Semi-rotary and Linear Actuators for Compressed Air Energy Storage and Energy Efficient Pneumatic Applications 9815179101, 9789815179101

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Semi-rotary and Linear Actuators for Compressed Air Energy Storage and Energy Efficient Pneumatic Applications Authored By Alfred Rufer

Ecole Polytechnique Fédérale de Lausanne (EPFL) Lausanne, Switzerland

Semi-rotary and Linear Actuators for Compressed Air Energy Storage and Energy Efficient Pneumatic Applications Author: Alfred Rufer ISBN (Online): 978-981-5179-09-5 ISBN (Print): 978-981-5179-10-1 ISBN (Paperback): 978-981-5179-11-8 © 2023, Bentham Books imprint. Published by Bentham Science Publishers Pte. Ltd. Singapore. All Rights Reserved. First published in 2023.

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CONTENTS PREFACE ................................................................................................................................................ i CHAPTER 1 INTRODUCTION AND SUMMARY .......................................................................... 1. INTRODUCTION ...................................................................................................................... 1.1. Historical Background of the Development: The System Gallino .................................. 1.2. Contents of the Book .......................................................................................................

1 1 4 6

CHAPTER 2 COMPRESSED AIR SYSTEMS AND STORAGE .................................................... 1. THE PHYSICAL PRINCIPLES RELATED TO COMPRESSED AIR ............................... 1.1. Adiabatic, Polytropic and Isothermal Compression and Expansion ................................ 2. ADVANTAGES AND DRAWBACKS OF CLASSICAL PNEUMATIC DEVICES .......... 2.1. Energy Loss due to the use of a Pressure Reduction Valve ............................................. 2.2. The Poor Energetic Performance of the Classical Pneumatic Actuators ......................... 3. COMPRESSED AIR ENERGY STORAGE WITH LOW PRESSURE - THE UNDERWATER CAES ................................................................................................................. 3.1. The Model of the Storage Infrastructure .......................................................................... 3.2. Examples of UWCAES Realizations ...............................................................................

9 9 14 16 16 18

CHAPTER 3 INCREASING THE ENERGETIC EFFICIENCY OF PNEUMATIC DEVICES 1. RECOVERY OF THE PNEUMATIC ENERGY .................................................................... 1.1. Operating Principle, Defaults and Improvements of the Truglia Motor .......................... 1.2. Expansion in a Separated Chamber with Sequential Strokes (The MDI Motor) ............. 1.3. Expansion in a Separated Chamber with Reciprocating Strokes .....................................

24 24 26 30 32

CHAPTER 4 COUPLING TWO ROTARY-TYPE ACTUATORS ................................................. 1. CONTEXT AND MOTIVATION ............................................................................................. 1.1. Structure of the System .................................................................................................... 1.2. The Mechanical Motion Rectifier .................................................................................... 1.3. Operating Principle .......................................................................................................... 2. SIMULATION OF THE SYSTEM ........................................................................................... 2.1. Parameters of the System ................................................................................................. 2.2. The Pressure Variation during the Expansion .................................................................. 2.3. From the Pressure to the Torque ...................................................................................... 2.4. The Effect of the Anti-Return Valve ............................................................................... 2.5. Exhaust Temperature ....................................................................................................... 3. EFFICIENCY CONSIDERATIONS ........................................................................................ 3.1. Efficiency of the Coupled Actuators ................................................................................ 3.2. Isothermal or Adiabatic .................................................................................................... 4. EXPERIMENTAL SET-UP ...................................................................................................... 5. DISPLACEMENT AND EXPANSION WORK IN ONE SINGLE ACTUATOR ............... 5.1. Basic Principle ................................................................................................................. 5.2. Closed Loop Operation of the Semi-Rotary Actuator ..................................................... 5.3. Torque Generated in Adiabatic and Isothermal Conditions ............................................ 6. SIMULATION OF THE SINGLE ACTUATOR SYSTEM WITH SENSORS AND CLOSED LOOP CONTROL ........................................................................................................ 7. EXPERIMENTAL SET-UP ...................................................................................................... 7.1. The 180° Actuator ............................................................................................................ 7.2. Control Circuits ................................................................................................................ 7.3. Sensor System for the 180° Actuator ............................................................................... 7.4. The Complete Assembly .................................................................................................. 7.5. Measurements ..................................................................................................................

34 34 34 35 36 37 37 39 40 43 44 45 45 47 49 52 52 54 55

19 20 22

56 61 61 62 62 62 63

8. THE REVERSIBILITY OF THE SYSTEM BASED ON SEMI-ROTARY ACTUATORS 8.1. The Crankshaft and Piston Rod System Instead of the Motion Rectifier ........................ 8.2. The Question of the Inertia of the Oscillating Vane-Rotor .............................................. 8.3. Combining the Operations of Compression and Expansion of Semi-Rotating Actuators 8.4. Experimentation with a Vane-Type Actuator Operating as a Compression Machine ..... 8.5. Reducing the Footprint of the Reversible System ........................................................... DISCLOSURE ................................................................................................................................

