staging, (12) temperature control valve, (13) hot end outlet, (14) gas inlet, (15) cold air outlet, (16) cold air nozzle

248

8 Temperature Field Model and Experimental Verification on Cryogenic …

Fig. 8.8 Schematic diagram of grinding force and grinding temperature measurement

Measuring equipments: the TIME3220 surface roughometer is applied to measure surface roughness of the workpiece after grinding. The workpiece surface morphology and grinding debris morphology after processing are observed and measured by using the S-3400N SEM (Hitachi). The surface tension is measured by the BZY-201 automatic surface tension meter. Viscosity of nanofluid and contact angle of oil film are measured by the DV2TLV digital viscometer and JC2000C1B contact angle gauge, respectively. The i-speed TR high-speed camera is used to measure the atomizing angle of nanofluid droplets sprayed from the nozzle. The gas flow rate is measured by using the DN15 vortex flow meter. The measuring equipments are shown in Fig. 8.9. To assure accuracy of experimental results and the same experimental conditions, the grinding wheel was dressed before each group of experiment and the dressing parameters of grinding wheel are listed in Table 8.5.

8.3.2 Experimental Materials Ti-6Al-4 V (80 mm × 20 mm × 40 mm) was used as the workpiece material in the experiment. Due to a series of good machining and mechanical properties like the high hardness, high strength, good thermos ability, corrosion resistance and rich reserves, Ti alloy is applied more and more in airline, aerospace, navigation and other industrial sectors. Nevertheless, Ti alloy becomes a kind of difficult-to-process materials due to hard hardness and low thermal conductivity, and it may produce high-temperature and high stress in processing, thus deteriorating the surface quality of workpieces and serious wearing of cutters [3, 4]. Ti-6Al-4 V is one type of Ti alloy which is applied the most extensively. Therefore, how to improve processing quality of Ti-6Al-4 V effectively and control grinding burn of boards is of important significance. Element composition of workpiece materials is presented in Table 8.6. The physical properties of materials are exhibited in Table 8.7.

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Fig. 8.9 Measuring equipments Table 8.5 Dressing parameters of grinding wheel Dressing parameters

PCD dresser

Single-point dressing volume (mm)

0.01

Horizontal feed rate (mm/rev)

0.5

Number of stroke

30

Table 8.6 Element composition of Ti-6Al-4 V Workpiece materials

Workpiece base

Alloy element (wt/ %)

Other elements (wt/%)

Ti-6Al-4 V

Ti

Al

V

Fe

Si

C

N

H

O

5.5–6.75

3.5–4.5

0.3

0.1

0.08

0.05

0.015

0.01

Table 8.7 Physical characteristics of Ti-6Al-4 V Thermal conductivity (W/m·K)

Specific heat (J/ kg·K)

Density (g/ cm3 )

Modulus of elasticity / GPa

Poisson’s ratio

Yield strength / MPa

Tensile strength / MPa

7.955

526.3

4.42

114

0.342

880

950

Table 8.8 Composition and boiling point of the synthesis lipid Components

Dearomatization

Bisadipate

Pentaerythritol ester

Tricresyl phosphate (TCP)

Content (%)

60

20

10

10

Boiling point (°C)

105

109

380.4

265

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8 Temperature Field Model and Experimental Verification on Cryogenic …

Table 8.9 Physical properties of Al2 O3 nanoparticles Grain size (nm)

Crystal structure

Melting point (°C)

Apparent density (g/ cm3 )

Thermal conductivity (W/ m K)

Color

Moh’s hardness

50

Hexagonal close packing

2050

0.33

36

White

8.8.9.0

In this experiment, KS-1008 synthesis lipid was chosen as the base oil of MQL and Al2 O3 nanofluid lubricant (volume fraction: 2%) was prepared by using Al2 O3 nanoparticles as the additives. According to Wang’s study [8], Al2 O3 nanoparticles have good lubrication and tribological properties compared to other nanoparticles. Since nanoparticles are very easy to agglomerate in base oil, adding appropriate amount of dispersing agent into the suspension liquid is conducive to improve dispersion stability of nanofluid. Some study has found that adding the surfactant of sodium dodecyl sulfate (SDS) into nanofluid can hardly influence the tribological properties of nanofluids, but can increase the dispersion and stability of nanofluid effectively [9]. In this experiment, Al2 O3 nanofluid was prepared by a two-step method. Firstly, Al2 O3 nanoparticles were added into the KS-1008 MQL base oil in the proportion of 2% (volume fraction). Next, 0.1% (volume fraction) SDS was added in, followed by the mechanical stirring and oscillation in the ultrasonic oscillator (KQ3200DB) for a period (2 h) to improve dispersion and suspension stability of nanofluids [10]. The component contents and boiling point of KS-1008 synthesis lipid are listed in Table 8.8. The physical properties of Al2 O3 nanoparticles are listed in Table 8.9.

8.3.3 Experimental Design The Ti-6Al-4 V was used as the workpiece material to explore cooling and heat transfer performances in the grinding zone under low-temperature cold air (CA), NMQL and CNMQL modes. The grinding experimental parameters are shown in Table 8.10. Through measurement of thermocouple and vortex flow meter, the fluid temperature and gas flow rate at nozzle outlet under three cooling modes are gained (Table 8.11).

8.3.4 Experimental Results The variation curves of grinding temperature with time in the grinding process under three cooling modes are shown in Fig. 8.10. The maximum temperatures of grinding zone under three cooling modes are shown in Fig. 8.11, and the error bars represent standard deviation (SD) of grinding temperature. Clearly, the maximum grinding

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251

Table 8.10 Grinding experimental parameters Grinding type

Plane grinding

Grind wheel type

SiC ceramic grinding wheel with binding agent

Cooling mode

CA, NMQL, CNMQL

Linear velocity of grinding wheel V s (m/s)

30

MQL flow rate (ml/h)

50

Feeding speed of workpiece V w (mm/min)

4000

Cutting depth ap (μm)

10

Gas flow rate (m3 /h)

25

Nozzle distance d (mm)

12

Nozzle angle α (°)

15

Atmospheric pressure P (MPa)

0.7

Table 8.11 Fluid temperature and gas flow at nozzle outlet Lubrication modes

Fluid temperature at nozzle (°C)

Gas flow rate (m3 /h)

CA

−5

10

NMQL

25

25

CNMQL

−5

10

temperature (214.1 °C) is achieved under NMQL, which reflects the insufficient cooling effect of NMQL mode. Due to the excellent cooling and heat transfer capacity of cold air, the grinding temperature of CA is 197.5 °C, which is about 17 °C lower compared to that under NMQL. CNMQL has advantages of both NMQL and CA. With good cooling and lubrication effects, CNMQL acquires the lowest grinding temperature (155.9 °C), which is about 42 °C (21%) lower than that under CA and about 60 °C (28%) lower than that under NMQL.

8.3.5 Comparison of Simulation and Experimental Results The comparison of simulation and experimental results of workpiece surface temperature under CNMQL is shown in Fig. 8.12. The variation curve of the simulated temperature is basically consistent with that of measured temperature. According to comparison between simulation and experimental data of highest workpiece surface temperature, it found that the difference between simulation and experimental results is only 7.9 °C, with a small error of 5.1%. Moreover, the simulation temperature on workpiece surface is higher than experimental temperature for following reasons. During simulation calculation, the model hypothesizes that heats transferred into the workpiece during grinding are not dissipated into external environment any more. In fact, some heats transferred into the workpiece will continue to transfer into the

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8 Temperature Field Model and Experimental Verification on Cryogenic …

Fig. 8.10 Relation curves of grinding temperature and time under different conditions

Fig. 8.11 Maximum grinding temperature under different conditions

workpiece and some will transfer to the side surface of workpiece materials. Besides, partial heats on workpiece surface are carried away by grinding fluid and surrounding air. Finally, heats which actually enter into the workpiece materials decrease [11]. As

8.4 Experimental Results Analysis and Discussion

253

Fig. 8.12 Comparison between simulation and experimental results of workpiece surface temperatures

a result, the measured temperature is lower than the simulation temperature. Generally speaking, the simulation temperature and experimental temperature agree highly and the model has some reliability.

8.4 Experimental Results Analysis and Discussion 8.4.1 Specific Grinding Force Grinding force can represent lubrication effect on the grinding wheel-workpiece interface. The smaller grinding force implies the lower energy consumption for the same volume of material removal, the better lubrication effect and the better grinding performances. Grinding force is mainly characterized by tangential and normal grinding forces. Specific grinding force refers to the mean loads that is actually born by grinding wheel per unit width. The calculation formulas of specific tangential grinding force and specific normal grinding force are: Ft' =

Ft b

(8.19)

Fn' =

Fn b

(8.20)

254

8 Temperature Field Model and Experimental Verification on Cryogenic …

Fig. 8.13 Specific grinding force under different conditions

where F' t and F' n are specific tangential grinding force and specific normal grinding force, respectively (N/mm). b refers to the workpiece width (mm). F n and F t are the corresponding actual tangential grinding force and normal grinding force (N), respectively. The specific tangential grinding force and specific normal grinding force under CA, NMQL and CNMQL are shown in Fig. 8.13. Error bars represent SD of grinding forces. It can be seen from Fig. 8.13 that under three cooling and lubrication modes, CNMQL gets the minimum specific tangential grinding force (2.17 N/mm) and specific normal grinding force (2.66 N/mm). The specific tangential grinding force and specific normal grinding force under NMQL and CA are increased to different extents. Specifically, the specific tangential grinding force and specific normal grinding force under NMQL are 2.43 and 3.06 N/mm, which are increased by 12.3% and 15.0% than those under CNMQL, respectively. The specific tangential grinding force and specific normal grinding force under CA are the highest (3.66 and 4.36 N/ mm), which are increased by 69.1% and 63.9% compared to those under CNMQL. Due to the lubrication of lubricant, CA generates a great specific grinding force and the energy consumption for material removal per unit volume is far higher than those under NMQL and CNMQL. Since nanofluid has good lubrication effect in the grinding zone, NMQL gains smaller specific grinding force than CA. CNMQL integrates advantages of CA and NMQL, and achieves the optimal lubrication effect. The specific grinding force is decreased significantly and the processing quality of workpiece is increased under CNMQL.

8.4 Experimental Results Analysis and Discussion

255

8.4.2 Cooling Performance Evaluation Under Different Working Conditions According to comparison of grinding temperatures under CA, NMQL and CNMQL, it concludes that CNMQL presents the optimal cooling performances, followed by CA and NMQL successively. Although the lubricant consumption is extremely small under NMQL, based on transportation of high-pressure gases, the nanofluid lubricant can break the air barrier produced by rotation of the grinding wheel and enter into the grinding zone to form lubricating oil film, thus providing good lubrication effect. This decreases grinding force to some extent and decreases heat generation in the grinding process [12]. Al2 O3 is a kind of compact packing crystal with extremely strong lattice energy as well as extremely melting and boiling points [13]. The melting point of Al2 O3 reaches as high as 2050 °C and it possesses good heat resistance. Hence, Al2 O3 nanoparticles can increase thermos ability of the lubricating oil film and strengthen the friction and wearing performances under high temperature. Moreover, Moh’s hardness of Al2 O3 can reach 8.8–9.0. Due to the high hardness, Al2 O3 has excellent anti-wear properties and it can decrease the actual grinding wheel-workpiece contact area as well as grinding force effectively. Therefore, Al2 O3 can weaken furrow effect of microbulges on grinding wheel surface to some extent. On the other hand, the lubricating oil film formed by nanofluids in the grinding zone also hinders heat transmission into the workpiece to some extent. With respect to the cooling mechanism, heats in the grinding zone are carried away through forced convection of normal-temperature air and vaporization and absorption of minimum quantity lubricating oil under high temperature, thus lowering the temperature of the grinding zone. As a result, the cooling performance is unsatisfying. Finally, the highest grinding temperature is gained. CA acquired lower grinding temperature than NMQL. Without lubricant, it fails to form good lubrication effect in the contact zone under CA, thus resulting in the great grinding force and heat consumption for workpiece material removal. With respect to cooling mechanism, the grinding zone cooling by normal-temperature cold air under CA and NMQL conditions belongs to forced convective heat transfer, but there’s a difference in temperature of compressed air involved in the forced convection. The low-temperature cold air is carried by the low-temperature high-pressure air. The temperature gap between the low-temperature cold air and grinding contact surface is widened and the convective heat transfer effect is strengthened, thus carrying away more heats. As a result, temperature of grinding zone is decreased. Although AC lacks of lubricant and may consume plenty of heats during material removal through grinding, the excellent cooling and heat transfer capacity offset such disadvantages. AC achieves better cooling effect than NMQL. CNMQL achieves the optimal cooling and lubrication effect and thereby gets the lowest grinding temperature since it integrates advantages of both NMQL and CA. CNMQL has better cooling effect than NMQL and CA for following reasons. Firstly, the lubrication effect of grinding fluid under CNMQL condition is better

256

8 Temperature Field Model and Experimental Verification on Cryogenic …

than that under NMQL, thus consuming fewer heats for grinding of workpiece materials. Nanofluid properties change with temperature of grinding zone. Due to the lower temperature, the lubricating oil film formed on the workpiece surface in the grinding zone has better lubrication performances and energy consumption for material removal is decreased, thus achieving better lubrication effects. The viscosity of lubricant is negatively related with temperature. Temperature of grinding zone under CNMQL is about 60 °C lower than that under NMQL, thus showing the higher liquid viscosity. With the increase of viscosity, the lubricant presents excellent stickiness on the grinding wheel-workpiece interface. Additionally, the formed oil film is relatively thick, which improves the lubrication performance and prolongs time of lubrication, thus decreasing energy consumption during grinding effectively. under NMQL, the nanofluid lubricant has a lower value of viscosity due to the high temperature in the grinding zone and viscosity of lubricant is poorer than that under CNMQL. The formed lubricating film is relatively thin and the lubrication effect is unsatisfying, which incurs a great energy consumption. Because of the insufficient heat transfer capacity of NMQL, the lubricating oil film is extremely easy to break under high temperatures, which decreases the lubrication effect and increases inputs of grinding force and grinding heats. Adding lowtemperature cold air increases stability of the lubricating oil film and decreases inputs of grinding heats. Besides, the heat transfer effect under CNMQL is better compared to those under NMQL and CA. The maximum temperature of the grinding zone under CNMQL is 155.9 °C, which decreases by 28% (about 60 °C) than that under NMQL. The low-temperature cold air is carried by low-temperature high-pressure air. It expands the temperature gap between heat transfer medium and grinding wheelworkpiece contact zone. The low-temperature cold air is far superior to normaltemperature air in term of enhanced convective heat transfer effect. Hence, the lowtemperature cold air carries away more heats from the grinding zone and thereby decreases temperature of grinding zone.

8.4.3 Boiling Heat Transfer Analysis Among heats carried away from the grinding zone, most heats are carried away by boiling heat transfer of grinding fluid except for a small amount of heats carried away by the enhanced convective heat transfer in the grinding zone. When grinding temperature reaches a specific value, grinding fluid may be boiled and vaporized after entering into the grinding zone [14]. Mao et al. [1] studied the heat transfer mechanism on workpiece surface in the grinding process and constructed a boiling heat transfer model of workpiece surface. According to an experimental study, they found that their heat transfer mechanism was credible. Boiling heat transfer is a heat transfer mode that bubbles move to carry away heats and realize cooling effect. It is a violent evaporation process that a lot of steam bubbles are produced, grown and carry away heats by transforming working medium from liquid state to gas state. Boiling

8.4 Experimental Results Analysis and Discussion

257

Fig. 8.14 Schematic diagram of boiling heat transfer in grinding zone

heat transfer in the grinding zone is a heat transfer process accompanied with gas– liquid changes of grinding fluid. According to flow characteristics of boiling fluid, boiling can be divided into pool boiling and flow boiling. Boiling heat transfer in the grinding process can be approximately viewed as flow boiling heat transfer, because nanofluid cooling liquid is carried by low-temperature high-pressure gases and moves toward a direction, thus causing boiling heat transfer phenomenon in the high-temperature grinding zone [15]. The boiling heat transfer in the grinding zone is shown in Fig. 8.14. In the beginning of boiling heat transfer in the grinding process, grinding fluid absorbs latent heats on workpiece, pipelines of debris tubes and surface cracks, generating and becoming the vaporization core [16]. The bubble volume continues to increase with the continuous heat transfer from high-temperature surface into the vaporization core. Heats are carried away until they leave from the workpiece surface under the action of buoyancy force. With the continuous supply of cooling liquid by the low-temperature compressed gas, countless bubbles are generated, grown and finally vaporized to absorb and carry away grinding heats. This process repeats continuously until realizing the goal of lowering temperature of the grinding zone. The boiling heat transfer process of liquid generally can be divided into two stages: (1) vaporization and absorption of latent heat (hereinafter referred as Stage 1); (2) vaporization and heat transfer (hereinafter referred as Stage 2). Latent heat means the absorbed or released heat in the process that substances changes from one phase to another phase under the constant temperature. It is a state variable. It won’t cause temperature rise (or drop) when the substance absorbs (or releases) latent heats. Latent heat only has potential effects on temperature changes. Latent energy is composed of two parts. One is difference between two phases of internal energy (internal latent heat) and power to overcome external pressure during phase change (external latent heat). Some absorbed latent heats at boiling of liquid are used to overcome attractive forces among molecules, and the rest are used to resist atmospheric pressure in the swelling process. Let U 1 and U 2 be the internal energy of Phase-1 and Phase-2 per unit mass, and V 1 and V 2 be the volumes of Phase-1 and Phase-2 per unit mass. Hence, the latent heats of phase change which are absorbed by unit mass substance during transformation from Phase-1 to Phase-2 can be expressed as follows:

258

8 Temperature Field Model and Experimental Verification on Cryogenic …

I = (U2 − U1 ) + (V2 − V1 ) = h 2 − h 1

(8.21)

where h1 and h2 are enthalpies of phase-1 and phase-2 per unit mass. (U 2 − U 1 ) refers to the internal latent heat absorbed by vaporization of liquid. p·(V 2 − V 1 ) denotes the external latent heat absorbed by vaporization of liquid. The initial temperature of cooling liquid carried by low-temperature cold air (−5 °C) under CNMQL (hereinafter referred as the former one) is significantly lower than the temperature (25 °C) of cooling liquid carried by normal-temperature cold air under NMQL (hereinafter referred as the later one). Since kinetic energy of liquid molecules decrease with the drop of temperature, the difference between gas and liquid phases is intensified accordingly. Moreover, since mean initial volume of evaporation core of the former one is smaller than that of the later one, it requires a lower energy for gasification and it is easier to be evaporated. Hence, (U 2 − U 1 ) of the former one is significantly higher compared to that of the later one and vaporization of liquid has to absorb fewer heats from the external environment. As a result, absorbed heats in the grinding zone in Stage 1 are far higher than that of the later one. In Stage 1, liquid only absorbs heats from the grinding zone, but its temperature is always kept constant. After finishing this stage, it enters into Stage 2: heats are transferred into the vaporization core continuously from the high-temperature surface. The steam bubbles grow continuously and temperature keeps rising until they leave from the workpiece surface and carry away heats under action of buoyant force. At this moment, the boiling heat transfer is completed. Given the same specific heat of cooling liquid, the temperature gap of cooling fluid from Stage 1 to the saturated temperature under CNMQL condition is higher than that under NMQL condition, so the heats absorbed in Stage 2 is also higher than that of the later one. Based on above analysis, heats carried away from the grinding zone under CNMQL condition in both Stage 1 and Stage 2 are higher compared to those under NMQL condition, indicating the better comprehensive heat transfer effect of CNMQL mode.

8.4.4 Effects of Workpiece and Debris Surface Characteristics on Cooling Heat Transfer In grinding process of metal materials, the key whether grinding fluid can develop the optimal cooling effect fully and effectively lies in that whether the grinding fluid can spread over the grinding zone timely and fully and thereby carry away heats produced in the grinding zone through boiling heat transfer. Due to the blocking effect of the strong hydrodynamic pressure produced by the air barrier on surface, only 5%-40% cooling fluid arrive at the grinding contact zone actually to provide cooling effect [17]. A lot of grinding fluid cannot enter into the grinding zone and grinding burn of the workpiece occurs, thus resulting in the poor surface quality of processed workpiece [1].

8.4 Experimental Results Analysis and Discussion

259

Since the grinding surface is composed of abundant irregular scattering grains, the workpiece surface may develop furrows, plastic deformation layer and microcracks with different depths in the grinding process. Meanwhile, some grinding debris is easy to be adhered onto the workpiece surface again under high temperature rather than separating from the grinding zone timely, forming micro-bulges. Because of these tribological properties of interfaces, micron-sized long and thin pipelines with different depths are produced on the grinding wheel and workpiece surface. The surface microtopography of workpieces under NMQL and CNMQL conditions is shown in Fig. 8.15, showing great differences. Under NMQL condition, there are obvious plastic deformation layers and deep and long furrows on the workpiece surface, accompanied with serious adhesion and material deposition phenomenon. These hinders longitudinal flow and transverse spreading effect of lubricant on workpiece surface along pipelines to some extent, which further influences the overall penetration process of lubricant on workpiece surface and weakens the lubrication effect, thus increasing energy consumption and heat accumulation. Given insufficient lubrication performances, grains are embedded into the workpiece during processing and cut furrows with different depths on the workpiece surface. The removed grinding debris cannot be separated from the grinding zone timely and effectively, and thereby is adhered onto the high-temperature workpiece surface with the continuous feeding and extrusion of the grinding, thus forming plastic deformation layers. The workpiece surface has relatively explicit and smooth grinding pipeline textures under CNMQL mode, accompanied with mild plastic deformation and material adhesion. Furrows are hardly developed. Due to the small barrier against flowing and spreading of lubricant along pipelines, the lubricant has better overall penetration effect on the workpiece surface. Meanwhile, micro-sized pipelines will be formed on the grinding wheel-debris contact surface due to scratching and ploughing effects when grinding debris moves and is removed along the rotation direction of the grinding wheel. The low-temperature grinding fluid for MQL sprayed by the nozzle through the grinding process will flow into these micro-sized pipelines successively. The grinding fluid flows in from ends of pipelines and flows forward quickly along

Fig. 8.15 Surface microtopography of workpiece

260

8 Temperature Field Model and Experimental Verification on Cryogenic …

Fig. 8.16 Bottom surface topography of debris

them by the high kinetic energy brought by high-pressure gases, forming a layer of cooling oil film with good spreading effect on the workpiece and debris surfaces [8]. Furthermore, the spreading area of cooling liquid is expanded due to the geometric shape of pipelines on workpiece and debris surfaces. Lattice displacement of stresses may occur on the workpiece material as a response to the continuous scratching, ploughing and cutting effects by the grinding wheel in the grinding process, which further brings plastic deformation and hardening phenomenon. As a result, the bottom surfaces of grinding debris are curled up gradually during material removal and present corrugated gullies in Fig. 8.16. The geometric shapes of such corrugated gullies increase the surface area of grinding debris significantly. The spreading and dynamic heat transfer areas of cooling liquid are expanded greatly because of geometric shapes of workpiece and debris surfaces, so that more cooling liquid can carry away heats from the grinding zone through boiling heat transfer, thus realizing the cooling and heat transfer effect. The total heat exchange capacity of the grinding zone is: ϕ = q A = AhΔt

(8.22)

where q refers to the heat transfer amount between solid surface and heat transfer fluid in the grinding zone per unit area in unit time (J/[m2 K s]). A refers to the heat transfer area of the grinding zone (mm2 ) and h expresses the overall heat transfer coefficient of the grinding zone (W/[m2 K]). Δt refers to the temperature gap between the grinding zone and cooling fluid (°C) and it increases by low-temperature cold air. The value of h under CNMQL condition is also increased to some extent compared to traditional working conditions. The dynamic heat transfer area (A) of the grinding zone also expands due to the morphological features of the workpiece and debris, which brings an increase in the total heat transfer amount in the grinding zone. The cooling and heat transfer effect under the CNMQL conditions is improved significantly compared

8.5 Summary

261

to that under traditional conditions. To sum up, CNMQL achieves the most excellent cooling and heat transfer effect under the collaborative action of low-temperature cold air and nanoparticles.

8.5 Summary Simulation analyses and verification experiments of plane grinding temperature field of Ti–6Al–4 V under CA, NMQL and CNMQL conditions are carried out in this chapter. Moreover, simulated and experimental temperatures of grinding zones are compared. The cooling and lubrication mechanism of the grinding zone under different cooling modes is further discussed from perspectives of grinding force, viscosity of nanofluid, stability of oil film, morphological features of workpiece and debris as well as boiling heat transfer effect. Some major conclusions could be drawn: 1. With reference to theories of boiling heat transfer and grinding heat transfer, heat transfer coefficients of the grinding zone and FDM models under different cooling modes (CA, NMQL and CNMQL) are constructed based on the fact that different boiling heat transfer states are corresponding to different heat transfer capacities. 2. Numerical simulation analyses of temperature field in the grinding zone under CA, NMQL and CNMQL modes are carried out based on numerical models. The simulation laws conform to the variation trend in actual grinding process. Verification experiments of plane grinding are conducted based on theoretical simulation, and the same laws are acquired in model simulation and experiments. CNMQL achieves the optimal cooling effect and the lowest grinding temperature (155.9 °C), followed by CA and NMQL successively. Besides, CNMQL shows the best lubrication effect and the minimum specific tangential grinding force (2.17 N/mm) as well as the minimum normal grinding force (2.66 N/mm), indicating the excellent cooling and heat transfer effect of CNMQL. Generally speaking, the simulation data conforms highly to experimental data and the simulation model is reliable to some extent. 3. The maximum temperature of the grinding zone under CNMQL condition is decreased by nearly 60 °C than that under NMQL condition. Hence, the lubricant has the higher viscosity and shows good stickiness on the grinding wheelworkpiece interface. Besides, the formed oil film is relatively thick, which improves the lubrication performances and prolongs the lubrication time. On one hand, it decreases energy consumption in the grinding process effectively and achieves better lubrication effect. On the other hand, it can decrease the occurrence of high temperature-induced breakage and evaporation of the oil film for its characteristics and the low grinding temperature. As a result, it decreases the probability for local dry friction in a short period, improves stability and lubrication effect of oil film, and reduces inputs of grinding force as well as heats.

