3D FEA Simulations in Machining 9783031240379, 9783031240386

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SpringerBriefs in Applied Sciences and Technology

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This series fosters information exchange and discussion on all aspects of manufacturing and surface engineering for modern industry. This series focuses on manufacturing with emphasis in machining and forming technologies, including traditional machining (turning, milling, drilling, etc.), non-traditional machining (EDM, USM, LAM, etc.), abrasive machining, hard part machining, high speed machining, high efficiency machining, micromachining, internet-based machining, metal casting, joining, powder metallurgy, extrusion, forging, rolling, drawing, sheet metal forming, microforming, hydroforming, thermoforming, incremental forming, plastics/composites processing, ceramic processing, hybrid processes (thermal, plasma, chemical and electrical energy assisted methods), etc. The manufacturability of all materials will be considered, including metals, polymers, ceramics, composites, biomaterials, nanomaterials, etc. The series covers the full range of surface engineering aspects such as surface metrology, surface integrity, contact mechanics, friction and wear, lubrication and lubricants, coatings an surface treatments, multiscale tribology including biomedical systems and manufacturing processes. Moreover, the series covers the computational methods and optimization techniques applied in manufacturing and surface engineering. Contributions to this book series are welcome on all subjects of manufacturing and surface engineering. Especially welcome are books that pioneer new research directions, raise new questions and new possibilities, or examine old problems from a new angle. To submit a proposal or request further information, please contact Dr. Mayra Castro, Publishing Editor Applied Sciences, via [email protected] or Professor J. Paulo Davim, Book Series Editor, via [email protected]

Panagiotis Kyratsis · Anastasios Tzotzis · J. Paulo Davim

3D FEA Simulations in Machining

Panagiotis Kyratsis Product and Systems Design Engineering University of Western Macedonia Kila Kozani, Greece

Anastasios Tzotzis Product and Systems Design Engineering University of Western Macedonia Kila Kozani, Greece

J. Paulo Davim Mechanical Engineering University of Aveiro Aveiro, Portugal

ISSN 2191-530X ISSN 2191-5318 (electronic) SpringerBriefs in Applied Sciences and Technology ISSN 2365-8223 ISSN 2365-8231 (electronic) Manufacturing and Surface Engineering ISBN 978-3-031-24037-9 ISBN 978-3-031-24038-6 (eBook) https://doi.org/10.1007/978-3-031-24038-6 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

1 A Comparative Study Between 2D and 3D Finite Element Methods in Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Comparison Between 2D and 3D FEM Analysis Techniques . . . . . . . 3 1.2.1 Evaluation of Cutting Forces and Torque . . . . . . . . . . . . . . . . . 3 1.2.2 Chip Formation and Dimensions Assessment . . . . . . . . . . . . . 4 1.2.3 Examination of Residual Stresses . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.4 Temperature and Tool-Wear Assessment . . . . . . . . . . . . . . . . . . 6 1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Fundamentals of 3D Finite Element Modeling in Conventional Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 FEM-Based Studies in Machining . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Advantages and Limitations of FEM . . . . . . . . . . . . . . . . . . . . . 2.2 Finite Element Modeling in Machining . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Meshing and Element Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Mesh Adaptivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Tool-Workpiece Representation . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 Material Flow Stress Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.6 Friction Modeling and Contact Description . . . . . . . . . . . . . . . 2.2.7 Material Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.8 Tool Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Typical FEM-Based Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Cuttings Forces, Torque, and Residual Stresses . . . . . . . . . . . . 2.3.2 Chip Morphology, Temperature Distribution, and Wear . . . . . 2.4 Conclusions and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

3 FEM-Based Study of AISI52100 Steel Machining: A Combined 2D and 3D Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Machining Process Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Preliminary FE Model Assessment . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Numerical Modeling of the Turning Process in Three Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Results and Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Machining Forces Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Chip Geometry Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Experimental and 3D Numerical Study of AA7075-T6 Drilling Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Layout of Experimental Testing . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Finite Element Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Results and Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Cutting Forces and Torque Analysis . . . . . . . . . . . . . . . . . . . . . 4.3.2 Chip Morphology Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Temperature Distribution Analysis . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3D Finite Element Simulation of CK45 Steel Face-Milling: Chip Morphology and Tool Wear Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Experimental Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Face-Milling CAD-Based Setup . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Numerical Modeling of the Face-Milling Process . . . . . . . . . . 5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Chip Formation Analysis and Temperature Distribution Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Tool Wear Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1

A Comparative Study Between 2D and 3D Finite Element Methods in Machining

Abstract The Finite Element Method (FEM) is arguably one of the most valuable tools when studying manufacturing processes. Therefore, it is widely used for the development of models that are able to predict the behavior of a manufacturing process under a variety of conditions with acceptable accuracy. Especially as computational resources develop, so does the FEM, making it an integral part of modern studies. Even though FEM can nowadays be implemented in 3D, 2D modeling still holds an important role. In the present work, a comparison between the application of 2D and 3D FEMs in machining was made, with both the advantages and disadvantages in mind. Specifically, an effort was made to capture the effectiveness of each method when studying standard machining results such as the cutting forces and torque, the temperatures, the residual stresses, and the tool wear. Keywords 2D FEM · 3D FEM · Machining · Cutting forces · Residual stresses · Tool wear · Cutting temperature

1.1 Introduction The Finite Element Method (FEM) is a well-known tool, implemented often in machining studies. The fact that it can reduce the experimental work and that it allows the investigation of variables that cannot be examined in other manners, makes it an integral part of modern machining studies. Both 2D and 3D FEM studies display a number of advantages and disadvantages. Even though at the moment it seems that the one supplements the other, it is considered that the 3D FEM will replace the 2D due to the restrictions that exist in the two dimensions. Cepero Mejias et al. [1] used a 2D FEM technique to study the orthogonal machining of thick unidirectional laminates. To obtain realistic results, the authors implemented a novel linear stiffness degradation coupled with a continuum damage mechanic model. Similar strategies, especially for the damage propagation [2] were applied to investigate the machining of unidirectional composites, focusing on the influence of the rake and relief angle of the tool, as well as the cutter edge radius. Zhou et al. [3] simulated the machining of alloy ZL109 in two dimensions with © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al., 3D FEA Simulations in Machining, Manufacturing and Surface Engineering, https://doi.org/10.1007/978-3-031-24038-6_1

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a polycrystalline diamond (PCD) tool to acquire the optimal finishing parameters and to study the effects of the cutting parameters on the residual stresses, cutting forces, and temperature. The authors verified the simulation results with experimental work. Peng et al. [4] developed a 2D FEM chip formation model for the cutting forces prediction during machining of aged Inconel 718, by using a Coupled Eulerian–Lagrangian (CEL) method. Carbide-cutting tools of different cobalt percentages have been utilized, to generate varying tool wear. Mishra et al. [5] studied the turning process with uncoated-textured and coated-textured tools on Ti6Al4V by using 2D Finite Element (FE) simulations. The authors made a comparison with equivalent plain tools and evaluated the performance of the tool with regard to the cutting forces, friction coefficient, contact length, chip behavior, and shear stress. Tagiuri et al. [6] established a 2D numerical model for the prediction and study of the effects of tool nose morphology combined with a number of cutting parameters when machining AISI1045 steel. The performance parameters studied, were the cutting temperature and developed forces, the effective stress, as well as the tool wear. Numerous studies such as [7–13] still use 2D FEM for the examination of several characteristics that are involved in machining. Typical materials studied are AISI1045, AISI630, and AISI4140 steels, Inconel 718, titanium alloys such as Ti6Al4V and Ti-5553, composites, as well as aluminium alloys. The aforementioned studies focus mostly on the investigation of the generated cutting forces and temperatures, the developed stresses, the chip morphology, and tool wear under dry conditions with both coated and uncoated tools. In some cases, cryogenic conditions were implemented, and the microstructure of the material was examined. The Arbitrary Lagrangian–Eulerian (ALE) and the CEL were the two common methods for the development of the FE models, with modifications related to the friction and the flow stress models. 3D FEM studies can be utilized for the investigation of similar parameters and characteristics of machining. Liu et al. [14] implemented 3D FEM in their study related to 17-4PH stainless steel machining. The developed 3D model enabled the investigation of the cutting performance of various micro-grooved tools. Studies that involve textured tools benefit greatly from the use of 3D FEM, since the complexity of the tool models cannot be easily approximated otherwise. Similar studies [15, 16] for the machining of AISI1045 steel and Ti6Al4V alloy, use FEM in three dimensions to examine the machinability under certain conditions with micro-grooved and textured tools. The increasing number of 3D studies in the past few years [17–23] proves the necessity of the 3D FEM in machining. Tzotzis et al. [24] utilized 3D FEM to predict the developed machining forces during AISI4140 turning with ceramic tools. The authors developed a 3D FE model implementing tool CAD models of high precision, for the study of the tool nose influence on the generated cutting forces. Xu et al. [25] utilized 3D FE techniques for the modeling of titanium composites drilling, in order to provide an understanding of the interface damage progression. In this work, a number of key points related to the techniques used in FEM-based studies of machining were extracted from recent advances in the field. Therefore, an effort was made to compare different approaches utilized in 2D and 3D FEM-based researches, focusing mainly on the modeling of the machining forces and torque, the

1.2 Comparison Between 2D and 3D FEM Analysis Techniques

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chip formation, the residual stresses, the generated temperatures, and the progression of tool wear.

1.2 Comparison Between 2D and 3D FEM Analysis Techniques Either 2D or 3D, the studies that implement FEM focus on the investigation of aspects that affect machining processes in order to analyze their mechanisms. A high number of variables involved in machining can be examined via FEM, but the number of dimensions used enables different approaches each time.

1.2.1 Evaluation of Cutting Forces and Torque Evaluation of the forces generated during machining is a topic widely discussed among researchers, since it can provide valuable insight into the tool wear and performance, as well as the machinability of a material. Most studies related to this topic include an examination of the cutting conditions’ influence on the produced machining forces, which is possible to be carried out with either 2D or 3D FE models. The difference is that a 2D model can approximate only the cutting force F c and the thrust force F p , whereas a 3D can simulate the feed force F f as well. Despite this difference, the 2D model cannot be considered obsolete by any means, since feed force is not that important when compared to both the cutting and the thrust force. In fact, the measured feed force values will always be lower compared to the other two force components. Thus, it does not contribute much to the generated resultant cutting force. However, when it is required to evaluate feed force as well, the 3D model is the only option. Finally, Fig. 1.1a illustrates an example force analysis on the plane, whereas Fig. 1.1b depicts the equivalent analysis in three dimensions. Because 2D simulations run much faster compared to 3D ones, many researchers [26–28] utilized this advantage to perform preliminary studies in two dimensions. Such studies are used for evaluation purposes of several aspects involved in the development of the FE model, such as the friction coefficients, the flow stress, and the damage progression constants. Similarly, cutting torque can be determined by both 2D and 3D FE models. However, a 3D model can deliver more accurate results at the cost of long running times. Torque can provide valuable information on the required machine power and allow the engineers to assess the ongoing machining process. A number of studies focused on the study of drilling, utilized 3D FE modeling in order to output combined results related to the cutting forces and torque with the chip formation [29, 30] or temperature distribution with the chip formation [31]. In contrast, Matsumura and

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Fig. 1.1 Machining force analysis in 2D (a) and 3D (b)

Tamura [32] established a hybrid simulation model, which implemented 2D simulations for cutting force prediction. The simulations focused on the energy analysis, where the three-dimensional chip flow was modeled on the plane, including both the cutting and the chip flow directions. Concluding, the selection of the appropriate method for the assessment of the cutting forces and torque depends to a great extent on the computational resources and the influence of the assumptions made during a 2D analysis.

1.2.2 Chip Formation and Dimensions Assessment Regarding the understanding of the chip formation mechanisms, the utilization of 3D FE modeling clearly provides an edge over the equivalent 2D method. In such studies,

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the implementation of the third dimension is critical, since it provides a more accurate approximation of both the chip formation and morphology. The chip flow in two dimensions can be predicted with reasonable accuracy. A number of 2D studies [6, 10, 11, 33] focused on the examination of the strain distribution and reported findings on the chip flow of acceptable reliability, approximating many types of chip such as continuous, discontinuous, with built-up-edge and serrated. However, according to Thepsonthi and Özel [34], the 2D chip tends to be accumulated in front of the tool’s edge, due to the lack of the third dimension. Hence, the 2D chip flow is based on assumptions that negatively affect the accuracy of the results. Especially when studying more complex processes such as drilling and milling, the implementation of the third dimension is imperative as shown in several studies [34–37]. Chip breakage [16] is a topic that cannot be easily examined without the implementation of the third dimension. A 3D study can reveal both the breakage points, as well as the critical dimensions and morphology at these points. Figure 1.2a illustrates an example of chip formation at the initiation of the cutting process in 3D turning, whereas Fig. 2b illustrates the equivalent process in 2D. Moreover, Fig. 1.2c depicts the chip formation during 3D milling. It is evident that the first two images present some similarities, the fact that proves the possibility to approximate the chip flow to some extent. However, Fig. 1.2c points out that more complex machining processes produce equally complex chips, making their study less efficient in two dimensions. In addition, 3D studies enable the examination of burr formation [38, 39], as well as allow the consideration of the tool run-out [26] and other machine errors, which cannot be taken into account in 2D. Furthermore, it is possible to study the performance of the cutting tool, regardless of its shape and geometrical characteristics [14, 40]. Finally, it is highlighted that the 3D FE modeling allows the investigation of more aspects related to the chip flow, compared to the 2D one.

1.2.3 Examination of Residual Stresses To access the residual stresses induced during the machining of materials, many researchers prefer a combination of 2D and 3D FE modeling. It is common to utilize 2D simulations for the identification of the loading zones, whereas 3D simulations are used for the fundamental modeling of the residual stresses. This technique leads to reduced simulation times, without compromising the reliability of the results. Rami et al. [27] managed to replace the tool-chip interface with the generated thermomechanical loadings. By using 2D FEM, the authors identified the depth where the residual stresses state appears and next, implemented 3D FEM in their study to obtain more realistic results by applying the loadings on a 3D model. Additionally, Salvati and Korsunsky [41] analyzed the microscale residual stresses in Electric Discharge Machining (EDM) with the aid of thermomechanical FEM solely in a planar domain. It must be noted, however, that the identification of the stress field can be realized completely in 3D without the need for 2D simulations [42, 43]. According

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Fig. 1.2 Example chip flow in 3D turning (a), 2D turning (b), and 3D milling (c)

to Attanasio et al. [44], the use of the 3D FEM model enables the study of complex tool geometries, as well as the identification of the optimal cutting parameters that can yield the lowest possible residual stress values. Valiorgue et al. [42] simulated the residual stress without the chip removal process, by applying the equal to the thermomechanical loadings onto the cut surface in three dimensions, simulating a multiple-pass cutting process.

1.2.4 Temperature and Tool-Wear Assessment Cutting temperatures are directly related to the generated tool wear, making the prediction of these variables critical. Even though both methods are able to yield results for the temperatures and tool wear, there are cases where 3D is a one-way solution, whereas, in other cases, a combination between the two can be more effective. Similar to the variables mentioned in the previous sections, 3D modeling is the preferred method over 2D for temperatures generated during more complex processes such as drilling and milling. In addition, when tools with special geometries are involved, the 2D method simply cannot yield acceptable results, since too many assumptions and simplifications must be made. According to Ebrahimi et al. [12], the length where contact exists between the primary cutting edge and the workpiece

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is considered to be the same as in a 2D analysis. Therefore, the authors combined 2D and 3D FEMs for the prediction of the chip morphology and the cutting forces respectively. On the other hand, some studies [4, 6] preferred to use solely the 2D method to model tool wear progression with respect to typical tool characteristics such as rake angle and nose radius. However, the majority of the researchers, resort to the 3D method for the development of FE models that involve complex processes and tool geometries, in addition to more realistic approaches. Malakizadi et al. [45] investigated the flank tool wear and the developed temperatures during turning in three dimensions, considering several cutting conditions, by utilizing dense 3D mesh distributions on the tool’s areas of interest. Majeed et al. [31] utilized 3D FE modeling to assess the temperature allocation on the chip and the test piece during drilling, with an aim to evaluate tool life. Similarly, Lotfi et al. [46] examined the connection between the built-up heat and the tool flank wear in drilling with the 3D method. Magalhães et al. [47] approximated the temperature distribution and the tool rake face wear, on the rounded edges of the tool, discretized with multiple chamfers. Moreover, Lotfi et al. [48] utilized 3D modeling for the prediction of the temperature interface and tool wear rates, among other variables, during turning with both coated and uncoated tools. Especially for the case of the coated tools, the models included the full geometrical aspects that can be captured only in three dimensions. Figure 1.3 illustrates sample temperature results for 3D drilling (Fig. 1.3a), 2D turning (Fig. 1.3b), and 3D turning as well (Fig. 1.3c). In specific, Fig. 1.3a depicts the temperature distribution along the cutting edges of the twist drill in three dimensions. It is noted that the temperature changes with respect to the depth of penetration, since the contact volume is analogous to the depth. Moreover, because a 2D model cannot simulate the contact volume of the tool, it is not possible to approximate the equivalent developed temperatures. Figure 1.3a, b compare the temperature distribution across the surface of the generated chip in two and three dimensions accordingly, for identical cutting conditions and at similar cutting step. Despite the similarities that can be found between the two methods, regarding the temperature values, as well as the distribution zones, the 2D method cannot highlight the volumetric boundaries of each one of these zones, in contrast to the 3D one. The same limitations and restrictions can be observed when investigating tool wear as well.

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Fig. 1.3 Example temperature distribution along a twist drill’s edges in 3D (a), on the 2D chip during turning (b), and on the 3D chip, respectively (c)

1.3 Conclusions This study introduced a number of points that derive from the comparison of the approaches made with 2D and 3D FEM during standard machining processes. The variables that are affected by the application of the FEM techniques, and are discussed in the present chapter, are the cutting forces, torque, temperature distribution on the cutting edges, as well as on the chip surface, the tool wear development, the chip flow and the generated stresses. By collecting and comparing information found in the literature, the following conclusions can be drawn. Additionally, Table 1.1 summarizes some key points related to the benefits and the limitations that emerge when using FEM in these types of studies, that were identified during the literature review. • The 2D FEM constitutes an effective tool for preliminary simulations and sensitivity studies due to the simple setup and short run times. • In contrast, the 3D FEM is a more resource-intensive method compared to the 2D one, the fact that is responsible for the long simulation times. In spite of this disadvantage, the 3D FEM provides more realistic results when compared to equivalent 2D analyses, and in some cases is the only way to generate certain output.

1.3 Conclusions

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Table 1.1 Summary of the advantages and disadvantages of 2D and 3D FEM 2D FEM Model setup is simple Run times are short Is effective for trial-and-error testing Provides accurate approximation of most types of chip morphology • Can be used to identify the residual stress’s depth • Can output the generated temperatures, flank, and rake tool wear with acceptable accuracy

3D FEM

(+) • • • •

• Utilizes the full tool geometry, thus, enabling the use of complex tools • Provides realistic chip formation, which includes several phenomena that occur during machining such as chip breakage, tool run-out, and burr formation • Enables the study of every chip dimension • Enables the prediction of all force components • Allows the full simulation of the residual stresses • Can output volumetric tool wear • Enables the study of the temperature distribution zones in three dimensions

(−) • Utilizes simplified tool geometry, thus, only the rake angle, the clearance angle, and the nose radius participate in the process • The study takes place in the plane, neglecting several important characteristics of the process • Prediction of the forces is not as accurate as in 3D

• Depends heavily on the computational resources • Run times can become very long • Model setup is more complicated compared to 2D • Some output variables are difficult to be measured

• The prediction of the cutting forces and torque is more accurate in 3D due to the modeling of the full tool geometry and contact region. • Modeling of the chip morphology can be determined accurately with both methods. However, the 3D chip flow can yield results that include parameters which cannot be easily implemented in a 2D analysis, such as the burr formation, chip breakage, and the complete dimensions of the chip. • The residual stresses, in terms of appearance depth and domain, can be identified by both methods with success. To acquire a deeper understanding of this phenomenon, however, the three-dimensional analysis seems a more efficient approach. • Finally, prediction of the temperatures that develop on the tool-chip interface can be carried out reliably by both methods. The same applies for the tool wear, with respect to both flank and rake regions. Nevertheless, the implementation of the third dimension, enables the use of the complete geometry of a tool, thus, allowing the examination of the full contact domain between the cutting tool and the material.