66 66 68 69 71 73 74

CHAPTER 5 THE PNEUMATIC MOTOR WITH LINEAR CYLINDERS ................................. 1. BASIC PRINCIPLE ................................................................................................................... 2. OPERATING PRINCIPLE OF THE MOTOR WITHOUT EXPANSION ......................... 2.1. Mathematical Description of the Piston/Crankshaft Assembly ....................................... 2.2. Simulation of a Motor with one Double Acting Cylinder ............................................... 2.3. Energetic Efficiency ......................................................................................................... 3. A PNEUMATIC MOTOR WITH ENHANCED EFFICIENCY – ADDING AN EXPANSION CHAMBER WITH RECIPROCATING STROKES ......................................... 3.1. Simulation Results ........................................................................................................... 3.2. Position and Velocity of the two Pistons ......................................................................... 3.3. Contributions of the 16 mm Piston .................................................................................. 3.4. Contributions of the Second Piston .................................................................................. 3.5. Total Torque of the Motor ............................................................................................... 4. SYSTEM WITH PISTONS IN PHASE AND CROSS CONNECTED EXPANSION WAYS .............................................................................................................................................. 4.1. Contributions of the Small Cylinder ................................................................................ 4.2. Contributions of the Larger Cylinder ............................................................................... 4.3. Total Torque of the Motor ............................................................................................... 5. ENERGY CONVERTED AND CALCULATION OF THE EFFICIENCY ........................ 5.1. Converted Energy ............................................................................................................ 5.2. Efficiency of the System with Expansion ........................................................................ 6. COMPARISON OF THE MECHANICAL WORK ............................................................... 7. EXPERIMENTAL SET-UP ...................................................................................................... 8. DISPLACEMENT WORK AND EXPANSION WORK IN THE SAME CYLINDER ...... 8.1. Basic Principle ................................................................................................................. 8.2. Asymmetrical Evolution of the Piston and Design of the Intake Angles ........................ 8.3. Control of the Valves ....................................................................................................... 8.4. Evolution of the Volumes of the Chambers ..................................................................... 8.5. Force Exerted on the Piston ............................................................................................. 8.6. Torque and Power ............................................................................................................ 8.7. Mechanical Work Produced ............................................................................................. DISCLOSURE ................................................................................................................................

75 75 76 77 79 83

CHAPTER 6 LINEAR PNEUMATIC CYLINDER ASSEMBLY WITH REDUCED AIR CONSUMPTION ..................................................................................................................................... 1. INRODUCTION ......................................................................................................................... 1.1. New Cylinder Assemblies ................................................................................................ 2. OPERATING PRINCIPLE AND CONTROL ........................................................................ 3. THE PRESSURE VARIATION DURING THE EXPANSION ............................................ 4. SIMULATION OF THE PROPOSED SYSTEM .................................................................... 4.1. Simulation Results ........................................................................................................... 5. EFFICIENCY OF THE NEW ASSEMBLY ............................................................................ 5.1. Comparison of Performance ............................................................................................ 6. EXPERIMENTAL SET-UP ......................................................................................................

84 86 86 86 90 92 93 93 94 95 95 95 96 97 97 100 100 100 103 105 106 107 108 108 110 110 110 113 114 114 115 119 120 122

6.1. The Parasitic Effect of the Dead Volumes ....................................................................... 6.2. A System with Greater Volumes ..................................................................................... 6.3. Control with a Simplified Tubing and Valve System (Supposed less dead volumes) – using 5/2-way Valves .............................................................................................................. 6.4. Experiment with the 100 mm Assembly .......................................................................... DISCLOSURE ................................................................................................................................

122 125 129 130 131

CHAPTER 7 THE EFFECT OF THE DEAD VOLUMES AND PRE-EXPANSION ON THE PRODUCED WORK .............................................................................................................................. 1. INTRODUCTION ...................................................................................................................... 1.1. Discontinuity of the Pressure ........................................................................................... 1.2. Torques Developed with a Pre-Expansion Factor of 0.6 ................................................. 1.3. Comparison of Energetic Performances ..........................................................................

132 132 133 134 136

CHAPTER 8 APPLICATION EXAMPLE: A PNEUMATIC DRIVEN HYDROGEN COMPRESSOR WITH INCREASED EFFICIENCY ........................................................................ 1. INTRODUCTION ...................................................................................................................... 2. DATA AND PERFORMANCE OF THE ORIGINAL BOOSTER ....................................... 3. DESIGN OF A SYSTEM WITH INCREASED PERFORMANCE ...................................... 3.1. Design of the New System ............................................................................................... 4. ADVANTAGE OF THE NEW SOLUTION REGARDING AIR SAVINGS ....................... 5. DYNAMIC SIMULATION .......................................................................................................

138 138 140 141 143 148 149

CHAPTER 9 CONCLUSION .............................................................................................................. 153 CONCLUSION ............................................................................................................................... 153 REFERENCES ........................................................................................................................................ 156 APPENDIX 1 ........................................................................................................................................... A1. ENERGY CONTENT OF AN AIR RESERVOIR ............................................................... A1.1. Description of the System ............................................................................................. A1.2. Mechanical Work by Expansion ...................................................................................

158 158 158 158

APPENDIX 2 ........................................................................................................................................... A2. MECHANICAL FORCES AND ENERGETIC PROPERTIES OF THE 100 MM LINEAR CYLINDER ASSEMBLY ............................................................................................. A2.1. Introduction ................................................................................................................... A2.2. Quasi-Static Behavior of the new Assembly ................................................................

161 161 161 161

SUBJECT INDEX .................................................................................................................................... 166

L

PREFACE In the context of the many challenges to society related to energy and environmental issues, the utilisation and the storage of electrical energy appear at a front level of needed industrial developments, accompanied by academic research and other investigations. The technology of compressed air is a simple and reliable technique widely used in the sector of industrial handling and actuators but has recently become an attractive means for energy storage in different forms. The main argument behind the use of compressed air energy storage is given by the use of simple mechanisms issued from reversible physics in comparison to electrochemical principles, where the calendric and cycle ageing mechanisms have been the centre of questions for many years. The question of recycling elementary materials is another aspect related to the battery industry and public services. Regarding the sustainability aspects of the use of energy, the general question of efficiency is now the centre of many considerations worldwide, and more and more studies and comparisons are made at the system level, where the different individual or cascaded energetic transformations are evaluated. A strong example comes from the automotive sector, where the classic ICE (Internal Combustion Engine) vehicles with their reservoirs are compared to Hydrogen powered vehicles with fuel-cells, or further with BEV (Battery Electric Vehicles). Back to the technique of compressed air, the industrial world uses from long time pneumatic actuators for their simplicity, reliability and low costs. But regarding the energetic balance, this technology presents, in its actual form, many disadvantages that can be qualified as energetic aberrations. And the use of pneumatic devices for the transformation from compressed air energy to mechanical and electrical power must be reconsidered. This book tries to give answers to the questions of the energetic efficiency of pneumatic devices and tries to use new arrangements for an application to energy storage. When speaking about energy storage, the question of the reversibility of the transformations or energy flows is also addressed. Even when the actual or classical industrial pneumatic devices are not foreseen for an operation as compression stages, the principle of using them as such is considered, and will need adaptations of those devices, especially at the level of their sealing elements. The compressed air energy storage principle is used in the industrial world in the form of air reservoirs used as buffers feeding the pneumatic actuators and motors. Here the buffering function serves to power devices with a strong flow of pneumatic energy, and normally, pressure regulating valves are rarely used. But several proposals are made in the sense of using compressed air stored at a higher level of pressure and with an adaptation element to the application. The properties of such pressure reduction elements are also discussed in this book. Further in the direction of realizing compressed air energy storage, a low pressure storage system called the underwater compressed air energy storage (UWCAES) is described and represents one of the ways for storing energy and using pneumatic converting elements for which the actually used pressure level fits the UWCAES system.