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4. The initial temperature (−5 °C) of cooling liquid carried by low-temperature cold air under CNMQL condition is far lower than the temperature (25 °C) of cooling liquid carried by the normal-temperature cold air under NMQL condition. Under the CNMQL condition, there’s a great temperature gap (Δt) between grinding fluid and its saturated temperature. Since the kinetic energy of liquid molecules decreases with the reduction of temperature, the temperature gap between gas and liquid phases also expands accordingly. Moreover, the vaporization core in the former one has smaller mean initial volume and it absorbs more energy for vaporization of droplets. Therefore, it can absorb and carry away more heats in the whole boiling heat transfer process. 5. There are explicit and smooth grinding pipelines on workpiece surface under the CNMQL condition, accompanied with mild plastic deformation and material adhesion phenomena. However, furrows are hardly developed. With small barriers against flowing and spreading of lubricant along pipelines, the overall penetration effect of lubricant on workpiece surface is better. Meanwhile, the bottom surfaces of grinding debris are curled up gradually upon stresses in the process of material removal and present corrugated gullies, which expands the adsorption area of grinding fluid. The spreading and dynamic heat transfer areas of cooling liquid are expanded significantly due to geometric shapes of workpiece and debris surface, so that more cooling liquid can carry away heats in the grinding zone through boiling heat transfer. It achieves good cooling and heat transfer effect. 6. Based on experimental results and analysis, CNMQL which integrates advantages of CA and NMQL shows excellent grinding performances and achieves excellent cooling and lubrication effects. Moreover, it has promising application prospects in the processing field for its low cost and environmental-friendly characteristics.

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Chapter 9

Convective Heat Transfer Coefficient Model Under Nanofluid Minimum Quantity Lubrication Coupled with Cryogenic Air Grinding Ti-6Al-4V

9.1 Introduction The numerical simulation and experimental study of grinding temperature field have proved that CNMQL grinding can increase cooling and heat transfer capacity of the grinding zone significantly to lower local temperature and control grinding burns [1]. Nevertheless, adding low-temperature cold air may influence temperature and flow rate of nanofluids sprayed onto the grinding zone, and thereby influence its viscosity, surface tension, contact angle and breaking state of droplets, finally affecting the lubrication performances of nanofluids. Based on Chap. 8, the lubrication mechanism of CNMQL grinding is further explored in this chapter.

9.2 Experimental Design 9.2.1 Experimental Equipments Experimental and measuring equipments are consistent with those in Sect. 8.2.1. Experimental equipments: a precise NC grinder, a YDM-III99 three-way grinding dynamometer, MX100 thermocouple, SiC ceramic grinding wheel with binding agent, KS-2106 minimum quantity lubrication supply device and VC62015G vortex tube. Measuring equipments: TIME3220 surface roughometer, S-3400N SEM, BZY201 automatic surface tension meter, DV2TLV digital viscometer, JC2000C1B contact angle gauge, i-speed TR high-speed camera, and DN15 vortex flow meter.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_9

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9.2.2 Experimental Materials The used experimental materials and treatment are also completely the same with those in Sect. 8.2.2. Ti-6Al-4V was chosen as the workpiece material and KS-1008 synthesis lipid was used as the base oil of MQL. The 2% (volume fraction) Al2 O3 nanofluid lubricant was prepared by using Al2 O3 nanoparticles as the additive and SDS as the surfactant. Al2 O3 nanofluid was prepared by using two-step method.

9.2.3 Experimental Schemes Ti-6Al-4V was chosen as the workpiece material. Given the other grinding parameters, numerical values of specific grinding energy and friction coefficient under CA, NMQL and CNMQL modes were compared. Lubrication performances of CA, NMQL and CNMQL modes were further discussed from oil film state of the grinding zone, atomization angle and workpiece surface morphology. Since the workpiece surface quality when the flow rate of the MQL oil was 50 ml/h was not satisfying in Chap. 8 and it had some phenomena of plastic deformation and material adhesion, the flow rate of the MQL oil was adjusted to 90 ml/h. The rest grinding parameters were consistent with those in Chap. 8.

9.3 Experimental Results 9.3.1 Specific Grinding Energy Specific grinding energy not only is an important index to measure grinding efficiency, but also characterizes lubrication effect on the grinding wheel-workpiece grinding interface. The smaller specific grinding energy indicates the lower energy consumption for removing the same volume of materials, and the better lubrication effect and grinding performances [2]. In the measurement process, means of data measurement results of 10 grinding strokes were calculated as the experimental results of grinding force. The measured tangential grinding force was brought into Eq. (9.1) to calculate specific grinding energy under different lubrication conditions. The specific grinding energy under CA, NMQL and CNMQL modes are shown in Fig. 9.1 and the error bars represent SD. Clearly, CNMQL gets the minimum specific grinding energy 51.96 J/mm3 , while the specific grinding energy under NMQL and CA is increased to different extents. Specifically, the specific grinding energy under NMQL is 58.37 J/mm3 , which is increased by 12.3% than that under CNMQL. The specific grinding energy under CA is the highest (87.84 J/mm3 ), which is 69.1% higher compared to that under CNMQL.

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Fig. 9.1 Specific grinding energy under different conditions

Grinding power, or known as the specific grinding energy, refers to the energy consumed for material removal per unit volume. Its calculation formula is [3]: U=

P Ft · vs = Qw vw · a p · b

(9.1)

U indicates specific grinding energy (J/mm3 ). P is the total energy consumption in grinding (J). Qw is the total volume of workpiece material removal. vs and vw are feeding speeds of the grinding wheel and workpiece, respectively (mm/s). F t is the tangential grinding force (N). ap and b are grinding depth and workpiece width (mm).

9.3.2 Friction Coefficient The smaller friction coefficient indicates the better lubrication state of the grinding wheel-workpiece interface in the grinding zone; otherwise, the higher friction coefficient reflects the poorer lubrication effect [4]. The friction coefficients under CA, NMQL and CNMQL modes are shown in Fig. 9.2. The variation laws of friction coefficients under three lubrication modes are basically similar with those of specific grinding energy. The lubrication effect of CA is the poorest, and the maximum friction coefficient (0.73) is gained. The lubrication effect of NMQL is better than that of CA and the friction coefficient is 0.65, which is decreased by 12.3% than that of CA. The lubrication effect of CNMQL is the best and the friction coefficient is 0.60, which is 7.7 and 17.8% lower compared to those of NMQL and CA. With comprehensive consideration to specific grinding energy and friction coefficient, a great grinding force is generated in the grinding process under CA mode since the grinding zone is in the dry friction state without medium-based lubrication. Energy consumption for the same volume of material removal is far higher than those under NMQL and CNMQL. Hence, the maximum specific grinding energy

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Fig. 9.2 Friction coefficients under different conditions

and friction coefficient are achieved under CA mode. The grinding force and energy consumption under NMQL mode are decreased to some extent due to the good lubrication effect of nanofluid in the grinding zone, thus getting smaller specific grinding energy and friction coefficient than those under CA mode. CNMQL integrates advantages of CA and NMQL, and achieves the optimal lubrication effect and decreases energy consumption during grinding significantly. It achieves the minimum specific grinding energy and friction coefficient.

9.4 Experimental Results Analysis and Discussion 9.4.1 Lubrication Performance Evaluation Under Different Working Conditions According to comparison of specific grinding energy and friction coefficients under three lubrication modes, CNMQL achieves the best lubrication effect, followed by NMQL and CA successively. Although the continuously supplied low-temperature cold air under CA can lower temperature of the grinding zone effectively and decrease thermal damages of the workpiece, it fails to form good lubrication effect in the grinding contact zone due to the absence of lubricating medium. The grinding wheelworkpiece interface is in the dry friction state during grinding and it has to consume a lot of energy to remove workpiece materials, thus getting the highest specific grinding energy and friction coefficient [5]. Under NMQL condition, the nanofluid lubricants which are carried by highpressure gas and have relatively high speed and impact force can pass through the gas barrier layer effectively, arrive at the processing zone directly and form effective spreading of droplets on the workpiece surface. A layer of stable lubricating oil film is

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formed on the grinding wheel-workpiece contact surface to provide good lubrication effect [6]. Al2 O3 nanoparticles added into the nanofluid lubricants also improve lubrication performances of the lubricants significantly [7]. Reasons are analyzed as follows. Firstly, nanoparticles have significant small-sized effect and the atomized microsized droplets can be sprayed easily onto the grinding wheel-workpiece interface in the grinding zone through the compressed gas. Secondly, Al2 O3 nanoparticles are spheres and can roll freely on the grinding wheel-workpiece interface, serving as “bearing-like” effect on the interface and transforming the grinding zone into a sliding-rolling combined frictional state. Hence, it decreases the shearing stress and energy consumption in the grinding process significantly, lowering the friction coefficient and specific grinding energy. Furthermore, workpiece surface after processing by grains becomes uneven for scratches, microcracks or furrows. Some nanoparticles can deposit or adhere into these small uneven valleys on the workpiece surface to fill up and flat the workpiece. Accordingly, the grinding force and specific grinding energy are decreased, thus strengthening the lubrication effect of the grinding zone [8]. Additionally, the melting point of Al2 O3 reaches as high 2050 °C, showing good resistance to high temperature. Adding Al2 O3 nanoparticles improves hightemperature stability and high-temperature friction performances of the lubricating oil film [9]. The lubrication effect of Al2 O3 nanoparticles in the grinding zone is shown in Fig. 9.3. CNMQL combines advantages of both CA and NMQL. Firstly, nanofluid lubricants expand the temperature gap between carrying medium of low-temperature and high-pressure air and grinding contact surface, strengthen the convective heat transfer effect, and increase boiling heat transfer capacity. They can carry away more heats from the grinding zone and lower temperature of grinding zone effectively. As a

Fig. 9.3 Lubrication effect of Al2 O3 nanoparticles in grinding zone

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result, the breakage and evaporation of oil film under high temperature are decreased, and the probability of local area in a short period in dry friction state is decreased. The stability of oil film is better. Moreover, the properties of nanofluid lubricants change with temperature of grinding zone. Due to the low temperature of grinding zone, a lubricating oil film with good lubrication performances in the grinding contact zone can be formed, which reduces energy consumption in the grinding process, achieves the optimal lubrication effect as well as the minimum specific grinding energy and friction coefficient [10].

9.4.2 Effects of Temperature on Lubrication Performances Due to different grinding temperatures in the grinding wheel-workpiece contact zone under different lubrication conditions, temperature of grinding zone has important influences on physiochemical properties, stability and spreading infiltration effect of nanofluid lubricants on the grinding interface, thus influencing lubrication performances of the lubricants. Since there’s no lubricating media under CA, the lubricating effect is the poorest. In the following text, key attention is paid to influences of temperature on lubrication performances of nanofluid under NMQL and CNMQL conditions. The highest temperatures of the grinding zone under NMQL and CNMQL conditions are shown in Fig. 9.4. Error bars represent SD of grinding temperature. Clearly, the grinding temperature under NMQL condition is the highest (209.1 °C). The cooling and heat transfer effects under CNMQL are improved significantly, which is attributed to the low-temperature cold air. The grinding temperature of CNMQL is 151.3 °C, which decreases by about 53 °C (25%) compared to that of NMQL. Fig. 9.4 Maximum grinding temperature under different conditions

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When the liquid makes laminar motion under external stresses, there’s an internal frictional force between two adjacent layers of fluid molecules to hinder liquid flow. Such characteristic is called as stickiness of liquid. Viscosity is a physical variable that measures stickiness [11]. Viscosity is also an important parameter that reflects mobility and lubrication performances of the lubricating oil. Generally speaking, lubricants can hinder the flowing trend to some extent with the increase of viscosity and it can show good retention on the grinding wheel-workpiece interface. The lubrication performances and lubrication time of the oil film are increased accordingly, thus improving processing quality of the workpiece, decreasing wearing loss of grinding wheels effectively, and prolonging the service life of the grinding wheel. When the viscosity of lubricating oil is too low, the lubricating oil film formed on the grinding wheel-workpiece interface in the grinding zone is relatively thin and has very poor stability, showing unsatisfying lubricating effect. When the viscosity of lubricating oil is too high, it may form excessive inhibition against its flowing trend and the lubricating oil film almost stagnates in the grinding zone. It is approximately a layer of solid film and the lubrication performances are relatively poor [12, 13]. In the grinding process, viscosity of nanofluid lubricants changes with grinding temperature under different conditions, thus leading to different lubricating effects. The viscosity-temperature curves of Al2 O3 nanofluids are shown in Fig. 9.5. With the increase of temperature, viscosity of nanofluid lubricants decreases gradually. It changes quickly in the low-temperature range, but slowly in the high-temperature range. It shows the good viscosity-temperature characteristics and high-temperature stability of Al2 O3 nanofluids in the high-temperature range. Viscosity of fluid reflects mutual attraction among fluid molecules and intensity of momentum transfer. Since the irregular moving speed of nanofluid molecules is extremely low, the interaction force among molecules is the primary influencing factor of nanofluid viscosity. With the increase of temperature, the relative distance among nanofluid molecules increases, thus weakening the interactive force among molecules and decreasing the viscosity of fluid [14]. The relation between nanofluid viscosity and temperature is going to be calculated by the Reynolds viscosity equation: u = Re−at

(9.2)

where u is the dynamic viscosity (cP). t is temperature (°C). R and a are constants which are calculated by the viscosity-temperature curves which are measured in experiments. Next, viscosity values of nanofluid lubricants corresponding to temperature of grinding zone under NMQL and CNMQL are calculated according to the viscosity equation. According to calculation, the nanofluid viscosity is 7.84 cP under CNMQL and it decreases by about 70.5% to 1.11 cP under NMQL. Viscosity under CNMQL is higher than that under NMQL, which is consistent with theoretical analysis results. The cooling and heat transfer effect under CNMQL is improved significantly, which is attributed to the low-temperature cold air. The temperature of grinding zone under CNMQL is only 151.3 °C, which decreases by about 53 °C compared to that under NMQL. Hence, CNMQL achieves the higher viscosity.

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Fig. 9.5 Viscosity-temperature curves of Al2 O3 nanofluids

Nanofluids in the grinding zone under CNMQL have the higher viscosity and lubricants present excellent stickiness on the grinding wheel-workpiece contact surface. The formed lubricating film is relatively thick and it improves the lubrication performances and prolongs the lubrication time, thus decreasing energy consumption in the grinding process effectively. As a result, CNMQL achieves relatively low specific grinding energy and friction coefficient. Under NMQL, viscosity of nanofluid is relatively low due to the high temperature in the grinding zone and viscosity of lubricants is poorer compared to that under CNMQL. Moreover, the formed lubricating film under NMQL is relatively thin and shows unsatisfying lubricating effect, thus increasing specific grinding energy and friction coefficient to some extents compared to those under CNMQL. The contact angle refers to the included angle (θ) between the tangent line of gas–liquid interface and solid–liquid boundary line at the intersection point of gas, liquid and solid phases. It is an important parameter to measure wetting degree and lubrication performances of droplets. As the contact angle decreases, the infiltration area of droplets increases gradually and the lubricating oil film can cover and lubricate wider effective areas, bringing better lubrication effect during grinding [15]. The contact angle measurement of the grinding wheel-workpiece contact surface under different lubrication conditions is shown in Fig. 9.6. The contact angle under NMQL is 30.5°, which is increased by about 38% to 41.5° under CNMQL. Reasons can be explained as follows. The droplet surface has an automatic shrinking trend due to the surface tension of liquid. When temperature rises, kinematic energy of thermal movement of droplet molecules increases, thus increasing the separation and diffusion trends of molecules under the same external stresses and weakening interaction forces among molecules. Hence, the surface tension of droplets declines. The temperature of grinding zone under NMQL is 209.1 °C, which is increased by about

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Fig. 9.6 Contact angle measurement under different conditions

53 °C than that under CNMQL. Surface tension of droplets is negatively related with temperature. The surface energy which has to be overcome for nanofluids continue to spread and diffuse after they are sprayed onto the grinding wheel-workpiece contact surface decreases accordingly. Hence, the contact angle under NMQL is smaller than that under CNMQL, but the infiltration and spreading effects of oil film are better. According to experimental results, specific grinding energy and friction coefficient under NMQL are higher than those of CNMQL, indicating that the lubrication effect of oil film in the grinding zone is a product of collaborative action of multiple factors. Contact angle is only one of influencing factors rather than a decisive factor. On the other hand, stability of lubricating oil film on the grinding wheel-workpiece contact surface is also an important factor that influences lubricating effect of oil film. Under NMQL, lubricants are carried by normal-temperature air into the grinding zone and have insufficient cooling and heat transfer effect. In particular, abundant heats will be generated during the grinding of difficult-to-process materials (e.g. Ti alloy) due to the high strength and high hardness. The generated heats are accumulated in the grinding zone and the temperature of grinding zone can exceed 200 °C. Moreover, the oil film has stronger liquidity and is thinner under NMQL for the lower viscosity and smaller contact angle of lubricating oil compared to those under CNMQL. Due to high temperature in the grinding zone and oil film characteristics under high temperature, the lubricating oil film is extremely easy to break and evaporate. Hence, local areas are in the dry friction state of direct contact between the grinding wheel and the workpiece in a short period. Lubricating oil film can only be formed again until secondary infiltration of nanofluids. This deteriorates the lubrication performances and thereby affects processing quality of workpieces. Under CNMQL, nanofluid lubricants are carried into the grinding zone by low-temperature cold air. This not only expands the temperature gap between heat transfer medium and grinding contact zone and decreases temperature of grinding zone effectively, but also increases viscosity, contact angle, stickiness and thickness of the oil film. Hence, the stability of lubricating oil film is improved to some extent and the lubricating effect is increased significantly. In a word, CNMQL achieves relatively small specific grinding energy and friction coefficient.

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9.4.3 Atomizing Angle Analysis The atomization process of lubricant is introduced as follows: lubricant and highpressure gas are mixed in the nozzle. The mixture spreads into a liquid layer when it flows through edges of nozzle hole. Under influences of aerodynamics, the liquid layer is firstly pulled into cylinders with similar size of tube hole and then broken and atomized into small droplet groups. Later, these small droplet groups are sprayed onto the grinding wheel-workpiece contact surface [16]. Atomization is the product of mutual completion between external stresses and internal stresses of the liquid. Droplets are atomized and broken into small droplets in the spraying process due to the aerodynamics and fluid pressure. The surface tension of droplets can keep droplets spherical and prevent deformation. Under this circumstance, the surface area and surface energy of droplets are the smallest. Moreover, the viscosity force of liquid may prevent deformation of the liquid. When external stresses on the liquid are enough to overcome its surface tension and viscosity force, the stress equilibrium state of the liquid will be broken. The liquid develops surface disturbance and finally is broken and atomized into many small droplet groups. Atomization angle is an important index to measure the atomization effect. There are two definitions of atomization angle in the technological manual of nozzle [17], as shown in Fig. 9.7. One is to define the included angle between two tangent lines from middle point of the nozzle outlet to the envelope line beyond the spraying distance as the atomization angle. The other is the common engineering expression method: by centering at the nozzle, the included angle between connecting lines of the intersection points between the nozzle end and spraying curve is defined as the atomization angle, or known as the conditional atomization angle. In this study, the common engineering conditional atomization angle was applied. The atomization angles under two lubrication conditions are shown in Fig. 9.8. To decrease contingency of measurement results, atomization angles at 10 time points were measured under each condition, and the mean results of each condition were chosen as atomization angle. According to measurement, θ is 30.36° under NMQL, which is increased by about 12°–42.08° under CNMQL. There’s a speed difference between compressed gas and lubricant. According to the principle of conservation of energy, energy exchange between gas and liquid phases occur when the compressed air carrying lubricants is sprayed out from the nozzle. Some energy of the gas increases the spraying speed of lubricants, and some is consumed for breaking and atomization of droplets. Energy and speed of droplets are increased, while speed of the compressed air declines for the loss of some energy. Due to energy exchange, the two-phase jet flow has some divergence angle and impact speed. It is finally sprayed onto the grinding zone for cooling and lubrication effect. According to Table 7.11, the gas flow rate under NMQL is 25 m3 /h, which is far higher than that under CNMQL. Since the liquid flow rates under NMQL and CNMQL are the same, the impact speed of gas–liquid flows sprayed to the grinding zone and their pressure difference with surrounding air under NMQL are higher than those under CNMQL. The disturbance effect of gas–liquid flows by surrounding air and the atomization angle under NMQL are smaller than those under CNMQL,

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thus resulting in the smaller spreading area on the grinding wheel-workpiece contact surface. Moreover, it can be observed obvious changes in droplet density in middle and boundary regions in the whole atomization and spraying region under NMQL, and the atomization effect is moderate. The spreading area of droplets is relatively small and the droplet distribution is uneven, resulting in the moderate lubrication effect. Under CNMQL, the spraying speed of gas–liquid flows from the nozzle and its pressure gap with surrounding air are relatively small due to the low flow rate of gases (10 m3 /h). The spraying boundaries are disturbed more by surrounding air and the atomization angle is larger. In the experiment, it also observed that density of droplets in the whole atomization and spraying region is relatively uniform, without obvious changes of density in middle and boundary areas. Hence, there’s good atomization effect. Droplets have larger spreading area in the grinding zone and droplets distribute uniformly, thus bringing better lubrication effect.

Fig. 9.7 Two definitions of the atomization angle

Fig. 9.8 Measurement of atomization angle under different conditions

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9.4.4 Surface Roughness and Surface Morphology Surface quality of workpiece can reflect lubrication effects under different working conditions. The better lubrication effect indicates the higher surface quality of workpieces. Surface quality under different conditions is evaluated by surface roughness (Ra) and surface microtopography (RSm). Ra and RSm values of workpieces under CA, NMQL and CNMQL modes are shown in Fig. 9.9a, b. The SEM images of surface microtopography of workpieces under CA, NMQL and CNMQL modes are shown in Fig. 9.10. It can be known from Fig. 9.9 that among three lubrication modes, CA achieves the poorest lubrication effect and the maximum Ra and RSm values (0.535 μm and 0.078 mm, respectively). Due to the lubrication effect of nanofluids, the Ra and RSm values under NMQL are 0.426 μm and 0.064 mm, which are 20.4 and 17.9% lower compared to those under CA. CNMQL achieves the optimal lubrication effect and gains the minimum Ra and RSm values (0.375 μm and 0.059 mm), which are 29.9% and 29.4% lower than those under CA. According to comparison of surface microtopography, there are great differences in workpiece surface morphologies under different lubrication modes. Surface roughness and surface microtopography of workpieces show high consistency under three

Fig. 9.9 Ra and RSm values of workpiece surface under different conditions

Fig. 9.10 SEM images of surface microtopography of workpieces under different conditions

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lubrication conditions. CNMQL presents the best lubrication effect and achieves the optimal surface quality and the lowest surface roughness, followed by MQL. CA achieves the poorest surface quality. Under CA condition, the grinding wheelworkpiece interface is in the dry friction state during grinding due to the lack of medium-based lubrication effect. The processed workpiece surface has obvious plastic deformation layers, deep and long furrows, serious debris adhesion and material deposition, showing the poorest surface quality. Under MQL, there are hardly large furrows and plastic deformation layers on workpiece surface due to the lubrication effects of nanofluids. The grinding textures are relatively clear, but dense scaly adhesions are developed. The debris adhesion might be formed for following reasons: some grinding debris removed from workpiece surface cannot be separated from the grinding zone timely and effectively, and they adhere onto the high-temperature workpiece surface again with the continuous feeding and extrusion of grinding wheel, forming scaly adhesion phenomena. CNMQL achieves the best lubrication effect, manifested by clear and smooth grinding textures on the workpiece surface. There are hardly furrows. Moreover, scaly adhesions are small-sized and scatter around. Hence, workpieces achieve relatively high surface quality under CNMQL mode. Grinding wheel surface is composed of abundant irregular grains in discrete distribution. In the grinding process, workpiece surface may develop scratches, furrows and microcracks with different depths along the grinding direction, forming close micro-sized long and thin pipelines with different depths. The spreading and infiltration of nanofluid lubricants in micro-sized pipelines on workpiece surface is shown in Fig. 9.11. In the grinding process, the nanofluid lubricants sprayed from nozzle continuously supplement into these micro-sized pipelines successively. Grinding fluid flows in from ends of pipelines and flows quickly forward along the pipelines by the impact kinetic energy from the high-pressure gas, and spread quickly on the grinding wheel and workpiece surfaces into a layer of lubricating oil film for lubrication of the grinding zone. Although the grinding textures under MQL are relatively clear, there are still dense scaly adhesion and material accumulation, which hinder flowing of lubricant along pipelines to some extent. These influence spreading and infiltration effect of lubricant and decrease the lubrication effect of lubricant. Energy consumption during material removal is high, thus bringing high specific grinding energy and proportional coefficient of energy. Under CNMQL condition, the workpiece surface not only has relatively clear and smooth grinding pipelines, but small and scattered scaly adhesion. However, the material accumulation is not obvious and forms small barriers against flowing of lubricant along pipelines. The lubricant has better spreading and infiltration effect, and thereby provides better lubrication effect. It consumes less energy in the grinding process, finally getting lower specific grinding energy and coefficient of friction cases.