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References 1. Cepero Mejías F, Curiel Sosa JL, Phadnis VA (2018) Machining 2D FEM study of long fibre reinforced unidirectional laminates using a linear continuum damage technique. 6th Conf Comput Mech 2. Cepero-Mejías F, Curiel-Sosa JL, Zhang C, Phadnis VA (2019) Effect of cutter geometry on machining induced damage in orthogonal cutting of UD polymer composites: FE study. Compos Struct 214:439–450. https://doi.org/10.1016/j.compstruct.2019.02.012 3. Zhou Y, Sun H, Li A et al (2019) FEM simulation-based cutting parameters optimization in machining aluminum-silicon piston alloy ZL109 with PCD tool. J Mech Sci Technol 33:3457– 3465. https://doi.org/10.1007/s12206-019-0640-3 4. Peng B, Bergs T, Klocke F, Döbbeler B (2019) An advanced FE-modeling approach to improve the prediction in machining difficult-to-cut material. Int J Adv Manuf Technol 103:2183–2196. https://doi.org/10.1007/s00170-019-03456-0 5. Mishra SK, Ghosh S, Aravindan S (2019) Performance of laser processed carbide tools for machining of Ti6Al4V alloys: a combined study on experimental and finite element analysis. Precis Eng 56:370–385. https://doi.org/10.1016/j.precisioneng.2019.01.006 6. Tagiuri ZAM, Dao TM, Samuel AM, Songmene V (2022) A numerical model for predicting the effect of tool nose radius on machining process performance during orthogonal cutting of AISI 1045 steel. Materials (Basel) 15. https://doi.org/10.3390/ma15093369 7. Parida AK, Maity K (2019) Analysis of some critical aspects in hot machining of Ti-5553 superalloy: experimental and FE analysis. Def Technol 15:344–352. https://doi.org/10.1016/j. dt.2018.10.005 8. González G, Segebade E, Zanger F, Schulze V (2019) FEM-based comparison of models to predict dynamic recrystallization during orthogonal cutting of AISI 4140. Procedia CIRP 82:154–159. https://doi.org/10.1016/j.procir.2019.04.061 9. Chandra Mouli G, Prakash Marimuthu K, Jagadeesha T (2020) 2D finite element analysis of inconel 718 under turning processes. In: IOP conference series: materials science and engineering, pp 1–11 10. Yaich M, Ayed Y, Bouaziz Z, Germain G (2020) A 2D finite element analysis of the effect of numerical parameters on the reliability of Ti6Al4V machining modeling. Mach Sci Technol 24:509–543. https://doi.org/10.1080/10910344.2019.1698606 11. Xu X, Outeiro J, Zhang J et al (2021) Machining simulation of Ti6Al4V using coupled EulerianLagrangian approach and a constitutive model considering the state of stress. Simul Model Pract Theory 110. https://doi.org/10.1016/j.simpat.2021.102312 12. Ebrahimi SM, Hadad M, Araee A, Ebrahimi SH (2021) Influence of machining conditions on tool wear and surface characteristics in hot turning of AISI630 steel. Int J Adv Manuf Technol 114:3515–3535. https://doi.org/10.1007/s00170-021-07106-2 13. Prakash Marimuthu K, Kumar CSC, Prasada HPT (2018) 2D finite element thermo-mechanical model to predict machining induced residual stresses using ALE approach. Mater Today Proc 5:11780–11786. https://doi.org/10.1016/j.matpr.2018.02.147 14. Liu G, Huang C, Su R et al (2019) 3D FEM simulation of the turning process of stainless steel 17–4PH with differently texturized cutting tools. Int J Mech Sci 155:417–429. https://doi.org/ 10.1016/j.ijmecsci.2019.03.016 15. Mishra SK, Ghosh S, Aravindan S (2018) 3D finite element investigations on textured tools with different geometrical shapes for dry machining of titanium alloys. Int J Mech Sci 141:424–449. https://doi.org/10.1016/j.ijmecsci.2018.04.011 16. Wu L, Liu J, Ren Y et al (2020) 3D FEM simulation of chip breakage in turning AISI1045 with complicate-grooved insert. Int J Adv Manuf Technol 108:1331–1341 17. Mishra DK, Verma AK, Arab J et al (2019) Numerical and experimental investigations into microchannel formation in glass substrate using electrochemical discharge machining. J Micromech Microeng 29:1–13 18. Wan M, Ye X-Y, Wen D-Y, Zhang WH (2019) Modeling of machining-induced residual stresses. J Mater Sci 54:1–35. https://doi.org/10.1007/s10853-018-2808-0

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19. Lotfi M, Amini S, Akbari J (2020) Surface integrity and microstructure changes in 3D elliptical ultrasonic assisted turning of Ti–6Al–4V : FEM and experimental examination. Tribol Int 151:106492. https://doi.org/10.1016/j.triboint.2020.106492 20. Park CI, Wei Y, Hassani M et al (2019) Low power direct laser-assisted machining of carbon fibre-reinforced polymer. Manuf Lett 22:19–24. https://doi.org/10.1016/j.mfglet.2019.10.001 21. Tzotzis A, Tapoglou N, Verma RK, Kyratsis P (2022) 3D-FEM approach of AISI-52100 hard turning: modelling of cutting forces and cutting condition optimization. Machines 10:74. https:// doi.org/10.3390/machines10020074 22. Tzotzis A, Efkolidis N, Oancea G, Kyratsis P (2021) FEM-based comparative study of square & rhombic insert machining performance during turning of AISI-D3 steel. Int J Mod Manuf Technol 13:143–148. https://doi.org/10.54684/ijmmt.2021.13.2.143 23. He YL, Davim JP, Xue HQ (2018) 3D progressive damage based macro—mechanical FE simulation of machining unidirectional FRP composite. Chinese J Mech Eng. https://doi.org/ 10.1186/s10033-018-0250-5 24. Tzotzis A, García-Hernández C, Huertas-Talón J-L, Kyratsis P (2020) Influence of the nose radius on the machining forces induced during AISI-4140 hard turning: a CAD-based and 3D FEM approach. Micromachines 11:798. https://doi.org/10.3390/mi11090798 25. Xu J, Lin T, Li L et al (2022) Numerical study of interface damage formation mechanisms in machining CFRP/Ti6Al4V stacks under different cutting sequence strategies. Compos Struct 285:115236. https://doi.org/10.1016/j.compstruct.2022.115236 26. Davoudinejad A, Tosello G, Parenti P, Annoni M (2017) 3D finite element simulation of micro end-milling by considering the effect of tool run-out. Micromachines 8:1–20. https://doi.org/ 10.3390/mi8060187 27. Rami A, Kallel A, Sghaier S et al (2017) Residual stresses computation induced by turning of AISI 4140 steel using 3D simulation based on a mixed approach. Int J Adv Manuf Technol 91:3833–3850. https://doi.org/10.1007/s00170-017-0047-1 28. Pittalà GM, Monno M (2010) 3D finite element modeling of face milling of continuous chip material. Int J Adv Manuf Technol 47:543–555. https://doi.org/10.1007/s00170-009-2235-0 29. Tzotzis A, Markopoulos AP, Karkalos NE et al (2021) FEM based investigation on thrust force and torque during Al7075-T6 drilling. In: IOP conference series: materials science and engineering, p 012009 30. Dou T, Fu H, Li Z et al (2019) Prediction model, simulation, and experimental validation on thrust force and torque in drilling SiCp/Al6063. Int J Adv Manuf Technol 103:165–175. https:// doi.org/10.1007/s00170-019-03366-1 31. Majeed A, Iqbal A, Lv J (2018) Enhancement of tool life in drilling of hardened AISI 4340 steel using 3D FEM modeling. Int J Adv Manuf Technol 95:1875–1889. https://doi.org/10. 1007/s00170-017-1235-8 32. Matsumura T, Tamura S (2015) Cutting simulation of titanium alloy drilling with energy analysis and FEM. Procedia CIRP 31:252–257. https://doi.org/10.1016/j.procir.2015.03.045 33. Davim JP, Maranhão C (2009) Study on plastic strain and plastic strain rate in machining of steel AISI 1020 using FEM analysis. Mater Des 30:160–165. https://doi.org/10.1016/j.matdes. 2008.04.029 34. Thepsonthi T, Özel T (2015) 3-D finite element process simulation of micro-end milling Ti6Al-4V titanium alloy: experimental validations on chip flow and tool wear. J Mater Process Tech 221:128–145. https://doi.org/10.1016/j.jmatprotec.2015.02.019 35. Tzotzis A, García-Hernández C, Huertas-Talón J-L, Kyratsis P (2020) FEM based mathematical modelling of thrust force during drilling of Al7075-T6. Mech Ind 21:415. https://doi.org/10. 1051/meca/2020046 36. Tzotzis A, García-Hernández C, Huertas-Talón J-L, Kyratsis P (2020) 3D FE modelling of machining forces during AISI 4140 hard turning. Strojniški Vestn—J Mech Eng 66:467–478. https://doi.org/10.5545/sv-jme.2020.6784 37. Lotfi M, Amini S, Aghaei M (2018) 3D FEM simulation of tool wear in ultrasonic assisted rotary turning. Ultrasonics 88:106–114. https://doi.org/10.1016/j.ultras.2018.03.013

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38. Davoudinejad A, Tosello G, Annoni M (2017) Influence of the worn tool affected by builtup edge (BUE) on micro end-milling process performance: a 3D finite element modeling investigation. Int J Precis Eng Manuf 18:1321–1332. https://doi.org/10.1007/s12541-0170157-6 39. Guo YB, Dornfeld DA (2000) Finite element modeling of burr formation process in drilling 304 stainless steel. J Manuf Sci Eng Trans ASME 122:612–619. https://doi.org/10.1115/1.128 5885 40. Kyratsis P, Tzotzis A, Markopoulos A, Tapoglou N (2021) CAD-based 3D-FE modelling of AISI-D3 turning with ceramic tooling. Machines 9:4. https://doi.org/10.3390/machines9 010004 41. Salvati E, Korsunsky AM (2020) Micro-scale measurement & FEM modelling of residual stresses in AA6082—T6 Al alloy generated by wire EDM cutting. J Mater Process Tech 275:1–12. https://doi.org/10.1016/j.jmatprotec.2019.116373 42. Valiorgue F, Rech J, Hamdi H et al (2012) 3D modeling of residual stresses induced in finish turning of an AISI304L stainless steel. Int J Mach Tools Manuf 53:77–90. https://doi.org/10. 1016/j.ijmachtools.2011.09.011 43. Özel T, Ulutan D (2012) Prediction of machining induced residual stresses in turning of titanium and nickel based alloys with experiments and finite element simulations. CIRP Ann Manuf Technol 61:547–550. https://doi.org/10.1016/j.cirp.2012.03.100 44. Attanasio A, Ceretti E, Giardini C (2009) 3D FE modelling of superficial residual stresses in turning operations. Mach Sci Technol 13:317–337. https://doi.org/10.1080/109103409032 37806 45. Malakizadi A, Gruber H, Sadik I, Nyborg L (2016) An FEM-based approach for tool wear estimation in machining. Wear 368–369:10–24. https://doi.org/10.1016/j.wear.2016.08.007 46. Lotfi M, Amini S, Al-Awady IY (2018) 3D numerical analysis of drilling process: heat, wear, and built-up edge. Adv Manuf 6:204–214. https://doi.org/10.1007/s40436-018-0223-z 47. Magalhães FC, Ventura CEH, Abrão AM, Denkena B (2020) Experimental and numerical analysis of hard turning with multi-chamfered cutting edges. J Manuf Process 49:126–134. https://doi.org/10.1016/j.jmapro.2019.11.025 48. Lotfi M, Jahanbakhsh M, Farid AA (2016) Wear estimation of ceramic and coated carbide tools in turning of Inconel 625: 3D FE analysis. Tribol Int 99:107–116. https://doi.org/10.1016/j.tri boint.2016.03.008

Chapter 2

Fundamentals of 3D Finite Element Modeling in Conventional Machining

Abstract The present chapter introduces the fundamentals of Finite Element Method (FEM) applied in standard machining processes such as turning, drilling, and milling. The most broadly used models for material flow, friction, and material separation and evolution are presented. In addition, a short introduction is included to meshing, element types, contact interface, and boundary conditions. Finally, the most recent modifications and advances in the various models implemented in FEM are presented, as well as the state of the art, especially in three dimensions. Keywords 3D FEM · 3D simulation · Machining · Turning · Drilling · Milling · Cutting forces · Chip geometry · Cutting temperature

2.1 Introduction Computers are widely used in engineering to simulate optimal prototype design solutions that meet established performance criteria. Various computing tools are often used in setting, evaluating, and testing the design goals and specifications of a product or system. It is expected that in the near future, computer-based modeling methods and tools will simply require a description of the expected behavior or structure of a design idea, in order to perform the simulation with an aim to evaluate the idea in a fully automated manner. Computer-aided engineering (CAE) is a technology that utilizes computer systems to analyze the geometry of a system, allowing the engineer to simulate and study the behavior, as well as the performance of a model, in order to optimize certain parameters. CAE systems are available for a wide range of analyses, such as stress, thermal, and vibration. Several CAE software, such as ANSYS™, ABAQUS™, and ALTAIR™ can calculate the resulting stresses of a complex geometry, by determining loads using fundamental static equations and numerical methods. They can also be used to analyze heat transfer problems, fluid flow, electromagnetism, and other multidimensional problems. Many physical problems involve complex geometries, different materials, complex boundaries, and initial conditions. To solve complex problems, engineers © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al., 3D FEA Simulations in Machining, Manufacturing and Surface Engineering, https://doi.org/10.1007/978-3-031-24038-6_2

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must resort to numerical methods, especially when analytical methods cannot be of assistance. In general, any practical problem can be idealized as a mechanical problem, as shown in Fig. 2.1. Especially engineering problems are models of physical states, expressed mathematically. A great number of models contain differential equations, which are derived using fundamental laws of physics (e.g., Newton’s laws) and principles, such as the conservation of energy and mass, and momentum, with a set of limits and initial conditions. For simple problems, it is possible to find a specific solution in analytical form, where the solution is given via multiple variables and parameters, which are already available in Static Engineering, Strength of Materials, Fluid Engineering, and other fields of engineering. However, for problems of increased complexity, numerical methods are more appropriate. These include the Finite Difference Method (FDM), where derivatives are replaced by differential equations, the Finite Element Method (FEM), and the Boundary Element Method (BEM), which uses integrated formulations to produce a system of algebraic equations. With FEM, the whole analysis domain or geometry is discretized. This chapter deal with the implementation of FEM in machining processes, a method that meets an increased degree of acceptance in the past few years.

Fig. 2.1 Solution flow chart of an engineering problem

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2.1.1 FEM-Based Studies in Machining Despite the fact that FEM-based analyses usually take a long time to complete and require a great deal of computer resources, it is a preferred method to simulate complex processes such as most machining operations. With the advent of more advanced software and the technological evolution of computers, it is possible to simulate most conventional and non-conventional processes in a relatively straightforward way. The development of more specialized software, oriented towards machining and forming, such as DEFORM™, FORGE™, and AdvantEdge™, enabled the investigation of the machining processes in both two and three dimensions. Earlier, Ceretti et al. [1] modified the code of DEFORM™-2D to study the orthogonal cutting process of steel. To achieve reasonable accuracy, several changes were made to the material separation process model. Similarly, Klocke et al. [2] studied the turning of AISI-1045 steel with the aid of 2D FEM, at high speeds. The authors indicated that despite the fact that several assumptions were made regarding the model, the results were in accordance with their experimental testing. Maranhão and Davim [3] modeled the behavior of stainless steel during machining, to investigate the influence of friction on standard parameters that are involved. Moreover, Xie et al. [4] implemented commercially available software to predict the wear of turning tools. By using FEM, the authors managed to calculate the chip formation and heat transfer, which were then used to determine the wear on the tool, according to the applied cutting conditions. Besides typical industrial materials such as steel and aluminium, FEM-based study of machining in two dimensions can be extended to more advanced materials such as titanium [5, 6] and nickel alloys [7, 8]. These studies focus on the surface quality and integrity of the machined material, residual stresses, thermal behavior, chip morphology, and more. Furthermore, a number of 3D studies in machining exist in literature, dealing with both conventional and non-conventional processes. An early example is the study on hard turning by Guo and Liu [9]. The authors established a 3D FE model to study the machinability of hardened steel with ultra-high strength tools. Karpat and Özel [10] investigated turning with 3D simulations to predict generated forces and temperatures with regard to the microgeometry of the tools. Moreover, a set of experiments was conducted for comparison. Buchkremer et al. [11] proposed a calculation method, which details how the chip characteristics at the breakage point and the thermomechanical properties on the uncut surface are related. The necessary parameters were obtained by implementing experimentally generated chip geometries into the methodology. Similar studies in turning [12–14], investigate the generated cutting forces, chip geometry, temperature distribution, tool wear, and more. FEM can be applied to an equally important machining process such as drilling. Gao et al. [15] proposed a three-dimensional FEM model of drilling with a twist drill.

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In the study, the scraps forming process, the cutting forces, and the cutting temperatures are analyzed. Majeed et al. [16] studied the effect of the developed temperatures on tool life, during drilling steel 4140. The authors determined the temperatures at the drill bit and compared them with the equivalent experimental ones. Oezkaya et al. [17] investigated flow drilling with the aid of FEM. Their paper presented a three-dimensional FE model for predicting the performance of modified tools during flow drilling of AlSi10Mg. The study includes the performance of both preheated and non-preheated tools in comparison with experimental results. Additional studies demonstrate the implementation of FEM when modeling the drilling operation and its usefulness when exploring several performance parameters [18–20]. Similar to turning and drilling, milling is one of the most used processes in industry. Hence, several studies deal with the investigation of milling based on FEM. Maurel-Pantel et al. [21] described the simulation process of 304L stainless steel shoulder milling with FEM. A number of experiments were carried out for validation purposes, which delivered the generated milling forces. Davoudinejad et al. [22] presented a 3D FEM approach for the micro-milling process of Al6082-T6. The built-up edge (BUE) and its effects on the process performance were examined in terms of the chip flow, burr formation, and cutting forces. Moreover, experiments were conducted with ultra-high precision for comparison purposes. Gao et al. [23] developed a 3D Coupled Eulerian–Lagrangian (CEL) model for the simulation of aluminium end-milling processes. The chip flow was predicted with the proposed model, and all the stages of the formation were compared with experimental data. As seen in similar studies [24–27], the examination parameters that draw the attention of the researchers are the milling forces, the temperature distribution, the chip geometry, the tool wear, the residual stresses, the machining errors, and more. It must be noted that FEM has applicability to non-conventional processes also, especially as computer technology advances and computational time is decreased. Electrical Discharge Machining (EDM) is one of the standard non-conventional machining methods that can benefit from FEM. A number of studies indicate that it is possible to study several aspects of the process with significant accuracy, meaning that FEM is a reliable method for non-conventional machining processes as well. Such studies [28–31] usually investigate the behavior of hard-to-machine materials such as metallic glasses via EDM and ultrasonic-assisted machining, as well as the performance of the electrodes, the machinability of various materials, and the effects of the machining parameters on the machined surface. The present chapter introduces the implementation of FEM in standard machining processes and summarizes most of the available models and techniques for meshing, boundary conditions, material flow stress, friction, and material separation. Additionally, an effort is made to include indicative studies and the latest trends in the field.