Alfred Rufer Ecole Polytechnique Fédérale de Lausanne (EPFL) Lausanne, Switzerland

Semi-rotary and Linear Actuators, 2023, 1-8

1

CHAPTER 1

Introduction and Summary Abstract: The motivation for the use of compressed air as an energy carrier and as a storage means for many industrial applications resides in the simplicity and low-cost conditions of its implementation. However, conventional pneumatic technology suffers from a very low energetic efficiency even if the production, use and recycling of the components can be said to be environmentally friendly, and it does not use problematic materials. This introductory chapter positions pneumatic technology and discusses a possible extension of the applications to the sector of energy storage in a general manner. The chapter gives the historical background of the presented developments of the book and gives an overview of the content of the document.

Keywords: Energy storage, Efficiency, Low pressure storage, Pneumatic actuators, Pumped hydro, Battery energy storage, Ageing effects. 1. INTRODUCTION During the second half of the 20th century, many questions arose about the availability of fossil energy resources and about the greenhouse gas emissions linked to their combustion. These questions have prompted several efforts in the development of alternative energy sources, mainly photovoltaic systems and wind energy. The intermittent nature of these sources linked to day-night alternation and seasonal or weather conditions has triggered new developments downstream in the sector of energy storage technologies. As a complement to well-established storage facilities like pump-turbine hydropower plants, battery energy storage systems can be considered very well suited for supporting decentralized power producers. Successive iterations of battery technology have shifted battery applications from the older lead-acid or nickel-cadmium or nickel-metal-hydride cells to the new lithium-ion technique, which features higher energy and power densities and allows the realization of applications under much better economic conditions. Alfred Rufer All rights reserved-© 2023 Bentham Science Publishers

2 Semi-rotary and Linear Actuators

Alfred Rufer

Generally, for electrochemical batteries, the question arises of the materials available in the future if their development evolves in the direction of very large volumes. The particularly concerned areas of future electrical systems are distributed generation and electrical mobility. Not only the material resources available but also the indirectly related topics of the global life cycle and aging phenomena are becoming increasingly important, as well as the still open questions on the recycling of all components and materials used in the manufacture of an electrochemical accumulator. In the context of sustainable energy strategies, several alternative solutions for energy storage are investigated as technologies based on reversible physics like mechanical or thermodynamic principles. Compressed air energy storage (CAES) can be considered a potential solution, using only standard materials and established technology. Additionally, and in opposition to the electrochemical batteries, these systems can be repaired or refurnished, offering unbeatable longer life cycles. Another advantage of CAES is that their materials are not problematic for recycling [1 - 4]. The development of CAES systems includes the development of highperformance compression and expansion machines and must comply with the elementary rules of thermodynamics. By many different development projects, the focus has been set on isothermal compression and expansion [5 - 7], with the goal to reach the highest possible efficiency. Also elementary conversion means based on classical pneumatic equipment have been proposed, where the operating principle has led to limited performance. If the classical pneumatic devices are generally classified in the category of low efficiency devices, they present the advantages of limited costs. Regarding their efficiency, several solutions have been proposed, such as adding an expansion chamber to the original displacement volume in order to recover a significant part of the fluid’s enthalpy [8 - 10]. For the same category of classical pneumatic devices, the normal operating pressure is in the order of tens of bars. Using them in the context of CAES will have the consequence of strongly limiting the system’s energy density if the storage reservoir is designed for the same pressure level as the pneumatic converters. However, one possibility exists where the storage pressure is of limited value. This is the so-called Under Water CAES, where the reservoir consists of immerged bags with a highly deformable volume. Such systems can be

Introduction and Summary

Semi-rotary and Linear Actuators 3

placed underwater at an immersed depth of one or two hundred meters, leading to a storage pressure compatible with the low pressure of classical conversion devices [11 - 12]. Another advantage of UWCAES is that they can be operated under constant pressure for the whole range of their storage capacity. Last-but-not-least, the specially designed energy bags for UWCAES have the property of needing only very low energy for their realization, leading to storage equipment with very low grey energy [13]. In this book, proposals are made for the enhancement of the energy efficiency of systems based on classical industrial pneumatic devices used in energy storage based on low pressure. The main contributions concern the expansion process, where linear and rotational actuators are used as prime movers of an electric generator. Then, with the aim to use the same components in the compression process, the reversibility of the components and systems is analysed and measured. Regarding the use of vane-type rotational actuators, the enhancement of efficiency is proposed for an original system called the Gallino system, where an oscillating angular actuator drives the generator with the help of a so-called motion rectifier [14 - 15]. The main contribution concerns the pneumatic to mechanic conversion, where in addition to the classical displacement work of the actuators, an expansion volume is added to the system allowing to recover an important part of the primarily injected enthalpy. Additionally, the influence of a pressure regulation valve on global efficiency is discussed. Such a valve is used in the Gallino system as a pressure reduction element between the storage reservoir and the pneumatic actuator. Because the motion rectifier in the Gallino system does not allow the reversibility of the power flow, a solution for the interface between angular actuators and the electric generator is proposed. This solution is based on a crankshaft and connecting rod assembly. A two-channel system with two 90° shifted actuators is proposed, allowing low speed operation and starting from any angular position. Then, the study describes a generator drive using classical linear pneumatic cylinders. First, the operation and energetic performance of a single cylinder is simulated and calculated. In this system, the back-and-forth movement of the piston is transmitted to the generator through a classical crankshaft.