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Fig. 9.11 Spreading and infiltration of nanofluid lubricants on the pipelines of the workpiece surface

9.5 Summary Plane grinding experiments of Ti-6Al-4V under CA, NMQL and CNMQL modes are carried out. Through comparison of specific grinding energy and friction coefficients under different lubrication modes, the lubrication mechanism of grinding zones under CNMQL and NMQL are further analyzed from viscosity, contact angle, stability of lubricating oil film, atomization effect of droplets and workpiece topography. Some major conclusions can be drawn: (1) Among three lubrication modes, CNMQL achieves the minimums specific grinding energy (51.96 J/mm3 ) and friction coefficient (0.60). The specific grinding energy under NMQL and CA conditions are increased by 2.3 and 69.1% compared to that under CNMQL condition. Friction coefficient under the CNMQL condition is 17.8 and 7.7% lower compared to those under CA and NMQL conditions. (2) The cooling and heat exchange effect under CNMQL condition are increased significantly. It achieves the minimum grinding temperature (151.3 °C), which is about 53 °C lower than that under NMQL condition. Since the nanofluid lubricants have higher viscosity (7.84 cP) and larger contact angle (41.5°), the lubricating oil film is thicker and has better retention effect in the grinding wheel-workpiece contact surface. Moreover, the breakage and evaporation of oil film under high temperature are decreased because of its characteristics and the low grinding temperature. This decreases the probability of dry friction state of local areas in the short period. The oil film has better stability and lubrication effect. (3) Under CNMQL, the speed of gas–liquid flow and its pressure gap with surrounding air are low due to the small flow rate of gases (10 m3 /h). The spraying boundaries are disturbed significantly by surrounding air, thus getting the maximum atomization angle (42.08°) among three lubrication modes. The droplet density in the whole atomization and spraying region is relatively uniform, without obvious changes in density in middle and boundary regions. The atomization effect is relatively good. Hence, droplets have larger spreading area and uniform distribution in the grinding zone, thus bringing better lubrication effect.

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(4) CNMQL achieves the lowest Ra and RSm values. The workpiece surface not only has relatively clear and smooth grinding pipelines, but small and scattered scaly adhesion. The material accumulation is not obvious, which causes small barriers against flowing of lubricants along grinding pipelines. The lubricant has better spreading and infiltration effects, thus achieving better lubrication effect and consuming less energy in the grinding process. Finally, it achieves the lower specific grinding energy and coefficient of friction cases compared to those under CA and NMQL conditions. (5) Based on above results, CNMQL integrates advantages of both CA and NMQL modes. It has excellent grinding performances and achieves the optimal lubrication effect. Moreover, it has advantages of low cost and environmental-friendly characteristics. CNMQL mode possesses promising application prospects in the processing field.

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Chapter 10

Effects of Cold Air Fraction in Vortex Tube on Heat Transfer Mechanism in CNMQL Grinding

10.1 Introduction A vortex tube is applied as the low-temperature cold air supply device of CNMQL. The overall state of cold air medium is of important significance to realize effective cooling of the grinding zone, lower temperature of grinding zone and thereby improve processing quality of workpieces [1]. Cold air fraction of vortex tube may influence temperature and flow rate of nanofluids sprayed onto the grinding zone, thus influencing its viscosity, surface tension, contact angle and breaking state of droplets. Finally, it will influence the boiling heat transfer state and cooling heat transfer performances of nanofluids in the grinding zone. In this chapter, effects of cold air fraction of the vortex tube on heat transfer mechanism of CNMQL grinding are explored. A numerical simulation and experimental verification of grinding temperature field of Ti-6Al-4 V under CNMQL condition with different cold air fractions are carried out. The influencing laws of cold air fraction of vortex tube on cooling heat transfer performances during CNMQL grinding are further disclosed.

10.2 Numerical Simulation of Grinding Temperature Field Numerical simulation analysis of grinding temperature field is carried out by using FDM. The core idea of FDM is to replace differential by difference. It is an analytical and calculation method that discretizes the continuous region into a region composed of finite grids, and then solves the partial differential equation by establishing the finite difference equation set [2].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_10

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10.2.1 Mathematical Model of Grinding Temperature Field This section has the consistent content with mathematical model of temperature field in Sect. 8.2.1.

10.2.2 Determination of Simulation Parameters The same calculation process and calculation method of heat transfer coefficients in Sect. 8.2.3 are used. Parameters of gases and droplets which are measured in experiment and calculated when cold air fraction is 0.45 are listed in Table 10.1. Heat transfer coefficients at turning points of different heat transfer stages when cold air fraction is 0.45 are gained through interpolation calculation. On this basis, the actual heat transfer coefficient of the grinding zone is calculated hn = 4.34 × 104 W/m2 K. The heat transfer coefficient when cold air fraction is 0.45 is shown in Fig. 10.1 and Table 10.2. Similarly, heat transfer coefficients at turning points of different heat transfer stages under different cold air fractions are calculated by the same method [4]. The corresponding actual heat transfer coefficients under different cold air fractions are gained through interpolation method. The heat flux density and proportional coefficient of energy are calculated from Eqs. (10.1) and (10.2). The heat flux density into the workpiece is: qw =

qw vs Ft vs Ft = ·R= / ·R qtotal blc b ds a p

(10.1)

where qw is the heat flux density into the workpiece (J/[m2 K s]). qtotal is the total heat flux density (J/[m2 K s]). Ft refers to the tangential grinding force. vs denotes the linear velocity of grinding wheel (m/s). lc is the length of grinding wheel-workpiece contact arc (mm). b is the grinding width (mm). Ds is the equivalent diameter of the grinding wheel (mm). ap is the grinding depth (μm). The proportional coefficient of energy (R) transferred into the workpiece is [5]: 1/2

R=

kw vw

θ 1/2 1/4 1/4 max

qtotal βαw a p ds

(10.2)

where β is a constant, α w is the thermal diffusivity of workpiece (m2 /s), and θ max is the maximum temperature rise (°C).

10.3 Numerical Simulation Results

283

Table 10.1 Given parameters Given parameters

Numerical values Given parameters

Numerical values

Length of workpiece a (m)

0.08

105

Saturated temperature of nanofluid T s (°C)

Feeding speed of workpiece 0.067 vw (m/s)

Temperature at initial point 107.4 of nucleate boiling T n1 (°C)

Width of grinding debris b (mm)

20

Temperature at initial point 157.4 of transition boiling T n2 (°C)

Atmospheric pressure po (Mpa)

0.11

Temperature at initial point 231 of film boiling T n3 (°C)

Internal pressure of nozzle pa (Mpa)

0.6

Spreading radius of single droplet r su (μm)

145

Nanofluid supply in unit time Q' (μm3 /s)

2.2 × 1010

Specific heat capacity of droplets cl (J/(kg K))

1870

Included angle between 15 droplet jetting direction and the horizontal direction θ (°)

Latent heat of droplet vaporization hfa (J/kg)

384,300

Velocity of gas v (m/s)

310

Surface tension of droplet σ (N/m)

2.02 × 10–2

Nanofluid density ρ l (kg/m3 )

665

Heat conductivity coefficient of steam λv (W/m K)

0.02624

Nanofluid temperature T l (°C)

1.2

Dynamic viscosity of steam μv (Pas)

0.018448

Contact angle θ n (°)

51.86

Mass thermal capacity of steam cv (J/(kg K))

1004

10.3 Numerical Simulation Results A numerical simulation analysis of temperature field on workpiece surface under different cold air fractions of vortex tube is carried out by using the Matlab simulation platform. The overall changes of heat source in the grinding zone from cut-in to cut-out of the workpiece at a cold air fraction of 0.45 are shown in Fig. 10.2. Clearly, the grinding temperature in the grinding wheel-workpiece contact area is the highest (red region), and the workpiece temperature declines gradually after the heat sources passes by. Temperature rise mainly concentrates at the heat source point

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Fig. 10.1 Heat transfer coefficients at a cold air fraction of 0.45

Table 10.2 Calculation results Given parameters

Numerical values Given parameters

Numerical values

Single-droplet volume V l (μm3 )

7.77 × 106

Non-boiling heat transfer coefficient hn1 (W/m2 K)

2.7 × 104

Single-droplet diameter d 0 193 (μm)

Maximum heat transfer coefficient hn2 (W/m2 K)

10.86 × 104

Number of droplets N l

5800

Heat transfer coefficient at 1.84 × 104 initial point of the film boiling heat transfer hn3 (W/ m2 K)

Convective heat transfer coefficient of low-temperature air h' a (W/m2 :K)

301

Actual heat transfer coefficient when cold air fraction is 0.45 hn (W/m2 K)

4.34 × 104

Vertical velocity of droplet 110.2 impacting onto the heat transfer surface vn (m/s)

and the region that the heat source just passes by. Due to low heat conductivity coefficient of Ti alloy, temperature of the unprocessed surface is always close to the environmental temperature before the grinding wheel grinds to the grinding point, without showing obvious temperature changes. When the grinding wheel grinds to the grinding point, the workpiece surface temperature increases dramatically, but the temperature declines slowly after the grinding wheel leaves the point until

10.4 Experimental Verification

285

Fig. 10.2 Phase diagram of simulation changes of the grinding zone at a cold air fraction of 0.45

reaching the environmental temperature finally. The simulation results conforms to the variation trend of grinding temperature in the actual grinding process.

10.4 Experimental Verification 10.4.1 Experimental Equipments The used experimental equipments and measuring equipments are the same with those in Sect. 8.2.1.

10.4.2 Experimental Materials The used experimental equipments and treatments are also completely the same with those in Sect. 8.2.2.

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10.4.3 Experimental Design Vortex tube is used as a low-temperature cold air supply device of CNMQL. The volume percentage of cold air released from the cold end of the vortex tube in the total input compressed air is called as the cold air fraction of vortex tube. Cold air fraction of vortex tube is one of decisive factors of the refrigeration performances. The lower cold air fraction of vortex tube indicates the lower temperature of cold-end airflow and the smaller cold air flow rate, and vice versa. The overall state of cold air medium is of important significance to realize effective cooling of the grinding zone, lower temperature of grinding zone and thereby improve processing quality of workpieces. Cold air fraction of vortex tube may influence temperature and flow rate of nanofluids sprayed onto the grinding zone, thus influencing its viscosity, surface tension, contact angle and breaking state of droplets. Finally, it will influence the boiling heat transfer state and cooling heat transfer performances of nanofluids in the grinding zone [6]. Hence refrigeration performances of the vortex tube is the collaborative result of flow rate and temperature drop of cold air. According to previous academic studies on cold air fraction of vortex tube and pre-experimental results, influences of different cold air fractions of vortex tube on cooling heat transfer performances during CNMQL grinding when cold air fraction is 0.25, 0.35, 0.45, 0.55 and 0.65 are discussed in this experiment. Grinding experimental parameters are shown in Table 10.3. Table 10.3 Grinding experimental parameters Grinding type

Plane grinding

Grinding wheel type

SiC ceramic grinding wheel with binding agent

Cold air fraction

0.25, 0.35, 0.45, 0.55, 0.65

Linear velocity of grinding wheel V s (m/s)

30

Flow rate of MQL (ml/h)

90

Feeding speed of workpiece V w (mm/min)

4 000

Cutting depth ap (μm)

10

Gas flow rate of NMQL (m3 /h)

25

Nozzle distance d (mm)

12

Angle of nozzle α (°)

15

Atmospheric pressure P (MPa)

0.7

10.5 Experimental Results and Analysis

287

Fig. 10.3 Simulation and experimental curves of maximum temperature in grinding zone

10.4.4 Comparison of Simulation and Experimental Results Grinding temperature is the most intuitive parameter that characterizes the cooling heat transfer performances in grinding [7]. The variation curves of simulation and experimental results of maximum temperature in the grinding zone with time at the cold air fraction of 0.45 are shown in Fig. 10.3. The comparison between simulation and experimental results of maximum temperature of the grinding zone under different cold air fractions is shown in Fig. 10.4. According to experimental results, the maximum temperatures of the grinding zone are 200.7, 187.9, 192.3, 204.9 and 2110.4 °C when the cold air fraction increases from 0.25 to 0.65, respectively. Moreover, the maximum temperature of the grinding zone presents a V-shaped variation trend with the increase of cold air fraction. The maximum temperature of grinding zone declines gradually when the cold air fraction increases from 0.25 to 0.35, and reaching the minimum at 0.35. The specific grinding energy increases gradually when cold air fraction increases from 0.35 to 0.65. According to the maximum temperature of grinding zone, it can conclude that the cooling heat transfer effect of grinding zone decreases firstly and then increases with the increase of cold air fraction, and reach the peak at the cold air fraction of 0.35.

10.5 Experimental Results and Analysis 10.5.1 Specific Grinding Energy Specific grinding energy characterizes the energy consumed for material removal per unit volume and it is one of the most important grinding parameters in the grinding process. Specific grinding energy is closely related with service life of grinding wheel

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Fig. 10.4 The simulation and experimental results of maximum temperature in grinding zone

and workpiece surface quality. It not only is an important index to measure grinding efficiency, but also can characterize the lubrication effect of the grinding wheelworkpiece interface. The smaller specific grinding energy indicates the lower energy consumption for removing the same volume of materials, and better lubrication effect and grinding performances [8]. During measurement, mean of stroke force of 10 grinding experiments was chosen as the grinding force that is brought into Eq. (10.3) to calculate specific grinding energy under different cold air fractions. Grinding power, or known as specific grinding energy: energy consumed for removing the same volume of materials. The relevant calculation formula is [9]: U=

P Ft · vs = Qw vw · a p · b

(10.3)

U is specific grinding energy (J/mm3 ). P is the total energy consumption in grinding (J). Qw is the total volume of removed workpiece material. vs and vw are feeding speeds of grinding wheel and workpiece (mm/s), respectively. Ft is the tangential grinding force (N). ap and b are grinding depth and workpiece width (mm), respectively. It can be seen from Fig. 10.5 that specific grinding energy is 68.92, 611.07, 62.84, 71.20 and 72.07 J/mm3 when the cold air fraction increases from 0.25 to 0.65, respectively. Generally speaking, specific grinding energy presents a V-shaped variation with the increase of cold air fraction. It declines gradually when cold air

10.5 Experimental Results and Analysis

289

Fig. 10.5 Specific grinding energy under different cold air fractions

fraction increases from 0.25 to 0.45, and reaches the minimum at 0.45. Later, the specific grinding energy increases gradually when cold air fraction increases from 0.45 to 0.65. Specific grinding energy can reflect lubrication performances. Hence, it can conclude from specific grinding energy that the lubrication effect of grinding zone decreases firstly and then increases with the increase of cold air fraction, and the best lubrication effect is achieved at the cold air fraction of 0.45.

10.5.2 Effects of Nanofluid Viscosity on Heat Transfer Performances When the liquid makes laminar motion under external stresses, there’s an internal frictional force between two adjacent layers of fluid molecules to hinder liquid flow. Such characteristic is called as stickiness of liquid and it is measured by viscosity. Viscosity is also an important parameter that reflects mobility and lubrication performances of the lubricating oil. When fluid with some viscosity flows through the solid wall, the frictional resistance between the fluid and wall will inhibit the flowing trend of fluid. A speed boundary layer and a temperature boundary layer are formed between wall and fluid. Generally speaking, the speed boundary layer is thinner with the increase of viscosity. Hence, the momentum diffusivity is weaker, accompanied with the stronger frictional resistance between workpiece surface and lubricating oil film, and better stability and lubricating effect of the oil film. Accordingly, the energy consumption and heat input during material removal can be decreased effectively.

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Moreover, the temperature boundary layer is thinner with the increase of viscosity, which weakens the heat diffusivity and the enhanced heat transfer performances of nanofluid. Temperature of nanofluid lubricant changes with cold air fraction and the viscosity also varies. Interaction forces among nanofluid molecules take the dominant role in viscosity. With the increase of temperature, the relative distance among nanofluid molecules increases, thus weakening the interaction force of molecules and decreasing viscosity of the nanofluid [11, 12]. The variation curves of temperature and viscosity of Al2 O3 nanofluids sprayed into grinding zone under different cold air fractions are shown in Fig. 10.6. It can be seen from the table that in the low-temperature range, temperature of nanofluid sprayed into the grinding zone increases (from −7.6°C to 11.8°C) gradually when the cold air fraction increases from 0.25 to 0.65, while viscosity of the nanofluid decreases quickly. Temperature of the nanofluid is −7.6 °C when the cold air fraction is 0.25 and the corresponding viscosity is 2711.8cP. As the cold air fraction increases to 0.65, the temperature of nanofluid is 11.8 °C and the viscosity is 1610.3cP. With the increase of the cold air fraction from 0.25 to 0.65, temperature of nanofluid increases by 14.4 °C, while the viscosity drops dramatically by 111.5cP. In fact, viscosity of Al2 O3 nanofluid changes quickly in the low-temperature range, but slowly in the high-temperature range. It has excellent viscosity-temperature characteristics and high-temperature stability. From the perspective of viscosity, temperature of nanofluid increases with the increase of cold air fraction and its viscosity also increases dramatically. With the

Fig. 10.6 Temperature and viscosity curves of nanofluids sprayed into grinding zone

10.5 Experimental Results and Analysis

291

increase of viscosity, the speed boundary layer becomes thinner and the momentum diffusivity weakens. Given the stronger frictional resistance between lubricant and workpiece surface, the oil film has better stability and lubrication performances, thus enabling to decrease energy consumption and heat input during material removal. As a result, the workpiece quality is improved and the grinding temperature is lowered. Low viscosity has a positive effect on heat transfer: the frictional resistance between lubricant and workpiece surface is relatively small at a low viscosity. The formed lubricating oil film is thinner and has poorer stability, but stronger thermal diffusivity. It is easier to carry away heats from the grinding zone through boiling heat transfer. Hence, the heat transfer performance is better [13].

10.5.3 Effects of Surface Tension of Nanofluids on Heat Transfer Performances A surface layer will be formed upon contact between liquid phase and gas phase. There are mutual attractive forces in this liquid surface layer, that is, surface tension. Due to the surface tension, the liquid surface has a trend of automatic shrinkage and keeping spherical shape [14]. Surface tension is caused by the cohesive force among liquid molecules: molecules in the liquid surface layer are sparser than those inside the liquid and they bear a force pointing inside of the liquid, thus bringing the shrinkage trend of the liquid surface layer. Hence, the surface area of liquid is shrunk as much as possible. Surface tension is only related with properties and temperature of liquid. Generally speaking, surface tension is negatively related with temperature. With the increase of liquid temperature, the oscillation amplitude of molecules at the equilibrium position increases and the relaxation time prolongs dramatically, accompanied with accelerating diffusion of molecules. In this case, molecules with great kinetic energy of thermal motion can overcome attractive forces of liquid molecules and thereby become evaporation molecules. This decreases density of liquid, attractive forces among molecules and surface potential energy, thus decreasing surface tension accordingly. Similarly, there are surface layers and surface tension between the liquid and solid wall. Nanofluid is sprayed into the grinding wheel-workpiece contact surface as droplets after it is sprayed out of the nozzle to provide cooling and lubrication effect. The contact state between droplets and workpiece decides the cooling and lubrication effects. Contact angle refers to the included angle (θ ) between the tangent line of gas–liquid interface and solid–liquid boundary line at the intersection point of gas, liquid and solid phases. According to Young’s equation, the calculation formula of θ is (Fig. 10.7). cos θ =

γsv − γsl γlv

(10.4)

γ sv , γ sl and γ lv are solid–gas surface tension, solid–liquid surface tension and gas– liquid surface tension, respectively. Based on the above equation, θ increases with

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Fig. 10.7 Schematic diagram of contact angle

the increase of γ lv. In other words, the contact angle decreases with the increase of temperature, which conforms to the variation trend of viscosity with temperature. The variation curves of the measured surface tension and contact angle of Al2 O3 nanofluid under different cold air fractions are shown in Fig. 10.8. When the cold air fraction increases from 0.25 to 0.65, the surface tension of nanofluid decreases from 30.74 to 29.79 mN/m. With the reduction of surface tension, γ lv decreases from 511.26° to 410.37°. The experimental results conform to the theoretical analysis results. Given a small contact angle, the surface energy which has to be overcome for continuous spreading and diffusion of nanofluid after it is sprayed onto the grinding wheel-workpiece contact surface also decreases, while the infiltration area of droplets on the grinding wheel-workpiece contact surface expands. The oil film has better infiltration and spreading effect, thus having better cooling and lubrication effect. Furthermore, stability of the lubricating oil film on the grinding wheel-workpiece contact surface is also an important factor that influences cooling and lubrication effects of oil film. Temperature of nanofluids sprayed onto the grinding zone increases with the increase of cold air fraction, but viscosity and contact angle of the lubricating oil film decline. As a result, the oil film has stronger mobility and smaller thickness. Due to the high temperature of grinding zone, the lubricating oil film is extremely easy to be broken and evaporated. Consequently, the local grinding zone is in the dry friction state of direct contact between grinding wheel and workpiece in a short period. The lubricating oil film can only be formed again until secondary infiltration of nanofluids, which decreases the lubrication effect to some extent and thereby influences processing quality of workpiece. Given a low cold air fraction, viscosity and contact angle of oil film are higher, and the oil film has relatively high stickiness and thickness. These improve stability and lubricating effect of the oil film to some extent, and thereby decrease energy consumption as well as heat input during material removal. Given a low viscosity and contact angle of lubricating oil, the lubricating oil film has stronger thermal diffusivity and it is easy to carry away heats from the grinding zone through boiling heat transfer. It has better heat transfer ability.

10.5 Experimental Results and Analysis

293

Fig. 10.8 Curves of surface tension and contact angle of nanofluids

10.5.4 Effects of Atomizing Effect and Boiling Heat Transfer on Heat Transfer Performances Lubricant and high-pressure gas are mixed in the nozzle. The mixture spreads into a liquid layer when it flows through edges of nozzle hole. Under influences of aerodynamics, the liquid layer is firstly pulled into cylinders with similar size of tube hole and then broken and atomized into small droplet groups. Later, these small droplet groups are sprayed onto the grinding wheel-workpiece contact surface [15]. Atomization is the product of mutual completion between external stresses and internal stresses of the liquid. Droplets are atomized and broken into small droplets in the spraying process due to the aerodynamics and fluid pressure. The surface tension of droplets can keep droplets spherical and prevent deformation. Under this circumstance, the surface area and surface energy of droplets are the smallest. Moreover, the viscosity force of liquid also may prevent deformation of the liquid. When external stresses on the liquid are enough to overcome its surface tension and viscosity force, the stress equilibrium state of the liquid will be broken. The liquid is broken and atomized into many small droplet groups. Due to different physical properties of nanofluids sprayed onto the grinding zone under different cold air fractions and different flow rates of carried gases, the atomization effect of droplets varies, thus influencing the lubrication effect and cooling heat transfer performances of the nanofluids [16]. Gas flows of Al2 O3 nanofluids sprayed onto the grinding zone under different cold air fractions are shown in Fig. 10.9. With the increase of cold air fraction, gas flow of nanofluids sprayed onto the grinding zone increases gradually. It is nearly doubled

294

10 Effects of Cold Air Fraction in Vortex Tube on Heat Transfer Mechanism …

from 14.4 to 29.1m3 /h when the cold air fraction increases from 0.25 to 0.65. There’s a velocity gap between the low-temperature compressed gas and lubricant when they meet in the nozzle. From the perspective of energy, energy exchange occurs between the gas and liquid phases when the compressed air carrying lubricant is sprayed from the nozzle. Energy consumption of gas mainly includes the viscosity dissipation work to overcome stickiness of the liquid and the surface energy dissipation work to overcome surface tension. The rest energy is to increase momentum of lubricants. Due to energy exchange, the two-phase jet flow has some divergence angle and impact speed, and finally it is sprayed into the grinding zone as droplets to provide cooling and lubrication effects. Given the same flow rate of nanofluids, the atomized droplet size decreases with the increase of gas flow rate and the atomization quality is improved. This is because it has more energy under a higher gas flow rate, so that the gas–liquid flow gains higher total momentum and impact speed to further strengthen shearing effect of gas to droplets. Additionally, increasing gas flow rate can increase volume porosity of gas in the two-phase jet flow, and strengthen extrusion and impact onto the liquid, thus improving the breaking and atomizing effect of droplets. Hence, it is more conducive for droplets to break the wedge-shaped zone and enter into the grinding wheel-workpiece contact surface. To sum up, the higher cold air fraction brings the better atomization effect and the better cooling and lubrication effect of the grinding zone. Among heats carried away from the grinding zone, most are carried away through boiling heat transfer of grinding fluid except for a small proportion carried away by compressed air through enhanced convective heat transfer. When the workpiece surface temperature of grinding zone is higher than the saturated temperature of grinding fluid, the grinding fluid is vaporized by heats and abundant bubbles are

Fig. 10.9 Gas flow sprayed into the grinding zone

10.5 Experimental Results and Analysis

295

produced and escape from the workpiece surface, thus causing boiling phenomenon [15]. Boiling heat transfer of grinding zone is a violent evaporation process that a lot of steam bubbles are produced, grow and carry away heats by transforming working medium from liquid state to gas state. When the workpiece surface temperature exceeds the saturated temperature of grinding fluid and reaches a certain numerical value, grinding fluid firstly absorbs latent heats and produce bubbles in pits and microcracks of workpiece surface. These points that can produce bubbles are called as vaporization cores [17]. As heats continue to transfer from the hightemperature surface into the vaporization cores, the bubbles grow continuously and float upward until separating from the workpiece surface and carry away heats. Carried by low-temperature compressed gas, grinding fluid is sprayed into grinding zone continuously and lowers temperature of grinding zone through boiling heat transfer. The boiling heat transfer process of liquid generally can be divided into two stages: (1) vaporization and absorption of latent heat (hereinafter referred as Stage 1); (2) vaporization and heat transfer (hereinafter referred as Stage 2). If the temperature of nanofluids sprayed into the grinding zone is lower, the liquid molecules have lower kinetic energy and the gas–liquid energy gap is greater. Hence, it has to absorb more heats from external environment for vaporization of liquid. Nanofluids absorb more latent heats under a lower cold air fraction. After entering into the Stage 2, the grinding fluid with a lower temperature has a greater temperature gap (Λt) with its saturated temperature and it absorbs more heats from the grinding zone in this process. When cold air fraction increases from 0.25 to 0.65, the temperature of nanofluids sprayed into the grinding zone increases by 14.4 °C from −7.6 to 11.8 °C. Hence, it concludes that the lower cold air fraction brings the better overall boiling heat transfer effect. Temperature of the grinding zone is decided by cooling and lubrication effect of grinding fluid in the grinding zone together. The higher cold air fraction, the smaller atomized droplet size, the higher the impact kinetic energy of two-phase flow, and the better atomization quality. Hence, droplets are easier to be vaporized at vaporization cores of workpiece surface. Meanwhile, droplets further grow and float upward until separating from the workpiece surface to carry away heats. Besides, viscosity, surface tension and contact angle decrease with the increase of cold air fraction. The oil film becomes thinner and it is easier to break under high temperature. This decreases the lubricating effect and increases energy consumption for material removal to some extent. When the cold air fraction is relatively low, the oil film has higher viscosity, larger contact angle, stronger stickiness and greater thickness, thus improving its stability and lubricating effect to some extent. Although atomization effect under a low cold air fraction is inferior to that under a high cold air fraction, the high viscosity and large contact angle assure the strength and stability of the lubricating oil film in the grinding zone. The lubricating oil film has better lubrication effect and decreases energy consumption during material removal. According to experimental results of grinding temperature, the maximum temperature of grinding zone presents a V-shaped variation trend with the increase of cold air fraction and reaches the minimum (187.9 °C) at 0.35. Hence, we can conclude that there’s good lubricating

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10 Effects of Cold Air Fraction in Vortex Tube on Heat Transfer Mechanism …

effect and excellent heat transfer ability when the cold air fraction is 0.35, achieving the minimum temperature of grinding zone.