2.2 Finite Element Modeling in Machining

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2.1.2 Advantages and Limitations of FEM It is not easy to determine whether 2D or 3D modeling is a better method, since both have their advantages and disadvantages. Most of the time it depends on the type of study. Thus, in some cases, 2D may prove to be an ideal solution, whereas, in other cases, 3D is the only way to study a phenomenon. Regarding the 2D analysis, it enables the use of analytical rigid parts that reduce calculation time and can be used to simplify the mechanical problem, making it ideal for preliminary simulations. However, it cannot be used to simulate more complicated phenomena and geometries. On the other hand, a 3D analysis produces results closer to the real conditions, as it implements the full geometry of a cutting tool. 3D analyses are ideal for complicated simulations but are sensitive to computer resources. In general, FE modeling provides the user with several advantages: • • • • • • •

The full machining process can be visualized. Many machining aspects and variables can be thoroughly examined. Experimental testing can be reduced. Safety procedures can be eliminated. Costs related to production, as well as production times, can be minimized. A great deal of manufacturing failures and errors can be predicted. Finally, a number of machining results can be accurately predicted. As someone would expect, this method is followed by some limitations also:

• Idealization of real-life objects cannot be exact for very complex shapes. • The method yields approximate solutions. • The computation is very costly. For instance, as the mesh becomes finer, the requirement for computer resources grows. Thus, there is a computational limit based on the current computer resources. • Time needed for solving the problems, increases with the degree of fineness of the mesh, hindering the prospect of solving a model in full.

2.2 Finite Element Modeling in Machining 2.2.1 Meshing and Element Types During the discretization process of a model, the volume or the surface is divided into a discrete number of smaller elements, which are called finite elements. Elements can be one-dimensional if they are simple lines in the plane, two-dimensional if they are shapes in the plane (e.g., a triangle), usually called shell elements, and threedimensional if they are solids in space (e.g., tetrahedron, hexahedron, and pyramid). During the solution process, the equations that govern the behavior of a system are applied to each of the individual elements of a model. One-dimensional elements are used to discretize lengthy parts with a uniform cross section, such as shafts, beams,

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and others. Shell elements (two-dimensional) are usually used for models that have a small and uniform thickness (e.g., sheet-metal parts), while the solid elements (three-dimensional) are used in complex parts, which have a complex geometry (e.g., cast objects). Finally, 2D and 3D elements can be first-order (linear) or secondorder (parabolic), with the second-order elements having a greater number of nodes than the first-order, making them higher quality elements. Figure 2.2 illustrates the different types of elements. As shown in Fig. 2.2, nodes are the vertices of the forming elements of a grid. Also, they are the points of an element with which it contacts and connects with neighboring elements. Their number depends on the type of element, so for the first order, a triangular shell element will have three nodes, while a hexahedral solid element will have eight nodes. Correspondingly for the second order, the triangle will have 6, whereas the hexahedron 20. Figure 2.3 depicts typical examples of first- and second-order elements, respectively. Modern computer simulation systems enable the selection of the desirable element type and the edit of the mesh parameters. In addition, it is possible to use the embedded to the software mesh generator, which automatically selects the appropriate type of elements according to the problem. For example, once the user selects to process a

Fig. 2.2 Standard types of finite elements

2.2 Finite Element Modeling in Machining

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Fig. 2.3 Number of nodes based on the element’s order

problem in two dimensions with symmetrical geometry, the software suggests the use of the optimal type of elements, which in this case is the plane element. One of the most important mesh parameters is density, which refers to the size of the elements that will be generated within a boundary. Thus, the total number of elements in an area can be determined by their size. Most Finite Element Analysis (FEA) systems usually allow the user to either set the number of elements upfront or define the minimum/maximum size of an element. With the latter option, the mesh size is calculated according to either the minimum or the maximum size of an element. Secondary parameters that affect the mesh density are the sample grid resolution and the critical point tolerances. These parameters are considered to have lesser effect on the density, compared to the element size (Fig. 2.4).

Fig. 2.4 Typical mesh size parameters

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Fig. 2.5 Sample meshing for a typical machining process

Besides element size, the minimum element number in a circle or arc and the size ratio between neighboring elements are equally important mesh parameters. It is noted that not all elements within an area have the same size. Moreover, it is possible to set various element sizes for different regions within an area. This technique is usually implemented when a local refinement is desired, such as at the machined surface of the workpiece during machining (Fig. 2.5). The local mesh can be defined with the specified size ratio. The DEFORM™-3D software suggests a size ratio of 7:1 [14, 32, 33], irrespective of the machining operation. Some studies on turning [3, 13, 34] point out that 4:1 to 5:1 is an acceptable ratio, whereas a number of works in drilling [16, 35] applied a 10:1 ratio. More complex parts that are used during milling, were discretized with ratios in the range of 10:1–20:1 [36, 37]. In any case, the minimum element size (MES) is set to values in the order of fractions of an mm and is based on the experience and expertise acquired with FEA simulations. It is noted that especially for the DEFORM™-3D system, as a rule of thumb, a sufficient MES is usually equal to 25% of the feed for turning, or 50% of the feed per tooth for drilling and milling [38–41]. Early examples of 3D FEM-based studies in machining [9, 42], where the local mesh refinement was utilized, prove that a higher mesh density is usually applied at the area of interest, which is the contact area of the tool-work pair. This technique allows for increased precision and resolution of the geometry that participates in the machining operation. In addition, the field variables such as strain, temperature, and material damage become more accurate. However, this benefit comes with a drawback; The computational time that is required to solve the problem increases significantly, following a geometric progression pattern. Therefore, it is desirable for regions, where large deformations occur, to have a considerable number of smallsized elements. Contrarily, a coarser mesh (fewer small elements) is preferable in regions where the gradients of the state variables are negligible. The latter can greatly improve the conservation of computational resources. Finally, it is pointed out that a mesh with a density below an acceptable range may cause problems. More specifically, a low-quality mesh around corner edges or in regions with localized surface

2.2 Finite Element Modeling in Machining

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Fig. 2.6 Example tool model meshing

effects such as high damage, will most likely interfere with the remeshing process and cause mesh degradation. Regarding the tool model meshing, a similar practice is usually followed. Hence, the area around the tooltip or cutting edge that is in close proximity with the unmachined plane of the workpiece, is discretized with a denser mesh compared to the rest surface of the tool. A number of studies [13, 16, 34, 43] indicate that a 4:1 size ratio is adequate for the solution process, regardless of the machining operation and software used. In most cases, the tool is modeled to be rigid for simplification purposes of the under-study problem. As such, the nodes of the tool model cannot be deformed, contributing this way to the optimized simulation times. In the event that deformation effects must be investigated on the tool, it can be modeled as plastic. Either way, the complexity of the tool geometry can significantly affect the generated results, in addition to the completion time. It is pointed out that a rigid tool still should be meshed with this technique, in order to serve the thermal analysis. Figure 2.6 illustrates an example meshing with a 4:1 ratio for a turning insert and a twist drill model as well.

2.2.2 Mesh Adaptivity Remeshing is the most common method to prevent extreme element distortion during modeling of machining. There are three types of mesh adaptivity: h-adaptivity, padaptivity, and r-adaptivity. The first one is considered a general-use method and it enables the change of the element size, allowing this way the alteration of the mesh density and the node connectivity. The second type is less common since it is not effective in metal machining modeling. It increases the precision of the solution by changing the order of the interpolation polynomials. Finally, the third type is implemented in the Arbitrary Lagrangian–Eulerian (ALE) formulation and

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2 Fundamentals of 3D Finite Element Modeling in Conventional Machining

is capable of relocating the nodes. Therefore, the shape of the mesh elements is optimized without affecting the connectivity. Since large plastic deformations occur during machining, it is important that the conditions of the model’s initial mesh are continuously checked. In the event that mesh becomes unusable, the remeshing process is triggered, replacing the distorted mesh with a new undistorted one. Moreover, this process interpolates the field variables such as strain, temperature, node velocity, and damage from the unusable mesh to the new one. Most FEA software systems embed an algorithm that performs a check if certain criteria are met during the simulation process and handle both the remeshing and variable interpolation procedures at the same time. One standard criterion is the interference depth between the tool and the machined part, where the penetration depth of the primary into the slave object is monitored. A much higher value of penetration depth than the one needed will result in distorted elements, whereas a much lower value will increase the number of the remeshing processes, negatively affecting the run time. Another criterion for triggering the remeshing is the occurrence of the negative Jacobian matrix, which renders the mesh unusable. It is noteworthy that the remeshing technique is applied to the newly cut surface and the generated chip as well, to improve the convergence of the solution [44] and is based on the strain and strain rate values [24]. Modern versions of various FEA systems deal with the mesh distortion problem with local remeshing, rather than with a full replacement of the mesh. Lastly, there are three mathematical formulations that are used in continuum FEM: the Lagrangian, the Eulerian, and the ALE. Practically, the primary models are considered to be two, since the ALE is a combination of the Lagrangian and Eulerian. The updated Lagrangian formulation [16, 35, 44] is regarded as a major advancement in meshing techniques, allowing for improved computational times [45]. Additionally, the ALE formulation [17, 34, 46] enables the nodal adjustment, which allows the element nodes to adapt independently, preventing the occurrence of large deformations and maintaining the mesh topology. Nowadays, the Eulerian formulation is not the preferred choice of researchers in machining, because it requires the chip geometry to be predetermined and does not allow chip separation. In spite of the aforementioned disadvantages, this method employs a fixed space mesh, which completely disables the severe distortion problem [47]. Element deletion As damage in the material initiates, it will evolve and, eventually, the material will fracture. The criteria implemented in FEM that are used to model the chip separation and damage evolution are discussed in Sect. 2.7. Modern FEA systems include an option, as part of the remeshing procedure, that enables the deletion of extremely distorted elements to maintain the integrity of the mesh. Elements that exceed a defined critical damage value are removed from the mesh, making this method an effective way of modeling crack propagation. Due to the fact that element deletion may generate sharp edges at the area of interest, it is possible to select the degree of element deletion. Finally, coupled with local remeshing, compose an effective tool for the generation of a realistic chip. Figure 2.7 illustrates an example of chip generation

2.2 Finite Element Modeling in Machining

23

Fig. 2.7 Material separation and chip generation

and evolution during modeling of machining with DEFORM™-3D ver.12, where a remeshing technique is locally used, deletion for elements of specific size is enabled and Cockcroft-Latham criterion is implemented with the equivalent to the material damage constant.

2.2.3 Tool-Workpiece Representation Accurate representation of the tool-work interface is of great importance in FEMbased studies in machining. In most cases, the workpiece is a simplified part, which is easy to be designed in a CAD software. The tools, on the other hand, are usually more complex and require certain techniques to be accurately modeled. One source for tool models is the manufacturer’s website that usually contains several tool models. Unfortunately, most vendors do not upload accurate representations of their tools, but rather simplified ones. Even though a tool model with less information would contribute towards the improvement of the simulation time, the generated results would not be as reliable as it should. Even small misinterpretations in the geometry may alter significantly the results [48]. Therefore, for more accurate representations of complex tools, such as twist drills, specialized drills, and end-mills, an effective method is 3D scanning [21, 35, 44]. This method requires a 3D scanner and the equivalent piece of software that is able to convert the scanning process into a cloud of points and finally into a usable file format such as STL. Nonetheless, the method requires hardware and resources that are not always available. As a final resort, it is possible to design the tool in a CAD system, if all the critical geometric aspects of the tool are available. Moreover, it is feasible to implement programming to automatically generate parametrical tool models [49, 50], increasing this way the accuracy and improving the calculation process. Figure 2.8 compares the geometry and the design intent between a turning insert model from the vendor and the equivalent parametric model designed in a CAD system. In specific, it is shown that the origin point of the downloaded model is not ideally positioned, making the insertion of the model into the FEA system more complicated. Furthermore, it does not include a honing feature on the cutting edge, reducing this way the efficiency of the simulation and the reliability of the generated

24

2 Fundamentals of 3D Finite Element Modeling in Conventional Machining

Fig. 2.8 Model comparison with regard to the FEM aspects of a sample CNGA120408 tool

results [49]. Finally, lower tessellation in general, let alone of a critical geometrical aspect of the tool, tends to reduce the simulation precision. In addition, the size of the STL file for each of the two models is of the same order. Concluding, the generated CAD model contains extra geometrical features and thus implements a great deal of insert variations.

2.2.4 Boundary Conditions The conditions that express the borders between the tool and the workpiece are usually applied in such a way so that the tool is able to advance towards the fixed workpiece or the tool is constrained from translating along the feed path and at the same time is allowed to rotate (for processes such as milling and drilling). In any case, the movement of the tool and the workpiece is related to each other and equal to the cutting speed. The standard parameters that are set during the boundary conditions setup are the cutting speed, the feed, the cutting direction, the depth and the width of cut where applicable, as well as the initial contact zone between the tool and the work, and the heat exchange. Figure 2.9 illustrates the set of the basic boundary conditions for three typical machining procedures, drilling with a twist drill (Fig. 2.9a), turning with an insert (Fig. 2.9b), and face milling with an insert (Fig. 2.9c). By observing Fig. 2.9a it is shown that the twist drill translates along the Z axis (feed) towards the workpiece while rotating around the Z axis (spindle speed) at the same time, similar to the real procedure. Moreover, workpiece is fixed so that all nodes at the bottom and on the periphery of the cylinder are fixed, allowing only the distortion of the nodes inside the pre-made hole. Figure 2.9b depicts the cutting path that the turning insert follows in order to perform the cut. Since the radius of the work is drawn on the Z axis, the cutting trajectory will be on the YZ plane. In this case, the cutting speed and feed are converted to tool simultaneous movement along the Y and Z axes. The work is fixed on the side and along the bottom so that

2.2 Finite Element Modeling in Machining

25

Fig. 2.9 Boundary conditions for three typical machining processes; drilling (a), turning (b), and face milling (c)

the velocities of the nodes on both the X and Z axes are equal to zero. In contrast to the real conditions, the workpiece is constrained, whereas the tool is the object that moves. At last, Fig. 2.9c shows the cutting path of the milling insert on the XY plane and the fixation of the work in a similar manner to the turning workpiece. In this process, the kinematics of the simulation are identical to the real ones, with the exception that only one tooth participates in the cut for simplification purposes. As long as the steady state is achieved, it is possible to design the workpiece as an orthogonal part, further simplifying the process. This applies to both turning and face milling or similar processes. However, the addition of the circularity to the part makes the setup more realistic and allows the full study of the procedure. Analysis domain A focused analysis area is often used [24, 32, 38, 51] to simplify the study of the cutting process. This way the phenomena that occur during machining can be studied to an extent without sacrificing vast amounts of resources and time. CAD systems are an ideal tool to extract the necessary geometrical aspects of the tool-work framework, position the tool and examine the kinematics of the system [43]. Figure 2.10 presents an example analysis domain for turning extracted with the aid of a commercially available CAD software. In Fig. 2.10a, the domain is an arc that belongs to the diameter of the work. In this instance, the tool uses a constant speed (U x ), usually expressed in mm/s, to replicate feed by moving linearly towards the uncut surface and a constant angular velocity (ωx ) for the revolution around the X axis. By projecting the arc-shaped part on a 2D plane, the center and the radius of the generated sector will be matched to the ones of the workpiece. Hence, the angular velocity in rad/s can be determined as ω = 2π f , with the frequency f given in rps. Moreover, the simulation time can be calculated by simply dividing the angle of the

26

2 Fundamentals of 3D Finite Element Modeling in Conventional Machining

Fig. 2.10 Analysis domain simplification for turning of arc-shaped (a) and rectangular work (b)

arc, plus any extra travel by the angular velocity. For example, for the machining of an arc-shaped part of 45° belonging to a workpiece with 100 mm diameter, at a constant cutting speed equal to 100 m/min, the angular velocity is calculated approximately 33.33 rad/s, and the simulation time is close to 24 ms. The second case (Fig. 2.10b) is simpler since no revolution is set. Here, the tool may perform two translations with constant speed, one towards the −X axis (feed) and one towards the +Y axis (cutting direction) with a speed equal to U y . Heat exchange Thermal modeling is an equally critical approximation to all other modeling procedures implemented in numerical simulations. Equation 2.1 calculates the conductive heat transfer Qt between the contact surfaces (chip and tool rake face) with a heat transfer coefficient h between material and environment that have temperature T w and T 0 , respectively. Hence, heat from the cut material is transferred to the tool. Q t = h(Tw − T0 )

(2.1)

Typical assumptions in heat transfer modeling are the fact that 100% of the friction work is converted to heat, with 90% of the work converted to heat and 10% stored in the material [35]. The heat flux Qd generated by the plastic distortion of the work w˙ p can be determined with Eq. 2.2, which takes into account the fraction of the mechanical energy losses to heat and the material density ρ.

2.2 Finite Element Modeling in Machining

27

Fig. 2.11 Heat exchange schematic in FEM-based study

Qd =

f w˙ p ρ

(2.2)

The heat generated due to the frictional forces Qf is given by Eq. 2.3 as a rate, where ηf is the friction-based work conversion coefficient, τ f denotes the frictional stresses, and us is the sliding velocity between the cutting tool and the part. Q f = η f τ f us

(2.3)

Finally, Fig. 2.11 shows the relationship between the surfaces that come in contact, as well as the heat flux between the materials and the environment, while machining a workpiece, as modeled with the FEM.

2.2.5 Material Flow Stress Modeling To achieve reasonable and reliable results, the use of material parameters as close to reality as possible is important. Since the phenomena that take place during machining are complex, properties such as flow stress, yield strength, fraction strain, friction, and elastic constants, as well as thermo-physical properties such as density, Poisson’s ratio, thermal conductivity, and thermal capacity, should be determined with the best possible accuracy for a wide range of strains, strain rates, temperatures, and pressures. Depending on the type of machining operation, the tools, and the materials that take place in the process, the occurrence of extreme conditions is expected; strains of 100–700%, strain rates up to 10−6 s, temperatures at the range

28

2 Fundamentals of 3D Finite Element Modeling in Conventional Machining

of 500–1400 °C, heating rates that can reach values close to106 °Cs−1 and pressures that may build up towards 3GPa [52]. Nowadays, a decent number of flow stress models exist, as well as the equivalent constants for a variety of known materials spanning from aluminium alloys, steel, and titanium to thermoplastics. The power law equation is one of the simplest models for flow stress. It is an elastoplastic model ideal for studying the relationship between flow stress and strain at low temperatures and strain rates. Equation 2.4 represents the model, which calculates flow stress in relation to strain, strain rate, and temperature. σ = C(T )ε n(T )

(2.4)

where σ is the flow stress usually expressed in MPa, C refers to the strength coefficient, T is the temperature, ε denotes the strain, whereas n is the exponent expressing strain hardening. The next parameters, C and n are in function with the temperature. Oxley [53] proposed a modified power law equation for the description of the material flow stress, by implementing the velocity-modified temperature into the model. Equation 2.5 shows the modified model, whereas Eq. 2.6 represents the modified temperature. σ = C(T mod )ε n(T mod ) T mod

  ε˙ = T 1 − u log ε˙ 0

(2.5)

(2.6)

where σ is the flow stress, T and T mod are the temperature and the modified temperature, respectively, C refers to the strength coefficient, ε denotes the strain, whereas ε˙ and ε˙ 0 the strain rate and the default strain rate in s−1 , respectively, n is the strain hardening factor, and finally, u is a constant. Both the coefficient for strength and the strain hardening exponent are in function with the modified temperature. Maekawa et al. [54] included the strain path-dependent loading effect, in their proposed model. Equation 2.7 presents the model, where the integral is assigned for the history effect. To implement this model in FEM, it is required to reduce it to a simpler form. ⎡  ˙ m   ˙ M ε ε ⎢ σ =C e−kT ⎣ 1000 1000

ε,T ≡ε˙

⎤N  ˙  −m N ε kT ⎥ eN dε ⎦ 1000

(2.7)

where σ is the flow stress, T is the temperature, C is the strength coefficient, ε denotes the strain, whereas ε˙ is the strain rate, M is the strain rate sensitivity, and k, N, and m are constants. A broadly accepted model is the one proposed by Johnson and Cook [55], which is used for stress analysis under extreme conditions that occur in deformations, followed by high strain rates and temperatures. The model was modified in the past decade

2.2 Finite Element Modeling in Machining

29

by many researchers, to meet the needs of different applications [56–62] involving machining, metal forming, material testing, and structural crashworthiness for a range of materials such as steel, aluminium, and titanium alloys. Equation 2.8 represents the generalized form of the Johnson–Cook equation, which is divided into three terms. The first term considers the strain, the second one the strain rate, and the third takes into account the temperature. It is shown that each term embeds each of the three aforementioned parameters separately. As long as the constants are experimentally determined, the model can be used for a variety of materials.       θ − θ0 m ε˙ 1− (2.8) σ = A + Bε n 1 + C ln θm − θ0 ε˙ 0 A, B, and C denote the material constants that relate to the stresses and strains accordingly, n and m are the strain hardening exponent and a coefficient related to temperature respectively. Finally, θ and θ 0 are the reference and bulk temperature accordingly, whereas θ m is the material melting temperature. The constitutive model developed by Zerilli and Armstrong [63] is based on the dislocation mechanics theory and takes into account the structure of metals. Therefore, authors suggested two models, one for each type of metal structure. Equations 2.9 and 2.10 correspond to the BCC and FCC structure, respectively, including the plastic strain hardening contribution.  σ = c0 + c1 exp −c3 T + c4 T ln ε˙ + c5 ε n

(2.9)

 σ = c0 + c2 ε n exp −c3 T + c4 T ln ε˙

(2.10)

where c0 to c5 and n are constants, that can be experimentally determined for a variety of metals. It is noteworthy that many FEA systems allow the expression of the material plastic behavior in a tabular form. Despite the fact that material plastic behavior is a non-linear phenomenon, a tabular data form enables the linear or logarithmic connection between strain, strain rate, and temperature. Therefore, any material can be represented as a function of these three parameters, as long as the data are available, making the tabular data form a versatile and robust approach. Equation 2.11 shows the model based on tabular data of strain, strain rate, and temperature.  ˙ T σ = f ε, ε,

(2.11)

where σ equals to the effective flow stress, ε is the effective strain, ε˙ is the effective strain rate, and T is the temperature.