4 Semi-rotary and Linear Actuators

Alfred Rufer

The kinematics of the crankshaft and connecting rod imposes a non-symmetric movement of the piston in the back and in forth motion, leading to different expansion works and displacements for the double-acting cylinders. This effect is the next motivation to analyse two different possibilities for the connection of the additional expansion cylinders. The behaviour of a two-cylinder system with a 180° crankshaft is first simulated, where the displacement and expansion volumes of the cylinders are on the same sides of the pistons. Second, a system with a 0° crankshaft is simulated where the expansion volume is on the opposite side of the displacement volume. The different forces, torques, mechanical power and converted energy are compared. The energetic performance of the enhanced linear system is also calculated. Finally, the principle of adding an expansion chamber is applied to conventional linear pneumatic cylinders. The principle allows increasing the poor energetic performance of the classical pneumatic cylinders which are intensively used in industry. The proposed solution represents a much cheaper solution in comparison with modern approaches that try to use electromechanical actuators instead of pneumatic ones. 1.1. Historical Background of the Development: The System Gallino Gianfranco Gallino, a brilliant inventor from southern Switzerland has developed and patented an original diving lamp, using the same cylinders as the breathing air as the energy reservoir. The conversion of energy from its pneumatic form into electrical power for the light bulb is accomplished by a pneumatic angular actuator driving an electrical generator. The oscillating movement of the actuator is transformed into a unidirectional rotation for the generator through a so-called motion rectifier [14 - 15]. Fig. (1.1) shows the patented system of Gallino with its main components as the high-pressure air bottle, the pneumatic actuator with the motion rectifier, the electric generator and the conversion circuits for the powering of the bulb.

Introduction and Summary

Semi-rotary and Linear Actuators 5

Fig. (1.1). The patented system proposed by Gianfranco Gallino [14].

A more detailed technical description of the Gallino system is given in Fig. (1.2), where the used components are represented through functional symbols. V1b r1 AX1

Not inverting (belt)

M1

FW1

Inverting (gear) FW1

Gen

P2

Pin AX2

PRV V1a Free-wheeling clk.-w.

Fig. (1.2). Schematic diagram of the Gallino system.

Free-wheeling c. clk.-w.

6 Semi-rotary and Linear Actuators

Alfred Rufer

At the left side of Fig. (1.2), the air reservoir is connected to a pressure reduction and regulation valve (PRV), which adapts the pressure of the air at the level of the reservoir to the operating pressure of the vane-type angular actuator. This actuator consists of two working chambers, fed alternately by pressurized air through the control valves. The alternating motion of the actuator is then transformed into a unidirectional rotation with the help of a motion rectifier [15]. The motion rectifier is made up of two motor trains, the first being of the non-inverting direct type, made with a toothed belt. The second train is an inverter train comprising two gears. Both trains are driven from the input shaft in their respective directions by two freewheel devices working clockwise and counter clockwise, resulting in a shaft of unidirectional rotation output. This output shaft is connected to the electric generator via a simple multiplier gear in order to achieve a sufficiently fast speed for the generator. 1.2. Contents of the Book In the second chapter of the book, elementary mechanisms and principles of compressed air technology are presented. For the compression and expansion processes, the physical principles according to adiabatic, polytropic and isothermal characteristic curves are described. The conditions of using compressed air under good efficiency are discussed, as the effect of using pressure reduction valves, or simply the level of the operating pressure. CAES (Compressed Air Energy Storage) with low pressure is presented in its version of using UWCAES Underwater CAES using so-called energy bags. In the third chapter, the basic principle of increasing the efficiency of pneumatic devices is presented. Examples of devices and machines where the pneumatic content of the pressurized air is recovered through thermodynamic expansion are given. The fourth chapter of the book is dedicated to the application of the principle of adding an expansion chamber to the already presented Gallino system based on the use of semi-rotational pneumatic devices. The structure of the system and its operational principle are presented. The evolution of the volumes and the resultant pressure are calculated. Then the acting forces and the torque components produced by the tandem running devices are evaluated. The goal of this study is to evaluate the energetic performance of the new system. The new principle allows to increase the efficiency from around 0.35 to nearly 0.7.

Introduction and Summary

Semi-rotary and Linear Actuators 7

Then a comparison of performances is made by changing the expansion characteristics, including isothermal and adiabatic expansions. An experimental setup is described with its control circuits. The same principle of adding expansion work to displacement work is then investigated by realising both phenomena in one device only. During the first part of the stroke, normal constant pressure work is achieved. And after that, the intake valve is closed and additional expansion work is produced during the rest of the normal stroke. The different quantities, pressure, forces and torques are simulated. The main result is that, according to this principle, the same average work is produced but with a stronger variation. Additionally, the proposed drive is simulated in a specific way of operation with position sensors allowing a closed-loop control. Experimental results are collected from a small experimental set-up. In the last part of the chapter, the reversibility of the generator driven by semirotary actuators is studied. This study is realized in correlation with the application of compressed air energy storage where not only air expansion is demanded but also air compression. Even if the available commercial devices are not able to work as compression stages, a system architecture is proposed for maintaining the oscillating operation of the semi-rotary actuators without using a motion rectifier. In this architecture, the coupling of the actuators with the electric generator is achieved through a classical crankshaft and coupling rods. In the fifth chapter of the book, a pneumatic motor using linear cylinders is presented. The same principle of combining constant pressure displacement work and expansion work within additional chambers is applied. Two cylinders of different sections and identical strokes are coupled on a common crankshaft. The piston rods are coupled with a phase-shift of 180 degrees. According to the mathematical description of the crankshaft and piston rod system, the different torque components are calculated. Again, the energetic performance of the new two-cylinder system with expansion is compared to the performance of a classical drive with one cylinder and without expansion. The obtained energetic performances in terms of efficiency are identical to the results obtained from the system described in Chapter 4. Then, for this system using linear cylinders, the principle of realizing the displacement work and the expansion work in the same cylinder is applied. An experimental set-up is finally described together with its control circuits.