10.6 Summary A simulation analysis and verification experiment of temperature field during plane grinding of Ti–6Al–4 V under different cold air fractions of vortex tube are carried out. Moreover, a comparative analysis of simulation and experimental temperatures of grinding zone is performed. The cooling and lubrication mechanism of grinding zone under different cold air fractions of vortex tube is further analyzed from perspectives of specific grinding energy, viscosity of nanofluids, surface tension and contact angle of nanofluids as well as atomization and boiling heat transfer effect of grinding zone. Some major conclusions can be drawn: (1) With reference to theories of boiling heat transfer and grinding heat transfer, heat transfer coefficients and FDM models of grinding zone under different cold air fractions of vortex tube (0.25, 0.35, 0.45, 0.55 and 0.65) are constructed based on different cooling heat transfer capacities of cooling liquid under different boiling heat transfer states. A simulation analysis of temperature field of grinding zone under different cold air fractions is carried out. The simulation laws conform to the variation trend in actual grinding. (2) A numerical simulation analysis of temperature field of grinding zone under different cold air fractions is performed based on the numerical model. The simulation laws conform to the variation trend in actual grinding. Based on theoretical simulation, a verification experiment of plane grinding is conducted. According to experimental results, the maximum temperature of grinding zone presents a V-shaped variation trend with the increase of cold air fraction and reaches the minimum (187.9 °C) at 0.35. Generally speaking, the simulation results agree highly with experimental results. The simulation model is reliable to some extent. Additionally, specific grinding energy decreases firstly and then increases with the increase of cold air fraction and reaches the minimum (62.84 J/ mm3 ) at 0.45. In other words, the best lubricating effect is achieved when the cold air fraction is 0.45. (3) The viscosity of nanofluid increases dramatically with the increase of cold air fraction. The lubricating oil film has a thinner speed boundary layer and a weaker momentum diffusivity, but better stability and lubrication performances, thus decreasing energy consumption during material removal. Finally, the workpiece quality is improved and grinding temperature is lowered. The frictional resistance between nanofluids and workpiece surface is weaker when the viscosity is low. The formed lubricating oil film is thinner and has poorer stability as well as stronger thermal diffusivity. It is easier to carry away heats from the grinding zone through boiling heat transfer, showing better heat transfer performances.

References

297

(4) Surface tension and contact angle of nanofluids also may influence heat transfer performances. The surface tension of nanofluids decreases from 30.74 to 29.79, while γ lv decreases from 511.26 to 410.37 when the cold air fraction increases from 0.25 to 0.65. Given a small contact angle, the surface energy which has to be overcome for continuous spreading and diffusion of nanofluids after being sprayed onto the grinding wheel-workpiece contact surface is lower, the infiltration area of droplets on workpiece surface is larger, and the infiltration and spreading effects of oil film are better, thus resulting in the better cooling and lubrication effects. Moreover, stability of the lubricating oil film is an important factor. With the increase of cold air fraction, the viscosity, contact angle and thickness of the lubricating oil film decline, while the liquidity increases. Due to the high temperature of grinding zone, the lubricating oil film is extremely easy to be broken and evaporated. Hence, there’s dry frictional state in local area in a short period, which decreases the lubricating effect and workpiece quality to some extent. However, it is easier to carry away heats through boiling heat transfer. The stability of lubricating oil film is better when the cold air fraction is relatively lower. (5) Atomization and boiling heat transfer effect also may influence cooling heat transfer performances. Given a higher cold air fraction, the gas flow sprayed to the grinding zone is higher, the atomized droplet size is smaller, and the atomization quality is better. Besides, the two-phase flows have more total kinetic energy and impact speed, which are conducive for lubricant to break the wedge-shaped zone to cool and lubricate the grinding zone. Given a lower cold air fraction, there’s a greater temperature gap (Λt) between grinding fluid and its saturated temperature, and a greater energy gap between gas and liquid phases. Hence, more heats are absorbed throughout the boiling heat transfer. (6) According to the comprehensive analysis of specific grinding energy, viscosity, surface tension, contact angle, atomization and boiling heat transfer effect, the actual temperature of grinding zone is decided by the cooling and lubrication effects of grinding fluid in the grinding zone. The maximum temperature of grinding zone presents a V-shaped variation trend with the increase of cold air fraction and reaches the minimum at 0.35. To sum up, it achieves good lubrication effect and excellent heat transfer performances when the cold air fraction is 0.35, thus getting the lowest temperature of grinding zone.

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4. Zou L, Huang Y, Zhou M, et al. Effect of Cryogenic Minimum Quantity Lubrication on Machinability of Diamond Tool in Ultraprecision Turning of 3Cr2NiMo Steel [J]. Materials and Manufacturing Processes, 2018, 33(9): 943–949. 5. Zhang D, Li C, Zhang Y, et al. Experimental research on the energy ratio coefficient and specific grinding energy in nanoparticle jet MQL grinding [J],The International Journal of Advanced Manufacturing Technology, 2015,78 (5-8) :1275–1288. 6. Yuan S, Liu S, Liu W. Effects of cooling air temperature and cutting velocity on cryogenic machining of Cr18Ni9Ti alloy [C]. Applied Mechanics and Materials. Trans Tech Publications, 2012, 148: 795–800. 7. Bagherzadeh A, Budak E. Investigation of machinability in turning of difficult-to-cut materials using a New Cryogenic Cooling Approach [J]. Tribology International, 2018, 119: 510–520. 8. Li, B., Li, C., Zhang, Y., Wang, Y., Jia, D., Yang, M., Zhang, N., Qu, Q., Han, Z., & Sun, K. (2017). Heat transfer performance of MQL grinding with different nanofluids for Ni-based alloys using vegetable oil. Journal of Cleaner Production, 154, 1–11. 9. Yin Q A, Li C H, Dong L, et al. Effects of the physicochemical properties of different nanoparticles on Lubrication Performance and Experimental Evaluation in the NMQL Milling of Ti6Al-4V[J]. International Journal of Advanced Manufacturing Technology, 2018, 99(9–12): 3091–3109. 10. Yang, M., Li, C., Zhang, Y., Jia, D., Li, R., Hou, Y., Cao, H., & Wang, J. (2019). Predictive model for minimum chip thickness and size effect in single diamond grain grinding of zirconia ceramics under different lubricating conditions. Ceramics International, 45(12), 14908–14920. 11. Zhang S, Liu, W, Wang, WM. Numerical Simulation of Physical Fields during Spark Plasma Sintering of Boron Carbide [J]. Materials, 2023, 16(11). 12. Cai C Y, Liang X, An Q L, et al. Cooling/Lubrication Performance of Dry and Supercritical CO2 -Based Minimum Quantity Lubrication in Peripheral Milling Ti-6Al-4V [J]. International Journal of Precision Engineering and Manufacturing-Green Technology, 2021, 8(2): 405–421. 13. Wika K K, Litwa P, Hitchens C. Impact of supercritical carbon dioxide cooling with Minimum Quantity Lubrication on tool wear and surface integrity in the milling of AISI 304L stainless steel [J]. Wear, 2019, 426: 1691–1701. 14. Yuan S, Zhang, Y, Gao, Y . Faraday instability of a liquid layer in ultrasonic atomization [J]. Physical Review Fluids, 2022, 7(3). 15. Wenhao Xu, Changhe Li, Yanbin Zhang, Hafiz Muhammad Ali, Shubham Sharma, Runze Li, Min Yang, Teng Gao, Mingzheng Liu, Xiaoming Wang, Zafar Said, Xin Liu, Zongming Zou. 2022. Electrostatic atomization minimum quantity lubrication machining: from mechanism to application. Int. J. Extrem. Manuf.4 042003 (2022). https://doi.org/10.1088/26317990/ac9652. 16. Yang, M., Li, C., Luo, L., Li, R., & Long, Y. (2021). Predictive model of convective heat transfer coefficient in bone micro-grinding using nanofluid aerosol cooling. International Communications in Heat and Mass Transfer, 125, 105317. 17. Min Yang, Changhe Li, Zafar Said, Yanbin Zhang, Runze Li, Sujan Debnath, Hafiz Muhammad Ali, Teng Gao, Yunze Long. Semiempirical heat flux model of hard-brittle bone material in ductile microgrinding, Journal of Manufacturing Processes, 2021, 71: 501–514.

Chapter 11

Effects of Nanofluid Concentration on Heat Transfer Performances in Cryogenic Nanofluid Minimum Quantity Lubrication Grinding

11.1 Introduction Recently, new green processing modes of NMQL and CA have attracted high attention from Chinese and foreign researchers and have been studied extensively. Chinese and foreign researchers have demonstrated through abundant studies that preparing nanofluid by adding appropriate amount of nanoparticles into lubricating oil can improve lubrication capacity and cooling heat transfer capacity of lubricant more effectively [1]. The plane grinding experimental results in Chaps. 8 and 9 also prove the excellent lubrication and cooling heat transfer performances of Al2 O3 nanofluid. Based on above studies, the effects of Al2 O3 nanofluid on improvement of cooling heat transfer effect in the grinding zone under CNMQL conditions were investigated in this chapter. Moreover, influences of Al2 O3 nanofluid concentration on lubrication and cooling effects under pure MQL condition were discussed. Adding cryogenic air will surely influence physicochemical properties and atomization effect of nanofluids, thus influencing cooling heat transfer performances of the grinding zone [2]. According to literature retrieval, no study has discussed the variation of cooling heat transfer effect with Al2 O3 nanofluid concentration under CNMQL condition. Therefore, a systematic study and deep analysis of above contents are carried out in this chapter.

11.2 Experimental Design 11.2.1 Experimental Equipments The used experimental equipments are completely the same with those in Sect. 8.2.2.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_11

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11.2.2 Experimental Materials The used experimental materials and treatments are also completely the same with those in Sect. 8.2.2. The nanofluid lubricants were prepared by using KS-1008 synthesis lipid as the base oil of MQL and Al2 O3 nanoparticles as the additive.

11.2.3 Experimental Schemes The experiment is to investigate cooling heat transfer effect of Al2 O3 nanofluids with different concentrations in the grinding zone under CNMQL condition, thus enabling to determine the optimal Al2 O3 nanofluid concentration. Except Al2 O3 nanofluid concentration, other grinding parameters and other input conditions of the experiments in this chapter were all the same with those in Sect. 9.2.1. In the experiments in this chapter, six volume concentrations of Al2 O3 nanofluid were chosen, including 0.5, 1.0, 1.5, 2.0, 2.5, and 7.0%. In experiments, Al2 O3 nanoparticles with different volume fractions were added into the base oil to prepare Al2 O3 nanofluids with different volume concentrations.

11.3 Experimental Results and Discussion 11.3.1 Grinding Temperature The variation curve of the measured grinding temperature when the Al2 O3 nanofluid concentration is 0.5% is shown in Fig. 11.1. The maximum temperatures of the grinding zone which are measured in experiments under different Al2 O3 nanofluid concentrations are shown Fig. 11.2. It can be seen from Fig. 11.2 that the maximum temperatures of the grinding zone are 197.6, 187.3, 187.5, 187.5, 190.2, and 1911.3 °C when the Al2 O3 nanofluid concentration increases from 0.5 to 3%. Generally speaking, the maximum temperature of the grinding zone decreases firstly and then increase with the increase of the Al2 O3 nanofluid concentration. When Al2 O3 nanofluid concentration increases from 0.5 to 1.5%, temperature of the grinding zone decreases gradually and it reaches the minimum at 1.5%. When Al2 O3 nanofluid concentration increases from 1.5 to 3%, temperature of the grinding zone increases gradually. In view of general temperature changes, the nanofluid has some influences on grinding temperature. The maximum temperature gap of the grinding zone caused by different nanofluid concentrations is about 13 °C. The influences of Al2 O3 nanofluid concentration on temperature of the grinding zone are far weaker than those of cold air fraction.

11.3 Experimental Results and Discussion

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Temperature (

)

Peak temperature 193.6

Time (s)

Peak grinding temperature (

)

Fig. 11.1 Variation curve of grinding temperature under 0.5% of Al2 O3 concentration

220 200 180 160 140 120 100 80 60 40 20 0

193.6

0.5

187.3

1

183.5

187.5

1.5 2 Concentration (%)

190.2

196.3

2.5

3

Fig. 11.2 Maximum temperature of the grinding zone under different Al2 O3 concentrations

11.3.2 Specific Grinding Energy Specific grinding energy is one of important characterization parameters of grinding performances. The lower specific grinding energy indicates the less generation of grinding heats in removal of workpiece material per unit volume, the better lubrication effect, and the better workpiece surface quality after processing [3]. The specific grinding energy under different volume fractions of Al2 O3 nanofluids is shown in Fig. 11.3. Clearly, specific grinding energy is 74.8, 70.97, 68.6, 65.98, 64.74, and

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69.33J/mm3 when the Al2 O3 nanofluid concentration increases from 0.5 to 3%. Generally speaking, specific grinding energy decreases slowly and then increases with the increase of Al2 O3 nanofluid concentration. When Al2 O3 nanofluid concentration increases from 0.5 to 2.5%, the specific grinding energy decreases slowly and reaches the minimum at 2 and 2.5%. When Al2 O3 nanofluid concentration increases from 2.5 to 3%, the specific grinding energy increases significantly. Specific grinding energy can characterize lubrication performances directly. Hence, it can conclude from results of specific grinding energy that lubrication effect of grinding zone decreases firstly and then increases with the increase of Al2 O3 nanofluid concentration. The optimal lubrication effect is achieved at 2 and 2.5% of Al2 O3 nanofluid concentration. As Al2 O3 nanofluid concentration increases gradually, specific grinding energy declines gradually. This proves the good anti-wear, anti-friction performances and lubrication effect of Al2 O3 nanoparticles. Al2 O3 nanoparticles have excellent grinding and lubrication performances due to their spherical structures, high surface energy and surface activity, “bearing-like” effect and high hardness. The lubrication mechanism of Al2 O3 nanofluid in the grinding zone has been analyzed thoroughly in Chap. 4. With the further increase of nanoparticles, the lubrication effect declines rather than improves. This might be because nanoparticles agglomerate under high concentration condition, thus weakening lubrication performances of the lubricating oil film on grinding contact surface. This also proves that high-concentration nanoparticles are against lubrication of grinding zone [4, 5]. There’s an optimal nanoparticle concentration range to develop the best cooling and lubrication effect.

Specific grinding energy (J/mm3)

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74.8

70.97

70

68.6

65.98

64.73

69.33

60 50 40 30 20 10 0

0.5

1

1.5 2 Concentration (%)

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Fig. 11.3 Specific grinding energy under different Al2 O3 concentration

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11.3 Experimental Results and Discussion

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11.3.3 Effects of Viscosity and Contact Angle of Nanofluids on Heat Transfer Performances Viscosity of Al2 O3 nanofluids with different volume fractions at 0 °C is shown in Fig. 11.4. Clearly, viscosity presents the nonlinear increasing trend with the increase of Al2 O3 nanofluid concentration. It achieves the greatest growth when Al2 O3 nanofluid concentration increases from 0.5 to 1.5%, but the growth slows down from 1.5 to 3% and it reaches the maximum (235.8 cp) at 3%. Viscosity presents a great growth rate in the low Al2 O3 nanofluid concentration range. Since nanoparticles have very small volume size and strong irregular Brownian movement, it will increase irregular movement and energy exchange degree in nanofluids significantly, thus increasing viscosity of nanofluids. With the increase of concentration, such irregular movement and energy exchange are stronger, thus increasing viscosity gradually. If there’s excessive concentration of nanoparticles in the nanofluid suspension, particles may collide mutually and form clusters in the process of irregular movement. As a result, some nanoparticles finally agglomerate and sink for losing the original dynamic stability. Therefore, nanoparticles have an optimal concentration range to develop the best cooling and lubrication effect. This also can be well proved by specific grinding energy under different concentrations. The lubricant with higher viscosity is more beneficial to improve lubrication effect of the grinding zone. With the increase of viscosity of lubricant, the momentum diffusibility ability weakens. The frictional resistance between lubricant and workpiece surface increases, while the oil film has better stability and longer detention time. As a result, the lubrication performances of the grinding zone are improved and energy consumption during material removal is decreased. However, a higher viscosity will lead to the thinner temperature boundary layer, which will further weaken heat diffusibility of nanofluids and thereby weaken the heat exchange performances [6, 7]. The contact angle of Al2 O3 nanofluids with different concentration at 0 °C is shown in Fig. 11.5. It can be seen from Fig. 11.5 that the contact angle presents an approximate decreasing trend when the Al2 O3 nanofluid concentration increases from 0.5 to 2.5%, but it increases quickly from 2.5 to 3%. This can be interpreted from the following aspects. Molecular size of base oil is generally nanometers, while the grain size of Al2 O3 nanoparticles is about 50nm. The grain size and distribution density of Al2 O3 nanoparticles are both higher than those of base oil molecules. Al2 O3 nanoparticles can apply stronger acting pressures onto oil drops along the internal direction perpendicular to droplet surface, thus decreasing contact angle of oil droplets. With the increase of volume concentration of nanoparticles, such squeezing effect is strengthened gradually, thus resulting in the decreasing trend of contact angle [8]. However, the contact angle increases gradually after the Al2 O3 nanofluid concentration exceeds 2.5%. Reasons are explained as follows. Excessive nanoparticle concentration in nanofluid suspension finally will make some nanoparticles lose the original dynamic stability and sink, thus losing the original squeezing effect to internal structure of droplets. Hence, the contact angle increases. Given a small contact angle, the surface energy that has to be overcome for nanofluid to

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Dynamic viscosity (cP)

240 235.8

220

227.6 220.1 211.9

200 196.3

180 182.8 160 0.0

0.5

1 1.5 2.0 Concentration (%)

2.5

3.0

Fig. 11.4 Viscosity of Al2 O3 nanofluids with different concentration at 0 °C

Contact angle (°)

continue to spread on the grinding wheel-workpiece contact surface after it is sprayed decreases, while infiltration area of droplets on the grinding wheel-workpiece contact surface increases. The infiltration and spreading effect of oil film is improved, thus achieving better cooling lubrication effect. Viscosity and contact angle of nanofluid also may influence atomization effect of lubrication. The nanofluid lubricants sprayed from the nozzle are broken and

Concentration (%) Fig. 11.5 Contact angle of Al2 O3 nanofluids with different concentration at 0 °C

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atomized into small droplet groups under the disturbance of aerodynamics. These small droplet groups are sprayed onto the grinding wheel-workpiece contact surface for cooling lubrication effect [9]. Atomization is the result of mutual competition between external force and internal force of the liquid. Aerodynamics in the spraying process of liquid and fluid pressure will facilitate atomization and breaking of droplet, but surface tension of droplets make them keep spherical shape and hinder their deformation. At this moment, the surface area and surface energy of droplets are the lowest. Moreover, viscosity force of liquid also may hinder deformation of liquid. When the external force on liquid is enough to overcome surface tension and viscosity force of the liquid, the state of stress equilibrium of the liquid will be broken and the liquid is broken and atomized into fine droplet groups. In the process that lubricant carried by the low-temperature compressed air is sprayed from the nozzle, there’s energy exchange between the gas and liquid phases. Gas energy is mainly consumed to by the viscous dissipation action to overcome viscosity of the liquid and surface energy dissipation action to overcome surface tension. The rest energy is to improve kinetic energy of lubricant. Due to the energy exchange process between the gas and liquid phases, the two-phase jets have some divergence angle and impact speed, and they are finally sprayed onto the grinding zone as droplets to provide cooling lubrication effect. In view of atomization alone, the viscosity dissipation action and surface energy dissipation action losses of the gas are lower if the viscosity and surface tension of lubricant are lower. The impact kinetic energy of two-phase jets is higher and the atomization quality of droplet particles is better, thus providing better cooling lubrication effect in the grinding zone.

11.3.4 Effects of Nanoparticle Dispersibility on Heat Transfer Performances It can be seen from Fig. 11.1 that as Al2 O3 nanofluid concentration increases from 0.5 to 3%, the maximum temperature of the grinding zone declines firstly and then rises, and it decreases gradually when the Al2 O3 nanofluid concentration increases from 0.5 to 1.5%, but it begins to increase again from 1.5 to 3%. Such temperature variation trend is related with dispersibility of nanoparticles with different concentrations to some extent. Dispersibility of nanoparticles in lubricant will influence overall heat exchange effect of lubricant. According to the theory of Xuan et al. [10], nanoparticles in nanofluid are in relative uniform distribution. When there’s no agglomeration, most nanoparticles are in stable Browian movement and mutual collision form. They can further enhance heat exchange ability of suspension liquid, thus bringing the fluid better heat exchange performances. Through an experimental study of Xie et al. [11, 12], the theory that the looser agglomeration structure of nanoparticles in nanofluid brings the higher effective heat exchange volume and stronger overall heat exchange

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ability was proposed. Nanoparticles which agglomerate to some extent are beneficial to strengthen heat exchange for following reasons. Nanoparticles immersed in fluids are covered by an extremely thin layer of liquid film. Influenced by atoms on nanoparticle surface, this covering liquid film tends to solid phases, thus having thermal conductance ability similar with that of solids. Space among nanoparticles decreases continuously with the increase of nanoparticle volume content. When space among nanoparticles decreases gradually and reaches some extremum, this covering liquid film will form mutual connections and even develop compressive overlapping phenomenon (Fig. 11.6). Under this circumstance, nanoparticles are in direct contact and lap contact, decreasing the defect of poor thermal conductance of liquid under the solid–liquid–solid transfer states. The phenomenon of “hot short circuit” of direct heat transfer among solid nanoparticles is formed, thus decreasing the contact thermal resistance significantly [13, 14]. There’s some contact pressure among nanoparticle contact surfaces under direct contact and lap contact states, making the prominent part deformed. As a result, the cracks are narrowed and the contact area is expanded, thus further decreasing the contact thermal resistance. This enhances thermal conductance and overall heat transfer effect of Al2 O3 nanofluid suspension liquid [15]. It can be concluded from results of specific grinding energy and grinding temperature that Al2 O3 nanofluid concentration can keep a relatively stable dispersion effect at about 2% and has excellent lubrication and cooling heat transfer performances. As a result, it gets relatively low specific grinding energy and grinding temperature. When the nanoparticle concentration is too high, the irregular Brownian movement in suspension will be influenced. Finally, some nanoparticles lose the original dynamic stability and agglomerate and sink, thus weakening heat transfer capacity of suspension liquid. Among heats carried away from the grinding zone, most are carried away through boiling heat transfer of grinding fluid except for some carried away by strengthened convective heat transfer through compressed air. When the workpiece surface temperature of the grinding zone is higher than the saturation temperature of grinding fluid, the grinding fluid is gasified after being heated and a lot of steam bubbles are generated and escape from the workpiece surface, thus Al2O3 nanoparticles

Cladding layer (a) Dispersion

(b) Agglomeration

Fig. 11.6 Schematic diagram of “hot short circuit” of nanoparticle lap

11.4 Summary

307

Abrasives Wheel MQL nozzle

Gaps are filled with nanoparticles

Fig. 11.7 Schematic diagram of “filling blocking” effect of nanoparticles

causing boiling phenomenon. Boiling heat transfer of grinding zone is a violent evaporation process that a lot of team bubbles are produced, grow and transform the working medium from liquid state to the steam state to carry away heats. When the workpiece surface temperature exceeds the saturated temperature of grinding fluid and reaches some numerical value, the grinding fluid firstly absorb latent heats at pits and cracks on workpiece surface to produce steam bubbles. These points which can produce steam bubbles are called as vaporization cores [16]. As the heats are transferred continuously from high-temperature surface to vaporization cores, the volume of steam bubbles increases continuously and they float up until separating from the workpiece surface, thus carrying grinding heats away. It is easy to have gas residues in small pits and cracks on workpiece surface with boiling phenomenon, which are viewed as the best vaporization cores. However, nanoparticle agglomeration and sedimentation due to excessive concentrations may form “filling blocking” effect, thus decreasing the gas accommodation capacity of vaporization cores and number of cores. As a result, the boiling heat transfer capacity of lubricant in the grinding zone is weakened, thus increasing grinding temperature [17]. The “filling blocking” effect of nanoparticles is shown in Fig. 11.7.