30

2 Fundamentals of 3D Finite Element Modeling in Conventional Machining

Table 2.1 Sample flow stress models for 3D studies of steel A (MPa)

B (MPa)

C

n

m

Material-process

Source

546

487

0.25

0.027

0.631

AISI1045 turning

[11]

553.1

600.8

0.234

0.0134

1.0

AISI1045 drilling

[64]

595

580

0.023

0.133

1.03

AISI4140 turning

[65]

598

768

0.0137

0.2092

0.807

AISI4140 turning

[12]

950

725

0.015

0.375

0.625

AISI4340 turning

[16]

688.17

150.82

0.043

0.336

2.77

AISI52100 turning

[66]

Table 2.2 Sample flow stress models for 3D studies of aluminium alloys A (MPa)

B (MPa)

C

n

m

Material-process

Source

546

678

0.024

0.71

1.56

AA7075-T6 drilling

[67]

527

575

0.017

0.72

1.61

AA7075-T6 drilling

[68]

214.25

327.7

0.00747

1.31

0.504

AA6082-T6 milling

[26]

370.4

1789.37

0.0128

0.73315

1.5282

AA6061-T6 milling

[69]

324

114

0.002

0.42

1.34

AA6061 turning

[70]

Table 2.3 Sample flow stress models for 3D studies of Ti6Al4V A (MPa)

B (MPa)

C

n

m

Material-process

Source

1098

1092

0.014

0.93

1.1

Drilling, milling

[71, 72]

1000

780

0.033

0.47

1.02

Milling

[25]

1080

1007

0.01304

0.6349

0.77

Milling

[73]

782.7

498.4

0.028

0.28

1

Drilling

[74]

862.5

683.1

0.012

0.35

1

Turning

[75]

Material constants The accuracy of the flow stress model is a factor that greatly affects the generated results. The model constants are obtained via experimental testing and usually require fine-tuning depending on the process studied, the conditions, and the tool-workpiece geometries. The next Tables 2.1, 2.2, and 2.3 present a comparison between sample constitutive models for a number of typical industry-standard materials such as steels, aluminium alloys, and titanium accordingly.

2.2.6 Friction Modeling and Contact Description Friction between two bodies is a complex phenomenon where extreme pressures and temperatures are generated. Especially for machining, three distinct heat generation

2.2 Finite Element Modeling in Machining

31

Fig. 2.12 The deformation zones in metal cutting

zones are present, the primary zone where deformation occurs, also called shear zone, where the elastoplastic deformation occurs, and the maximum heat is generated. The secondary deformation also called the friction zone, where plastic deformation is present, and the rest of the heat is produced between the moving chips and the tool, due to friction. And finally, the tertiary zone, which is the tool-workpiece interface zone where elastic deformation occurs. In this zone, the heat generated is minimal compared to the sum of the other two. Figure 2.12 illustrates the three deformation zones during metal cutting. A number of models that deal with the friction description are available in the literature. Coulomb’s law is the most commonly used model, providing an adequate estimation of the friction that occurs in the sliding subzone. This model (Eq. 2.12) describes the relationship between frictional and normal stress via a coefficient. τ f = μσn

(2.12)

where τ f is the stress, μ the coefficient for friction, and σ n the normal stress. This formula is easy to implement, however it does not yield very accurate results, especially after a certain critical value of the normal stress. Despite this fact, it is still used [24, 65, 76] for its simplicity and the adequate approximation it offers under certain conditions (i.e. low cutting speeds for turning) in the sliding region, which is of great importance in machining. According to Zorev [77] the interface where the chip and the tool are in contact (secondary zone) can be discretized into two subregions, the sticking and the sliding. The author stated that the frictional stress in the shear zone cannot exceed the shear yield strength. Thus, the frictional stress in the sticking subzone can be determined in relation to the material’s shear yield strength as indicated by Eq. 2.13. σ τf = m√ 3

(2.13)

32

2 Fundamentals of 3D Finite Element Modeling in Conventional Machining

where m is the shear friction constant and σ the effective stress. The combination of the two models can provide a better approximation for friction, considering that the frictional stresses in the sticking region can be calculated by the material’s shear strength, and in the sliding region they increase based on Coulomb’s formula. Many simulation systems allow the implementation of a hybrid friction model, where the user can input both shear and Coulomb friction constants. Advancement of friction models led to the description of the intermediate region (transitional subzone) that connects the sticking to the sliding subzone. Usui and Shirakashi [78] proposed a model based on Zorev’s assumptions, which implements non-linearity for the stress expression. Their empirical description is represented by Eq. 2.14.   τ f = k 1 − e−(μσn /k)

(2.14)

where k is the material flow stress and μ the friction coefficient as used in Coulomb’s law, which can be calculated by Eq. 2.15 after determining the feed force F f and the cutting force F c experimentally, in addition to the rake angle γ . The formula is based on Merchant’s analysis [79] and does not take into account the effect of ploughing. A modification by Albrecht [80] is available that considers the condition of the tool. μ=

F f + Fc tan γ Fc − F f tan γ

(2.15)

Childs et al. [81] proposed a refined version of Eq. 2.14, for a smoother transition between the two subzones by implementing two factors, m and n, as shown in Eq. 2.16. The first coefficient ensures that the frictional stresses do not exceed flow stress at high values of normal stress and the latter is responsible for the smooth transition from the sticking to the sliding subzone. Both coefficients can be calculated with experimental testing (split tool technique).   n 1/n τ f = mk 1 − e−(μσn /mk)

(2.16)

Another approach is the one from Iwata et al. [82] where the hardness of the material is taken into account, as well as the pressure that is developing between the newly created surface and the tool face. The empirical formula is shown in Eq. 2.17 where H V is the hardness in the Vickers scale and p is the pressure usually expressed in MPa.   0.07μp HV (2.17) tanh τf = 0.07 HV Additional models were proposed by researchers in the past few years. Sekhon and Chenot [83] derived a computationally convenient form from Norton’s law, which utilizes the relative sliding velocity, given between the tool and the chip.

2.2 Finite Element Modeling in Machining

33

Yang and Liu [84] proposed a stress-based friction model in which frictional and normal stresses are related with the aid of fourth-order polynomial. Zemzeni et al. [85] investigated the possibility of identifying a friction model and determining a coefficient for the tool, as well as the workpiece and chip area of interest when drymachining AISI4142 steel. Similar works [86, 87] led to the identification of friction parameters for machining modeling widening the range of materials and conditions. Moreover, Palanisamy et al. [88] examined recently the friction modeling of Ti6Al4V machining, in addition to the constitutive modeling. Friction coefficients Despite that Coulomb’s law is oversimplified in terms of the approximation degree of the frictional forces, it is used in many FEM studies, both 2D and 3D. As already discussed, FEM investigations on processes with complexities, require more sophisticated models for friction in order to generate accurate results. Table 2.4 summarizes the implementation of friction models by a number of studies focused on the machining of typical materials in three dimensions. Most works implement a static Coulomb coefficient, however, a hybrid model, sometimes with variable values, is expected to yield results of better accuracy. Arrazola et al. [89] proposed a new approach for friction modeling, by using variable coefficients, and reported increased accuracy compared to static modeling. Table 2.4 Friction modeling in 3D machining Model

Coefficient

Process

Material

Source

Coulomb

μ = 0.3

Turning

Ti6Al4V

[75]

Coulomb

μ = 0.5

Milling

Ti6Al4V

[27]

Coulomb

μ = 0.7

Milling

AA6082-T6

[26, 90]

Coulomb

μ = 0.17

Turning

AA2024-T351

[91]

Coulomb

μ = 0.6

Turning

AISI-D2

[92]

Coulomb

μ = 0.577

Turning

AISI-4140

[43]

Coulomb

μ = 0.32

Turning

AISI-4140

[65]

Coulomb

μ = 0.8

Milling

AISI-306L

[21]

Shear

m = 0.82

Turning

AISI-1045

[93, 94]

Hybrid

μ = 0.7 m = 0.9

Drilling

Ti6Al4V

[95]

Hybrid

μ = 0.5 m = 1.0

Milling

Aluminium 6000

[24]

34

2 Fundamentals of 3D Finite Element Modeling in Conventional Machining

2.2.7 Material Separation As soon as the tool model begins to penetrate the workpiece, the sum of the mathematical formulae for contact, friction, flow stress, material separation, etc., that constitute the machining process, comes into effect. Material separation due to damage, is the stage at which the elements forming the cut surface, begin to separate so that the undeformed chip can be shaped. Similar to friction, flow stress, etc., modeling the chip separation and evolution is a complex task. When a ductile material starts losing its ability to resist deformation, structural failure begins to occur according to stiffness degradation. Moreover, when the stiffness no longer exists, the material fails. Figure 2.13 illustrates a typical stress–strain curve visualizing the stress–strain response of a ductile material. The line between points (a) and (b), represents the linear elastic zone. Curve (b–c) is characterized by the plastic yielding with strain hardening. Damage initiates at point (c) and from that point on, the material begins to lose its load-carrying capacity. Finally, point (d) translates into total fracture. The region between points (b) and (c) can be modeled using a flow-stress model, whereas the rest of the curve past point (c) requires a damage criterion. A well-established criterion for damage modeling is the Johnson–Cook shear failure model [96], which depends on the strain rate, temperature, pressure, and equivalent stress. Equation 2.18 represents the aforementioned criterion.   σ  m ε f = D1 + D2 exp D3 [1 + D4 ln ε˙ ][1 + D5 T ] σ

(2.18)

where εf is the equivalent strain to fracture, D1 –D5 are the material damage constants, σ m is the average given by the three normal stresses, σ˜ is the equivalent stress, ε˙ is the strain rate, and T the temperature. The material damage parameters are usually determined experimentally with tensile [97–99] or impact tests [100–102] for a variety of standard materials such as carbon steels and aluminium alloys. An equally important criterion of ductile fracture is the one presented by Cockcroft and Latham [103], which considers the maximum normal stress that is operating. Fig. 2.13 Uniaxial stress–strain response for ductile specimen

2.2 Finite Element Modeling in Machining

35

Equation 2.19 is the normalized version of the criterion proposed by the authors, that describes the occurrence of fracture when the integral is equal to the constant value Dc , for a given strain rate and temperature. ε f Dc = 0

σmax dε pl σ

(2.19)

where Dc is the material constant value, σ max denotes the maximum stress, whereas σ represents the equivalent stress. Additionally, εf is the upper limit of the integral, representing the fracture strain and εpl is the plastic strain. A modified adaptation of the criterion was used recently by Razanica et al. [104]. Other notable works on the damage initiation formula that can be implemented in FEM and are based on the concepts of effective stress and equivalent strain, come from McClintock [105], Rice and Tracey [106], Brozzo et al. [107], Chandrakanth and Pandey [108] and Obikawa et al. [109]. Damage evolution The damage progression is based on the fracture energy that is dissipated during the process [110]. Once the damage criterion is fulfilled, it is necessary that a new approach is used for the description of the material separation evolution, since the energy dissipated during the deformation decreases with remeshing. As such, a stressdisplacement response is necessary to minimize mesh dependency that the stress– strain relation produces. Fracture energy Gf in a totally fractured material is given by Eq. 2.20 [5, 111] with respect to the fracture toughness K c , the elastic modulus E, and Poisson’s ratio ν, which can be used to reduce the mesh dependency. G f = (K c )2

(1 − ν 2 ) E

(2.20)

Exponential damage behavior is considered to exist between the chip and the tool path zone, as described in Eq. 2.21. The formula is set in such a way that the energy dissipated during material separation is close to the fracture energy Gf , and the varying stiffness degradation D draws close to unity asymptomatically at an infinite equivalent plastic displacement, where σ and u are the equivalent stress and plastic displacement, respectively. ⎛ ⎜ D = 1 − exp⎝−

u f 0

⎞ σ ⎟ du ⎠ Gf

(2.21)

36

2 Fundamentals of 3D Finite Element Modeling in Conventional Machining

In the case that stiffness degradation attains unity, the flow stress tensor σ for the failed element can be described by Eq. 2.22. σ = (1 − D)σ

(2.22)

2.2.8 Tool Wear Prediction modeling of the tool wear phenomenon has been studied by many researchers. Usually, these models approximate the rate of material volume loss on the contact face, such as the rake or the flank face, with respect to the contact area and the temporal development of the wear effect. Furthermore, it is required that the material characteristics and the cutting parameters are included in the models. One of the first approaches to approximate the wear mechanism between flat surfaces was made by Archard [112]. The author established a simple equation to describe sliding-based wear, according to the asperity contact theory, which was implemented in many studies related to cutting tool wear, with modifications. Palanikumar and Davim [113] developed a formulation to predict tool wear during machining of composite components. Marksberry and Jawahir [114] modified a model from previous work to be used with near-dry machining. Their model for dry machining is shown in Eq. 2.23. km T = TR n n f 1d 2



VR V

(1/n c ) (2.23)

where T is the tool wear, T R denotes the tool wear reference for 1 min, V is the cutting speed, whereas V R is the reference cutting speed when tool wear is measured for one minute, nc is a factor for the coating effect, f is the depth of cut, d the tool nose radius, and finally, k, n1 , and n2 are empirical constants. An early study on tool wear was carried out by Takeyama and Murata [115]. Hao et al. [116] analyzed the tool wear schema and mechanisms for Inconel 718 dry cutting. Zhang et al. [117] researched the wear for diamond tools used in precision machining and investigated ways of implementing the equivalent modeling to analytical and numerical methods. More recent studies [118–122] focus on the prediction of tool wear with the aid of methods such as neural networks, machine learning, and fuzzy logic. Typical steels, aluminium, and titanium alloys are the materials of choice for many works. It is noteworthy that the model from Usui et al. [123] for crater and flank wear, that takes into consideration the interface pressure and temperature, as well as the sliding velocity, can be implemented in FEM with success. Equation 2.24 represents the tool wear over time as an integral. dW = apvs exp(−b/T ) dt

(2.24)

2.3 Typical FEM-Based Results

37

where W is the wear, p is the contact pressure, vs the sliding velocity, T denotes the temperature at the contact area and, lastly, a and b are experimentally determined coefficients.

2.3 Typical FEM-Based Results FEM-based studies can generate a variety of predicted state variables and parameters such as cutting forces, torque, temperature distribution, residual stresses, and tool wear. The accuracy provided by the use of FEM is acceptable; however, it strongly depends on the models used for the rheology of the material, the friction, and so on. According to Melkote et al. [124], a tendency to predict lower thrust forces in FE metal cutting is present, probably due to the oversimplification of the friction coefficient values, pointing out the importance of friction modeling.

2.3.1 Cuttings Forces, Torque, and Residual Stresses The cutting forces prediction is crucial for all machining processes since it constitutes an indicator for the stress of the machine, the quality of the machined part, as well as the longevity of the tool. Higher values of forces than expected, usually lead to faster tool wear, frequent machine maintenance, and production of lower quality parts. Torque is a parameter of great interest as well, since it is directly related to the machining power. Thus, knowledge of the produced torque during an operation can provide the user with useful insight into the amount of power that is required, the cost, and so on. Furthermore, prediction of the stresses that remain on the microstructure of the metal after the machining operation, enables the assessment of the material’s surface integrity. The degree of residual stresses that appear is a parameter that affects the quality of the machined part directly. With this in mind, many studies [14, 61, 68, 75] include the assessment of the predicted forces and other parameters for optimization purposes. By implementing statistical techniques and machine learning, it is possible to determine the optimal cutting conditions, such as depth of cut, tool geometrical aspects, feed, and cutting speed for a specific scope. The numerical results are often compared with analogous experimental data for verification. Experimental testing is the most effective way to calibrate the developed FE model and fine-tune the corresponding factors that participate in the modeling procedure. Multi-component dynamometers and data acquisition systems are the mean for acquiring the force components, as well as torque. Sreeramulu et al. [34] modeled the oblique cutting procedure of Al7075-T6 with coated tools, in DEFORM™-3D, with respect to feed, cutting speed, and depth of cut, generating results for the cutting force. Oezkaya and Biermann [125] worked on the modeling of AISI1045 steel tapping by simulating the process in DEFORM™3D. They examined the generated torque with tool production in mind and developed

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a mathematical model for the generation of torque during a total load cycle. Rami et al. [65] investigated the ability to determine the residual stresses during machining of AISI4140 steel with a FE model developed in ABAQUS™. Moreover, the authors simulated several tool passages under various conditions and examined the effect of the thermo-mechanical loadings, as well as of the feed. Similar studies [20, 126, 127] exhibit the advantages of FEM in machining modeling and the ability to investigate the aforementioned parameters.

2.3.2 Chip Morphology, Temperature Distribution, and Wear Temperature allocation on both the tool and the part, as well as the chip geometric characteristics are considered to be factors of equal significance to tool wear and deflection. Thermally induced errors contribute a large proportion of the total machining error. Temperature-based factors affect friction conditions and altogether influence the generated chip morphology and the rate of tool wear. Pittalà and Monno [24] investigated the chip temperature and the cutting forces generated while facemilling aluminium 6000. The 3D FE model of this case was built with DEFORM™3D. The authors performed a friction sensitivity analysis to improve the model. Lotfi et al. [35] studied the drilling process of AISI1045 with the aid of FEM with regard to the heat built-up, the tool wear, and the BUE. Attanasio et al. [93] developed a 3D FE model for studying the turning of AISI-1045 within a range of f and V c . The chosen software was DEFORM™-3D. The authors focused on the tool wear investigation by utilizing a modified tool wear model, coupled with experiments. Paktinat and Amini [128] made a comparison between the conventional drilling procedure and the drilling of Al7075 assisted ultrasonically. In a similar manner to previous studies, they developed a FE model in three dimensions for the examination of the developed stresses, the BUE formation, as well as the chip morphology, and the temperature distribution. Analogous works [26, 129, 130] focused on three-dimensional modeling and simulation of machining proceedings were carried out, expanding the range of knowledge in the field, coupled with experimental work in order to investigate variables similar to the ones mentioned in this paragraph. It should be mentioned that a number of papers are available in the bibliography that focus on other factors and actions that are involved in machining, such as the effect of cutting fluids, the tool runout, the minimization of machining errors, and more. Figure 2.14a presents the formation of the chip during dry drilling of aluminium alloy 7075 with a 5-mm HSS twist drill, while Fig. 2.14b illustrates the temperature distribution on the drill’s surfaces that are in contact with the work, with the aid of the color gradient. It is evident that by observing the figures it is possible to extract useful information for the tool performance and the evolution of the process.