8 Semi-rotary and Linear Actuators

Alfred Rufer

In chapter six of the book, linear cylinders are studied in their application as linear actuators. For these applications, new cylinder assemblies are proposed where the same principle of combining displacement work and expansion work can be achieved. Two original architectures are proposed. In the first one, the assembly comprised four cylinders of identical volume. One of them is placed in the centre of the arrangement, and three others are placed around the first one. The stators of the cylinders are coupled mechanically, as also their moving parts. In this first system, the displacement work is realized within the central cylinder, and the expansion work is achieved through a transfer of the air into the three other cylinders placed around the first. For the second architecture, three cylinders compose the new assembly. One cylinder is used for the production of displacement work, and the two others are placed laterally to the first one. The expansion work is produced while transferring the air from the central one to the two lateral ones. In order to achieve a sufficiently high expansion factor, the volumes of the two lateral cylinders are higher than the volume of the central one. In this chapter, a specific parasitic effect is considered where dead volumes of the tubing and the valves introduce a parasitic effect of pre-expansion when the valves are operated. The consequence is a reduction of the globally produced mechanical work. The energetic advantages of the linear cylinder assemblies are presented as well as experimental results. In the seventh chapter, the parasitic effect of the pre-expansion phenomenon due to dead volumes is discussed in more detail. Chapter eight of the book gives a special application of the previously described principle, namely an application to a so-called gas booster driven by a pneumatic cylinder. The study evaluates the potential savings in pressurized air for an equivalent output work. Chapter nine of the book serves as a conclusion to the global study and newly proposed systems and principles.

Semi-rotary and Linear Actuators, 2023, 9-23

9

CHAPTER 2

Compressed Air Systems and Storage Abstract: The elementary principles related to compressed air are presented, describing the basic compression and expansion characteristics. The adiabatic, polytropic and isothermal phenomena are described together with the definitions of the energy content of a given volume. Different loss factors related to compressed air are enumerated together with the advantages and drawbacks of pneumatic technology. Then, the possibility of storing energy under low pressure conditions as the so-called Underwater CAES system is discussed. Such systems have the interesting property of being realized with a very low amount of grey energy.

Keywords: Adiabatic characteristic, Compression of air, Expansion of air, Energy content, Isothermal characteristic, Loss factors, Low pressure storage, Properties of energy storage, Polytropic characteristic, Pressure reduction valve, Underwater CAES. 1. THE PHYSICAL PRINCIPLES RELATED TO COMPRESSED AIR A compressed air energy storage system is based on elementary principles of thermodynamics [9]. According to the general scheme of compressed air energy storage, two main types of components are used, namely compression/expansion machines, where mechanical work is the main input vector, as well as storage vessels, where the mechanical work is equal to zero. The two types of components are represented in Fig. (2.1). Both components can be considered as separate control volumes and respond to the rate form of the First Law of thermodynamics.

Wi

Qe  me ˜ he  mi ˜ hi 

dU dt d

Alfred Rufer All rights reserved-© 2023 Bentham Science Publishers

(2.1)

10 Semi-rotary and Linear Actuators

Qe

Alfred Rufer

mi ˜ hi

Wi

Compression / expansion machine me ˜ he

Qe

Wi

mi ˜ hi

0

Reservoir me ˜ he

Fig. (2.1). Main components of a CAES.

Wi and Qe are the work and heat flows transferred to the gas from the external environment, mi and me are the input and exit mass flows, and he , hi are the corresponding specific enthalpies [J/kg].

The compression and expansion machine’s main function is to change the thermodynamic state of the gas inside the control volume, and further to maintain the input and exit flow rates. The reservoir itself is characterized by the absence of work transferred to the gas (= 0). The description of a compression machine is based on the assumption of the air being considered as an ideal gas (PV = mRT), and further on the basic relations for the work and the heat.

W

³ pdV

(2.2)

Compressed Air Systems and Storage

Semi-rotary and Linear Actuators 11

Q H c Ac (T  Tw )

(2.3)

Hc is the heat transfer coefficient, Ac is the cylinder surface area exposed to convection, Tw is the temperature of the surface area and T the instantaneous gas temperature. For a compressor, assuming steady state conditions where no energy is accumulated in the device, the following relation can be written as a combination of the First and Second Laws [16].

(  (1

W

T0  )Q  m ˜\ T

(2.4)

Where ψ is the flow energy defined by:

\

(h  h0 )  T0 (s  s0 )

(2.5)

h and s are the specific enthalpy and entropy, and the subscript 0 indicates that the properties are taken at reference temperature and pressure (T0 =20°C, po = 1bar). The exergy flow (usable energy) of the produced air stream is then expressed as:

X

m m[[h  h0  T0 (s  s0 )]

(2.6)

In the case of an ideal gas flow:

h  h0 s  s0

c p (T  T0 ) c p ln

T p  R ln T0 p0

(2.7) (2.8)

The air stream exergy can be split into two parts, the pneumatic part and the thermal part, as follows:

X

X ( pn )  X (th )

(2.9)

12 Semi-rotary and Linear Actuators

Alfred Rufer

Where,

X ( pn )

X (th )

p p0

m mR T0 ln mRT

(2.10)

§ T · m p ¨ T  T0  T0 ln ¸ mc T0 ¹ ©

(2.11)

The compression work can lead to various ratios between pneumatic and thermal parts, according to the various processes, e.g., isothermal, adiabatic or polytropic ones. The compressed air is stored in the reservoir, where further the thermal exergy can be dissipated by cooling down, leading to a decrease in the pressure [9]. The final pressure in the reservoir becomes:

p2

p

T0 T

(2.12)

The exergy of the compressed air in the reservoir after reaching the thermal equilibrium with the ambient can be obtained by integrating the recoverable exergy of the air stream after cooling down.