11.4 Summary The cooling heat transfer effect of Al2 O3 nanofluids with different concentrations in the grinding zone was investigated. Influences of specific grinding energy, viscosity and contact angle, dispersibility of and atomization effect of nanoparticles under different concentrations of Al2 O3 nanofluids on cooling heat transfer were analyzed. Some conclusions could be drawn: (1) Volume fraction of Al2 O3 nanoparticles will influence cooling and lubrication of grinding processing. When nanofluid concentration increases from 0.5 to 3%, specific grinding energy decreases slowly and then increases, reaching the minimum specific grinding energy (65.98 and 64.74J/mm3 ) and the best

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lubrication effect at 2 and 2.5%The maximum temperature of the grinding zone decreases firstly and then increases with the increase of nanofluid concentration. When the Al2 O3 nanofluid concentration from 0.5 to 1.5%, the temperature of the grinding zone declines and reaches the minimum grinding temperature (187.5 °C) at 1.5%. When the Al2 O3 nanofluid concentration from 1.5 to 3%, temperature of the grinding zone increases gradually. (2) Viscosity and contact angle of nanofluid will influence heat transfer performances of grinding zone. With the increase of Al2 O3 nanofluid concentration, viscosity presents a nonlinear growth trend and reaches the maximum (235.8 cp) at 3%. The contact angle presents a variation trend of approximate linear reduction and quick growth. With the increase of viscosity, the oil film weakens the kinetic diffusibility and gains better stability and longer retention time, thus improving lubrication performances and thereby decreasing energy consumption in material removal. However, high viscosity will lead to thinner temperature boundary layer and weaken heat diffusibility of oil film, thus weakening the heat transfer performances. The smaller contact angle brings the less surface energy to overcome for nanofluids to continue to spread and diffuse after being sprayed onto the grinding wheel-workpiece contact surface. Accordingly, the infiltration area of droplets on the grinding wheel-workpiece contact surface expands and the infiltration and spreading effect of oil film are better, thus getting better cooling lubrication effect. (3) Viscosity and surface tension may influence cooling heat transfer. From the perspective of atomization, the lower viscosity and surface tension of nanofluid lubricants causes the less loss of viscosity dispersion action and surface energy dissipation action of gas, the greater impact energy of two-phase flows, and the higher atomizing quality of droplet particles. As a result, the cooling lubrication effect of grinding zone is better. (4) Dispersibility of nanoparticles in lubricant will influence the overall heat transfer effect of lubricant in grinding zone. Nanoparticles immersed in fluid will be covered by an extremely thin layer of liquid film and its heat conductivity coefficient is far higher than that of base liquid. The space among nanoparticles decreases continuously with the increase of volume content, and nanoparticles are in direct and mutual lap contact state, thus decreasing the contact thermal resistance in heat conduction process significantly. Hence, it strengthens heat conductance and heat exchange capacity of nanofluid suspension liquid. However, agglomeration and sinking of nanoparticles for excessive concentrations will form the “filling blocking” effect, thus decreasing gas carrying capacity of vaporization cores and number of cores. Hence, it weakens boiling heat transfer capability of lubricant in the grinding zone, thus increasing the grinding temperature.

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References 1. Hayat T, Nadeem S. Heat transfer enhancement with Ag-CuO/water hybrid nanofluid[J]. Results In Physics, 2017, 7: 2317–2324. 2. Mingzheng Liu, Changhe Li, Min Yang, Teng Gao, Xiaoming Wang, Xin Cui, Yanbin Zhang, Zafar Said, Shubham Sharma, Mechanism and enhanced grindability of cryogenic air combined with biolubricant grinding titanium alloy, Tribology International, 2023, 108704. 3. Mao C, Zou HF, Huang Y, et al. Research on heat transfer mechanism in grinding zone for MQL surface grinding [J]. China Mechanical Engineering, 2014, 25 (6). 4. Sayuti M, Sarhan A A D, Hamdi M. An investigation of optimum SiO2 nanolubrication parameters in end milling of aerospace Al6061-T6 alloy[J]. The International Journal of Advanced Manufacturing Technology, 2013, 67(1–4): 833–849. 5. Bianchi E C, Rodriguez, RL, Hildebrandt, RA, et al. Application of the auxiliary wheel cleaning jet in the plunge cylindrical grinding with Minimum Quantity Lubrication technique under various flow rates [J]. Improving minimum quantity lubrication in CBN grinding using compressed air wheel cleaning, 2019, 233(4): 1144–1156. 6. Mao C, Zou H, Huang Y, et al. Analysis of heat transfer coefficient on workpiece surface during minimum quantity lubricant grinding[J]. International Journal of Advanced Manufacturing Technology, 2013, 66(1–4):363–370. 7. Yang, M., Li, C., Luo, L., Li, R., & Long, Y. (2021). Predictive model of convective heat transfer coefficient in bone micro-grinding using nanofluid aerosol cooling. International Communications in Heat and Mass Transfer, 125, 105317. 8. Chinnam J, Das D, Vajjha R, et al. Measurements of the contact angle of nanofluids and development of a new correlation[J]. International Communications in Heat and Mass Transfer, 2015, 62: 1–12. 9. Min Yang, Changhe Li, Zafar Said, Yanbin Zhang, Runze Li, Sujan Debnath, Hafiz Muhammad Ali, Teng Gao, Yunze Long. Semiempirical heat flux model of hard-brittle bone material in ductile microgrinding, Journal of Manufacturing Processes, 2021, 71: 501–514. 10. Xiaoming Wang, Changhe Li, Yanbin Zhang, Wenfeng Ding, Min Yang, Teng Gao, Huajun Cao, Xuefeng Xu, Dazhong Wang, Zafar Said, Sujan Debnath, Muhammad Jamil, Hafiz Muhammad Ali. Vegetable Oil-based Nanofluid Minimum Quantity Lubrication Turning: Academic Review and Perspectives, Journal of Manufacturing Processes, 2020, 59, 76–97. 11. Xiaoming Wang, Changhe Li, Yanbin Zhang, Hafiz Muhammad Ali, Shubham Sharma, Runze Li, Min Yang, Zafar Said, Xin Liu, Tribology of enhanced turning using biolubricants: A comparative assessment, Tribology International, 2022, 107766. 12. Gao, T., Li, C., Zhang, Y., Yang, M., Jia, D., Jin, T., Hou, Y., & Li, R. (2019). Dispersing mechanism and tribological performance of vegetable oil-based CNT nanofluids with different surfactants. Tribology International, 131, 51–63. 13. Jalili B, Aghaee N, Jalili P, et al. Novel usage of the curved rectangular fin on the heat transfer of a double-pipe heat exchanger with a nanofluid[J]. CASE Studies in Thermal Engineering, 2022, 35: 102086. 14. Sheikholeslami M, Ghasemi A. Solidification heat transfer of nanofluid in existence of thermal radiation by means of FEM[J]. International Journal of Heat and Mass Transfer, 2018, 123: 418–431. 15. Rashidi S, Eskandarian M, Mahian O, et al. Combination of nanofluid and inserts for heat transfer enhancement[J]. Journal of Thermal Analysis And Calorimetry, 2019, 135(1): 437– 460. 16. Sheikholeslami M, Rokni H B. Simulation of nanofluid heat transfer in presence of magnetic field: A review[J]. International Journal of Heat and Mass Transfer, 2017, 115: 1203–1233. 17. Sheikholeslami M, Sadoughi M K. Simulation of CuO-water nanofluid heat transfer enhancement in presence of melting surface[J]. International Journal of Heat and Mass Transfer, 2018, 116: 909–919.

Chapter 12

Performances of Al2 O3 /SiC Hybrid Nanofluids in Minimum-Quantity Lubrication Grinding

12.1 Introduction Grinding process is a machining technology to improve processing quality and processing accuracy of key parts. It is mainly applied to the final processing procedure of workpiece [1]. Nevertheless, a lot of friction, high-temperature and highpressure phenomenon in the grinding zone during grinding [1, 2]. Therefore, the lubrication performances of lubricant play an extremely important role in friction interface between the grinding wheel and workpiece in the grinding zone [1]. When there’s insufficient lubricant or poor lubrication performance of lubricants in the grinding zone, the grinding force increases, and workpiece surface quality declines, thus causing damages to workpiece surfaces, such as large surface furrows, plastic deformation, scratches and cracks [3]. All of these will decrease antifriction performances and anti-fatigue performances of workpieces [4]. Hence, these not only decrease service reliability and service life of parts, but also deteriorate grinding performances and processing accuracy of the grinding wheel. The MQL mechanism of mixed nanofluids and evaluation parameters that characterize grinding performances were analyzed. The relevant grinding mechanism of ultrasonic vibration grinding and motion trails and damage formation mechanism of grains in relative to workpiece were investigated. Research conclusions lay theoretical foundations to follow-up experimental studies.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_12

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12.2 MQL Mechanism of Mixed Nanofluids 12.2.1 Thermophysical Properties of Al2 O3 and SiC Nanoparticles Al2 O3 nanoparticles are similar with characteristics of laminated structure and porosity. A lot of base oil can be adhered onto Al2 O3 nanoparticle surface, which can repair the oil film when they enter into the grinding zone with grinding fluid and increase coverage area of the oil film in the grinding zone. Hence, it can provide good lubrication effect [5]. Since heat transfer coefficient of Al2 O3 is very low (20W/m K), adding Al2 O3 fails to improve heat transfer performances of nanofluids significantly. SiC nanoparticles have a relatively high heat conductivity coefficient (83.6 W/ m K), and its atomic structure is formed by alternating lamellar stacking of carbon atoms and silicon atoms. It has some self-lubrication characteristics [6]. Therefore, adding SiC nanoparticles into base oil increases the heat conductivity coefficient of the mixed grinding fluid, and strengthens energy transfer process, thus enhancing heat transfer performances of nanofluids. Moreover, it strengthens the lubrication performances of grinding fluid to some extent. However, adding SiC cannot improve lubrication performances of nanofluids significantly due to the multi-angular appearance and high intensity. Moreover, both Al2 O3 and SiC nanoparticles can be used as abrasives of grinding wheel. Their Moh’s hardness reaches 9 level and 9.5 level, respectively. Hence, thermo-physical performances after mixing of Al2 O3 and SiC nanoparticles can be supplemented. With the hardness and special particle shapes, the mixture of Al2 O3 and SiC nanoparticles can serve for grinding and polishing on the grinding wheelworkpiece interface, thus improving workpiece surface quality effectively.

12.2.2 MQL Mechanism of Base Oil In MQL grinding, the mixture of extreme minimal quantity of lubricant and compressed air arrived at the grinding zone after being vaporization to achieve the same lubrication effects with traditional pouring grinding or even better. Reasons are explained as follows: (1) During grinding process, boundary lubrication takes the dominant role in lubrication on the grinding wheel-workpiece interface. The lubrication effect is not proportional to supply of lubricant. Therefore, lubrication effect is decided by lubricant consumption which has some ranges [7]. The consumption range of lubricant has a direct close relationship with properties of grinding wheel, workpiece material and lubricant, abrasive particle size and workpiece surface roughness. When grinding debris flows out along the front end of abrasives, there are small spaces with the front end face of abrasives, which can be filled by only

12.2 MQL Mechanism of Mixed Nanofluids

313

minimal quantity of lubricant. This lubricant consumption is far lower than that in traditional pouring grinding. (2) Although the lubricant consumption of traditional pouring grinding is considerable, only less lubricant enters into the grinding zone actually due to small pressure and low flow rate. Most lubricant only serves for cooling surrounding the grinding wheel and has poor lubrication effect. The lubricant utilization of pouring lubrication is not very high. (3) In MQL grinding, lubricant is sprayed into the grinding zone at a high speed and energy under the influence of compressed air. Compared with pouring lubrication, lubricant spray generated by MQL has a series of characteristics, including high velocity, low viscosity, small grain size, low average molecular weight and high momentum. It can easily enter into extremely small spaces where are difficult for pouring lubricant to access to, generate a very effective boundary lubrication oil film, and realize relatively good lubrication and infiltration characteristics. The lubrication effect generated by lubricant is mainly attributed to boundary lubrication film on the metal surface after lubricant infiltrates and enters into the grinding wheel-workpiece interface. The permeability of lubricant and the bonding strength between workpiece and abrasive surfaces decide the lubrication effect of boundary lubrication film. The boundary lubrication film generally can be divided into following two types: (1) Physical adsorption boundary lubrication film The boundary lubrication film formed by physical adsorption is the lubrication film formed by mutual adsorption between polar atoms and polar groups in grinding fluid molecules and metal lattice molecules [8]. The gravity field generated by metal lattice often can make the surface adsorb dozens or even hundreds of molecular adsorption layers of lubricant. “Oiliness” of lubricant oil decides lubrication performances of lubricant. Oiliness refers to adsorption strength and adsorption capacity of polar groups or polar atoms in lubricants with metal lattices. Lubricant often contains polar atoms like S, N, O and P, or polar groups like –CN, –NH2 , –OH, –COOH, –CHO, –COOR, –NCS, – COR, –NHCH3 , –NH3 , and –NROH. These components and material surfaces have excellent compatibility activity and physical adsorption phenomenon through Van der Waals’ force and molecules on metal material surface. This physical film serves for antifriction in the grinding process, thus decreasing grinding force. The length of carbon chain contained in lubricant molecules determines the adsorption durability of physical film and grinding temperature of the relatively long carbon chain is relatively high. This improves protection of such adsorption film on the workpiece surface. Due to existence of Van der Waals’ force, the physical adsorption film often has reversibility of adsorption. The adsorption layer formed at low temperature is relatively stable, but it is resolved as temperature increases gradually. Temperature for the physical film to keep adsorption performances generally is lower than 200°C-250°C. It is completely insufficient to have

314

12 Performances of Al2 O3 /SiC Hybrid Nanofluids in Minimum-Quantity …

lubrication based on physical film during grinding process. Moreover, it is necessary to add in extreme pressure additive in lubricating oil to form chemical adsorption boundary lubrication film with the metal surface. (B) Chemical adsorption boundary lubrication film The chemical adsorption boundary lubrication film is also called extreme pressure lubricating film. This film is formed chemical reaction between the extreme pressure additives in lubricating oil and workpiece metals. Such extreme pressure additives generally contain S, Cl, P and other elements. These extreme pressure additives will be decomposed in the grinding zone under high temperature and release elements with strong activity to make chemical reaction with metals on workpiece surface. Many compounds are generated on metal surface, such as ferric chloride, iron phosphide, ferric sulfide, etc. This layer of compound is the extreme pressure lubricating film. With a low melting point, low hardness and shearing strength, this extreme pressure lubricating film can decrease friction and wearing loss effectively. Fatty acid compounds are very easy to form a temporary fatty acid metallic soap with the metal surface under high temperature conditions during grinding. This is known as the “saponification reaction of metals”. During reaction, hydrogen atoms in the carboxyl –COOH are replaced with atoms on metal surface, thus forming monolayer semi-chemically bonded oily lubricating film. This adsorption film structure is composed of monolayer molecules or multi-layer molecules. This adsorption film has vertical adsorption characteristics on metal surface and it is adsorbed onto workpiece material surface tightly under the molecular interaction, thus improving lubrication of grinding zone positively. Chemical adsorption boundary lubrication film can exist stably in the grinding zone with a high temperature. If the chemical film is damaged and peeled off during processing, a new chemical film will be generated immediately on the new workpiece surface as supplementation. Hence, it can assure existence of sufficient reaction lubricating film in the grinding zone.

12.2.3 Lubrication Mechanism of Mixed Nanoparticles Nanoparticles have a higher heat conduction coefficient than lubricant in MQL and they can improve heat transfer efficiency of lubricant effectively. Moreover, nanoparticles have higher specific surface energy and specific interface energy. Lubricant can be adhered onto surfaces of nanoparticles effectively, thus increasing infiltration area of lubricant in the grinding zone. Additionally, nanoparticles have high antifriction characteristics and extreme pressure performances (Fig. 12.1). The action mechanisms of nanoparticles mainly include the following types: (1) Ball mechanism [9] On the contact surface with good smoothness, spherical or approximately spherical nanoparticles can form ball bearing effect on the friction surface and change

12.2 MQL Mechanism of Mixed Nanofluids

315

Fig. 12.1 Antifriction mechanism of Al2 O3 /SiC mixed NPs on the grinding zone

the rolling friction into rolling friction, thus decreasing friction coefficient. Hence, nanoparticles show excellent antifriction performances. (B) Filling mechanism [10] Relatively small nanoparticles can fill in furrows and damage positions on the friction surface, thus providing self-repair effect. Hence, roughness and friction coefficient are decreased. (C) Surface grinding and polishing mechanism [11] Adding some relatively hard nanoparticles into lubricating oil as abrasives is a types of polishing-like processing technique and can process relatively smooth surface. The contact area of friction pair after polishing expands and the roughness decreases, thus decreasing friction coefficient significantly. Moreover, the pressure stress of contact surface may decrease, thus improving extreme pressure performances of lubricating oil effectively. (D) Lubrication mechanism of chemical reaction film [12] Due to the high ductility performances and diffusion performances, nanoparticles form a relatively ideal diffusion layer and infiltration layer with good friction performances on metal base through infiltration and diffusion in the grinding wheelworkpiece interface. Moreover, some elements in nanoparticles may infiltrate into the base surface and even the secondary surface, and bond in the form of solid solution. They also may have chemical reaction on metal base surface to produce a chemical film with good friction performances. Mixed nanoparticles maintain all action mechanisms of nanoparticles and make uses of surface effect of nanoparticles based on original action mechanisms. Atoms on the surface layer are in the asymmetric force field, resulting in the imbalanced stresses on internal atoms. Atoms on the surface layer mainly bear action forces from the internal size, resulting in unsaturated number of atomic coordination. They are very easy to combine with external atoms and tend to be stable. Hence, two types or

316

12 Performances of Al2 O3 /SiC Hybrid Nanofluids in Minimum-Quantity …

more types of nanoparticles form the “physical coating” effect, that is, the “physical synergistic effect” of mixed nanoparticles. Such “physical synergistic effect” integrates excellent physical and chemical properties of two or more types of nanoparticles, develops the cooling lubrication effect of nanoparticles to the maximum extent, avoids thermal damages of workpieces effectively, and improves lubrication effect of mixed nanofluid on the grinding wheel-workpiece interfaces.

12.3 Performance Evaluation Parameters of Mixed NMQL 12.3.1 Grinding Force Grinding force is mainly from squeezing action of workpiece by abrasives, thus generating elasticoplastic deformation, and causing grinding debris and friction effect. It is an important parameter of grinding process, and can influence service life of grinding wheel, workpiece surface quality, grinding stability and power consumption directly. Hence, grinding force was used to diagnose various conditions in the grinding process. Grinding force can be divided into cutting force, ploughing force and sliding force. Relations are shown in Eqs. (13.1) and (13.2). Specifically, sliding force is generated by friction between abrasive-workpiece and abrasive-grinding debris interface. It is related with workpiece, material properties of grinding wheel and grinding parameters, and it is even influenced by lubrication conditions. Changing the lubrication condition may change lubrication performances in the grinding zone, thus decreasing the sliding force. However, cutting force may not change. Therefore, it shall calculate the sliding force and micro-friction coefficient to characterize lubrication performances in studies on grinding force. These can reflect influencing laws of changes of NMQL jetting parameters on sliding force. Ft = Ft,c + Ft, p + Ft,sl

(12.1)

Fn = Fn,c + Fn, p + Fn,sl

(12.2)

where F t is the tangential grinding force, F t,c is the tangential cutting force, F t,p is the tangential ploughing force, F t,sl is the tangential sliding force, F n is the normal grinding force, F n,c is the normal cutting force, F n,p is the normal ploughing force, and F n,sl is normal sliding force. (1) Calculation of single-grain cutting force The cutting force is related with grinding parameters, material properties of grinding wheel and workpiece, but it is unrelated with lubrication condition. Many scholars have carried out theoretical modeling of cutting force under dry grinding and solved it. Zhang et al. [7] considered single grain as a cone with a vertex angle of 2θ (Fig. 12.2), and got the calculation formula of cutting force of single-grain:

12.3 Performance Evaluation Parameters of Mixed NMQL

317

Fig. 12.2 Model of conical grinding grain

' Ft,c = (π/4)Fp ag2 sinθ

(12.3)

' Fn,c = Fp ag2 sinθ tanθ

(12.4)

Furthermore, Zhang et al. [13] brought the correlation coefficient of materials (k) and average grinding debris area (Am ) into the Eqs. (12.3) and (12.4), thus getting the single-grain cutting force related with materials: ' Ft,c = (3/2cosθ)k Am−ε ag2

(12.5)

' Fn,c = (6/π cosθ )k Am−ε ag2 sinθ tanθ

(12.6)

where F p is the unit grinding force (N/mm2 ), ag is the average cutting depth formed by single grain (mm), and ε ranges 0.2–0.5. (B) Calculation of single-grain ploughing force The ploughing force is to squeeze workpiece by grains and make the workpiece develop plastic deformation to form furrows. This is only related with grinding parameters, material properties of grinding wheel and workpiece, but has no direct relationship with lubrication condition. Ploughing is actually plastic deformation of materials under the action of ploughing force. The plastic deformation limit of materials is the limit of yielding [14]. Due to material isotropism, plastic deformation forces on grain surface are all perpendicular to surface and have equal values. Therefore, the single-grain ploughing force is: π

Ft,' p =

2

δs · a 2p · tan θ · sin ϕdϕ

(12.7)

0

Fn,' p = 0.5(tanθ)2πδs ap2

(12.8)

318

12 Performances of Al2 O3 /SiC Hybrid Nanofluids in Minimum-Quantity …

Fig. 12.3 The probability distribution of grain size

where δ s is the limit of yielding of workpiece materials and ap is the average ploughing depth of single grain (mm). (C) Probability calculation of number of cutting grains and ploughing grains Grain distribution on grinding wheel surface is uneven and random, and heights of grains are uneven. In Fig. 12.3, it hypothesizes that distribution of protrusion height of grains on grinding wheel agrees with normal distribution. In the grinding arc zone, the cutting depth of grains into workpiece is different due to the inconsistent protrusion height of grains. This is because grains in the grinding arc zone mainly exists following states: cutting, ploughing, scratching, contact and non-contact. Grains in cutting, ploughing and scratching states take the dominant role in grinding process. These three states are different from cut-in depth of grains. Therefore, the probability function of different cut-in depths can be calculated through the probability function of different heights of grains, thus enabling to calculate the proportion of grains in cutting, ploughing and scratching states in total grains. The number of grains per unit area (Ns) was calculated according to the maximum diameter (d max ), minimum diameter (d min ) of grains in grinding wheel as well as percentage of grains (w):  Ns =

8 w π(dmax − dmin )3

 23 (12.9)

Therefore, the total grain number in the grinding arc zone (N total ) is calculated according to diameter of the grinding wheel (D), grinding width (b) and grinding depth (ap ):  Ntotal = Ns · b · D · arccos

D − ap D

 (12.10)

Zhang et al. [13] established a formula of micro material removal rate (V ana ). According to the law that macro material removal rate (V exp ) is equal to V ana in the grinding process, the difference (hin ) between d max and d min is gained:

12.3 Performance Evaluation Parameters of Mixed NMQL

Vana

1 = l · Ntotal √ 2π

+∞

319

gx2 · tan θ · e−x

2

/2

dx

(12.11)

xcut min

where l is the grinding arc length and x cut min is the x-coordinate corresponding to the minimum cutting grains. According to hin , x value corresponding to diameter of ploughing grains is calculated:   10 dmax − dmin xcon min = (12.12) − h in · 2 dmax − dmin According to modern grinding theory, cutting effect occurs when the cut-in depth of grains reaches 0.05 times of radius of cutting grains and x-value corresponding to the minimum diameter of cutting grains is: xcut min = xcon min + 0.05

  10 dcut min 2 dmax − dmin

(12.13)

On this basis, the proportion of ploughing grains (Pplow ) and the proportion of cutting grains (Pcut ) can be calculated:

Pplow

Pcut

1 =√ 2π 1 =√ 2π

+∞

e−x

2

/2

dx

(12.14)

xcon min

+∞

e−x

2

/2

dx

(12.15)

xcut min

(D) Calculation of cutting force and ploughing force Based on above analysis, F tc , F nc , F tp , F np , Pplow and Pcut all can be calculated according to above theoretical formulas. Therefore, the total cutting forces (F tc , total , F nc , total ) and the total ploughing forces (F tp , total , F np , total ) at a fixed moment can be calculated: Ftc,total = Ftc Pcut Ntotal

(12.16)

Fnc,total = Fnc Pcut Ntotal

(12.17)

Ftp,total = Ftp Pplow Ntotal

(12.18)

Fnp,total = Fnp Pplow Ntotal

(12.19)

320

12 Performances of Al2 O3 /SiC Hybrid Nanofluids in Minimum-Quantity …

12.3.2 Micro-friction Coefficient Friction coefficient also can be defined as force ratio. It is calculated from the ratio between tangential grinding force (F t ) and normal grinding force (F n ). The friction coefficient directly reflects lubrication effect on the grinding wheel-workpiece interface. The smaller friction coefficient indicates the better lubrication effect between grains and workpiece in the grinding zone. The calculation formula is: μ=

Ft Fn

(12.20)

where F t is the tangential grinding force, F n is the normal grinding force, and μ is the friction coefficient. In the grinding process, the friction coefficient generally ranges within 0.2–0.7. The value of friction coefficient has no direct relationship with the contact area, but it has direct relationship with surface roughness of workpiece. Micro friction coefficient (μsl ) is the ratio between the tangential sliding force (F t,sl ) and normal sliding (F n,sl ), as shown in Eq. (12.21). It characterizes lubrication effect on the grinding wheel-workpiece interface and grinding wheel-grinding debris interface. Since influences of cutting force and ploughing force are eliminated, μsl can reflect lubrication performances of the grinding zone which change with lubrication conditions more intuitively. μsl =

Ft,sl Fn,sl

(12.21)

12.3.3 Specific Grinding Energy Specific grinding energy (U) is the energy consumption per unit volume of material removal and its calculation formula is: es =

P Ft vs = Qw vw a p b

(12.22)

where P is the total energy consumption per unit time (J). Qw is the volume of workpiece removal in unit time (mm3 ). Ft is the tangential grinding force (N). vs is the circumferential velocity of grinding wheel (m/s). vw is the feeding speed of workpiece (mm/s). ap is the grinding depth (mm). b is the grinding width (mm). The specific grinding energy also reflects the lubrication effect of the grinding wheel-workpiece interface. Given the same grinding condition and materials, a low specific grinding energy is corresponding to a good lubrication effect; otherwise, the lubrication effect is relatively poor. In this plane grinding test, the total energy consumed per unit time (P), the volume of workpiece removal in unit time (Qw ),

12.3 Performance Evaluation Parameters of Mixed NMQL

321

rotating speed of grinding wheel (vs ), workpiece feeding speed (vw ), grinding depth (ap ) and grinding width (b) were fixed. The tangential cutting forces (Ft) of each group was the mean. These parameters were brought into Eq. (12.22) to get the corresponding specific grinding energy.