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Fig. 2.14 Example chip generation (a) and tool-tip temperature distribution and b in drilling

2.4 Conclusions and Perspectives This chapter introduces the most important aspects of FE modeling in machining by summarizing concepts on the representation of the tool-workpiece interface, the meshing process, the set of boundary conditions, the friction phenomenon, and the material separation. Furthermore, it includes several works in the field from the early years until recently, as well as references on standard models and formulae that can be implemented by modern FEA software, to model most machining processes in three dimensions with adequate precision. It is concluded that 3D FEM in machining is a highly valued tool that provides several advantages, especially compared to 2D FEM, in the investigation of the machinability of materials and the performance of the processes. However, it should be pointed out that despite the advantage of the computational resources, 3D FEA still requires hefty amounts of run-time. Moreover, many models for material flow, damage, etc., are not optimized for three-dimensional studies. Therefore, it is imperative that new models and modifications are developed for 3D applications. Finally, it is anticipated that 3D models will increase in number with time, especially with the advent of more sophisticated technologies and computational resources, expanding the field of work to non-conventional methods on aerospace, energy, and biomechanics applications.

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85. Zemzemi F, Rech J, Ben SW et al (2008) Identification of a friction model at tool/chip/workpiece interfaces in dry machining of AISI4142 treated steels. 9:3978–3990. https://doi.org/10.1016/j.jmatprotec.2008.09.019 86. Sun Y, Chen T, Qiong C, Shafai C (2016) A comprehensive experimental setup for identification of friction model parameters. Mech Mach Theory 100:338–357. https://doi.org/10.1016/ j.mechmachtheory.2016.02.013 87. Behera BC, Ghosh S, Rao PV (2018) Modeling of cutting force in MQL machining environment considering chip tool contact friction. Tribol Int 117:283–295. https://doi.org/10.1016/ j.triboint.2017.09.015 88. Palanisamy NK, Lorphèvre ER, Gobert M et al (2022) Identification of the parameter values of the constitutive and friction models in machining using EGO algorithm: application to Ti6Al4V. Metals (Basel) 12:1–21 89. Arrazola PJ, Ugarte D, Domínguez X (2008) A new approach for the friction identification during machining through the use of finite element modeling. Int J Mach Tools Manuf 48:173– 183. https://doi.org/10.1016/j.ijmachtools.2007.08.022 90. Davoudinejad A, Parenti P, Annoni M (2017) 3D finite element prediction of chip flow, burr formation, and cutting forces in micro end-milling of aluminum 6061–T6. Front Mech Eng 12:203–214. https://doi.org/10.1007/s11465-017-0421-6 91. Asad M, Mabrouki T, Ijaz H et al (2014) On the turning modeling and simulation: 2D and 3D FEM approaches. Mech Ind 15:427–434. https://doi.org/10.1051/meca/2014045 92. Hu HJ, Huang WJ (2014) Tool life models of nano ceramic tool for turning hard steel based on FEM simulation and experiments. Ceram Int 40:8987–8996. https://doi.org/10.1016/j.cer amint.2014.01.095 93. Attanasio A, Ceretti E, Rizzuti S et al (2008) 3D finite element analysis of tool wear in machining. CIRP Ann Manuf Technol 57:61–64. https://doi.org/10.1016/j.cirp.2008.03.123 94. Attanasio A, Ceretti E, Giardini C (2009) 3D FE modelling of superficial residual stresses in turning operations. Mach Sci Technol 13:317–337. https://doi.org/10.1080/109103409032 37806 95. Ucun ˙I, Aslantas K, Özkaya E, Cicek A (2017) 3D numerical modelling of micro-milling process of Ti6Al4V alloy and experimental validation. Adv Mater Process Technol 3:250–260. https://doi.org/10.1080/2374068X.2016.1247343 96. Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48 97. Murugesan M, Dong-Won J (2019) Johnson Cook material and failure model parameters estimation of AISI-1045 medium carbon steel for metal forming applications. Materials (Basel) 12:1–18. https://doi.org/10.3390/ma12040609 98. Bal B, Karaveli KK, Cetin B, Gumus B (2019) The precise determination of the Johnson– Cook material and damage model parameters and mechanical properties of an aluminum 7068-T651 alloy. J Eng Mater Technol 141. https://doi.org/10.1115/1.4042870 99. Zhang D, Shangguan Q, Xie C, Liu F (2015) A modified Johnson–Cook model of dynamic tensile behaviors for 7075–T6 aluminum alloy. J Alloys Compd 619:186–194. https://doi.org/ 10.1016/j.jallcom.2014.09.002 100. Stopel M, Skibicki D (2018) Determination of the Johnson-Cook damage parameter D 4 by Charpy impact testing. Mater Test 60:974–978 101. Banerjee A, Dhar S, Acharyya S et al (2015) Determination of Johnson cook material and failure model constants and numerical modelling of Charpy impact test of armour steel. Mater Sci Eng A 640:200–209. https://doi.org/10.1016/j.msea.2015.05.073 102. Wang X, Shi J (2013) International journal of impact engineering validation of Johnson-Cook plasticity and damage model using impact experiment. Int J Impact Eng 60:67–75. https:// doi.org/10.1016/j.ijimpeng.2013.04.010 103. Cockcroft MG, Latham DJ (1968) Ductility and the workability of metals. J Inst Met 96:33–39 104. Razanica S, Malakizadi A, Larsson R et al (2020) FE modeling and simulation of machining Alloy 718 based on ductile continuum damage. Int J Mech Sci 171:105375. https://doi.org/ 10.1016/j.ijmecsci.2019.105375

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105. McClintock FA (1968) A criterion for ductile fracture by the growth of holes. J Appl Mech 35:363–371. https://doi.org/10.1115/1.3601204 106. Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:201–217 107. Brozzo P, Deluca B, Rendina R (1972) A new method for the prediction of formability limits in metal sheets. In: Proc. 7th biennal Conf. IDDR 108. Chandrakanth S, Pandey PC (1995) An isotropic damage model for ductile material. Eng Fract Mech 50:457–465 109. Obikawa T, Sasahara H, Shirakashi T, Usui E (1997) Application of computational machining method to discontinuous chip formation. J Manuf Sci Eng 119:667–674. https://doi.org/10. 1115/1.2836807 110. He YL, Davim JP, Xue HQ (2018) 3D progressive damage based macro-mechanical FE simulation of machining unidirectional FRP composite. Chin J Mech Eng. https://doi.org/10. 1186/s10033-018-0250-5 111. Zhang YC, Mabrouki T, Nelias D, Gong YD (2011) Chip formation in orthogonal cutting considering interface limiting shear stress and damage evolution based on fracture energy approach. Finite Elem Anal Des 47:850–863. https://doi.org/10.1016/j.finel.2011.02.016 112. Archard JF (1953) Contact and rubbing of flat surfaces. J Appl Phys 24:981–988. https://doi. org/10.1063/1.1721448 113. Palanikumar K, Paulo Davim J (2007) Mathematical model to predict tool wear on the machining of glass fibre reinforced plastic composites. Mater Des 28:2008–2014. https:// doi.org/10.1016/j.matdes.2006.06.018 114. Marksberry PW, Jawahir IS (2008) A comprehensive tool-wear/tool-life performance model in the evaluation of NDM (near dry machining) for sustainable manufacturing. Int J Mach Tools Manuf 48:878–886. https://doi.org/10.1016/j.ijmachtools.2007.11.006 115. Takeyama H, Murata R (1963) Basic investigation of tool wear. J Eng Ind 85:33–37. https:// doi.org/10.1115/1.3667575 116. Hao Z, Gao D, Fan Y, Han R (2011) New observations on tool wear mechanism in dry machining Inconel718. Int J Mach Tools Manuf 51:973–979. https://doi.org/10.1016/j.ijm achtools.2011.08.018 117. Zhang SJ, To S, Zhang GQ (2017) Diamond tool wear in ultra-precision machining. Int J Adv Manuf Technol 88:613–641. https://doi.org/10.1007/s00170-016-8751-9 118. Peng B, Bergs T, Schraknepper D et al (2019) A hybrid approach using machine learning to predict the cutting forces under consideration of the tool wear. Procedia CIRP 82:302–307. https://doi.org/10.1016/j.procir.2019.04.031 119. Wang J, Li Y, Zhao R, Gao RX (2020) Physics guided neural network for machining tool wear prediction. J Manuf Syst 57:298–310. https://doi.org/10.1016/j.jmsy.2020.09.005 120. Xu X, Wang J, Zhong B et al (2021) Deep learning-based tool wear prediction and its application for machining process using multi-scale feature fusion and channel attention mechanism. Meas J Int Meas Confed 177:109254. https://doi.org/10.1016/j.measurement.2021.109254 121. Li Y, Wang J, Huang Z, Gao RX (2022) Physics-informed meta learning for machining tool wear prediction. J Manuf Syst 62:17–27. https://doi.org/10.1016/j.jmsy.2021.10.013 122. Seeholzer L, Krammer T, Saeedi P, Wegener K (2022) Analytical model for predicting tool wear in orthogonal machining of unidirectional carbon fibre reinforced polymer (CFRP). Springer, London 123. Usui E, Shirakashi T, Kitagawa T (1984) Analytical prediction of cutting tool wear. Wear 100:129–151. https://doi.org/10.1016/0043-1648(84)90010-3 124. Melkote SN, Grzesik W, Outeiro J et al (2017) Advances in material and friction data for modelling of metal machining. CIRP Ann Manuf Technol 66:731–754. https://doi.org/10. 1016/j.cirp.2017.05.002 125. Oezkaya E, Biermann D (2017) Segmented and mathematical model for 3D FEM tapping simulation to predict the relative torque before tool production. Int J Mech Sci 128–129:695– 708. https://doi.org/10.1016/j.ijmecsci.2017.04.011

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126. Wei L, Wang D (2019) Comparative study on drilling effect between conventional drilling and ultrasonic-assisted drilling of Ti-6Al-4V/Al2024-T351 laminated material. Int J Adv Manuf Technol 103:141–152. https://doi.org/10.1007/s00170-019-03507-6 127. Ucun ˙I (2016) 3D finite element modelling of drilling process of Al7075-T6 alloy and experimental validation. J Mech Sci Technol 30:1843–1850. https://doi.org/10.1007/s12206-0160341-0 128. Paktinat H, Amini S (2017) Ultrasonic assistance in drilling: FEM analysis and experimental approaches. Int J Adv Manuf Technol 92:2653–2665. https://doi.org/10.1007/s00170-0170285-2 129. Ezilarasan C, Senthil VS, Velayudham A (2014) heoretical predictions and experimental validations on machining the Nimonic C-263 super alloy. Simul Model Pract Theory 40:192– 207. https://doi.org/10.1016/j.simpat.2013.09.008 130. Malakizadi A, Gruber H, Sadik I, Nyborg L (2016) An FEM-based approach for tool wear estimation in machining. Wear 368–369:10–24. https://doi.org/10.1016/j.wear.2016.08.007

Chapter 3

FEM-Based Study of AISI52100 Steel Machining: A Combined 2D and 3D Approach

Abstract In this research, the cutting forces that are induced during AISI52100 turning and the geometrical characteristics of the generated chips are studied by means of combined 2D and 3D Finite Element (FE) analyses. A number of 2D simulation tests were performed according to a design of experiments in order to evaluate the accuracy of three friction models, as well as a flow stress model at a given range of cutting conditions. Upon the comparison of the numerical results with the equivalent experimental ones, in terms of the thrust and cutting force, the model with the best fit was selected and, consequently, the establishment of a 3D FE model was achieved based on the 2D concepts. The three force components, as well as the chip’s geometrical aspects, were studied and visualized. Keywords AISI52100 machining · FEM · DEFORM™ · ANSYS™ · Thrust force · Cutting force · Chip geometry

3.1 Introduction Nowadays, it is evident that the utilization of Finite Element Method (FEM) in machining is an integral part of the studying procedure. A range of studies that are available in the bibliography, indicate that FEM is an indispensable tool for the accurate investigation of several parameters that are involved in machining and manufacturing, that in some cases would not be possible to study otherwise. The minimization of the experimental testing, the cost reduction, and the repeatability, are only some of the benefits that are expected from the use of FEM. Typical manufacturing processes such as drilling, milling, and turning, as well as more modern operations such as Electrical Discharge Machining (EDM), can be studied with the aid of FEM, for a variety of materials. Three-dimensional Finite Element (FE) studies specifically seem to gain ground compared to 2D works. However, it is noted that two-dimensional tools are still used by many researchers, since they are considered to be effective for a wide range of applications, as well as time efficient. Material plastic behavior and friction modeling are two of the most

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al., 3D FEA Simulations in Machining, Manufacturing and Surface Engineering, https://doi.org/10.1007/978-3-031-24038-6_3

47

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3 FEM-Based Study of AISI52100 Steel Machining: A Combined 2D …

important parameters that greatly affect the numerical results and are usually thoroughly investigated by the researchers. The most common material flow stress model is the one proposed by Johnson and Cook [1], applied to virtually any process. Several other models are also used, either modified or with minor adjustments. On the other hand, friction modeling is an aspect that is frequently debated due to the nature of the phenomena that occur during machining. Coulomb, shear, or hybrid models are typically used with constant coefficients after a calibration procedure, while, in some cases, more complex models are coupled with variable coefficients. Xiong et al. [2] investigated the performance of a metal matrix composite in terms of typical cutting and chip geometric parameters. The study was based on a 2D concept with Johnson–Cook flow stress modeling. The work by Salvati and Korsunsky [3] focused on the characterization of the residual stresses yielded during the EDM cutting of AA6082-T6. The authors performed two passes, one main cut and one trim cut, examined the surface morphology, and carried out the equivalent experiment in a simulated environment. Liu et al. [4] evaluated the performance of microtextured tools during machining of stainless steel 17-4PH. A 3D FE model was developed for this purpose and several tool textures were tested. In addition to the cutting forces, chip morphology was also studied. Similarly, Lotfi et al. [5] investigated the ultrasonic-assisted turning of AISI4140 steel by using a 3D model and performing experimental work. The authors focused on the tool wear analysis of the process. Kyratsis et al. [6] investigated the influence of typical conditions on the cutting forces induced while turning AISI-D2 tool steel, simulated by a 3D FE model. Studies related to drilling, usually focus on investigating the generated thrust force, cutting torque, chip characteristics and evolution, residual stresses, temperatures, tool wear, built-up-edge (BUE), and more, as can be seen in the next papers [7–12]. In a similar manner, investigations that are based on milling processes [13–17], tend to examine the machinability of industry-related materials, the parameters that affect the performance of the cutting tools and the performance of the available cutting fluids and cooling methods in general. In most cases, the ultimate purpose of examining the influence of several parameters on the process, is the prediction of these factors and the development of models that can forecast the behavior of the tool-workpiece system. Current work presents a 3D FE model for AISI52100 steel machining, with the combined implementation of a CAD-based and a two-dimensional FE setup. The first method enabled the quick and accurate derivation of the tool geometry aspects, as well as the machining area of interest, whereas the latter, allowed the relatively straightforward calibration of the rheological and the friction model by comparing the generated 2D simulation runs results, with equivalent experimental ones. The summarized workflow of the study can be seen in Fig. 3.1.

3.2 Materials and Methods

49

Fig. 3.1 The workflow of the present study

3.2 Materials and Methods 3.2.1 Machining Process Framework A CAD-based setup resembling the tool-part interaction was utilized prior to the development of the three-dimensional FE model, in order to facilitate the extraction of the required parameters that affect the process, as well as to verify the positioning. Setups that rely on CAD systems are an effective way to design and plan the machining operation without the need for time-consuming and costly experimental setups. Moreover, such a setup allows the user to effortlessly change any parameter that participates in the process. In addition, basic assembly and collision detection features are available in most CAD systems, including freeware versions.

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3 FEM-Based Study of AISI52100 Steel Machining: A Combined 2D …

Fig. 3.2 The CAD-based framework of the machining process

On the other hand, experimental working is of course an integral part of the modeling procedure, since it is required for calibration purposes. The under-study process is the external longitudinal turning of a Ø56 cylindrical bar made by AISI52100 steel, with Cubic Boron Nitride (CBN) tools. The ISO code for the tool is SNGA120408T01020, meaning that it is a square-shaped negative insert, with a 0.8 mm nose radius and honed cutting edge with 0.1 mm width and 20° angle. The equivalent number for the toolholder is PSBNR2525M12. Turning with standardized tools and toolholders provides several advantages such as accurately fixed cutting angles and interchangeability. The cutting angles were extracted during the CAD modeling procedure; the tool cutting edge angle (KAPR) is 75°, the clearance angle is 6° and, finally, both the rake (GAMO) and the inclination (LAMS) angle are equal to −6°. Figure 3.2a illustrates the CAD assembly for the workpiece, the tool, and its toolholder. The model of the toolholder was downloaded, since it is available online by many manufacturers, whereas both the insert and the work were modeled in SolidWorks™ 2021. Especially the tool model was designed with the aid of an applet [18]. Figure 3.2b depicts the most important geometric characteristic of the tool.

3.2.2 Preliminary FE Model Assessment The machining parameters applied to the current study were chosen according to the recommendations of several manufacturers for this type of inserts, that are intended for hardened material cutting. Therefore, the selected values of cutting speed are 125, 176, and 246 m/min, respectively, the feed is equal to 0.08, 0.12, and 0.16 mm/rev accordingly, and finally the depth of cut is 0.45 mm for all tests, as seen in Table 3.1.