X ( pn )2

mR mRT0 ln mRT

p p2

X2

³

p p0

p § T0 · ¨ ¸ p0 © T ¹

p p2

X ( pn ))2dp

³

p p0

mRT0 ln

(2.13)

p § T0 · ¨ ¸dp p0 © T ¹

ª §p · p º § 1 · p2V ¨  ln( p2 )  1¸ m1RT0 «ln ¨ 2 ¸  0  1» © p2 ¹ ¬ © p0 ¹ p2 ¼

(2.14)

Isothermal compression and expansion represent the best conditions for storage

Compressed Air Systems and Storage

Semi-rotary and Linear Actuators 13

because the thermal energy exportation towards the external atmosphere allows, in addition to the high efficiency, a greater energy density inside of the storage vessel. As shown in Fig. (2.2), the phenomenon can be easily understood, from the example of a hand pump, with the orifice closed [9]. By adding a supplementary pressure of 1.5 bar, from a stabilized initial condition of 1 bar of pressure in a unity volume at 15°C, the piston will go down, reducing the volume to a new value of 0.5, while the temperature increases up to 101°C in totally adiabatic conditions (first step).

1 Adiabatic

F  F1

2.5

1

V

0.5

T

15qC

T

101qC

Isobaric

Po lyt

4

rop F  F1

P

2.5

V  0.5 T  101qC

4 F

P 1 V

0.77

T

51qC

Isobaric

Isobaric

Qe

Po

lyt

51qC

ic rop

T

ic

0.77

2 Qe

al

V

rm

the

Iso

P 1

F

Isobaric

P

V

P 1

F

Adiabatic

3

2 F  F1

P

2.5

V

0.4

T

15qC

Fig. (2.2). The basic compression and expansion cycle.

When in the second step, the thermal energy corresponding to the added mechanical work is exported through the external ambient air by new temperature stabilization at 15°C, the volume will be reduced again down to 0.4. The pressure is kept at the previous level of 2.5 bar. Then, by removing the additional pressure (third step), the piston comes up again, bringing the volume up to 0.77. During this expansion, adiabatic conditions would decrease the temperature down to −51°C.

14 Semi-rotary and Linear Actuators

Alfred Rufer

The temperature equalization (fourth step) will then increase the volume from 0.77 up to its initial value of 1. The match of the initial pressure and temperature conditions indicates that the energy added by isothermal compression can be recovered by isothermal expansion. The energy efficiency is then ideally equal to 1. During isothermal compression, the internal energy of the cylinder has not been changed. This actually means that the energy is stored in the form of heat in the surrounding during compression and restored during expansion. The quality of heat transfer is, therefore, a key element for the performance of the storage process [17, 18]. 1.1. Adiabatic, Polytropic and Isothermal Compression and Expansion Adiabatic, Polytropic and Isothermal compression/expansion have different energetic properties and can be described by the elementary formulations as: Adiabatic

PV k = constant

(2.15)

Polytropic

PV n = constant

(2.16)

Isothermal

PV = constant

(2.17)

where n k

c p / cv

(2.18)

Compression: Significant energy is accumulated through increasing the gas pressure. In Fig. (2.3), the dark grey surface represents the spent energy for bringing the thermodynamic state of the gas from its initial volume Vi, to the final one Vf, when the compression is realized in isothermal conditions. The surfaces under the mid grey (polytropic) and light grey (adiabatic) curves are larger, and therefore the compression work is higher than under isothermal conditions. The adiabatically reached point (2) from state (1) corresponds to a state with increased temperature. After such compression, the cooling down to the initial temperature (as at point 1) brings the system to point (3), where the stored energy is identical to the energy accumulated by isothermal compression.

Compressed Air Systems and Storage

P Pf

Semi-rotary and Linear Actuators 15

(2)

(3)

adiabatic polytropic isothermal

(1)

Pi

Vi

Vf Fig. (2.3). Compression in adiabatic, polytropic and isothermal conditions.

Expansion: In Fig. (2.4), the dark grey surface represents the recovered energy from bringing the thermodynamic state from Vi to Vf when the expansion is realized in isothermal conditions. The surface under the mid grey (polytropic) and under the light grey (adiabatic) curves is smaller, and therefore the expansion work is smaller than under isothermal conditions.

P Pi

(3)

adiabatic polytropic isothermal

(1)

Pf

(2')

Vi

Vf

Fig. (2.4). Expansion in adiabatic, polytropic and isothermal conditions.

The adiabatically reached point (2’) from state (3) corresponds to a state with decreased temperature. After such an expansion, the heating up of the gas to the

16 Semi-rotary and Linear Actuators

Alfred Rufer

initial temperature (as at point 3) brings the system to point (1), where the remaining energy is identical to that resulting from an isothermal expansion [9]. 2. ADVANTAGES AND DRAWBACKS OF CLASSICAL PNEUMATIC DEVICES The Gallino system presented in section 1.2 is a very compact assembly, allowing to power a diver lamp from the compressed air bottle where a significant amount of energy is stored. The presence of a pressure reduction valve allows to use compressed air driven actuators designed for low pressure. Another advantage of industrial air driven actuators is that they exist in a very wide range of sizes and powers, as well as in their rotary and linear execution. This widely spread technique has been optimized over decades, reaching high reliability, and last-bu-not least, these devices benefit from very low prices due essentially to the very high volume of production. The vane-type rotary actuator used in the Gallino system is a pneumatic-tomechanical converter whose particularity is to extract energy within a limited space, meaning that no external space is needed for any crankshaft or connecting rod, neither any emerging piston shaft while expanding. 2.1. Energy Loss due to the use of a Pressure Reduction Valve The energy density of CAES is increased using a higher storage pressure. This leads to the use of complex and heavy compression and expansion equipment. For the compression device, multistage compressors can be used, and the storage reservoir must be designed in consequence. For the inverse conversion (the expansion), cylinders or expansion stages are often used where their operating pressure is reduced. Between the storage reservoir and the expander, a pressure reduction valve (PRV, Fig. 2.5) must be used. This component has a consequence on global energy efficiency. In Fig. (2.5), the converting element from pneumatic to mechanical energy at the output is a conventional pneumatic actuator. Such devices usually operate at constant low pressure, which also has a consequence on the conversion efficiency, as discussed in the next section. Let us first consider the effect of the use of a PRV valve on the usable energy in the discharge process.