12.3.4 Removal Parameters of Workpiece The workpiece removal parameter (Λw ) can be used to evaluate grinding efficiency and grinding difficulty of workpiece. The physical significance is the volume of cutting metals by unit normal force in the unit time [15]. Λω =

VW Fn

(12.23)

The higher value of Λw indicates the higher grinding efficiency. V W refers to volume of cutting metals in unit time and F n is normal force.

12.3.5 Workpiece Surface Quality The surface quality of workpiece is an important evaluation standard of grinding performances and surface roughness is an important evaluation parameter of surface quality. It is usually used to characterize workpiece surface quality directly and has significant influences on usability of mechanical parts. A low surface roughness indicates the high surface evenness of workpiece. (1) Arithmetic mean height of profile (Ra) The arithmetic mean height, or known as the central line mean, is the most common roughness parameter in general quality control. This parameter is defined as the irregular mean absolute deviation of roughness of mean line within a sampling length. The mathematical definition of arithmetic mean height is: 1 Ra = l

l |y(x)|d x

(12.24)

0

where l is the sampling length (mm) and y(x) is the longitudinal coordinate at the x-coordinate. (B) Mean width of profile unit (RSm) This parameter is defined as the mean distance among profile peaks of the mean line and it is expressed by RSm. The profile peak is the highest point of the upper and

322

12 Performances of Al2 O3 /SiC Hybrid Nanofluids in Minimum-Quantity …

lower mean lines and the mathematical definition is: n 1  RSm = Si N i=1

(12.25)

where N is the number of units in the sampling length and S i is the width of each unit. (C) Profile supporting length rate (Rmr) All characteristics of workpiece surface roughness contain both Ra value along the height direction and the transverse space parameter of RSm. These two parameters are insufficient to reflect influences on usability of parts. Since profile curves have different shapes between peaks and valleys, these might have different degrees of influences on using performances of parts. Therefore, it also need shape feature parameters that can characterize microscopic unevenness. Hence, profile supporting length rate (t p ) and profile supporting length rate curve were introduced in. The value of t p is the only one parameter to evaluate the microscopic surface shape characteristics and it can reflect friction and wearing performances of workpiece surface directly. t p is the profile supporting length rate on the unit length and it is expressed in percentages. The mathematical expression of t p is:  n   t p = (η p )/l = bi /l

(12.26)

i=1

where η p is the sum of lengths of sections formed by lines parallel to the midline in the sampling length l and the profile.

12.4 Research on Grinding Surface Homogeneity 12.4.1 Autocorrelation Analysis of Workpiece Surface Profile The rough surface profile measured by the Stylus profilometer is mainly viewed as a mathematical model of ordinary random process (Fig. 12.4). τ is a space coordinate. x(t) and x(t + τ ) are heights above the profile parameter baseline. Traditional transversal and longitudinal roughness parameters can express finite geometric information of surface profile blindly. The application of autocorrelation function on surface morphology is used to express degree of similarity at the same displacement difference between two profile waveforms (τ 0 ) [16]. The autocorrelation function is calculated as:

12.4 Research on Grinding Surface Homogeneity

y

x(t+τ)

x(t)

323

Contour curve

x τ Fig. 12.4 Autocorrelation function

1 Rx (τ) = L

L x(t)x(t + τ)dt

(12.27)

0

where τ is the lateral displacement and L is the evaluation length. The digital estimation formula is: AC F(r h) =

N −r −1 1 Yn Yn+r (r = 0, 1, 2, 3, . . . , m; m Mix(1:2) > Mix(1:1). The “physical encapsulation” structure has not been formed completely under Mix(1:2) and Mix(1:1) nanofluid MQL conditions, and the lubrication effect is not ideal. There’s friction coefficient µ = 0.28, specific grinding energy U = 60.68 J/mm3 and Ra = 0.323 μm under Mix(2:1) nanofluid MQL condition, which are 6.7, 20.1 and 29.3% lower than those under pure Al2 O3 nanofluid MQL condition. Therefore, Mix(2:1) achieves the best lubrication performances among mixed nanoparticles. Therefore, Mix(2:1) is the optimal mixing ratio.

References 1. Jia DZ, Li CH, Zhang YB, et al. Specific energy and surface roughness of minimum quantity lubrication grinding Ni-based alloy with mixed vegetable oil-based nanofluids[J].

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13 Grinding Performances of Al2 O3 /SiC Mixed Nanofluid MQL … Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology, 2017, 50: 248–262. Zhang X, Li C, Zhang Y, et al. Lubricating property of MQL grinding of Al2 O3 /SiC mixed nanofluid with different particle sizes and microtopography analysis by cross-correlation[J]. Precision Engineering 2017; 47: 532–545. Zhang X, Li C, Zhang Y, et al. Performances of Al2 O3 /SiC hybrid nanofluids in minimumquantity lubrication grinding[J]. International Journal of Advanced Manufacturing Technology, 2016, 86: 3427–3441. Xiaotian Zhang, Changhe Li, Zongming Zhou, et al. Vegetable Oil-Based Nanolubricants in Machining: From Physicochemical Properties to Application. Chinese Journal of Mechanical Engineering (2023) 36:76. Yuan SW, Feng YH, Wang X, et al. Molecular dynamics simulation of thermal conductivity of mesoporous α-Al2 O3 [J]. Acta Physica Sinica, 2014, 63(1):220–227. X. Cui, C.H. Li, W.F. Ding, et al. Minimum quantity lubrication machining of aeronautical materials using carbon group nanolubricant: from mechanisms to application, Chinese Journal of Aeronautics, 2022, 35(11):85–112. Jia D, Li C, Zhang Y, et al. Experimental research on the influence of the jet parameters of minimum quantity lubrication on the lubricating property of Ni-based alloy grinding[J]. International Journal of Advanced Manufacturing Technology, 2016, 82(1–4): 617–630. Malkin S, Cook N H. Wear of Grinding Wheels. Part 1. Attritious Wear[J]. Journal of Engineering for Industry, 1971, 93(4). Prestigiacomo C, Biondo M, Galia A, et al. Interesterification of triglycerides with methyl acetate for biodiesel production using a cyclodextrin-derived SnO@gamma-Al2 O3 composite as heterogeneous catalyst. 2022, Fuel, 321:15. Tran G T, Nguyen N T H, Nguyen N T T, et al. Plant extract-mediated synthesis of aluminum oxide nanoparticles for water treatment and biomedical applications: a review. Environmental Chemistry Letters, 2022, 21(4):2417–2439. Shao Y, Fergani O, Li B, et al. Residual stress modeling in minimum quantity lubrication grinding[J]. The International Journal of Advanced Manufacturing Technology, 2016, 83(5): 743–751. Zhang Y, Li C, Yang M, et al. Experimental evaluation of cooling performance by friction coefficient and specific friction energy in nanofluid minimum quantity lubrication grinding with different types of vegetable oil[J]. Journal of Cleaner Production, 2016, 139: 685–705. Yanbin Zhang, Hao Nan Li, Changhe Li, et al. Nano-enhanced biolubricant in sustainable manufacturing: From processability to mechanisms. Friction. 2021, 10(6): 803–841. Yang M, Li C, Zhang Y, et al. Maximum undeformed equivalent chip thickness for ductilebrittle transition of zirconia ceramics under different lubrication conditions[J]. International Journal of Machine Tools & Manufacture, 2017, 122. Wang Y, Li C, Zhang Y, et al. Comparative evaluation of the lubricating properties of vegetable-oil-based nanofluids between frictional test and grinding experiment[J]. Journal of Manufacturing Processes, 2017, 26: 94–104 Zhang LD. Nano materials and nano structure. Bull Chin Acad Sci, 2001, 6(06): 444–445. Yang M, Li C, Zhang Y, et al. Microscale bone grinding temperature by dynamic heat flux in nanoparticle jet mist cooling with different particle sizes[J]. Materials & Manufacturing Processes, 2017: 1–11. Zakaria R, Ruyet D L. Theoretical Analysis of the Power Spectral Density for FFT-FBMC Signals[J]. IEEE Communications Letters, 2016, 20(9):1748-1751. Yuying YANG, Min YANG, Changhe LI, Runze LI, Zafar SAID, Hafiz Muhammad ALI, Shubham SHARMA. Machinability of ultrasonic vibration assisted micro-grinding in biological bone using nanolubricant. Front. Mech. Eng. 2022, https://doi.org/10.1007/s11465-0220717-z. Li L, Gu ZM, Gu C, et al. Research on the tribological properties of mixtures of nano-particles of CeO2 and TiO2 as lubricating oil additives. Mar Technol, 2007, 5: 41–43.

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Chapter 14

Lubricating Property of MQL Grinding of Al2 O3 /SiC Mixed Nanofluid with Different Particle Sizes and Microtopography Analysis by Cross-correlation

14.1 Introduction The lubrication performances of nanofluid take the dominant role in processing performances of MQL grinding. Improving lubrication performances of nanofluid effectively becomes a major research trend at present. Specifically, different mixing ratios may generate different “physical synergistic effect” and “physical encapsulation” effect. The lubrication performances of nanofluid is optimized through optimization of grain size combination of nanoparticles in nanofluid. It is one of effective ways to improve processing performances of MQL grinding. Previous scholars have studied influences of grain size of single nanoparticle on tribological properties and lubrication performances of nanofluid. However, only few scholars have studied influences of mixed nanoparticles with different grain sizes on lubrication performances of MQL grinding. Hence, the tribological characteristics of grinding wheel-workpiece interface during NMQL grinding are improved by optimizing the mixing of nanoparticles with different grain sizes. Moreover, it can decrease grinding force, improve workpiece surface quality, and realize low-carbon green cleaning production with high efficiency, low energy consumption, environmental protection and resource saving. Al2 O3 and SiC nanoparticles with different grain sizes were mixed, which was then mixed with base oil to prepare nanofluid. Experiments of NMQL grinding of highhardness material Ni-based alloy were carried out. The size ratio of Al2 O3 /SiC mixed nanofluid to generate the best lubrication performances was explored by analyzing grinding performance parameters (specific grinding force, workpiece removal parameters, surface roughness (Ra, RSm and profile supporting length rate), morphology of grinding debris and contact angle) as well as cross correlation analysis of workpiece surface profile curves.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_14

353

354

14 Lubricating Property of MQL Grinding of Al2 O3 /SiC Mixed Nanofluid …

14.2 Experimental Design 14.2.1 Experimental Equipments The grinding equipments and parameters in experiments are the same with those in Sect. 3.2.1. The contact angle between droplets and workpiece is measured by using JC2000C1B contact angle gauge.

14.2.2 Experimental Materials Al2 O3 /SiC mixed nanoparticles at the volume fraction ratio of 2:1 (hereinafter referred as Mix(2:1)) was applied to prepare nanofluid. In previous studies [1], the nanofluid prepared by Mix(2:1) and base oil was sprayed onto the grinding zone as droplets through the MQL device, thus achieving the best lubrication effect [2] and the best workpiece surface quality. Therefore, the mixing volume ratio was determined 2:1 in experiments in this section. Bluebe #LB-1 synthesis lipid was applied as the base oil. It has following advantages: (1) it is composed of vegetable oil, non-toxic, harmless, no odor and nonvolatile. (2) Excellent lubrication performances: it can prolong service life of grinding wheel under various conditions and maintain bright and perfect workpiece surface without damages [3]. (3) Good cooling performances: low viscosity. It can eliminate stresses on grinding wheel and workpiece produced by temperature changes, and has outstanding cooling effect. (4) Environmental protection: it conforms to international environmental protection regulations and it is easy to be decomposed, conforming to sustainable development strategies.

14.2.3 Experimental Schemes The size ratio of mixed Al2 O3 and SiC nanoparticles was recorded as mix(x:y) in experiments. A total of 9 groups were divided according to size ratios of mixed Al2 O3 and SiC nanoparticles, which were mix(30:30), mix(50:50), mix(70:70), mix(30:50), mix(30:70), mix(50:30), mix(50:70), mix(70:30), and mix(70:50), respectively. These 9 groups of mixed nanoparticles were mixed with synthesis lipid at the 2% volume fraction to prepare grinding fluid for NMQL. The tangential grinding force (F t ) and normal grinding force (F n ), surface roughness (Ra and RSm) and contact angle of droplets on workpiece in 9 groups of experiments were measured, respectively. The experimental designs are shown in Table 14.1.

14.3 Experimental Results

355

Table 14.1 Experiment schemes Experiment No. 1

2

3

mix(30:30)

Grain size (nm) Al2 O3

SiC

Volume fraction (vol %)

Mixing ratio of volume fraction

30

30

2

2:1

mix(30:50)

50

2

2:1

mix(30:70)

70

2

2:1

mix(50:30)

30

2

2:1

mix(50:50)

50

2

2:1

mix(50:70)

70

2

2:1

mix(70:30)

50

30

2

2:1

mix(70:50)

70

50

2

2:1

mix(70:70)

70

2

2:1

14.3 Experimental Results 14.3.1 Specific Grinding Force Specific grinding force is divided into specific tangential grinding force (Ft' ) and specific normal grinding force (Fn' ). The calculation formulas are: Ft' =

Ft b

(14.1)

Fn' =

Fn b

(14.2)

where F t is the tangential grinding force, F n is the normal grinding force, and b is the width of grinding wheel. According to calculation formulas of specific grinding force [Eqs. (14.1) and (14.2)], specific grinding forces of 9 groups of different grain size were gained (Fig. 14.1). Given the fixed grain size of Al2 O3 nanoparticles, the specific normal grinding force in Al2 O3 /SiC mixed NMQL grinding increases gradually with the increase of SiC grain size. However, the specific normal grinding force generally presents a decreasing trend with the increase of Al2 O3 grain size. Specifically, mix (70:30) achieves the lowest specific normal grinding force (2.645 N/mm), accompanied with a relatively low SD. It is 28.2% lower compared to mix (30:70) = 3.683 N/mm. Compared to specific normal grinding force, the variation trend of specific tangential grinding force is not obvious. Specific tangential grinding forces in 9 groups of experiments were compared. The maximum specific tangential grinding forces were achieved in mix(30:30), mix(50:50), and mix(70:70), which were 1.226 N/mm, 1.196 N/mm and 1.296 N/mm, respectively. The lowest specific tangential grinding force

356

14 Lubricating Property of MQL Grinding of Al2 O3 /SiC Mixed Nanofluid …

Fig. 14.1 Specific grinding forces of different size ratios of Al2 O3 /SiC mixed nanoparticles

was achieved in mix(70:30), which was 0.809 N/mm, accompanied with a relatively high SD. It is 37.6% lower than the maximum specific tangential grinding force: mix(70:70) = 1.296 N/mm. Clearly, mix(70:30) achieved the lowest specific normal grinding force and specific tangential grinding force among 9 groups of experiments, showing the best lubrication effect.

14.3.2 Removal Parameters of Workpiece The grinding efficiency and degree of difficult-to-grind of workpiece can be evaluated by the workpiece removal parameter (Λw ). It refers to volume of the removed metals by unit normal force in unit time [4]. It is expressed as Eq. (2.23). Λw reflects the grinding efficiency of workpieces and a high value reflects the high grinding efficiency of workpiece. The workpiece removal parameters under 9 working conditions were calculated according to Eq. (2.23). Results are shown in Fig. 14.2. It can be seen clearly from Fig. 14.2 that among Al2 O3 /SiC mixed nanofluids, the workpiece removal parameter when the Al2 O3 grain size is 70 nm has obvious advantages compared to the rest two grain sizes. Specifically, mix(70:30) gets the highest workpiece removal parameter (189.05 mm3 /(s·N)), showing the highest grinding efficiency. Moreover, mix(30:70) achieved the minimum workpiece removal parameter (135.77 mm3 /(s·N)), showing the lowest grinding efficiency. With the increase of

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Fig. 14.2 Workpiece removal parameter

grain size of SiC, the workpiece removal parameter presented a decreasing trend. Accordingly, grinding efficiency of workpiece declined gradually and it was inversely proportional to grain size of SiC.

14.3.3 Surface Roughness of Workpiece Yang [5] established a mathematical model for weight analysis of surface roughness evaluation parameters and discussed weights of Ra, Rz, RSm and Rmr that influence surface roughness. In this study, it has found that Ra contains most information of micro-unevenness and it is enough to characterize surface features and usability of surface roughness. Hence, Ra was chosen firstly to characterize surface roughness. However, it cannot characterize intervals of roughness, while RSm can characterize interval of roughness well. Rmr characterizes the roughness profile shape and it is related with frictional wear of surface and can reflect the contact area of surface directly [6]. In a word, Ra was the main indicator of surface roughness, assisted with RSm and Rmr. 1. Arithmetic mean height of workpiece surface profile (Ra) and mean width of profile unit (RSm) Ra and its SD under Al2 O3 /SiC mixed nanofluid MQL grinding with different size ratios were measured by a TIME3220 roughness tester. Results are shown in Fig. 14.3. The RSm and its SD are shown in Fig. 14.4.

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0.386

70:50 70:30

0.352 0.347

Partical size ratio

50:70 50:30

0.298 0.308

30:70

0.331

30:50 70:70

0.389

50:50

0.355 0.314

30:30 0.00

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Ra (μm)

Fig. 14.3 Ra and SD of MQL grinding using different nanofluids

70:50

0.0396 0.0381

Partical size ratio

70:30

0.0451

50:70

0.0408

50:30 30:70

0.0414

30:50

0.0416

70:70

0.0453

50:50

0.0388

30:30

0.0392

0.00

0.01

0.02

0.03 0.04 RSm (mm)

0.05

0.06

Fig. 14.4 RSm and SD of MQL grinding using different nanofluids

It can be seen from Fig. 14.3 that Ra under mix(30:30), mix(50:50) and mix(70:70) MQL conditions were 0.314 μm, 0.355 μm and 0.389 μm, respectively. With the increase of grain size of the mixed nanoparticles, Ra increases gradually. Secondly, given the fixed SiC grain size in the Al2 O3 /SiC mixed nanofluid, Ra increases significantly with the increase of Al2 O3 grain size. Hence, changes of Al2 O3 grain size in the Al2 O3 /SiC mixed nanofluid could influence Ra significantly. Under 9 working conditions, mix(50:30) achieved the lowest Ra (0.298 μm), which was 23.4% lower compared to the maximum value (mix(70:70) = 0.389 μm). Besides, the SD was relatively low (1.92 × 10−2 ), indicating the small dispersion degree of Ra at different

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points on the workpiece to the mean. In other words, the whole workpiece surface has a relatively high precision. On workpiece surface after grinding, RSm reflects the diameter of “furrows” when grains cut the workpiece. A large diameter of “furrows” will lower surface quality of the workpiece. It can be seen from Fig. 14.4 that SiC grain size in the Al2 O3 /SiC mixed nanofluid influences RSm more obviously. For example, RSm(70:30) = 0.0381 mm, RSm(70:50) = 0.0396 mm, and RSm(70:70) = 0.0452 mm. In other words, RSm increases gradually with the increase of SiC grain size when the Al2 O3 grain size is fixed, and the “furrows” on workpiece surface are larger. Specifically, mix(70:30) gets the lowest RSm, indicating the small diameter of “furrows” when grains cut the workpiece. This reveals that a high-quality workpiece surface is formed. However, SD of RSm is relatively high. The RSm at different points on the workpiece has great dispersion degree to means, indicating the low precision of workpiece surface. 2. Profile supporting length rate (Rmr) Sometimes, Ra and RSm are not enough to characterize all features of surface roughness. They cannot reflect influences on part performances [7]. Different shapes between peaks and valleys of the profile curve have different influences on usability of parts. Therefore, it is necessary to involve shape feature parameters that characterize microscopic unevenness. Hence, profile supporting length rate (t p ) and profile supporting length rate curve were introduced in [8]. Abbott and Firestone analyzed functional characteristics of surface by using profile supporting length rate [9]. They acquired 3 parameters from the AbbottFirestone profile supporting length rate curve, namely, peak roughness, middle roughness and valley roughness. These three parameters were corresponding to three parts of the profile supporting length rate curve, which were profile peak, core profile and profile valley [10]. Specifically, profile supporting length rate Mr1 (%) is determined for a transversal which is used to separate the profile peak from the core profile of roughness. The profile supporting rate Mr2 (%) is determined for a transversal which is used to separate profile valley from the core profile of roughness [11]. Under 9 working conditions, the relatively low Ra was achieved under mix(30:70) and mix(50:30), which were 0.308 and 0.298 μm. A relatively low RSm (0.0381 mm) was gained under mix(70:30). Hence, profile supporting length rate curves of workpiece surface under mix(30:70), mix(50:30) and mix(70:30) were analyzed, as shown in Fig. 14.5, respectively. Obviously, given the same horizontal intercept of profile, Mr2 under mix(30:70) was closer to the right. Moreover, profile supporting length rate (t p ) under mix(30:70) was longer than those under mix(70:30) and mix(50:30), which reaches 90%. In other words, the overall distribution of microscopic peaks on workpiece surface is more precise and uniform. When the friction surface of workpiece is worn to some extent, a large supporting area will be produced, showing high surface supporting performances. This means that the workpiece surface quality is relatively good. The profile valley areas on the profile supporting length ratio curve under mix (50:30) and mix (70:30) are relatively large. This implies that there are more and deep “furrows” on workpiece surface, and the surface quality is relatively poor. Due to the large profile valley area, it has good oil storage performances,

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Fig. 14.5 Profile supporting length rate curve

thus improving the lubrication effect effectively. Hence, the lowest specific normal grinding force and specific tangential grinding force in Group 2 and Group 3 were acquired under mix(50:30) and mix(70:30) in Fig. 14.1, showing good lubrication performances.

14.4 Analysis and Discussion 14.4.1 Lubrication Mechanism of Al2 O3 /SiC Mixed Nanofluids with Different Physical Encapsulation Effects Al2 O3 nanoparticles and SiC nanoparticles have different physical properties and shape characteristics. The nanofluid formed by mixing Al2 O3 nanoparticles and SiC nanoparticles at different size ratios and the lubricating oil provides different lubrication effects during MQL grinding. Al2 O3 nanoparticles are hard materials and they are approximately spherical, showing a relatively high specific surface area and adsorption. There are very strong polarity of chemical bonds between Al3+ and O2− , accompanied with great lattice energy. As a result, Al2 O3 nanoparticles have high melting point, high strength and good chemical stability [12]. SiC, or known as carborundum, belongs to a type of hard material and have multiangular shapes. The Moh’s hardness of SiC can reach 0.5. It is a compound formed carbon atoms and Si atoms through covalent bonds. It has hexahedral crystal structure similar with diamond, and has very high hardness and melting point. Moreover, SiC has remarkable chemical stability and thermal stability as well as excellent mechanical and heat conduction performances [1]. Scholars have proposed some mechanisms for nanoparticles to improve performance of lubricating oil successively during experimental studies on lubrication

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performances by using nanoparticles as additives [13–15]. In a word, the mechanism for hard nanoparticles like Al2 O3 and SiC to improve performances of lubricating oil include: (1) ball mechanism: for contact surface with good smoothness, spherical or approximately spherical nanoparticles can form ball bearing effect on the friction surface and change sliding friction into rolling friction, thus decreasing friction coefficient and showing excellent antifriction performances. (2) Filling mechanism: relatively small nanoparticles can fill in furrows and damages on friction surface, thus providing self-recovery effect, decreasing roughness and lowering the friction coefficient. (3) Surface grinding and polishing mechanism: it is a precise polishing technique to add some hard nanoparticles into lubricating oil as polishing materials, and it can process super-smooth surface. The roughness of friction pairs after polishing decreases and the contact area increases, thus decreasing the friction coefficient. Moreover, the pressure stress of contact surface decreases and the carrying capacity of lubricating oil increases. The Al2 O3 /SiC mixed nanoparticles was used as lubricant additive and mixed with lubricating oil to form nanofluid. The nanofluid was sprayed onto the grinding zone through a MQL system, thus realizing good lubrication effect. The microstructure of Al2 O3 nanoparticles is approximately spherical and has high loading capacity and good chemical stability, they adhere onto the grinding wheel-workpiece interface after sprayed by the MQL nozzle. As a result, the sliding friction between the grinding wheel and interface was changed into rolling friction, providing the “ball effect” and improving antifriction effect and extreme pressure performances of nanofluid [16]. Secondly, small nanoparticles can fill in “furrows” and other positions on workpiece friction surface to improve lubrication effect of nanofluid. Additionally, Al2 O3 nanoparticle surfaces have relatively strong adsorption and they could be adhered with base oil well, which can increase coverage area of oil film on the grinding zone and thereby enhances lubrication performances of nanofluid [17]. Different from Al2 O3 nanoparticles, SiC nanoparticles have irregular and multiangular shapes, so they cannot achieve the ideal “ball effect” on the grinding wheel-workpiece interface as same as that of spherical Al2 O3 nanoparticles. The major mechanism for SiC nanoparticles to improve lubrication performances of base oil is attributed to the grinding polishing mechanism of the workpiece friction surface and self-lubrication characteristics of SiC. They not only offer good lubrication performances and extreme performances of base oil, but also produces grinding effect on the workpiece effect and decreases workpiece surface roughness effectively. Combining with characteristics of Al2 O3 nanoparticles and SiC nanoparticles, it achieves complementary lubrication effect and avoids their adverse effects on lubrication performances in MQL after they are mixed, thus realizing the “physical synergistic effect”. This is mainly manifested by physical modification effect between Al2 O3 nanoparticles and SiC nanoparticles, which is known as the phenomenon of “physical encapsulation”. The phenomenon of “physical encapsulation” is attributed to surface effect of nanoparticles. With the decrease of nanoparticle size, the proportion of atoms on nanoparticle surface in total atoms increases dramatically, and the specific surface area of nanoparticles increases quickly. Moreover, decreasing grain size will produce higher specific surface energy and specific interface energy [18].