3.2 Materials and Methods Table 3.1 The cutting parameters and the levels used in the study

51 Level

V c (m/min)

f (mm/rev)

ap (mm)

+1

246

0.16

0.45

0

176

0.12

0.45

−1

125

0.08

0.45

The nine tests correspond to the three levels of the two factors. However, several 2D FE tests were carried out before attempting to run the 3D tests, in order to calibrate the model. The two-dimensional simulations were choseThe cutting parameten for the short run time and minimal preparation work. Figure 3.3 illustrates the generalized 2D model used in this study, along with the boundary conditions. The two-dimensional setup was developed in the ANSYS™ module, Explicit Dynamics 2021 R2. Each test was allowed to run until the steady state was achieved, thus up to approximately 1 mm, and lasted for about one hour and a half. This way, excessive chip accumulation in the cutting edge of the tool was avoided, making the comparison of the thickness between the 2D and 3D results possible, as discussed later in Sect. 3.3.2. Both the rheological and friction models were calibrated according to experimental data that are available in the literature [19], with the following method. Flow stress modeling A tabular data format was used in this study, by extracting the values of flow stress from the diagram of Fig. 3.4, which is tuned for the machining of AISI52100, at similar conditions [20]. This way the flow stress is represented as a function of strain, strain rate, and temperature. The tabular data format is considered to be a robust method for representing the material flow stress, as long as an adequate number of data points are available. Each curve of strain rate was converted to a column in the table and each strain value to a line. Thus, the flow stress value that corresponds to the points of strain (0.05, 0.1, 0.2, 0.4, 0.7, 1.0, 2.0, and 5.0) for each strain rate

Fig. 3.3 The 2D FE model setup

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3 FEM-Based Study of AISI52100 Steel Machining: A Combined 2D …

Fig. 3.4 The flow stress chart for AISI52100 steel at 20 °C

curve at the given temperature, were extracted. Minor adjustments were made by performing a small number of 2D simulations, to tune the simulated values as close to the test results as possible, for the applied depth of cut. The properties, regarding mechanical and thermal behavior, of the tool-work materials, are presented in Table 3.2, where the thermal properties for the workpiece are expressed with respect to the temperature. It should be noticed that the tool was set to behave as rigid, however, its thermal properties were set so that the thermal analysis can be carried out. Friction modeling In a similar manner to the flow stress calibration, friction model was calibrated according to the experimental results. Due to the fact that in 2D simulations feed force is neglected, the comparison was done between the experimental and the simulated thrust (F p ) and cutting (F c ) forces. At first, two sets that contain nine tests each were carried out to examine the influence of the shear and the Coulomb friction coefficient, respectively. The three levels for each coefficient are depicted in Table 3.3. It is noted that the initial coefficients were selected based on the default values of several software used in FEA, such as DEFORM™, LS-DYNA™, and ABAQUS™, and the literature [22]. Furthermore, the number of simulations for each set was defined according to an L9 Taguchi orthogonal array design, instead of the full factorial design that implements 27 runs, to reduce the workload without compromising the fidelity of the model. Table 3.4 includes the tests in their run order and the parameters involved. A comparison between the results was performed upon completion of the tests. In general, the runs yielded results with underestimated cutting forces. Moreover, the

3.2 Materials and Methods Table 3.2 Standard properties for the AISI52100 work [21] and CBN tool [22]

53 Mechanical properties

AISI52100

CBN Rigid

E [GPa]

210

ρ [kg/m3 ]

7,850

ν

0.30

Thermal properties

AISI52100

CBN

C [J/kg K]

278 → 93 °C

20,000

324 → 316 °C 579 → 649 °C 718 → 871 °C α

[°C−1 ]

k [W/mK]

11.9 × 10−6

4.5

24.57 → 149 °C

60

24.4 → 349 °C 24.23 → 477 °C 24.75 → 604 °C

Table 3.3 The friction coefficients used in the preliminary tests

Table 3.4 The 2D preliminary tests

Level

m

μ

+1

0.8

0.50

0

0.6

0.35

−1

0.4

0.20

Run

V c (m/min)

f (mm/rev)

m

µ

1

125

0.08

0.4

0.20

2

125

0.12

0.6

0.35

3

125

0.16

0.8

0.50

4

176

0.08

0.6

0.35

5

176

0.12

0.8

0.50

6

176

0.16

0.4

0.20

7

246

0.08

0.8

0.50

8

246

0.12

0.4

0.20

9

246

0.16

0.6

0.35

initial value of both the shear and the Coulomb coefficient predicted the cutting forces more accurately. Afterward, an evaluation of a hybrid model was done by selecting the coefficient values that fitted the experimental values the best. The conclusion was that a hybrid model with a shear constant equal to m = 0.6 and a coefficient of μ = 0.35 generated error, equal to 18.7%, being the lowest value. In order to evaluate the coefficients, the relative error between the experimentally generated cutting forces and the FE results was calculated for all the possible combinations and utterly the

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3 FEM-Based Study of AISI52100 Steel Machining: A Combined 2D …

Fig. 3.5 Comparison graph for the different friction models and coefficient values tested

total resultant error, expressed in percentage, was generated with the aid of Eq. 3.1. Where ∆x is the relative error calculated by the numerical and the experimentally acquired value of thrust force and cutting force, a represents the number of the runs for each combination (i.e., a = 3 for friction coefficient m = 0.6) and, finally, b is the number of the cutting force components, which is equal to two. Figure 3.5 visualizes the comparison between the selected coefficients by presenting the total error.

err ortotal =

| |∑ b | a ∑ ∆x 2 | | i=1 j=1 a×b

× 100

(3.1)

3.2.3 Numerical Modeling of the Turning Process in Three Dimensions For the development of the 3D-FE model, DEFORM™-3D ver. 12.0 was utilized, which implements the Lagrangian modeling method coupled with an embedded remeshing technique for the treatment of the mesh distortion during the chip generation procedure. The criterion applied during the remeshing affects the size control according to the proportions of the elements around the distorted mesh. It is a common practice to simplify the area where the cutting process takes place in order to shorten the simulation run time. The CAD-based setup allowed the

3.2 Materials and Methods

55

extraction of a simplified version of the workpiece (Fig. 3.6a). Therefore, the work was modeled as an arc-shaped, one-eighth fraction of the full bar. To further improve the simulation time, a predefined cut surface was shaped on the workpiece model. Regarding the behavior of the models, the workpiece was set to be deformable and approximately 46,000–91,000 tetrahedron elements comprised its mesh, based on the applied value of feed, whereas the tool was set to be non-deformable and discretized with a high number of elements, approximately 50,000. Since the tool was set to act rigidly, the mesh size had a minimal effect on the results. However, a denser mesh on the tool and especially on the cutting tip produces a better visual representation of the process, without sacrificing computational resources [20]. The size of the smallest element in the workpiece’s mesh was defined to be 25% of the value of feed [23], thus ranging between 0.02 and 0.04 mm for this study. Furthermore, to optimize the mesh at the contact area, the small-to-large size ratio of mesh elements was set to 7:1 (Fig. 3.6b) for the work and 4:1 (Fig. 3.6c) for the tool, respectively. As a result of the simplification process, the workpiece did not rotate around axis Z as it would in real time, rather it was fixed allowing the tool to follow the trajectory illustrated in Fig. 3.6a to achieve the cut. Finally, to represent the heat exchange of the workpiece-tool system, due to both convection and conduction, with the environment (T ambient = 20 °C), the equivalent coefficients were applied. For dry cutting, their values are as follows, hconv = 20 W/(m2 × °C) and hcond = 4.5 × 104 W/(m2 × °C), respectively [21]. To approximate the damage process, where the material separation occurs, the normalized Cockcroft-Latham criterion [24] was applied. Equation 3.2 represents the criterion, which in general is a simplified formula that relates the material damage constant to both the maximum and the effective stress.

Fig. 3.6 The 3D FE model setup; the analysis domain (a), the meshed part (b), and the tool (c)

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3 FEM-Based Study of AISI52100 Steel Machining: A Combined 2D …

/ε f Dc = 0

σmax dε pl σ

(3.2)

Dc represents a material constant that enables the fracturing, σ max denotes the maximum tensile stress and σ˜ the effective stress. The limit of the integral, εf represents the limit fracture strain, whereas εpl the plastic strain. In addition, the fraction of the plastic work that is converted to heat, was set to 90%, so that the remaining 10% was allowed to be stored in the workpiece.

3.3 Results and Findings 3.3.1 Machining Forces Evaluation The average run time of each of the 3D simulations was about 10 h with a deviation of a couple of hours depending on the feed value, on an AMD Ryzen 3.6 GHz CPU, 96 GB RAM, and SSD technology hard disk. It was observed that the fraction of the workpiece used, was enough to allow the steady state to occur in a total 8 ms cut. Therefore, the force values versus the time were extracted for each of the runs and the mean value was calculated for all three force components after applying a first-order exponential smoothing on the time series. Next, a comparison was made with the experimentally acquired values. The comparison graphs of Fig. 3.7 visualize the results of the three cutting-force elements. In specific, Fig. 3.7a illustrates the results for the thrust force, Fig. 3.7b for the cutting force, and Fig. 3.7c for the force at the feed direction. It is evident that the agreement levels are high, especially for the cutting force, which is the component that contributes the most to the resultant force. The relative error comparing the numerical results with the experimental range from −11.2 to 26.6% for the thrust force F p , −5.9 to 16.9% for the cutting force F c, and 14.6 to 28.7% for the feed component F f . The relatively increased error that is observed among the feed values is possibly related to the fact that the calibration was done based on 2D tests. As already discussed, two-dimensional tests neglect the feed force, thus an underestimation is expected. In any case, the feed force is the component with the smallest degree of contribution to the resultant machining force. Regarding the 3D tests, it is noted that they were run in the same order as the 2D ones. By studying Fig. 3.7, the following observations can be made. First, the cutting force F c contributes the most to the resultant force F resultant , as proven by solving Eq. 3.3 and then calculating the ratio between the squares of F c and F resultant . The contribution percentage varied between 67.5 and 76.6%. As an example, thrust, cutting, and feed force for numerical test number 2 are equal to approximately 169N, 358N, and 103N, respectively. Thus, the resultant force is equal to 409.1N, yielding a contribution percentage for F c close to 76.6%.

3.3 Results and Findings

57

Fig. 3.7 Comparison graphs between the experimental and the simulated machining forces; thrust force (a), cutting force (b), and feed force (c)

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3 FEM-Based Study of AISI52100 Steel Machining: A Combined 2D …

Fresultant =

(

F p2 + Fc2 + F 2f

(3.3)

Next, it is obvious that the feed acts increasingly on all machining force components. On the contrary, any changes in the cutting speed values do not affect the generated forces significantly. In fact, both thrust and feed force exhibit light changes in their values, with cutting force being an exception, since it is evident that an increase in cutting speed reduces cutting force value noticeably. Moreover, the most impactive feed value is equal to 0.16 mm/rev. For instance, the percentage of increase for the cutting force, when shifting from 0.08 to 0.16 mm/rev, reaches 15.2, 23.2, and 47.4% for cutting speed equal to 125, 176, and 246 m/min accordingly.

3.3.2 Chip Geometry Evaluation Chip morphology possesses a key role in determining material machinability and tool-wear prediction when machining. The geometric characteristics of the generated chip enable the understanding of the influence of several parameters on the machining operation. Feed, cutting speed, depth-of-cut, and cutting angles are some of the most important factors that affect the performance of the tool and the overall machinability. FEM allows the modeling of the machining operation with respect to the aforementioned parameters, for prediction purposes of several results that some decades ago could not be predicted with another way, except with experimental working. In the present study, the chip formation and morphology were examined with the aid of both the 2D and 3D simulations and evaluated in terms of the agreement level between the numerical values and analytical calculations. Specifically, the deformed chip thickness hc and the chip width b, as well as the shear angle ϕ were the parameters that were evaluated. The chip thickness was measured directly in the 2D FE model and indirectly for the 3D model as described later on, whereas the width was measured only in the three-dimensional model. Additionally, the shear angle was calculated with Eq. 3.4 [25] and measured with the aid of the 3D model as well. The shear angle ϕ, usually expressed in degrees, is determined by the rake angle γ and the cutting ratio r c , which essentially is the ratio of the undeformed chip thickness h0 to the deformed hc . Thus, it is valid that rc = h 0 / h c . ϕ = tan−1

(

rc cos γ 1 − rc sin γ

) (3.4)

The chip thickness can be expressed in mm as well, but it is common to use µm. To determine the undeformed chip thickness with respect to feed f and major cutting-edge angle κ r , it is possible to use Eq. 3.5 [26]. h 0 ≈ f sin κr

(3.5)

3.3 Results and Findings

59

Fig. 3.8 The chip geometry evaluation schematic; chip width in 3D (a), chip thickness in 3D (b), and chip thickness, as well as shear angle in 2D (c)

To avoid assuming that the chip width is constant across its length, assumption that is common for 2D strategies, the width was measured between multiple opposite nodes of the chip (Fig. 3.8a) at approximately 1 mm length of cut and then the mean value was calculated. In a similar manner, the chip thickness was measured on multiple points across its section to determine the mean value. To facilitate the measurement and ensure adequate accuracy, the workpiece model was exported to the CAD system (Fig. 3.8b). The machined workpiece model was sectioned in the middle of the chip’s width, across the XY plane, revealing this way the planar chip morphology. By observing Fig. 3.8b it is evident that the curling of the chip is similar to the one of the 2D simulation. In addition, the chip thickness was measured in the 2D FE model, by recording a number of measurements along the periphery of the prescribed circle that was formed around the curling of the chip (Fig. 3.8c). Finally, the shear angle was measured with the aid of the twodimensional model as seen in Fig. 3.8c. Moreover, it was calculated with Eq. 3.4 by using as inputs the known rake angle, the cutting-edge angle, and the feed, in addition to the simulated chip thickness. It is noted that the measurements and calculations of Fig. 3.8 regard the conditions used in test number 2. To visualize the comparison between the generated chip thickness and the shear angle, the results and calculations were summarized in the charts of Fig. 3.9. Chip width was excluded from the comparison study since it did not exhibit any particular interest. The reason behind this decision is the fact that the parameters that affect the chip width such as the cutting-edge angle, the depth-of-cut, and the tool-nose radius remain constant for all tests, thus no significant variation was expected in the results.

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3 FEM-Based Study of AISI52100 Steel Machining: A Combined 2D …

Fig. 3.9 The deformed chip thickness graph (a) and the shear angle graph (b)

Figure 3.9a illustrates the chip thickness yielded in both 2D and 3D simulations. It is evident that the values exhibit a high level of accordance, meaning that the twodimensional tests are ideal when a quick assessment of the chip thickness is required. As shown in the graph, it is concluded that the feed has a significant impact on the chip thickness, acting increasingly. The same applies to the cutting speed, but the level of influence is lower compared to the effect of the feed. Mhamdi et al. [27] reported similar findings during their experimental work under cutting conditions of the same magnitude (feed between 0.05 and 0.2 mm/rev and cutting speed ranging from 50 to 250 m/min) for AISI-D2 steel. Specifically, the authors determined the chip thickening ratio, which increases with the rise of the feed value. An increasing trend is also present in Fig. 3.9b, where it is shown that the shear angle is influenced increasingly by higher values of feed. Despite the presence of a few wider values of error in this diagram, the trend remains clear.

References

61

3.4 Conclusions Concluding, the present study highlighted the importance of the establishment of a three-dimensional FE model as well as the value of 2D simulations and CAD-based tools when studying the effects of the cutting parameters in machining. Moreover, evaluated a range of friction coefficients and their influence on the development of a numerical model. In terms of the generated machining forces and the chip geometry, some useful conclusions can be drawn. • The FE model yielded results close to the experimental findings with adequate levels of error. • All machining force components are greatly affected by higher levels of feed. This, however, is not true for the cutting speed since its effect is marginal, especially for both the thrust and feed force. The effect on the cutting force, on the other hand, is slightly more significant. • Especially the feed value equal to 0.16 mm/rev boosts the forces significantly. • Furthermore, it is shown that the cutting force F c (tangential) is the dominant component. • Finally, both the feed and the cutting speed act increasingly on the produced deformed chip thickness, especially the feed. • The same applies to the estimated shear angle, with the exception of the cutting speed, which seems to have a negligible effect on the angle.

References 1. Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48 2. Xiong Y, Wang W, Jiang R et al (2018) Mechanisms and FEM simulation of chip formation in orthogonal cutting in-situ TiB2/7050Al MMC. Materials (Basel) 11:1–19. https://doi.org/10. 3390/ma11040606 3. Salvati E, Korsunsky AM (2020) Micro-scale measurement & FEM modelling of residual stresses in AA6082- T6 Al alloy generated by wire EDM cutting. J Mater Process Tech 275:1– 12. https://doi.org/10.1016/j.jmatprotec.2019.116373 4. Liu G, Huang C, Su R et al (2019) 3D FEM simulation of the turning process of stainless steel 17–4PH with differently texturized cutting tools. Int J Mech Sci 155:417–429. https://doi.org/ 10.1016/j.ijmecsci.2019.03.016 5. Lotfi M, Amini S, Aghaei M (2018) 3D FEM simulation of tool wear in ultrasonic assisted rotary turning. Ultrasonics 88:106–114. https://doi.org/10.1016/j.ultras.2018.03.013 6. Kyratsis P, Tzotzis A, Markopoulos A, Tapoglou N (2021) CAD-based 3D-FE modelling of AISI-D3 turning with ceramic tooling. Machines 9:4. https://doi.org/10.3390/machines9 010004 7. Kheireddine AH, Lu T, Jawahir IS, Hamade RF (2013) An FEM analysis with experimental validation to study the hardness of in-process cryogenically cooled drilled holes in Mg. 8:588– 593. https://doi.org/10.1016/j.procir.2013.06.156

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8. Xu J, Lin T, Li L et al (2022) Numerical study of interface damage formation mechanisms in machining CFRP/Ti6Al4V stacks under different cutting sequence strategies. Compos Struct 285:115236. https://doi.org/10.1016/j.compstruct.2022.115236 9. Tzotzis A, García-Hernández C, Huertas-Talón J-L, Kyratsis P (2020) FEM based mathematical modelling of thrust force during drilling of Al7075-T6. Mech Ind 21:415. https://doi.org/10. 1051/meca/2020046 10. Gao X, Li H, Liu Q et al (2011) Simulation of stainless steel drilling mechanism based on Deform-3D. Adv Mater Res 160–162:1685–1690. https://doi.org/10.4028/www.scientific.net/ AMR.160-162.1685 11. Lotfi M, Amini S, Al-Awady IY (2018) 3D numerical analysis of drilling process: heat, wear, and built-up edge. Adv Manuf 6:204–214. https://doi.org/10.1007/s40436-018-0223-z 12. Tzotzis A, García-Hernández C, Huertas-Talón J-L, Kyratsis P (2020) 3D FE modelling of machining forces during AISI 4140 Hard Turning. Strojniški Vestn. J Mech Eng 66:467–478. https://doi.org/10.5545/sv-jme.2020.6784 13. Thepsonthi T, Özel T (2015) 3-D finite element process simulation of micro-end milling Ti6Al-4V titanium alloy: experimental validations on chip flow and tool wear. J Mater Process Tech 221:128–145. https://doi.org/10.1016/j.jmatprotec.2015.02.019 14. Soo SL, Dewes RC, Aspinwall DK (2010) 3D FE modelling of high-speed ball nose end milling. Int J Adv Manuf Technol 50:871–882. https://doi.org/10.1007/s00170-010-2581-y 15. Afazov SM, Ratchev SM, Segal J (2012) Prediction and experimental validation of micromilling cutting forces of AISI H13 steel at hardness between 35 and 60 HRC. Int J Adv Manuf Technol 62:887–899. https://doi.org/10.1007/s00170-011-3864-7 16. Man X, Ren D, Usui S et al (2012) Validation of finite element cutting force prediction for end milling. Procedia CIRP 1:663–668. https://doi.org/10.1016/j.procir.2012.05.019 17. Li S, Sui J, Ding F et al (2021) Optimization of milling aluminum alloy 6061–T6 using modified Johnson-Cook model. Simul Model Pract Theory 111:102330. https://doi.org/10.1016/j.sim pat.2021.102330 18. Tzotzis A, García-Hernández C, Huertas-Talón JL, Kyratsis P (2020) CAD-based automated design of FEA-ready cutting tools. J Manuf Mater Process 4:1–14. https://doi.org/10.3390/ jmmp4040104 19. Bouacha K, Athmane M, Mabrouki T, Rigal J (2010) Statistical analysis of surface roughness and cutting forces using response surface methodology in hard turning of AISI 52100 bearing steel with CBN tool. Int J Refract Met Hard Mater 28:349–361. https://doi.org/10.1016/j.ijr mhm.2009.11.011 20. Tzotzis A, Tapoglou N, Verma RK, Kyratsis P (2022) 3D-FEM approach of AISI-52100 hard turning: modelling of cutting forces and cutting condition optimization. Machines 10:74. https:// doi.org/10.3390/machines10020074 21. Scientific Forming Technologies Corporation (2016) DEFORM V11.3 (PC) Documentation 22. Arrazola PJ, Özel T (2008) Numerical modelling of 3D hard turning using arbitrary Lagrangian Eulerian finite element method. Int J Mach Mach Mater 3:238–249 23. Tzotzis A, García-Hernández C, Huertas-Talón J-L, Kyratsis P (2020) Influence of the nose radius on the machining forces induced during AISI-4140 hard turning: a CAD-based and 3D FEM approach. Micromachines 11:798. https://doi.org/10.3390/mi11090798 24. Cockcroft MG, Latham DJ (1968) Ductility and the workability of metals. J Institue Met 96:33–39 25. El-Hofy H (2018) Fundamentals of machining processes: conventional and nonconventional processes. CRC Press 26. Agmell M (2018) Applied FEM of metal removal and forming, 1st edn. Studentlitteratur, Lund 27. Mhamdi MB, Ben SS, Boujelbene M, Bayraktar E (2013) Experimental study of the chip morphology in turning hardened AISI D2 steel. J Mech Sci Technol 27:3451–3461. https:// doi.org/10.1007/s12206-013-0869-1