Compressed Air Systems and Storage

Semi-rotary and Linear Actuators 17

P P1 P1

P2 PRV

E1 W2 W2d

P2 Pa

V1

V2

V

Fig. (2.5). Use of a pressure reduction valve between reservoir and expander.

The P-V diagram in Fig. (2.5) shows the different quantities of energy to be recovered from a reservoir at a pressure P1 in a volume V1. The maximum amount of energy is noted with E1, and corresponds to the expansion energy from P1 down to the atmospheric pressure Pa under isothermal conditions. This value can be calculated as

E1

§ P1 P · PV 1 a ¸ 1 1 ¨ ln P1 ¹ © Pa

(2.19)

W2 is the mechanical work produced with the cylinder while the pressure is maintained constant through the PRV valve. It is calculated through: W2

( P2  Pa ) ˜ (V2  V1 )

(2.20)

For the calculation of the effect of the PRV valve alone, it must be considered that the energy conversion at constant pressure in the cylinder is completed by an expansion process that uses the rest of the energy amount available. The last surface W2d of the diagram in Fig. (6.13) is then considered in the efficiency calculation. This last surface corresponds again to an isothermal expansion from P2 down to Pa and is equal to:

W2 d

§ P2 P · PV 1  a ¸ 2 2 ¨ ln P2 ¹ © Pa

(2.21)

18 Semi-rotary and Linear Actuators

Alfred Rufer

Finally, the efficiency of the discharge process while using a PRV valve can be estimated through:

K

W2  W2 d E1

(2.22)

Fig. (2.6) shows the influence of the use of a pressure reduction valve on the discharge process from a reservoir at P1 = 300 bar. The equivalent efficiency factor is given through rel. 2.22. 2.2. The Poor Energetic Performance of the Classical Pneumatic Actuators In a classical pneumatic actuator, mechanical work is obtained from the displacement of the piston under constant pressure. At the end of the stroke, the pressure in the fully deployed cylinder is released into the atmosphere by opening the exhaust valve, allowing the free return of the piston. This corresponds to renounce the pneumatic energy content inside the cylinder. The pneumatic energy content of the deployed cylinder can be illustrated by the W2d surface in the diagram of Fig. (2.5). In other words, it corresponds to the expansion energy of a V2 from a P2 pressure. A corresponding efficiency or energy loss factor can be defined as:

K pneum _ act

W2 W2  W2 d

(2.23)

K (efficiency)

1.0 0.8 0.6 0.4 0.2

1

50

100

150

200

PRV output pressure [bar] (Preservoir = 300 bar)

Fig. (2.6). Equivalent efficiency due to the PRV valve.

250

Compressed Air Systems and Storage

Semi-rotary and Linear Actuators 19

The energy loss factor of the classical pneumatic actuator is represented in Fig. (2.7). This diagram shows that such actuators can only be designed for pressure levels under 50 bar. The energetic performance is still very poor. 3. COMPRESSED AIR ENERGY STORAGE WITH LOW PRESSURE THE UNDERWATER CAES The studied pneumatic actuators are characterized by their low pressure. Consequently, storage means with similar pressure conditions must be chosen. An interesting solution has been proposed recently with the concept of immerged Energy Bags [11, 12]. This principle utilizes an immerged variable volume for the storage of compressed air. The intent of the submerged installation is to use the surrounding hydrostatic pressure for compensation of the pressure of the stored air, with the advantage of highly reducing the requirements of the vessel’s structure. The function of the Energy Bag is reduced to providing a membrane boundary between air and water. In the system represented in Fig. (2.8), the compression/expansion station is on shore and the pressurized air is fed down to the Energy Bag through a pipe.

Kpneum_act (efficiency)

1.0 0.8 0.6 0.4 0.2

1

50 100 150 Operating pressure [bar]

Fig. (2.7). Energy loss factor of a classical pneumatic actuator.

200

20 Semi-rotary and Linear Actuators

Alfred Rufer

Compression /expansion station

Distendable underwater enegy bags Anchorage to the sea- or lakebed Fig. (2.8). Underwater CAES system using Energy Bags.

Due to the Archimedes principle, the immerged volume undergoes a buoy effect that needs strong anchoring to a sufficient heavy ballast. The Energy Bags can be realized as scalable and flexible reservoirs as described in [18]. Other inflatable buoying systems used for underwater lifting can be easily adapted. 3.1. The Model of the Storage Infrastructure The energy bag or other expandable reservoirs can be modelled according to the scheme of Fig. (2.9). The compression/expansion machine is a high-performance machine achieving compression/expansion under isothermal conditions. In Fig. (2.9), the compression and expansion machines are represented separately, but a reversible volumetric machine can also be used. In dependency on the depth of the energy bag, multiple stage compression/expansion equipment must be used. The storage reservoir can be modelled as an expandable reservoir undergoing constant pressure. The pressure related to the immersion depth of the energy bags depends on the atmospheric one and the gravimetric pressure of the water.

Compressed Air Systems and Storage

Semi-rotary and Linear Actuators 21

Pabs M

G Fig. (2.9). Model of the UWCAES.

The pressure around the bag is given by:

Pabs

Patm  U ˜ g ˜ h

(2.24)

Where, ρ is the density of the water (1.025 for sea water) and g is the standard gravity h is the depth of the bag The energy amount that is stored in the underwater bag corresponds to the sum of the work realized by the volume variation under constant pressure Wdispl and of the energy content of the corresponding volume being expanded under isothermal (or polytropic) conditions of the compression/expansion machine E as defined in rel. 6.1.