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Since atoms on nanoparticle surface layer are in an asymmetric force field, there are imbalanced stresses on internal atoms. Atoms on surface layer mainly undertake the stress from the internal side, which lead to unsaturated coordination number of atoms. Atoms on surface layer are very easy to tend to be stable by combining with external atoms. Hence, Al2 O3 /SiC mixed nanoparticles with different size ratios will produce diversified “physical encapsulation” effect after they are delivered to the grinding zone through the MQL system. The phenomena of “physical encapsulation” of Al2 O3 /SiC mixed nanoparticles with different size ratios are shown in Fig. 14.6. In 9 groups of experiment, relatively ideal grinding effects were achieved under mix(30:70), mix(50:30) and mix(70:30) due to such “physical synergistic effect”. The lowest specific tangential grinding force and relatively high surface quality in Group 1 were achieved under mix(30:70). Reasons can be explained as follows. Given the fixed volume fraction of nanofluid, the number of Al2 O3 nanoparticles increases with the decrease of grain size. Small Al2 O3 nanoparticles have good physical modification to large SiC nanoparticles, thus achieving good “physical encapsulation” effect. It can be seen from Fig. 14.6a that Al2 O3 nanoparticles generate good ball and filling effect in the grinding zone, thus achieving good lubrication effect. The large SiC nanoparticles only serves for auxiliary grinding. SiC nanoparticles under mix(50:30) and mix(70:30) have a small grain size. There are more SiC nanoparticles under mix(50:30) and mix(70:30) than other mixed nanofluid and they mainly serve for grinding, improving workpiece surface quality. It can be seen from Figs. 14.3 and 14.4 that the nanofluid under mix(70:30) fails to achieve the ideal workpiece surface quality, manifested by the high Ra and high SD of RSm. In other words, there are large “furrows” on workpiece surface. This is because the excessive small SiC nanoparticles intensify wearing of workpiece surface, which causes the opposite effect. Fig. 14.6 “Physical encapsulation” phenomenon of the Al2 O3 /SiC mixed nanoparticles with different grain sizes

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14.4.2 Effects of Contact Angle Between NMQL Droplet and Workpiece Surface on Lubrication Performances MQL grinding fluid is sprayed into the grinding zone as droplets after being sprayed from the nozzle to provide cooling and lubrication effect between workpiece and grinding wheel. Hence, the state when droplets fall onto the workpiece determine the lubrication effect. The state of droplet here refers to the contact angle between the droplet and the workpiece. During grinding process, a small contact angle of droplets represents a large infiltration area of droplets. This refers to the effective lubrication area of MQL grinding fluid. The larger infiltration area brings more sufficient lubrication effect of MQL grinding fluid and the better workpiece surface quality. If the contact angle of droplets is too large, it may cause inadequate infiltration area to produce full lubrication effect. Surface tension of droplets is an internal factor that influences the contact angle between droplets and workpiece. The smaller surface tension brings the smaller contact angle between droplets and workpiece [19]. The measurement of contact angle between nanofluid MQL droplets and Ni-based alloy is shown in Fig. 14.7. The Al2 O3 /SiC mixed nanofluid with different size ratios achieved different contact angles. The contact angles of droplets under 9 groups of Al2 O3 /SiC mixed nanofluid MQL conditions were compared (Fig. 14.7). Obviously, the contact angles of droplets

Fig. 14.7 Contact angle between nanofluid MQL droplets and workpiece

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under mix(30:70), mix(50:30) and mix(70:30) were relatively low, valuing 35.5°, 30.5° and 41.0°. This reflects that large infiltration areas were acquired in these three groups, which produced more sufficient lubrication effect on the grinding wheelworkpiece interface. Hence, good workpiece surface quality was achieved under mix(30:70), mix(50:30) and mix(70:30). Secondly, the smallest contact angle of droplets was achieved under mix(50:30), which was corresponding to the lowest Ra (0.298 μm). This confirms that the contact angle between droplet and workpiece has great influences on Ra.

14.4.3 SEM Analysis of Grinding Debris It is widely accepted that the metal grinding process is similar with turning and milling, and metal materials are removed through cutting process. Due to uneven distribution of abrasives, “furrows” are produced by ploughing and cutting of abrasives at some region of the workpiece, while bulges are formed at some region after the failure of cutting. The distances among furrows and buldges vary. As a result, the cutting thickness of abrasives in the next grinding process is different. A small thickness of grinding debris will be produced when abrasives arrive at the previous “furrows”, but the thickness is relatively high when they arrive at the previous buldges, which even may exceed the radial feeds sometimes. Due to the strong squeezing and high-temperature effects during formation of grinding debris, the grinding debris have complicated and diversified shapes, including cracking-like continuous chips, comma shapes, melting spheres under high temperature, and slim chips that may curl up. In Fig. 14.8, no melted spherical grinding debris under high temperature is observed in all 9 groups of working conditions. On contrary, a lot of slim grinding debris is produced. This reflects that the Al2 O3 /SiC mixed nanofluid MQL grinding achieves not only good lubrication effect, but also ideal heat transfer effect. By comparing grinding debris under 9 groups of Al2 O3 /SiC mixed nanofluid MQL grinding conditions, we can find: • Among grinding debris surface morphologies under 9 groups of Al2 O3 /SiC mixed nanofluid MQL grinding conditions, there are obvious buldges on surface of grinding debris in 7 groups except mix(30:70) and mix(70:30). This means that grinding debris under mix(30:70) and mix(70:30) is more even, which reflect the better workpiece surface quality. • The grinding debris under mix(30:70) is relatively wider, but the width is relatively uniform. Grinding debris under mix(50:30) and mix(70:30) have uneven width distributions, especially the grinding debris under mix(70:30). This demonstrates that the nanofluid droplets in the grinding zone have larger infiltration area under mix(30:70), which provide a more extensive lubrication effect on the grinding zone, thus getting relatively uniform grinding debris shapes. This is related with that more lubricating oil can be adsorbed by more Al2 O3 nanoparticles, thus improving the coverage area of oil film in the grinding zone effectively.

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Fig. 14.8 SEM images of grinding debris in different working conditions

14.4.4 Cross Correlation Analysis of Al2 O3 /SiC Mixed NMQL Under Different Size Ratios A cross correlation analysis of workpiece surface profile curves under mix(30:70), mix(50:30) and mix(70:30) was carried out, which verified influences of nanoparticle grain size on workpiece surface quality under NMQL grinding conditions. The workpiece surfaces under above three working conditions were measured, getting abundant original data which was brought into the mathematical model. According to the cross correlation function and digital calculation formula of cross correlation coefficient, programs were compiled with Matlab7.0 and diagrams were plotted. The cross correlation function curves and cross correlation coefficient curves under mix(30:70), mix(50:30) and mix(70:30) were gained, as shown in Fig. 14.9a–c. According to comparison of these cross correlation function curves and cross correlation coefficient curves, the maximum absolute of the cross correlation coefficients between mix(30:70) and mix(50:30) were lower than 0.25, the maximum absolute of the cross correlation coefficients between mix(50:30) and mix(70:30) was lower than 0.5, and the maximum absolute of the cross correlation coefficients between mix(30:70) and mix(70:30) was lower than 0.4. They all were small. It can

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Fig. 14.9 Cross correlation function curves and cross correlation coefficient curves of profiles among different workpiece surface

be seen from Zone A, B and C in Fig. 14.9 that cross correlation function curves between mix(30:70) and mix(50:30), between mix(50:30) and mix(70:30), as well as between mix(30:70) and mix(70:30) all had periodic features and long period, which were determined by randomness of textures formed by grinding wheel on workpiece surface during grinding. These demonstrated the small correlation between workpiece surface profile curves under two working conditions, showing anisotropism. In other words, Al2 O3 /SiC mixed nanofluid with different size ratios had great influences on workpiece surface quality during NMQL grinding. Therefore, it verifies that

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changes of nanoparticle size may influence workpiece surface quality after NMQL grinding to some extent. Secondly, the maximum absolute of cross correlation coefficient between mix(30:70) and mix(70:30) is higher than that between mix(30:70) and mix(50:30). Combining with the optimal Ra and RSm under mix(30:70) and profile supporting length rate, it can determine that the workpiece surface quality under mix(70:30) was better than that under mix(50:30).

14.4.5 Cross Correlation Analysis of Profile Curves at Two Points of the Same Workpiece Surface The roughness profile curves at two random points on the same workpiece surface under mix(30:70), mix(50:30) and mix(70:30) are shown in Fig. 14.10a–c, respectively. The homogeneity degree of different surface was disclosed through cross correlation analysis of profile curves at two points on the same workpiece surface. Abundant data was acquired from measurement at two random pints on the same workpiece surface under mix(30:70), mix(50:30) and mix(70:30), and then brought into the mathematical model. According to the cross correlation function and digital calculation formula of cross correlation coefficient, programs were compiled with Matlab7.0 and diagrams were plotted. The cross correlation function curves and cross correlation coefficient curves were gained, as shown in Fig. 14.10a–c. The cross correlation function curve and cross correlation coefficient curve at two random points on the workpiece surface under mix(30:70) are shown in Fig. 14.10a. Clearly, Rxy (τ ) reaches the maximum at τ = 0.05, indicating the high similarity between two profile curves. It can be seen from Zone A, B and C in Fig. 14.10a that periods of the cross correlation function curve increases gradually with the increase of lateral displacement (τ), and the period of the section when τ increases from 0 mm to 0.8 mm was relatively small. This reflects the dense ripples on the workpiece surface. The period of the section when τ increases from 0.8 mm to 1 mm prolongs to some extent, but it is shorter than those of other two groups and presents greater amplitudes. Combining with the cross correlation coefficient curve, the maximum absolute of cross correlation coefficient between two profile curves is 0.67, further proving the great similarity between them. In other words, the workpiece surface under mix(30:70) condition has some homogeneity and surface texture presents homogenous characteristics. The cross correlation function curve and cross correlation coefficient curve at two random points on the workpiece surface under mix(50:30) are shown in Fig. 14.10b. Rxy(τ) achieves the maximum at τ = 0.95, but the maximum absolute of cross correlation coefficient is lower than 0.59. This reflects that two profile curves are similar to some extent, but the similarity is not very high. Moreover, It can be seen from Zone D, E and F in Fig. 14.10b that periods of the cross correlation function curve are all long, indicating the production of wide “furrows” on the workpiece

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Fig. 14.10 Cross correlation function curves and cross correlation coefficient curves at two different points on the same workpiece surface

surface. Hence the workpiece surface precision under mix(50:30) is relatively poor and the surface quality is low. The cross correlation function curve and cross correlation coefficient curve at two random points on the workpiece surface under mix(70:30) are shown in Fig. 14.10c. with the increase of τ, the cross correlation function curve presents a rising trend and the cross correlation coefficient reaches the maximum (0.61). When τ exceeds 0.3 mm, the cross correlation function curve begins to decay gradually, without a rising trend. This reflects that two profile curves are similar to a large extent, but the area of similarity is relatively small. In other words, the workpiece surface quality has a low precision.

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It can be seen from Zone G, H and I in Fig. 14.10c that periods of the cross correlation function curve show similar variation trends with those under mix(30:70). They all presents a rising trend, but the periods are all long. Hence, the workpiece surface quality under mix(70:30) has some advantages compared to that under mix(50:30), but the precision retainability of workpiece surface is lower than that under mix(30:70). To sum up, the cross correlation coefficient of two profile curves under mix(30:70) is higher than those under mix(50:30) and mix(70:30). After τ increases to 0.95 mm, the cross correlation function curve climbs up quickly, indicating that workpiece surfaces under mix(30:70) show greater similarity compared to those under mix(50:30) and mix(70:30). Moreover, workpiece surfaces have homogeneity and surface textures have homogeneous characteristics. This also reflects that the workpiece surface under mix(30:70) has higher precision retainability. Combining with experimental results, it concludes that Ra and RSm under mix(30:70) are relatively low (0.308 μm and 0.0414 mm), accompanied with relatively low SD. Moreover, it achieves a high profile supporting length rate (90%). The optimal workpiece surface quality is achieved under mix(30:70).

14.5 Summary Lubrication performances of Al2 O3 /SiC mixed nanoparticles with different size ratios under nanofluid jet MQL grinding conditions are analyzed through experiments. By analyzing grinding performance parameters of specific grinding force, workpiece removal parameter, surface roughness (Ra, RSm and profile supporting length rate), morphology of grinding debris, contact angle and further cross correlation analysis of workpiece surface profile curves, some major conclusions could be drawn: (1) Under the Al2 O3 /SiC mixed nanofluid MQL grinding conditions, grain size of Al2 O3 nanoparticles can influence Ra greatly. Small Al2 O3 nanoparticles are corresponding to a low value of Ra. The grain size of SiC nanoparticles can influence RSm greatly and large SiC nanoparticles are corresponding to a high value of RSm. (2) In 9 groups of Al2 O3 /SiC mixed nanofluid with different size ratios, the workpiece removal parameter under mix(70:30) is relatively high (189.05 mm3 / (s·N)), showing relatively high grinding efficiency. Therefore, the combination of large Al2 O3 nanoparticles and small SiC nanoparticles can improve grinding efficiency of nanofluid jet MQL grinding effectively. (3) Through comparison of cross correlation function values and cross correlation coefficient under mix(30:70), mix(50:30) and mix(70:30), it confirms that size changes of Al2 O3 nanoparticles and SiC nanoparticles in the Al2 O3 /SiC mixed nanofluid can influence the workpiece surface quality in NMQL grinding significantly.

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(4) According to comprehensive analysis of mix(30:70), mix(50:30) and mix(70:30) which are three groups of Al2 O3 /SiC mixed nanofluid with good performances, the workpiece surface roughness (Ra = 0.308 μm and RSm = 0.0414 mm) under mix(30:70) is lower than those under the rest two group, while the profile supporting length rate is higher (90%). Additionally, the SEM analysis of grinding debris and cross correlation analysis further prove that the best grinding effect and workpiece surface quality are achieved when the size ratio of Al2 O3 /SiC mixed nanoparticles is 30:70.

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Chapter 15

Spraying Parameter Optimization and Microtopography Evaluation in Nanofluid Minimum Quantity Lubrication Grinding

15.1 Introduction The NMQL grinding is applied to replace the traditional flood grinding to solve environmental and health issues [1, 2]. Specifically, optimization of jet parameters is the prerequisite to guarantee the effectiveness of NMQL. Scholars have carried out qualitative analysis on influencing laws of single jet parameter (e.g. types of vegetable oil, nanoparticle concentration, air pressure, position and angle of nozzle, gas–liquid flow ratio and flow rate) on MQL performances. However, they neither have considered the collaborative influencing laws of jet parameters on grinding performances nor have explored the overall optimization scheme of jet parameters. Optimization of jet parameters is not only the prerequisite to guarantee the effectiveness of NMQL, but also the key to realize the new sustainable grinding process. Hence, this study optimized jet parameters for Al2 O3 /SiC mixed NMQL grinding through an orthogonal experiment, and carried out experimental verification based on several groups of relatively optimized jet parameters. Moreover, the optimal jet parameters were acquired through power spectral density (PSD) analysis of workpiece surface microtopography, analysis of workpiece surface morphology and grinding debris morphology. This experimental study can provide some technical guidance and important references for industrial process.

15.2 Experimental Design 15.2.1 Experimental Equipments The grinding devices, grinding parameters and grinding wheel dressing parameters in the experiments were the same with those in Sect. 13.2.1 except that gas regulator valve, gas flow valve and liquid flow valve of the MQL pump have to be adjusted to achieve the desired jet parameters in the experiments. Additionally, the morphologies © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024 C. Li, Thermodynamic Mechanism of MQL Grinding with Nano Bio-lubricant, https://doi.org/10.1007/978-981-99-6265-5_15

373

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15 Spraying Parameter Optimization and Microtopography Evaluation …

Fig. 15.1 Utilization of experimental equipments and visualization of the experimental sequence

of workpiece surface and grinding debris were observed under a S-3400N scanning electron microscope. The experimental equipments and experimental process are shown in Fig. 15.1.

15.2.2 Experimental Materials The used workpiece materials and size were the same with those of Sect. 13.2.2. The Al2 O3 /SiC mixed nanoparticles with a volume ratio of 2:1 and a size ratio of 30 nm:70 nm were used. According to research contents in Chaps. 3 and 4, it can achieve the best grinding effect and workpiece surface quality by spraying the Al2 O3 / SiC mixed nanoparticles into the grinding zone through a MQL system. Nanofluid is prepared in two-step method. The base oil includes synthesis lipid (KS-1108), palm oil and castor oil. SDS was used as the dispersing agent. The 100 ml oil-based Al2 O3 /SiC mixed nanoparticles with a volume fraction of 1%, 2% and 3% were prepared, respectively, assisted with 20 min ultrasonic vibration to make nanoparticles disperse in base oil uniformly and avoid agglomeration of nanoparticles [3].

15.2 Experimental Design

375

15.2.3 Experimental Schemes Jet parameters of NMQL grinding are grinding factors and they mainly include base oil categories, volume concentration of nanoparticles, air pressure and gas–liquid flow ratio. These factors and their level ranges were chosen according to study of Li Benkai, Jia Dongzhou and Zhang Yanbin et al. [4–6] In their studies, jet parameters in NMQL grinding play a crucial role in droplet size and cooling lubrication effect. The jet parameters and their response levels are shown in Table 15.1. The orthogonal experimental method is to find relatively good production technological conditions through some experiments and it is a high-efficiency, fast and economic experimental design method. In experiment, L9 orthogonal array was used for three-level and four-factor (34) experimental design. The L9 orthogonal array is shown in Table 15.2. In the matrix, each row represents an experiment and the sequence of experiments was random. The tangential grinding force (Ft), normal grinding force (Fn) and surface roughness (Ra and RSm) of 9 experiments were measured, respectively. Table 15.1 Levels of grinding factors Factors

Level 1

Level 2

Level 3

Base oil

Synthetic

Palm

Castor

Volume concentration (%)

1

2

3

Gas pressure (MPa)

0.4

0.5

0.6

Gas–liquid flow ratio

0.2

0.3

0.4

Table 15.2 L9 orthogonal array Experiment no.

Base oil

Volume concentration (%)

Gas pressure (MPa)

Gas–liquid flow ratio

1–1

Synthetic

1

0.4

0.4

1–2

Synthetic

2

0.5

0.3

1–3

Synthetic

3

0.6

0.2

1–4

Palm

1

0.5

0.2

1–5

Palm

2

0.6

0.4

1–6

Palm

3

0.4

0.3

1–7

Castor

1

0.6

0.3

1–8

Castor

2

0.4

0.2

1–9

Castor

3

0.5

0.4

376

15 Spraying Parameter Optimization and Microtopography Evaluation …

15.3 Experimental Results 15.3.1 SNR Analysis It can get better grinding force, microscopic friction coefficient and surface roughness by optimizing jet parameters of NMQL grinding. Therefore, the signal-to-noise ratio (S/N) was introduced into the experimental design. The optimal design scheme was chosen according to function evaluation of grinding performances under different jet parameters based on S/N. During optimization, S/N has three quality characteristics [8], including larger-the-better characteristics, smaller-the-better characteristics and nominal-the-type characteristics. The experiments are to get smaller grinding force, microscopic friction coefficient and surface roughness [9]. Therefore, S/N of smallerthe-better characteristics was used for evaluation of grinding performances and its calculation formula was:   n S 1  2 y (15.1) = −10 log N n i=1 i where yi is the experimental data, and n refers to the number of experimental data. The setting of jet parameter levels with the highest S/N will generate the grinding force, microscopic friction coefficient and surface roughness of minimum variance. Hence, jet parameter levels with the highest S/N were chosen. S/N for tangential sliding force (F t,sl ), normal sliding force (F n,sl ), microscopic friction coefficient and surface roughness (Ra and RSm) was calculated from the Eq. (15.1). Results are shown in Table 15.3. 1. S/N analysis of grinding force Table 15.3 Corresponding S/N ratios for the observations No. F t,sl (N) Fn,sl (N) μ

Ra (μm) RSm (mm) S/N ratios for F t,sl

S/N ratios for F n,sl

S/N S/N ratios ratios for μ for Ra

S/N ratios for RSm

1–1

9.17

53.06

0.173 0.228

0.043

–24.39 –36.49 14.96 12.82 27.21

1–2

9.49

52.23

0.182 0.187

0.026

–24.54 –36.38 14.66 14.56 31.78

1–3 10.77

57.29

0.188 0.211

0.055

–25.27 –37.03 14.17 13.42 23.97

1–4 13.63

57.92

0.218 0.227

0.047

–26.08 –37.10 12.95 12.78 25.60

1–5

9.71

45.72

0.212 0.188

0.031

–25.16 –35.37 14.35 14.52 30.18

1–6 11.54

55.07

0.210 0.213

0.030

–25.55 –36.77 13.51 13.43 30.37

1–7 19.74

60.18

0.328 0.251

0.042

–28.68 –37.43 9.52

1–8 18.85

65.41

0.288 0.242

0.037

–28.40 –38.00 10.48 12.29 28.64

1–9 18.71

64.99

0.289 0.219

0.038

–28.39 –37.95 10.77 13.18 28.01

11.94 27.42

15.3 Experimental Results

377

Grinding force mainly comes from elasticoplastic deformation of workpiece caused by abrasives, formation of grinding debris and friction effect. It is an important parameter in grinding process and can influence workpiece surface quality, service life of grinding wheel, power consumption and grinding stability directly [10] therefore, grinding force is often used to diagnose grinding conditions. Grinding force can be divided into cutting force, ploughing force and sliding force. The relations are shown in Eqs. (15.2) and (15.3). Specifically, sliding force is produced by friction on the abrasive-workpiece interface and abrasive-grinding debris interface. It is related with material properties of workpiece and grinding wheel as well as grinding parameters, and it is even influenced by lubrication conditions [11, 12]. Changing lubrication conditions may change lubrication performances of grinding zone, thus decreasing sliding force. However, the cutting force may not change accordingly. Therefore, it shall calculate the sliding force and microscopic friction coefficient to characterize lubrication performances in studies of grinding force. On this basis, the influencing laws of jet parameters of NMQL on sliding force can be revealed. Ft = Ft,c + Ft, p + Ft,sl

(15.2)

Fn = Fn,c + Fn, p + Fn,sl

(15.3)

where F t is the tangential grinding force, F t,c is the tangential cutting force, F t,p is the tangential ploughing force, F t,sl is the tangential sliding force, F n is the normal grinding force, F n,c is the normal cutting force, F n,p is the normal ploughing force, and F n,sl is the normal sliding force. The mean and SD of grinding force in 9 groups of experiments are listed in Figs. 15.2 and 15.3.

Fig. 15.2 Mean and SD of grinding force in 9 groups of experiments

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15 Spraying Parameter Optimization and Microtopography Evaluation …

Fig. 15.3 Main effect diagram of S/N ratios for tangential sliding force F t,sl

The F t,sl and F n,sl in experiments were calculated according to the theoretical calculation model of grinding force proposed by Zhang [13]. F t,sl and F n,sl under 9 groups of different jet parameters were acquired (Table 15.3). The main effect diagrams of S/N for F t,sl and F n,sl are shown in Fig. 15.4. According to analysis on the main effect diagram of S/N for tangential sliding force, it concluded the optimal combination of jet parameters that influence the tangential sliding force is synthetic MQL oil, 2%vol of nanoparticle concentration, 0.4 MPa of air pressure and 0.4 of gas–liquid flow rate. The highest S/N was achieved under these jet parameters. Moreover, base oil category can influence tangential sliding force more obviously. Synthesis lipid achieves the highest S/N, followed by palm oil. The castor oil achieves the lowest S/N. This demonstrates that synthesis lipid can decrease tangential sliding force and achieve good lubrication effect on the grinding wheel-workpiece interface. Subsequently, S/N for tangential sliding force presents a linear growth gradually with the increase of gas–liquid flow rate. This reveals that a higher gas–liquid flow rate brings a lower tangential sliding force and a better lubrication effect. Air pressure cannot influence the tangential sliding significantly. According to analysis on the main effect diagram of S/N for normal sliding force, it achieves the highest S/N under Palm MQL oil, 2%vol of nanoparticle concentration, 0.6 MPa of air pressure and 0.4 of gas–liquid flow rate. These are the optimal combination of jet parameters to get the lowest normal sliding force. Similarly, base oil category still has obvious influences on sliding force. The palm oil achieves the highest S/N, indicating the lowest normal sliding force and the relatively good lubrication effect. Moreover, influences of air pressure on S/N for normal sliding force

15.3 Experimental Results

379

Fig. 15.4 Main effect diagram of S/N ratios for normal sliding force F n ,sl

decrease firstly and then increase, and the highest S/N is achieved at 0.6 MPa. Influences of nanoparticle concentration and gas–liquid flow rate on normal sliding force are basically consistent with their influences on tangential sliding force. Based on above analysis, it can be seen from influences of jet parameters on tangential and normal sliding forces that it can achieve relatively ideal lubrication effect by using synthesis lipid or palm oil as base oil of NMQL under 2%vol of nanoparticle concentration, 0.6 MPa of air pressure, and 0.4 gas–liquid flow rate. 2. S/N analysis of microscopic friction coefficient (μ) The microscopic friction coefficient (μ) is the ratio between F t,sl and F n,sl [15], as shown in Eq. (15.4). By deleting the influences of cutting force and ploughing force, μ can reflect lubrication performance changes of the grinding zone with lubrication conditions more intuitively. μ=

Ft,sl Fn,sl

(15.4)

The main effect diagram of S/N for μ is shown in Fig. 15.5. According to analysis, the highest S/N is achieved under synthetic MQL oil, 2%vol of nanoparticle concentration, 0.4 MPa of air pressure and 0.4 of gas–liquid flow rate. These are the optimal combination of jet parameters for the lowest μ. It shows high similarity with variation trend in the main effect diagram of S/N for tangential sliding force. The base oil category still has significant influences on S/N for μ, while effects of other jet parameters are relatively small. This demonstrates that base oil category

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plays a crucial role in lubrication effect of grinding zone. S/N for synthesis lipid is the highest, indicating the lowest μ and good lubrication effect. S/N for palm oil is the second highest. Under the constant levels of other jet parameters, palm oil still achieves a high S/N. This reflects that palm oil still has good lubrication effects. 3. S/N analysis of surface roughness (Ra, RSm) Grinding is a type of finish machining technique. Hence, workpiece surface quality is an important criterion to evaluate grinding performances [14, 16]. Since surface roughness is an important parameter of workpiece surface quality, it is applied to characterize surface quality in experiments. The smaller surface roughness indicates the more smoothness of surface. Surface roughness influences usability of mechanical parts significantly. Experimental results of Ra and RSm are listed in Table 15.3. The main effect diagram of S/N for Ra and RSm are shown in Figs. 15.6 and 15.7. By analyzing main effect diagram of S/N for Ra, the highest S/N is achieved when using synthesis lipid or palm oil as base oil of NMQL, 2%vol of nanoparticle concentration, 0.5 MPa of air pressure and 0.4 of gas–liquid flow rate. These are the optimal combination of jet parameters to get the lowest Ra. It achieves the same S/ N by using synthesis lipid and palm oil, indicating that synthesis lipid and palm oil have the equal effect in reducing Ra, they are superior to castor oil from this aspect. Additionally, influences of nanoparticle concentration and air pressure on S/N for Ra increase firstly and then decrease. This reflects that a relatively low Ra is achieved under 2%vol of nanoparticle concentration and 0.5 MPa of air pressure. With the increase of gas–liquid flow rate, the S/N for Ra presents a linear growth gradually.