Chapter 4

Experimental and 3D Numerical Study of AA7075-T6 Drilling Process

Abstract Finite Element Method (FEM) in machining is a technique that is widely accepted by the research community in the past few years, because it offers increased accuracy, robust results, and simplified test repeatability. The 3D-FE modeling of 7075-T6 aluminium alloy drilling is being presented in this study, with the use of commercial Finite Element Analysis (FEA) software, namely DEFORMTM . The drilling process was simulated according to typical cutting parameters such as cutting speed and feed. The approximation of the process was achieved by implementing the most critical aspects, including flow stress of the material, tool geometry, friction behavior, and proper meshing. Prior to the development of the Finite Element (FE) model, an identical set of drilling tests was conducted with a CNC machine. Moreover, the results (thrust force and cutting torque) were outputted via a dynamometric system. The yielded numerical and experimental results demonstrated an increased agreement, with the relative error varying at reasonable levels for both cutting force and torque. Keywords AA7075 drilling · FEM · DEFORMTM · Thrust force · Cutting torque · Temperature distribution · Chip geometry

4.1 Introduction A significant number of studies in machining are responsible for the technological advancement of the field. Modern industries depend heavily on this technology for the manufacturing of a wide range of products, making any research tool in machining an invaluable asset. Statistical tools and mathematical models are among these tools that are used until today. Budak et al. [1] investigated the mechanics of cutting techniques for the prediction of cutting force components during milling. Moreover, the authors experimentally verified the milling cutting force coefficients prediction when milling Ti6Al4V alloy with respect to chatter, eccentricity, cutting conditions, and cutter geometry. Liu et al. [2] studied the influence of tool-nose radius and tool wear on the residual stress

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al., 3D FEA Simulations in Machining, Manufacturing and Surface Engineering, https://doi.org/10.1007/978-3-031-24038-6_4

63

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4 Experimental and 3D Numerical Study of AA7075-T6 Drilling Process

formation during machining of bearing steel. The results were presented for a variety of cutting conditions with CBN tools, on bearing steel. Especially for drilling and other conventional processes, many experimental investigations make use of well-established statistical methodologies such as the Response Surface Methodology (RSM), the Taguchi method, and the Artificial Neural Networks (ANN), which of course are extended to non-conventional machining processes as well. Kao et al. [3] investigated inverted drilling of Al7075 alloy to examine several parameters such as hole roundness, surface roughness, and hole enlargement. The authors applied a gray-Taguchi methodology for optimization purposes of the aforementioned characteristics. Kyratsis et al. [4] implemented RSM in their work related to drilling of Al7075. Both the thrust force and torque, based on standard cutting conditions, were studied and the equivalent mathematical models were derived for prediction purposes. Similar works [5, 6] were realized with the aid of RSM and ANN for drilling. The aim of these works was to investigate the effect of several factors on drilling force and torque, in addition to the development of prediction models for rapid and reliable calculation of the aforementioned parameters. Finite Element (FE) modeling is another well-established methodology that is widely used by researchers in the field of machining, despite the fact that the model preparation, as well as the computational stages, are time-consuming, in addition to the need for increased computational power. Davim et al. [7] examined the performance of diamond and cemented tools during the machining of 7075 aluminium alloy by utilizing a commercial Finite Element Analysis (FEA) software. Additionally, they studied the behavior of the alloy in terms of machinability. Maranhão and Davim [8] modeled the machining process of AISI-316 steel by means of FEA and determined the influence of the friction on several crucial machining parameters, for instance, cutting forces and temperature, strains, shear stresses, as well as residual stresses. Studies that are oriented towards drilling [11–13] have used the FE method as well, for developing models in three dimensions that can be used to study the influence of similar specifications. Moreover, Nan et al. [14] worked on the three-dimensional FEM model for the micro-drilling process of AISI-1045 steel. The authors carried out experimental testing to validate the model, studying at the same time the produced thrust force, torque, and chip morphology. In some cases [9, 10], the use of CAD-based techniques is observed as an alternative to the FEA. In this type of study, the programming via the software’s interface is used to develop a code that can calculate the related parameters, such as cutting forces, torque, and chip geometry, with increased accuracy. The code usually comprises Boolean operations that are responsible for considering the tool geometry, the cutting conditions, and the workpiece to solve the typical formulas that govern the machining process. The present study deals with the AA7075 drilling via 3D-FE modeling, in which typical cutting parameters, within a standard range, were taken into account. Lastly, the model results were validated via experimental testing, proving the reliability and accuracy of the model.

4.2 Materials and Methods

65

4.2 Materials and Methods 4.2.1 Layout of Experimental Testing Prior to developing the numerical model, nine physical tests were conducted to study the effect of standard cutting conditions on the drilling of Al7075-T6. The selected cutting conditions are three levels of cutting speed and feed as seen in Fig. 4.1. Moreover, the used cutting tool is a Ø10 carbide drill with designation number B041A10000CPG (KC7325 grade), which is a general-purpose carbide drill, able to cut aluminum and its alloys. Additionally, the cutting tool is coated with a double layer of TiN/TiAlN. Figure 4.1 illustrates the geometrical aspects of the physical drill and compares it with the CAD model used in the numerical study. The workpiece used for the drilling operations is an orthogonal plate made of aluminium alloy 7075-T6. The most important physical properties of the alloy are included in Table 4.1. The experimental work was carried out with the VF-1 CNC machining center. Furthermore, a type 9123C force measurement device was utilized along with the equivalent charge amplifier and data acquisition system, for the cutting force and torque measurement. To dissipate the generated heat, a typical oil-based coolant was used. Figure 4.2a contains the aforementioned parts and components. Furthermore, Fig. 4.2b, c include two sample diagrams indicating force and torque development versus time, respectively. Both diagrams were generated with the aid of Dynoware software type 2825D-02, outputting a mean thrust force value equal to approximately

Fig. 4.1 Physical tool and CAD model comparison

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4 Experimental and 3D Numerical Study of AA7075-T6 Drilling Process

Table 4.1 AA7075-T6 and WC mechanical and thermal properties [15, 16]

Mechanical properties

AA7075-T6

WC/Co

E [GPa]

71.7

Rigid

ρ [kg/m3 ]

2,810

ν

0.33

Thermal properties

AA7075-T6

WC/Co

C [J/kgK]

960

150

α [o C−1 ]

22 × 10−6

5 × 10−6

k [W/mK]

130

59

430N and a mean torque value close to 1800Nmm. It should be noted that the equivalent force and torque versus time diagrams for the simulated drilling tests were run for only a few milliseconds. As explained in Sect. 4.2.2, it is very time-consuming to run a simulation until the drill tip fully penetrates the workpiece. For this reason, most duplications were run until a steady state was reached and then halted to save time.

4.2.2 Finite Element Layout In order to visualize and study the drilling process in three dimensions, DEFORMTM 3D software was used, specialized in Finite Element Analysis (FEA). 9 simulation tests were carried out in accordance with the cutting conditions applied during the experimental phase. The Finite Element (FE) setup was based upon an example that is already available by DEFORMTM , whereas the tool model was obtained via the KENNAMETALTM online tool library. Despite the fact that the tool CAD model was already available by the manufacturer, some changes had to be made for the model to be properly used. One such change is the conversion of the model to STL file format. Regarding the FE setup, the kinematics of the process, as well as the tool-work interface were derived from the example as can be seen in Fig. 4.3. Moreover, the example was run to verify that it produces reasonable results; thrust forces, torque, chip morphology, and cut interface temperature. To reduce simulation time, the runs were halted when cutting force steady state was achieved. Furthermore, the round workpiece was designed with an alteration compared to the original from the example. That is a drill spot at the center, which enables a more rapid achievement of the steady state. This happens due to the fact that as soon as the cutting edge starts to rotate, a full chip fragment is removed. In addition, it was important to set a reasonable time step for the simulations, as it directly affects the completion time, as well as the quality of the visualized process. In this case, the time step was set to 5.24 × 10−5 s. To calculate the time step, the cutting speed must be converted to rotational speed of the drill in rounds per second. Next, the time the drill requires to complete a rotation can be derived. Finally, the

4.2 Materials and Methods

67

Fig. 4.2 The CNC machine coupled with the data acquisition system and dynamometer (a), a sample force-time diagram (b), and torque-time diagram (c)

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4 Experimental and 3D Numerical Study of AA7075-T6 Drilling Process

calculated time and the number of steps per revolution, the tool performs, can be used to determine the simulation time step. The number of the steps should be close to 360 or more [17] so that one step equals to no more than one degree. It is obvious that more steps lead to better accuracy but significantly increase run time. The part was modeled to act deformingly with a mesh of approximately 147,000 elements. Furthermore, the remeshing technique embedded in DEFORM™ was applied to maintain a mesh with a reasonable number of elements at the area of interest. It is noted that the size of the mesh changes dynamically as soon as the cutting process begins. Despite the fact that the round shape can keep the number of elements relatively low, a denser mesh at the center countermeasures this advantage, since the denser the mesh, the longer the simulation times. It is recommended to set the refined mesh in such a manner so that the largest element should not exceed 50% of the feed. For the present study, a 10:1 ratio was applied. On the contrary, the drill was modeled to behave rigidly and allowed the minimum number of elements to be produced. However, the mesh at the area of the drill tip was tuned with a 4:1 ratio, since it is in the direct proximity of the uncut surface of the part. The simulation of the aluminium alloy flow stress during the drilling numerical tests was achieved with the Johnson–Cook model in its generalized form, which is very common in such situations where high deformations occur, along with high strain and temperatures. Equation 4.1 represents the model.        T − T0 m ε˙ 1− σ = A + Bεn 1 + C ln ε˙ 0 Tm − T0

Fig. 4.3 The drilling process FE model setup

(4.1)

4.2 Materials and Methods

69

Table 4.2 Material model constants [18] A (MPa)

B (MPa)

C

n

m

T 0 (°C)

T m (°C)

546

678

0.024

0.71

1.56

20

635

Each one of the parameters of the aforementioned formula represents a specific component of the material model. Specifically, A, B, and C are material coefficients, based on the stress and strain properties of the material. ε represents the plastic strain, n the constant related to the strain hardening, whereas m to the thermal softening, ε˙ is the strain-rate and ε˙0 is the reference rate. Finally, T and T 0 represent the default and bulk temperature accordingly, whereas T m is the temperature where the workpiece melts. The equivalent for the AA7075-T6 constants is presented in Table 4.2, as found in the literature for similar conditions, with reference strain rate s−1 . To reduce the produced errors, slight calibration changes were made according to a small number of trial-and-error runs. The material separation process occurs when the bond between the nodes of the workpiece is broken. This process can be determined via a damage model. In the present case, the normalized Cockcroft-Latham criterion [19] was selected since it is widely used by many researchers when studying the separation process on similar materials. Equation 4.2 represents the criterion. ε f Dc = 0

σmax dε pl σ

(4.2)

Dc is a constant related to the material fracture, σ max is the maximum stress, whereas σ˜ represents the effective stress. Finally, εf and εpl are the fracture and the normal strain, respectively. Regarding the interaction between the tool and the produced chip, a hybrid model [20] was implemented to simulate friction in a simple fashion. In most cases, the approximation of the friction that develops at the friction zone where sliding occurs is adequate. However, an approximation of both the sliding and the sticking zone can yield better results. Thus, the simulations can benefit from the use of a hybrid model as long as the friction coefficients yield reliable results. The generated frictional stresses around the tip of the drill can be determined by Eq. 4.3. This area has a more sticking behavior; therefore, the frictional stress is assumed to be analogous to the weaker material’s shear strength [21]. σy τ f = kτ √ 3

(4.3)

In Eq. 4.3, τ f represents the stress due to friction, k τ denotes a constant and σ y is the uniaxial yield stress for the workpiece.

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4 Experimental and 3D Numerical Study of AA7075-T6 Drilling Process

On the other hand, friction across the sliding zone can be calculated by Coulomb’s law. This simplified formula can be used for most metal materials. τ f = μσn

(4.4)

where τ f is the friction-based stress, μ the coefficient, and σ n the normal stress at the tool-work interface. Both constant coefficients, the shear and Coulomb were set close to the default values of the software, which are m = 0.7 and μ = 0.6, according to the findings of similar studies [20, 22] for the same material. Consequently, the boundary conditions for the model were set. First of all, the side walls of the test piece were constrained in this fashion so that all nodes would remain fixed (U x = U y = U z = 0). Next, the heat exchange conditions were appointed to all surfaces of the test piece. Specifically, a coefficient for the coolant was assigned, to approximate convection, with a typical value of 2 × 103 W/(m2 × °C). [17]. In addition, the drill was allowed to revolve around the feed axis and translate in a similar manner as the example. Finally, a relationship was assigned for the contact between the part and the formed chips to approximate any possible collision between the material and the chips.

4.3 Results and Findings 4.3.1 Cutting Forces and Torque Analysis To make the comparison possible, both the experiments and the simulations were carried out under the same cutting conditions. The next values of cutting speed were used: 50, 100, and 150 m/min. The same applied for feed, having values ranging from 0.15 to 0.25 mm/rev. The produced results were compared so that the drilling process could be analyzed within the specified range of conditions. Figure 4.4 contains six graphs that summarize the aforementioned analysis. First of all, the agreement level for the compared numerical and experimental results was found to be rather high, considering that the relative error ranges between −15 and 9% for the thrust force and between −8 and 13% for the torque. It is shown that feed acts increasingly for both force F z and cutting torque M z . According to the numerical results, the percentage of increase for the torque, when shifting from the low level to the middle one, is 46.2, 26.2, and 30.3% for cutting speed equal to 50, 100, and 150 m/min, respectively. The equivalent percentages for the force are 27.7, 33.1, and 46.3% accordingly. Similarly, any increasing change in cutting speed affects both components increasingly, but the effect is weaker compared to the one generated by the feed.

4.3 Results and Findings

71

Fig. 4.4 Experimental versus numerical results for thrust force and torque

4.3.2 Chip Morphology Analysis Chip formation during drilling of AA7075-T6 exhibits similar patterns between the experimental process and the simulations. This fact can be observed in Fig. 4.5a, which depicts the formation of the simulated chip at the first level of feed and speed. In addition, a sample of the physical chip is illustrated for the same conditions. The conical shape for both cases (experimental and simulated) was noticeable, which remained the same for all test runs no matter the change in cutting speed or feed. Furthermore, the diameter of the curling was measured at various points of the chip’s length to receive a mean value. It was measured at approximately 5.233 mm for the simulated and 5.965 mm for the experimental one (Fig. 4.5b). The experimental

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Fig. 4.5 The simulated chip evolution (a), sample experimental chip dimensions (b), and simulated chip thickness measurement (c)

chip dimensions were measured with calipers and an electronic image taken from a microscope, whereas the simulated ones were with the aid of a CAD system, as shown in Fig. 4.5c. Specifically, the deformed model of the workpiece was exported to the CAD environment and sectioned across the plane of interest. In this way, the chip thickness was revealed, and several measurements were taken in order to generate an accurate mean value. The conditions applied were the same for both measurements, specifically for the simulation, the chip was measured as soon as full curling was formed. The percentage of agreement was calculated as high as approximately 85–89%. Similar findings were observed for the chip thickness as well.

4.3.3 Temperature Distribution Analysis Finally, the temperature distribution on the drill contact area was examined by means of FEA. This parameter is subject to the heat transfer that takes place between the drill and the work. A typical stage of the heat distribution was determined to be when the full length of the cutting edge was engaged and when the thermal steady state was achieved, which was equal to approximately 0.033 and 0.15 mm penetration depth, respectively. The temperature distribution for both stages is illustrated in Fig. 4.6 for an example run with the low value of both cutting speed and feed. It is seen that the maximum temperature for both stages (77 and 129 °C) were located on the cutting lips corner (Fig. 4.6a, b, respectively).

4.3 Results and Findings

73

Fig. 4.6 Temperature at the tools’ cutting lip corner at full engagement (a) and at the occurrence of the steady state (b)

By selecting cutting speed and feed at higher levels, a slight increase in temperatures was observed, probably due to the higher frictional forces that generate as the tool rotates faster.

4.3.4 Concluding Remarks Concluding, the present study proposed a FE model for AA7075 drilling in three dimensions. Typical parameters in three consecutive values, with the same drill, were the used cutting conditions, leading to nine simulation runs. An equal number of experiments were performed to investigate the fidelity of the FE model. By comparing the results yielded by the experiments and simulation tests, a good level of agreement was found, meaning that the model can produce reliable results within the applied range of conditions. In general, the error for both cutting forces and torque was determined to be acceptable. Moreover, the morphology of the produced chip was considered to be similar for all cases studied. Finally, the next conclusions can be deduced from the analysis: • The FE model can be effortlessly changed, in terms of the cutting parameters, material constants, and tool geometry, to extend the evaluation of the effects of the cutting conditions on similar materials. • Any increase in the feed rate can affect significantly the thrust force and the torque as well, specifically leading to an increase. • On the contrary, changing the cutting speed does not seem to greatly affect thrust force or cutting torque. • As expected, the conical shape of the generated chips is maintained regardless of the cutting parameters.

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References 1. Budak E, Altintas¸ Y, Armarego (1996) Prediction of milling force coefficients from orthogonal cutting data. J Manuf Sci Eng 118:216–224. https://doi.org/10.1115/1.2831014 2. Liu M, Takagi JI, Tsukuda A (2004) Effect of tool nose radius and tool wear on residual stress distribution in hard turning of bearing steel. J Mater Process Technol 150:234–241. https://doi. org/10.1016/j.jmatprotec.2004.02.038 3. Kao JY, Hsu CY, Tsao CC (2019) Experimental study of inverted drilling Al-7075 alloy. Int J Adv Manuf Technol 102:3519–3529. https://doi.org/10.1007/s00170-019-03416-8 4. Kyratsis P, Garcia-Hernandez C, Vakondios D, Antoniadis A (2016) Thrust force and torque mathematical models in drilling of Al7075 using the response surface methodology. In: Davim JP (ed) Design of experiments in production engineering. Springer International Publishing, Cham, pp 151–164 5. Kyratsis P, Markopoulos A, Efkolidis N et al (2018) Prediction of thrust force and cutting torque in drilling based on the response surface methodology. Machines 6:24. https://doi.org/ 10.3390/machines6020024 6. Garcia-Hernandez C, Marín R, Talón J et al (2016) WEDM manufacturing method for noncircular gears using CAD/CAM software. Strojniški Vestn J Mech Eng 62:137–144. https://doi. org/10.5545/sv-jme.2015.2994 7. Davim JP, Maranhão C, Jackson MJ et al (2008) FEM analysis in high speed machining of aluminium alloy (Al7075-0) using polycrystalline diamond (PCD) and cemented carbide (K10) cutting tools. Int J Adv Manuf Technol 39:1093–1100. https://doi.org/10.1007/s00170007-1299-y 8. Maranhão C, Paulo Davim J (2010) Finite element modelling of machining of AISI 316 steel: numerical simulation and experimental validation. Simul Model Pract Theory 18:139–156. https://doi.org/10.1016/j.simpat.2009.10.001 9. Kyratsis P, Bilalis N, Antoniadis A (2011) CAD-based simulations and design of experiments for determining thrust force in drilling operations. Comput Des 43:1879–1890. https://doi.org/ 10.1016/j.cad.2011.06.002 10. Kyratsis P, Tapoglou N, Bilalis N, Antoniadis A (2011) Thrust force prediction of twist drill tools using a 3D CAD system application programming interface. Int J Mach Mach Mater 10:18–33. https://doi.org/10.1504/IJMMM.2011.040852 11. Tzotzis A, García-Hernández C, Huertas-Talón J-L, Kyratsis P (2020) FEM based mathematical modelling of thrust force during drilling of Al7075-T6. Mech Ind 21:415. https://doi.org/10. 1051/meca/2020046 12. Tzotzis A, Markopoulos AP, Karkalos NE et al (2021) FEM based investigation on thrust force and torque during Al7075-T6 drilling. In: IOP conference series: materials science and engineering, p 012009 13. Tzotzis A, Markopoulos A, Karkalos N, Kyratsis P (2020) 3D finite element analysis of Al7075T6 drilling with coated solid tooling. In: MATEC web of conferences, pp 1–6 14. Nan X, Xie L, Zhao W (2016) On the application of 3D finite element modeling for smalldiameter hole drilling of AISI 1045 steel. Int J Adv Manuf Technol 84:1927–1939. https://doi. org/10.1007/s00170-015-7782-y 15. Jafarzadeh E, Movahhedy MR, Khodaygan S (2018) Prediction of machining chatter in milling based on dynamic FEM simulations of chip formation. Adv Manuf 6:334–344. https://doi.org/ 10.1007/s40436-018-0228-7 16. MatWeb L (2019) MatWeb Material Property Data: {http://www.matweb.com}. www.matweb. com. Accessed 29 Sep 2019 17. Scientific Forming Technologies Corporation (2016) DEFORM V11.3 (PC) Documentation 18. Brar NS, Joshi VS, Harris BW (2009) Constitutive model constants for Al7075-T651 and Al7075-T6. AIP Conf Proc 1195:945–948. https://doi.org/10.1063/1.3295300 19. Cockcroft MG, Latham DJ (1968) Ductility and the workability of metals. J Institue Met 96:33–39