Base oil

Volume concentration (%)

Gas pressure(MPa)

Fig. 15.5 Main effect diagram of S/N ratios for micro friction coefficient µ

Gas-liquid flow ratio

15.3 Experimental Results

381

It proves that a high gas–liquid flow rate can improve Ra and bring good lubrication effect (Figs. 15.6 and 15.7).

Fig. 15.6 Main effect diagram of S/N ratios for surface roughness Ra

Fig. 15.7 Main effect diagram of S/N ratios for surface roughness RSm

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According to analysis of main effect diagram of S/N for RSm, the highest S/ N is achieved when using palm oil as base oil of NMQL, 2%vol of nanoparticle concentration, 0.5 MPa of air pressure and 0.4 of gas–liquid flow rate. These are the optimal combination of jet parameters to get the lowest RSm. With respect to influences of base oil category on S/N for RSm, palm oil gets the highest S/N, indicating that palm oil can improve RSm to the maximum extent and its lubrication effect is better compared to those of synthesis lipid and castor oil. Additionally, influences of nanoparticle concentration, air pressure and gas–liquid flow rate on S/N for RSm are relatively consistent with their influences on S/N for Ra. Based on above analysis, it can be seen from influences of jet parameters on Ra and RSm that relative low values of Ra and RSm can be achieved by using palm oil as base oil of NMQL under 2%vol of nanoparticle concentration, 0.5 MPa of air pressure and 0.4 of gas–liquid flow rate.

15.3.2 Analysis of Variance The analysis of variance (ANOVA) is to test whether jet parameters have significant effects on experimental results through a statistical mean. In ANOVA, there are two important evaluation parameters, which are F-value and contribution rate (P%). Fvalue is compared with F α of F distribution critical table. When F > F0.05, it is believed that influences of factors on results are significant [17]. Generally speaking, changes of jet parameters have great influences on quality features when F-value is high. P% is the proportion of variance of mean of each significant factor in the total variance of mean in the experiment. It is a function of deviation sum of square and reflects relative contributions of each factor to reduction of total deviation [18]. If the factor level can be controlled accurately, the total error can be decreased according to P%. 1. ANOVA of grinding force To further analyze significance of influences of jet parameters on grinding force and influences of experimental error on experimental results, ANOVA is needed to experimental results in order to determine the optimal combination of jet parameters that can decrease grinding force to the maximum extent. Jet parameters were ranked according to their influencing degrees on tangential and normal sliding forces. Top three jet parameters in term of influencing degree were chosen as major influencing factors, while the jet parameter with the lowest influencing degree was chosen as the error term for ANOVA. ANOVA results of influences of jet parameters on tangential and normal sliding forces are shown in Tables 15.4 and 15.5, respectively. In ANOVA for tangential sliding force, P% of base oil category, nanoparticle concentration and gas–liquid flow rate to tangential sliding force was 97.37%, 0.78% and 1.62%, respectively. Obviously, base oil category had the maximum relative contribution to reduction of total deviation of tangential sliding force and it achieved the maximum F-value of 428.54 > F0.05(2,2). In other words, changes of base oil

15.3 Experimental Results

383

Table 15.4 ANOVA results for F t,sl Source

Degree of freedom

Seq SS

P%

Adj MS

F-value

Base oil

2

145.448

97.37

72.7240

428.54

Volume concentration (%)

2

1.167

0.78

0.0093

0.05

Gas–liquid flow ratio

2

2.421

1.62

1.2107

7.13

Error

2

0.339

0.23

0.1697

Total

8

149.376

100.00

Table 15.5 ANOVA results for F n,sl Source

Degree of freedom

Seq SS

P%

Adj MS

F-value

Base oil

2

207.520

62.60

103.760

2.50

Volume concentration (%)

2

36.441

10.99

7.617

0.18

Gas–liquid flow ratio

2

4.415

1.33

2.207

0.05

Error

2

83.150

25.08

41.575

Total

8

331.527

100.00

categories influenced experimental results of tangential sliding force significantly. Key attention should be paid to change base oil category to improve experimental results of tangential sliding force when we need a relatively low tangential sliding force and a relatively small total deviation of tangential sliding force. In ANOVA for normal sliding force, P% of base oil category, nanoparticle concentration and gas–liquid flow rate to normal sliding force was 62.60%, 10.99%, and 1.33%. Clearly, base oil category had the maximum relative contribution to reduction of total deviation of normal sliding force and the proportion of nanoparticle concentration increased. Key attention should be paid to change base oil category and nanoparticle concentration to improve experimental results of normal sliding force when we need a relatively low normal sliding force and a relatively small total deviation of normal sliding force. 2. ANOVA of microscopic friction coefficient Similarly, jet parameters were ranked according to their influencing degrees on μ. Top three jet parameters were chosen as the main influencing factor, while the jet parameter with the lowest influencing degree was chosen as the error term for ANOVA. ANOVA results of influences of jet parameters on μ are shown in Table 15.6. Base oil category, air pressure, gas–liquid flow rate were three major influencing factors. Their P% to reduction of total deviation of μ was 95.04%, 2.40%, and 0.44%, respectively. Base oil type achieved the maximum F-value (85.12 > F0.05(2,2)). Hence, it played the crucial role in the value of μ. Combining with above S/N analysis for μ, synthesis lipid achieved the highest S/N, so it had better antifriction effect than palm oil and castor oil, and improved lubrication effect on the grinding wheel-workpiece interface.

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Table 15.6 ANOVA results for μ Source

Degree of freedom

Seq SS

P%

Adj MS

F-value

Base oil

2

0.023314

95.04

0.011657

85.12

Gas pressure (MPa)

2

0.000588

2.40

0.000294

2.15

Gas–liquid flow ratio

2

0.000354

1.44

0.000177

1.29

Error

2

0.000274

1.12

0.000137

Total

8

0.024531

100.00

3. ANOVA of surface roughness (Ra, RSm) Firstly, jet parameters were ranked according to their influencing degrees on Ra and RSm. Top three jet parameters were chosen as the main influencing factor, while the jet parameter with the lowest influencing degree was chosen as the error term for ANOVA. ANOVA results of influences of jet parameters on Ra and RSm are shown in Tables 15.7 and 15.8. In ANOVA for Ra, P% of base oil category, nanoparticle concentration and air pressure which were three main influencing factors to reduction of total deviation of Ra was 42.04%, 36.73%, and 11.66%, respectively. According to comparison of Fvalue of these three jet parameters, base oil category and nanoparticle concentration both achieved relatively high F-values of 4.39 and 3.84, respectively. Hence, base oil category and nanoparticle concentration were important to decrease Ra and its total deviation. In ANOVA for RSm, nanoparticle concentration, air pressure, and gas–liquid flow rate were main influencing factors and their P% to reduction of total deviation of RSm Table 15.7 ANOVA results for Ra Source

Degree of freedom

Seq SS

P%

Adj MS

F-value

Base oil

2

0.001594

42.04

0.000797

4.39

Volume concentration (%)

2

0.001393

36.73

0.000696

3.84

Gas pressure (MPa)

2

0.000442

11.66

0.000221

1.22

Error

2

0.000363

9.57

0.000181

Total

8

0.003792

100.00

Table 15.8 ANOVA results for Rsm Source

Degree of freedom

Seq SS

P%

Adj MS

F-value

Volume concentration (%)

2

0.000276

40.48

0.000088

4.22

Gas pressure (MPa)

2

0.000067

9.89

0.000025

1.20

Gas–liquid flow ratio

2

0.000296

43.49

0.000025

7.09

Error

2

0.000042

6.13

0.000021

Total

8

0.000681

100.00

15.4 Experimental Verification and Discussion

385

was 40.48%, 9.98%, and 43.49%, respectively. According to comparison of F-value of these three jet parameters, nanoparticle concentration and gas–liquid flow rate both achieved relatively high F-values of 4.22 and 7.09, respectively. Hence, nanoparticle concentration and gas–liquid flow rate were important to decrease RSm and its total deviation. Combining with above S/N analysis for Ra and RSm, a relatively high S/N was achieved under jet parameters of palm oil, 2%vol of nanoparticle concentration and 0.4 of gas–liquid flow rate. Hence, these three levels of jet parameters could improve Ra and RSm to a large extent and they improved lubrication effect of the grinding wheel-workpiece interface.

15.3.3 Optimization Results According to above S/N analysis and ANOVA of tangential sliding force, normal sliding force, microscopic friction coefficient and surface roughness (Ra and RSm), four groups of relatively optimal jet parameters were acquired: (1) synthesis lipid, 2% of nanoparticle concentration, 0.6 MPa of air pressure, 0.4 of gas–liquid flow rate; (2) palm oil, 2% of nanoparticle concentration, 0.6 MPa of air pressure, 0.4 of gas– liquid flow rate; (3) synthesis lipid, 2% of nanoparticle concentration, 0.4 MPa of air pressure, 0.4 of gas–liquid flow rate; (4) palm oil, 2% of nanoparticle concentration, 0.5 MPa of air pressure, 0.4 of gas–liquid flow rate.

15.4 Experimental Verification and Discussion The above four groups of relatively optimal jet parameters in orthogonal experiments were verified through experiments. The experimental designs are shown in Table 15.9. Moreover, it can be seen from Table 15.3 that grinding force, microscopic friction coefficient and surface roughness all achieved the highest S/N under synthesis lipid, 2%vol of nanoparticle concentration, 0.5 MPa of air pressure and 0.3 of gas–liquid flow rate. They were used as the control experiment 2–5. Next, experimental results for verification were analyzed and discussed through power spectral density function (PSDF), morphology and EDS of workpiece surface, as well as morphology and EDS of grinding debris.

15.4.1 Power Spectral Density Analysis of Surface Profile Power spectral density function (PSDF) is composed of frequencies which describe the time-domain signals from the frequency domain [19]. A rough surface profile can be viewed as a random signal and it is composed of fitting of countless sine curves with different periods. Hence, it has continuous distribution on the frequency

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Table 15.9 Experimental design for verification Experiment no Base oil

Volume concentration Gas pressure (MPa) Gas–liquid flow ratio (%)

2–1

Synthetic 2

0.6

0.4

2–2

Palm

2

0.6

0.4

2–3

Synthetic 2

0.4

0.4

2–4

Palm

2

0.5

0.4

2–5

Synthetic 2

0.5

0.3

domain. Amplitude of PSDF can be expressed as relative proportion of frequency under different frequencies. A long period is corresponding to a low frequency, which is manifested by proportion of waviness on the surface profile. A short period is corresponding to a high frequency and it is manifested as proportion of roughness on the surface profile [20]. According to workpiece surface profile curve under five groups of experimental conditions, five groups of PSDF curves were acquired through programming, as shown in Fig. 15.8a–e. Zoning based on frequency distribution in PSDF curves in Fig. 15.8a–e was carried out, including Zone A (0–100 Hz), Zone B (101–400 Hz), Zone C (401–700 Hz) and Zone H (701–1000 Hz). Next, the areas enclosed by each section of PSDF curve and x,y axes were calculated through programming, which were SA, SB, SC and SH (Table 15.10). To disclose characteristics of PSDF curves in the full frequency domain more comprehensively, a proportionality coefficient (K) was introduced in. It is defined as the ratio between the area enclosed by PSDF curve of a frequency band and x, y axes and the area enclosed by the full frequency domain PSDF curve and x, y axes. The proportionality coefficient reflects the proportion of a frequency band in the full frequency domain. A higher value of K indicates a higher proportion of the frequency band in the full frequency domain. In other words, this frequency band takes the dominant role in workpiece surface profile characteristics and its calculation formula is: Ki =

Si Si = Stotal S A + S B + SC + S H

(i = A, B, C, H )

(15.7)

where S i is the area enclosed by the PSDF curve of frequency band i and the x, y axes. Stotal is the area enclosed by the full frequency domain PSDF curve and x, y axes, and i refers to a section of frequency domain. K values of different frequency bands were calculated according to Eq. (15.7). Results are shown in Table 15.10. It can be seen from Fig. 15.8 that with the increase of frequency, the PSDF curves under five working conditions of a, b, c, d, e all show a decreasing trend. This reflects that workpiece surface in NMQL grinding still has obvious texture features from the microscopic perspective. The PSDF curves and the maximum profile curve under a, c, e decline straightly in Zone H, while PSDF curve and the maximum profile curve under b and d show a rising trend. Meanwhile, several wave peaks with the maximum power spectral density (PSD) exceeding 20W/Hz are produced. This

15.4 Experimental Verification and Discussion 200 180

200

A

B

PSD curve 180 Mean curve Max contour curve

C

160

160

140

140

120

120

100

100

80

80

60

60

40

40

20

20 0

Power spectral density (W/Hz)

387

100

200

300

400

600

500

700

800

900

1000 0

a

200 180

180

160

160

140

140

120

120

100

100

80

80

60

60

40

40

20

20 0

100

200

300

400

100

200

300

400

600

500

700

800

900

500

600

700

800

900

1000

600

700

800

900

1000

b

200

1000 0

100

c

200

300

400

500

d 200 180 160 140 120 100 80 60 40 20 0

100

200

300

400

600

500

e

700

800

900

1000

Frequence (Hz)

Fig. 15.8 PSDF curves of five experimental conditions

Table 15.10 The area coefficients (S) and proportionality coefficients (K) of PSDF curves in different frequency bands No.

SA

SB

SC

SH

KA

KB

KC

KH

a

43.58

53.49

31.41

17.73

0.298

0.366

0.215

0.121

b

35.77

56.26

33.52

20.72

0.245

0.385

0.229

0.142

c

57.70

90.30

37.28

17.59

0.284

0.445

0.184

0.087

d

50.69

81.97

36.87

17.96

0.270

0.437

0.197

0.096

e

46.31

56.35

34.99

19.74

0.294

0.358

0.222

0.125

means that workpiece surfaces under b and d have higher PSD in high-frequency zones compared to those under a, c and e. Hence, workpieces under b and d show proportion of roughness on surface profile. There’s small average spaces among waves on the workpiece surface profile, and there’s a high corrugation density.

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Combining with K under different working conditions in Table 15.10, the second group achieves the lowest value in Zone A (K Ab = 0.245), and the highest value in Zone H (K Hb = 0.142). This indicates that the PSD in the low-frequency band is relatively low under the second group of experimental conditions, but the PSD of high-frequency band is relatively high. In other words, the second group of experiment shows obvious surface profile features dominated by roughness than other groups. The proportionality coefficient of Zone A under the fourth group is K Ad = 0.270, which is the second lowest, only next to that of the second group. The fourth group and the second group have the same working conditions, which are different from other three groups by using palm oil as the base oil. Therefore, it achieves better lubricating performances by using palm oil in NMQL grinding compared to synthesis lipid. According to comparison of a, c and e in Fig. 15.8, synthesis lipid and 2%vol of nanoparticle concentration are used as base oil for NMQL grinding in these three groups. However, PSDF curves are different among these three groups, indicating that air pressure and gas–liquid flow rate can influence lubrication effect of NMQL grinding to some extent. Under the third group of experimental conditions, the proportionality coefficients of Zone A and Zone B are K Ac = 0.284 and K Bc = 0.445, and the proportionality coefficients of Zone C and Zone H are K Cc = 0.184 and K Hc = 0.087, respectively. This reveals that PSDF curve in the low-frequency band has the highest energy distribution. The energy distribution in PSDF curve of high-frequency band is the lowest. In other words, the third group of experimental conditions show more obvious surface profile characteristics centered at waviness compared to other working conditions. Besides, the proportionality coefficients in the first group are similar with those in the fifth group. The fifth group is used as the control group. The proportionality coefficients of Zone C and Zone H in Fig. 15.8e are only next to those of the second group, which are K Ce = 0.222 and K He = 0.125, respectively. However, the proportionality coefficient of Zone A is K He = 0.125. This demonstrates that PSDF curves in the low-frequency band and high-frequency band have relatively high energy distribution. In other words, the workpiece surface profile of the fifth group is mainly manifested as roughness and the workpiece surface quality is superior to that of the third group. Hence, the best workpiece surface quality and the optimal lubrication effect are achieved under 0.5 MPa of air pressure and 0.3 of gas–liquid flow rate when synthesis lipid and 2%vol nanoparticle concentration are used as base oil for NMQL grinding.

15.4.2 Surface Morphology of Workpiece and EDS Due to uneven distribution of abrasives, some parts produce “furrows” through ploughing and cutting effects, while some parts form buldges for failure of material cutting, with uneven distances. Surface morphology and energy disperse spectroscopy (EDS) are important indexes to evaluate workpiece surface quality [21]. The surface morphology can reflect surface quality quantitatively, while content

15.4 Experimental Verification and Discussion

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changes of surface EDS elements can further make a quantitative judgment of surface quality. SEM images and EDS of workpiece surface morphology under five groups of different jet parameters are shown in Fig. 15.10. In Fig. 15.10a, c, e, the workpiece surface morphology and EDS are all gained by using synthesis lipid and 2%vol of nanoparticles as lubricating oil of MQL. Specifically, the best workpiece surface quality is achieved in Fig. 15.10 e and O content is the lowest (0.25%wt). therefore, the combination of jet parameters (base oil: synthesis lipid; volume fraction of nanoparticles: 2%; air pressure: 0.5 MPa; gas–liquid flow rate: 0.3) achieves better cooling lubrication performances compared to other two groups. This is because given the fixed base oil and volume concentration of nanoparticles, 0.5 MPa of air pressure and 0.3 of gas–liquid flow rate are beneficial for jet to penetrate through the gas barrier layer on the grinding wheel (Fig. 15.9), so that droplets enter into the grinding zone to form effective infiltration area and thereby improve lubrication ability. Workpiece surface in Fig. 15.10c show obvious furrows and O content is the highest (0.57%), indicating the poor lubrication effect. As a result, the workpiece surface is oxidized serious. In other words, a low air pressure and high gas–liquid flow rate are difficult for droplets to enter into the grinding zone to form effective infiltration area. The workpiece surface morphology and EDS in Fig. 15.10b, d are all gained by using palm oil and 2%vol of nanoparticles as lubricating oil of NMQL. The workpiece surface in Fig. 15.10b is the most flat, without obvious furrows and buldges. O content in surface EDS is the lowest (0.11%), without obvious surface oxidization. Hence, this combination of jet parameters (base oil: palm oil; volume fraction of nanoparticles: 2%; air pressure: 0.6 MPa; gas–liquid flow rate: 0.4) brings the best cooling lubrication performances. This is because palm oil contains abundant saturated fatty acids (palmitic acid and stearic acid). Polar groups (–COOH) in saturated fatty acid are adsorbed onto the metal surface through Van der Waals’ force, thus making it easier to form effective infiltration areas and improving lubrication performances of droplets on the workpiece-grinding wheel interface. Hence, it can achieve the ideal lubrication effect under high air pressure and gas–liquid flow rate when the palm oil is used as base oil for MQL.

Barrier layer of air Grinding wheel

Nanofluids Workpiece Fig. 15.9 The air barrier layer on grinding wheel surface

Nozzle

Fig. 15.10 SEM morphology and EDS of workpiece surface in five experiments for verification

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15.5 Summary

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15.4.3 Debris Morphology and EDS The contact surface between grinding debris and abrasives during formation of grinding debris is the front surface of grinding debris, and the other side is the back surface. The front surface of grinding debris is more smooth than the back surface. The back surface of grinding debris is corrugated due to squeezing shearing forces in the cutting process. Influenced by the strong squeezing and high temperature, the shape of grinding debris is more complicated and diversified, including cracking-like continuous chips, comma shapes, melting spheres under high temperature, and slim chips that may curl up as a response to the collaborative effect of heat and force. SEM images and EDX of grinding debris surface morphology under five groups of jet parameters are shown in Fig. 15.11. Generally, no melted spherical grinding debris under high temperature has been found. Instead, a lot of slim grinding debris is produced. This reflects that the combination of jet parameters after optimization by orthogonal experiment achieves not only good lubrication effect, but also ideal heat transfer effect. It can be seen clearly from Fig. 15.11c that curling grinding debris are produced under the coupling effect between grinding force and heat. Moreover, O content in EDX is the highest, reaching 2.28%. This demonstrates that the grinding force is large under this group of jet parameters and abundant heats are produced, thus resulting in serious oxidization of grinding debris surface and poorer lubrication effect than other groups. This is because synthesis lipid which is used as the base oil of NMQL has poorer lubrication performances than palm oil containing a lot of saturated fatty acid. Moreover, the air pressure is relatively low (0.4 MPa), so that nanofluid droplets has weak ability to break the gas barrier layer on the grinding wheel. The gas–liquid flow rate is relatively high (0.4), thus decreasing nanofluid supply to meet lubrication needs. Consequently, the lubrication effect declines. Relatively, long belt grinding debris is produced on workpieces in Fig. 15.11b, d, e, without obvious curing phenomenon. This reflect that deformation forces during grinding under these three groups of jet parameters are relatively small, and the fitness between abrasive material and workpiece material is good. The surface morphology of grinding debris in Fig. 15.11b is relatively flat and O content in EDX is the lowest (1.11%), indicating the coupling effect between grinding force and heats is the lowest, providing the best cooling lubrication effect. This further proves that the combination of palm oil, 2%vol of nanoparticle concentration, 0.6 MPa of air pressure and 0.4 of gas–liquid flow rate brings the optimal grinding performances.

15.5 Summary To study influences of different combinations of jet parameter on grinding performances under NMQL condition, S/N analysis and ANOVA are carried out to grinding performance parameters, including tangential sliding force, normal sliding

Fig. 15.11 SEM morphology and EDS of grinding debris in five experiments for verification

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force, microscopic friction coefficient and surface roughness (Ra and RSm). Moreover, PSD, surface morphology and EDS of workpiece surface profile, as well as morphology and EDS of grinding debris in experiments for verification are analyzed. Some major conclusions can be drawn: (1) The highest S/N for tangential and normal sliding forces is achieved when synthesis lipid or palm oil is used as the base oil of NMQL under 2%vol of nanoparticle concentration, 0.6 MPa of air pressure and 0.4 of gas–liquid flow rate. The contribution rates of base oil category to tangential and normal sliding forces are the highest, reaching 97.37% and 62.60%, respectively. Hence, synthesis lipid and palm oil are crucial to lubrication performances and they can decrease grinding force effectively. (2) In influences of jet parameters on microscopic friction coefficient, the highest S/N is achieved by using synthesis lipid as base oil of MQL under 2%vol of nanoparticle concentration, 0.4 MPa of air pressure and 0.4 of gas–liquid flow rate. This group of jet parameters can decrease microscopic friction coefficient effectively, thus getting good lubrication effect. Moreover, contribution rate of influences of synthesis lipid on microscopic friction coefficient is the highest (95.04%), and synthesis lipid influences lubrication performances in the grinding zone greatly. (3) It achieves the highest S/N for surface roughness (Ra and RSm) under the use of palm oil, 2%vol of nanoparticle concentration, 0.5 MPa of air pressure and 0.4 of gas–liquid flow rate. This group of jet parameters decreases surface roughness effectively. Contribution rates of base oil category, volume concentration of nanoparticles and gas–liquid flow rate to surface roughness are 42.04%, 40.48%, and 43.49%, respectively. They are important to decrease Ra and RSm as well as their total deviations. (4) In experiments for verification, the group of jet parameters (palm oil, 2%vol of nanoparticle concentration, 0.6 MPa of air pressure and 0.4 of gas–liquid flow rate) achieves the lowest proportionality coefficient in Zone A (K Ab = 0.245) and the highest in Zone H (K Hb = 0.142). In other words, the workpiece surface under this group of jet parameters show more obvious roughness-centered surface profile features and higher corrugation density. The workpiece surface quality is the best. (5) According to comprehensive analysis on morphology of workpiece surface and grinding debris as well as content changes in EDS elements in five experiments for verification, it further proves the better cooling lubrication performance of palm oil than synthesis lipid under 2%vol of nanoparticle concentration, 0.6 MPa of air pressure and 0.4 of gas–liquid flow rate.

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