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20. Ucun I (2016) 3D finite element modelling of drilling process of Al7075-T6 alloy and experimental validation. J Mech Sci Technol 30:1843–1850. https://doi.org/10.1007/s12206-0160341-0 21. Agmell M (2018) Applied FEM of metal removal and forming, 1stedn. Studentlitteratur, Lund 22. Melkote N, Grzesik W, Outeiro J et al (2017) Advances in material and friction data for modelling of metal machining. CIRP Ann Manuf Technol 66:731–754. https://doi.org/10.1016/ j.cirp.2017.05.002

Chapter 5

3D Finite Element Simulation of CK45 Steel Face-Milling: Chip Morphology and Tool Wear Validation

Abstract Nowadays, three-dimensional Finite Element (FE) modeling is used more often for the investigation of the machining processes, due to the increased approximation it provides and the fact that a number of variables cannot be examined by other means. The present work introduces a 3D FE model of CK45 (AISI1045) steel face-milling. In specific, it proposes a model for full immersion face-milling with a head mill. Moreover, it focuses on the comparison of the simulated chip formation process with experimental results, as well as the investigation of the tool wear in terms of the generated temperatures. The results of this study exhibit good agreement results for the generated chip morphology and dimensions. In addition, it is pointed out that tool wear is directly connected to cutting-edge temperatures and chip flow. Keywords AISI1045 · Face milling · FEM · DEFORM · Tool wear · Chip formation · Tool temperature

5.1 Introduction Milling is one of the most versatile processes used in the industry. Aerospace, vehicle, construction, and biomedical are only a few of the industries that utilize milling to produce a number of products such as mechanical parts, molds, implants, and more. Therefore, investigation of the process and its parameters is often the topic of many studies. The tools and techniques that are usually applied in such investigations involve experimental testing, statistical processing, and soft computing, as well as numerical modeling. Especially Finite Element (FE) modeling, constitutes a robust tool for the examination of several factors that participate in the milling process and in other machining procedures as well. Maurel-Pantel et al. [1] investigated the machinability of AISI304L stainless steel by means of the Finite Element Method (FEM). The authors examined the generated cutting forces and stresses and validated the results by comparing the numerical results with equivalent experimental ones. Gao et al. [2] presented a Coupled Eulerian–Lagrangian (CEL) model in 3D, for the simulation of AA6061-T6 end-milling, validated by experimental work. Two milling methods were tested, with the milling forces and the chip production being © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 P. Kyratsis et al., 3D FEA Simulations in Machining, Manufacturing and Surface Engineering, https://doi.org/10.1007/978-3-031-24038-6_5

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the objective investigation parameters. As seen in example studies that relate to other conventional machining processes such as drilling and turning [3–7], the typical investigation parameters are the generated chip morphology, the machining forces, and torque, the tool wear and life, the residual stresses, as well as the temperature generation across the tool cutting edge or the tool-workpiece contact interface. Micro-milling is another subject of increased interest, where FE modeling is applicable. In such delicate operations, tools of very small diameter are used, usually in the range of a few hundred microns. For example, Thepsonthi and Özel [8] studied three cases of micro-milling, the full-immersion of tool, and the half-immersion during standard milling techniques. The chip formation, the tool wear, the temperature allocation across the cutting-edge, and the cutting-edge roundness effect on the produced forces, were the main objective of the study. Similarly, Ucun et al. [9] worked on a three-dimensional approximation of micro-milling of Ti-6Al-4V alloy. The authors focused their study on the cutting forces generation, the chip aspects, and the tool stress. Additionally, experiments were carried out to verify the model. Similar works [10, 11] are available in the literature, focusing on parameters that cannot be easily examined via experiments, confirming the need for FE models. Especially models in three dimensions are considered to be tools of increased precision when dealing with the simulation of more complex processes. Face milling is the most common milling operation and can be performed with a variety of tools, each one designed for a specific operation. Pittalà and Monno [12] developed a 3D FE model and focused on the examination of the developed milling forces. A sensitivity study and an inverse method were utilized for the identification of the friction coefficients and the material constants respectively. Soo et al. [13] presented a Lagrangian-based, 3D FE model for simulating end-milling of Inconel718 superalloy with ball-nosed tools, at high speeds. The study included cutting force predictions, validated against corresponding experimental results, as well as tool-chip temperatures. Rao et al. [14] carried out an experimental analysis focused on the required energy and surface quality measurements, as well as cuttingtool metrics. The authors supplemented the experiments with a FEM-based tool wear model in terms of the contact interface temperature and stress, as well as the chip velocity. Nieslony et al. [15] developed a FE model in three dimensions for investigation purposes of the cutting power and specific cutting energy as to the rotation angle of the mill and the chip thickness. Similar works [16–18] studied face milling and several conditions that affect the process, such as burr formation, chip thickness, and cutting forces. This study utilizes well-established models and methods to develop a 3D FE model for CK45 (AISI1045) steel face-milling with coated tools. Moreover, the recommended by the manufacturer cutting conditions were applied. The study focuses mainly on the chip formation mechanisms, the tool wear, and temperature generation. In addition, the results regarding the chip development and tool wear were validated with experiments.

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5.2 Materials and Methods 5.2.1 Experimental Framework The experimental work was carried out on a four-axis HAAS VF-1 milling center without the use of coolant. The used workpiece is a CK45 steel plate with 150 mm length, 120 mm width, and 20 mm thickness. To perform the face milling on the plate, a general-purpose shell mill and the equivalent inserts were selected, with ISO designation numbers 50A04RS45SE14EG and SEPT1404AESNGB2, respectively. According to the manufacturer, the selected cutter system is designed for steel, stainless steel, and several high-temperature alloys. Moreover, the inserts are carbide with a 3.5 microns TiAlN + TiN coating. A mill arbor, with code 40.340.22 by HAIMER™, was used to clamp the shell mill to the machine. Finally, the machining conditions are available in the manufacturer’s catalogue for the CK45 steel, which belongs to the ISO P2 material group. Thus, the cutting speed was set to 230 m/min and the feed to 0.36 mm/tooth. The milling process was done with full immersion of the head at depth of cut equal to 2 mm, lower than the maximum allowed. The effective cutting diameter is 50 mm. Figure 5.1 illustrates the complete set of experimental work. Specifically, Fig. 5.1a depicts the assembly of the mill cutter, with a more detailed inspection of the milling insert, Fig. 5.1b shows the CNC machine and, lastly, Fig. 5.1c illustrates the plate that was used as a workpiece.

5.2.2 Face-Milling CAD-Based Setup The equivalent of the experimental setup was reproduced with the aid of a CAD system. This technique allows the examination of the setup in a simple and repeatable manner. Hence, in the present work, the positioning of the tool on the test piece was achieved, the angles involved in the milling procedure, as well as the force vectors, were extracted, and the FE setup was facilitated with respect to the CAD-based model. The workpiece was designed in the CAD system in such a way that it would resemble a part with an already cut region, based on the cutter’s effective diameter, as well as the insert’s shape and the selected cutting conditions (Fig. 5.2a). It is noted that the milling insert has an entering angle (KAPR) equal to 45° and an axial rake angle of 18°, with no inclination in the radial direction. Figure 5.2b illustrates the dimensions of the used tool. To further simplify the setup, only one of the four inserts was implemented.

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Fig. 5.1 The milling cutter assembly, with a closer view of the insert (a), the CNC milling center (b), and the used workpiece (c)

Fig. 5.2 The setup of the milling process in the CAD environment, with details (a) and the mill insert dimensions (b)

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5.2.3 Numerical Modeling of the Face-Milling Process Analysis of domain and boundary conditions The milling process FE model was set with the aid of DEFORM™-3D ver. 12 software that uses an updated Lagrangian formulation. First, the workpiece was designed, as seen in Fig. 5.3a, based on the CAD-based setup. Hence, it was designed according to the effective cut diameter, the depth of cut, the radius of the insert’s cutting edge, and the entering angle. A sectioned sketch of the work is illustrated in Fig. 5.3b. It is shown that it was sketched as an arc with an already cut region, to minimize the simulation time. Moreover, it was set to be plastic and was initially meshed with approximately 32,000 tetrahedral elements, based on the feed value. Since the simulated material separation process is identical to all machining processes, a rule of thumb is to use elements with a minimum size, equal to a portion of the feed value [19, 20]. The size ratio of 7:1 for the elements was applied on the contact area, which combined with the local remeshing criteria, shifted the total number of elements to 100,000. The tool, on the other hand, was meshed with roughly 125,000 elements. Even though the tool was set to behave as rigid, it was necessary to use a high number of mesh elements to achieve a better approximation of the thermal behavior of the tool, as well as to calculate its wear more accurately. It must be noted that the majority of the elements belong to the coating’s mesh, which was crucial to the wear calculation. Due to the subtle thickness of the coating (Fig. 5.3c), the size of the elements had to be very small. In addition, a 10:1 size ratio was used to refine the areas around both the primary and the secondary cutting edges (Fig. 5.3c). The primary cutting edge is the one that cuts most of the formed chip volume, whereas the secondary is the one that separates the chip from the bottom of the part. As discussed in Sect. 5.3.2, it is evident that less wear is induced on the secondary cutting edge. Finally, the detail of Fig. 5.3b depicts the average chip section that is expected to be formed due to the shape of the tool and the feed value. The boundary conditions for the model were set according to the milling kinematics. The workpiece was fixed on its bottom and side, as shown in Fig. 5.3b. In contrast, both a translation and a rotation were applied on the tool so it would be possible to follow the trajectory illustrated in Fig. 5.3a. This way, it was ensured that both the tool rotation and the table feed are simulated. Furthermore, the boundary conditions related to the heat transferred among the tool, the work, and the environment were attributed. The constants for both types of heat transfer were set to 20 and 4.5 × 104 W/(m2 × °C), respectively. Material and friction modeling To model the material’s behavior under the conditions that occur during machining, a tabular data format was used according to temperatures from 20 °C (ambient temperature) to the softening temperature of the material. Moreover, the strain values [21] used range from 0 to 5, for strain rates equal to 1, 10, 102 , 103 , 104 , 105 , and 5 × 105 , respectively. Therefore, the flow stress was modeled with respect to the temperature, the strain, and the strain rate for the aforementioned range of values. A number of

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Fig. 5.3 The milling process FE model setup: the analysis domain (a), the workpiece section (b), and the cutting-tool model (c)

extra points were interpolated in the table to yield more smooth flow stress curves. The approximation of the damage process and material separation, the normalized Cockcroft-Latham criterion [22] was applied, which links a material damage constant with both the maximum and the effective stress. Moreover, the mechanical workto-heat conversion factor was set to 0.9, with the rest of the work absorbed by the workpiece. In addition, Table 5.1 includes the standard properties of the part material used in the present study, as found in the software’s material library. It is noted that the thermal properties are expressed with respect to the temperature. Similar to the flow stress values, intermediate points were interpolated to fill the tabular data format for these properties. Finally, Table 5.2 displays the thermal properties of the tool material, as well as the coating, since they were taken into account during the calculations involved in the thermal analysis. In order to describe the frictional phenomenon that occurs between the tool and the part, a hybrid approach was followed. Specifically, the shear friction was modeled with a constant coefficient equal to m = 1 and the Coulomb coefficient was determined by the levels of the relative sliding velocity. According to the findings of Binder et al. [24], the friction coefficient between AISI1045 steel and coated carbides is close

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Table 5.1 CK45 steel thermomechanical properties [21] Mechanical properties E (GPa)

212.0 (20 °C)

ρ (kg/m3 )

7,850

ν

0.3

207.0 (100 °C)

192.0 (300 °C)

164.0 (600 °C)

69.44 (1500 °C)

Thermal properties Specific heat (J/kgK)

Thermal expansion × 10−6 (°C−1 )

Thermal conductivity (W/mK)

361.9 (20 °C)

11.9 (20 °C)

41.7 (20 °C)

389.4 (100 °C)

12.5 (100 °C)

43.4 (100 °C)

445.9 (300 °C)

13.6 (300 °C)

41.4 (300 °C)

610.7 (600 °C)

14.9 (600 °C)

34.1 (600 °C)

610.7 (1500 °C)

14.9 (1500 °C)

34.1 (1500 °C)

Table 5.2 Tool thermal properties [21, 23]

Thermal properties

Carbide

Coating

Heat capacity [J/kgK]

150

150

5×

Thermal expansion [°C−1 ] Thermal conductivity [W/mK]

10−6

9.2 × 10−6

100 °C

40.15

12.61

300 °C

48.55

14.01

500 °C

56.95

15.41

700 °C

65.35

16.81

900 °C

73.75

18.21

to 0.3 for sliding velocities that range from 1000 to 1500 mm/s. To identify the relative sliding velocity, a 3D simulation with a smaller workpiece was run. After the generation of a full chip curling (Fig. 5.4) and the achievement of the thermomechanical steady state, the relative sliding velocity for the present case was determined to be between 1000 and 1700 mm/s. Therefore, the Coulomb coefficient equal to μ = 0.3 was preserved.

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Fig. 5.4 The preliminary simulation run showing the sliding velocities at the direction of cut

5.3 Results and Discussion 5.3.1 Chip Formation Analysis and Temperature Distribution Evaluation A 3D chip flow analysis is more efficient compared to the equivalent 2D, since these models are limited in the XY plane. Because of the plane limitation, the chip accumulates in front of the tool’s cutting edge. Therefore, the chip flow predicted by a two-dimensional model is less accurate. Moreover, a three-dimensional simulation yields a more realistic flow, and it is possible to measure all dimensions of the chip. Figure 5.5a illustrates the chip flow during the cut, produced by the fully immersed tool. The generated chip’s section is found to be as expected (see Fig. 5.3b), based on the feed value and the 45° corner angle. Additionally, the phases where the chip formation was observed, reveal that the chip tends to form a small spring with one or two curls, which then slightly straightens (ϕ = 100°) and finally breaks into single curl chips, probably due to the contact with the workpiece. The temperature rise on the tool’s cutting edges was examined by collecting the maximum temperature and its zone, as well as the temperature distribution. Figure 5.5b shows the temperature rise along the cutting edges with respect to the revolution of the tool. It is shown that the area where the heat spreads, match the two wear zones, which is reasonable since these areas are in contact with the workpiece. In addition, it is evident that the temperature rises quickly as soon as the full engagement

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85

Fig. 5.5 The simulated chip morphology and chip flow in 3D (a) and the temperature distribution on the tool’s cutting edges (b)

of the tool occurs. This denotes a lower level of heat transferred between the cutting edges and the chip, due to the smaller contact zone compared to other types of inserts. This is reasonable considering that the 45° corner angle produces relatively thin chips, thus the contact area is smaller. Figure 5.6 presents a sample chip experimentally generated, compared to the equivalent simulated one. The parameters that are taken into account are the chip curling diameter, the deformed chip width, and thickness. The measurements of the aforementioned dimensions were performed on a number of chips. Especially the chip thickness, was measured on multiple points across the curling as seen in Fig. 5.6a, in order to derive an average value, since the tool run-out that is present in the system does not allow the generation of a uniform undeformed chip thickness. The same measurement technique was utilized for the simulated chip (Fig. 5.6b), within the CAD environment. As seen in Fig. 5.6b, the sample chip model was exported to the CAD system, where it was sectioned to achieve more accurate measurements. In general, it is shown that there are similarities between the simulated and the real chip. Moreover, the agreement percentage for all three dimensions, curl radius, width, and thickness, was found to be close to 85, 88, and 78%, respectively. It must be noted that the simulated chip was determined to be thicker compared to the real ones during all measurements.

5.3.2 Tool Wear Assessment The Usui et al. [25] model was utilized to predict the adhesive-based tool wear by using the results from the FEM runs, since the variables that participate in the model

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5 3D Finite Element Simulation of CK45 Steel Face-Milling: Chip …

Fig. 5.6 The experimental (a) and the simulated (b) sample chip formation

can be determined via FEM-based simulations. In specific, the thermomechanical load generated in the tool-work contact interface can be converted to nodal tool wear. In the present case, the average wear depth along the primary and the secondary cutting edges of the tool was determined at discrete points of time. Equation 5.1 represents the tool wear W with respect to time (dW /dt). In other words, the wear represents the wear volume with respect to time and area of contact. Where p is the contact interface pressure, vs represents the sliding velocity developed by the chip, T represents the interface temperature and, finally, a and b are coefficients related to the workpiece and the tool material, respectively, defined experimentally. dW = apvs exp(−b/T ) dt

(5.1)

The modeling variables, specifically the pressure, the sliding velocity, and the temperature generated at the area of interest, were extracted from the FEM simulations, whereas the values of the two constants were calculated considering the cutting data acquired after the full engagement of the mill head to the workpiece and the completion of three passes, thus approximately after 20 s. Moreover, they were compared to the constants used by studies [26, 27] that examined similar materials, to verify that they are of the same magnitude. It should be noted that the intention of this part of the study is to approximate the tool wear zones, rather than the tool wear rate. As seen in Fig. 5.7a, the tool wear is located at two distinct zones, the primary, and the secondary zone. The primary zone corresponds to the primary cutting edge, which is in contact with the material being removed, whereas the secondary zone corresponds to the secondary cutting edge, which is in contact with the bottom surface of the machined part. Once the full engagement of the tool occurs, the secondary cutting edge scratches continuously the bottom surface. However, due to the fact

5.4 Concluding Remarks

87

Fig. 5.7 The tool wear zones (a), the simulated wear pattern (b), and the predicted average tool wear depth (c)

that no chip is generated, the tool wear is rather small compared to the wear that is induced in the primary zone. The FEM simulations yielded a wear pattern similar to the actual one, as can be seen in the sample of Fig. 5.7b. Finally, Fig. 5.7c illustrates the average wear values that are formed along the cutting edge. This graph shows a rapid tool wear depth as soon as the engagement begins, but this increase is quickly limited. Furthermore, it is indicated that the wear progress is continuous but not its rate, rather it increases as the tool constantly wears with the cutting distance. However, it is evident that the increase occurs at a slower pace.

5.4 Concluding Remarks In this work, a 3D-FE model for the face-milling of CK45 steel was developed by implementing well-established methodologies and models. The developed model focused on the examination of the chip formation, the cutting-edge temperature distribution, and the tool wear. The results of the study can be related to the following remarks: • The generated chip follows a typical curl pattern. As the cut advances, the chip formed resembles a small spring with a couple of curls. Due to the contact with

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the workpiece, the chip slightly unfolds and breaks into smaller pieces. Moreover, the chip thickness is relatively small, with the average value being lower than the feed value. • Tool wear appears in two zones matching the two cutting edges of the tool. Most of the wear occurs across the primary cutting edge, due to the higher contact length compared to the secondary cutting edge, which scratches the bottom cut surface. • A rapid increase in the tool wear is evident as soon as the tool begins to cut, followed by a milder and at the same time, constant increase. The same applies to the generated maximum temperature, which is located on the primary cutting edge. This is reasonable since the temperature is related to the wear and both are influenced by the contact area.

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