Etot

Wdispl  Eexp an

ª §P · P º Pabs ˜V1  Pabs ˜V1 «ln ¨ abs ¸  1  a » Pabs ¼ ¬ © Pa ¹

(2.25)

From rel. 2.25, it is easy to calculate the energy density euw of the UWCAES. The value of euw in dependency of the depth is represented in Fig. (2.10).

22 Semi-rotary and Linear Actuators

Alfred Rufer

6

Energy density [kWh/m3]

5 4 3 2 1 50

100

150

200

250

300

350

400

450

500

Depth [m]

Fig. (2.10). Energy density of the UWCAES.

The UWCAES can be evaluated regarding the needed volume for the storage of an amount of 1MWh of energy and in dependence of the depth of immersion (Table 2.1). Table 2.1. Volume of the storage vessel. Immersion depth Volume of the UWCAES

h = 50 m

h = 100 m

h = 200 m

h = 500

3125 m

1428 m

555 m

234 m3

3

3

3

3.2. Examples of UWCAES Realizations Fig. (2.11) shows a prototype energy bag realized by “The Red Line Aerospace” for the University of Nottingham [12].

Fig. (2.11). Thin Red Line Aerospace Energy Bag designed and fabricated for the University of Nottingham UWCAES.

Compressed Air Systems and Storage

Semi-rotary and Linear Actuators 23

Another class of solutions for UWCAES can be found in the underwater lifting industry, where large lifting bags or cushions can be found Fig. (2.12).

Fig. (2.12). Underwater lifting systems (courtesy High Point La Rochelle).

24

Semi-rotary and Linear Actuators, 2023, 24-33

CHAPTER 3

Increasing the Energetic Efficiency of Pneumatic Devices Abstract: The chapter presents the main principle on which the proposals of this book are based. In this principle, the energetic efficiency of pneumatic actuators is strongly increased by adding an amount of expansion work to the classical work produced by constant pressure displacement. Such a principle has already been applied in steam machines at the beginning of the 20th century or in existing pneumatic converters used as motors for automotive vehicles.

Keywords: Constant Pressure Displacement Work, Expansion Work, The Truglia Motor, Compressed Air Car. 1. RECOVERY OF THE PNEUMATIC ENERGY In Section 2.3.2, the pressure-volume diagram related to the recovery of pneumatic energy is shown in Fig. (3.1) and the elementary principle is described.

P P1 P1

P2 PRV

E1 W2 W2d

P2 Pa

V0

V1

V2 V

Fig. (3.1). Energy recovery of the pressurized air.

In the case of the operation of a classical pneumatic cylinder, the mechanical work is produced only by the displacement of the piston under the condition of a constant pressure P2. At the end of the stroke, the pressurized air is released to the Alfred Rufer All rights reserved-© 2023 Bentham Science Publishers

Efficiency of Pneumatic Devices

Semi-rotary and Linear Actuators 25

external by opening an exhaust valve. In order to increase the resultant efficiency, the pressurized air of the cylinder’s chamber should be expanded within an additional step of the process. For such an expansion, two categories of principles will be described. For the first category, the constant pressure displacement and the expansion of the air occur in the same volume or in the same cylinder. Fig. (3.2a) illustrates this principle where the V1 volume corresponds to the volume with constant pressure and the sum of V1 and V2 to the volume of the expanded air. The change between the constant pressure work and the expansion is controlled by closing the intake valve when a volume V1 of air has been intaken. The principle of expanding the fluid had already been applied in steam machines at the beginning of the 20th century with the goal of reducing the consumption of steam [19]. A more recent example of such a process is given by the principle of the so-called Truglia motor [20]. The operation principle of the Truglia motor will be described in Section 1.1.

V1

V2

V1

V2 a)

b)

Fig. (3.2). Adding an expansion volume a) in the same cylinder, b) in an additional cylinder.

In the second category, the constant pressure displacement is realized in a first cylinder, and the expansion of the air is realized through a transfer of the air into a second cylinder Fig. (3.2b). This principle has been used for the MDI motor of the compressed air car [21]. This principle will be described in section 3.1.2. In this second category, the principles of sequential and reciprocating strokes will be discussed. The MDI motor is a sequential strokes machine (Section 3.1.2), the other principle of the reciprocating strokes is presented in a short way in Section 3.1.3. Further, this principle will be analyzed in more detail through two applications in Chapter 4 and 5. The first of these applications corresponds to improving the efficiency of vane-type rotary actuators. The second application corresponds to a pneumatic motor realized with two double effect linear actuators.

26 Semi-rotary and Linear Actuators

Alfred Rufer

1.1. Operating Principle, Defaults and Improvements of the Truglia Motor The pneumatic motor invented by Vito Truglia uses a classical base of an ICE motor, pistons, and crankshaft, together with all auxiliaries and a mechanical transmission system. Only the upper part, namely the cylinder-head is modified with its distribution components. The three main components of the Truglia motor cylinder-head are first an inlet valve controlled by the piston itself in the position around the upper dead center. Second, an exhaust valve controlled by a specific cam tree. The opening of the exhaust valve is done between the lower dead center and the opening of the inlet valve, allowing the exhaust of the expanded air. Finally, an anti-return valve is integrated into the cylinder-head in order to avoid the production of a negative torque when the expansion of the air reaches a level under the atmospheric pressure due to low inlet pressure. Fig. (3.3) shows the three valves of the Truglia motor.

a)

b)

c)

Fig. (3.3). The three specific valves of the Truglia motor a) Inlet valve, b) Exhaust valve, c) Anti-return valve

The position of the piston and the openings and closings of the valves are indicated in Fig. (3.4). In this figure, the horizontal axe corresponds to the time, under the condition of a mechanical frequency of 31.4 rad/s. The period of the piston cycle is equal to 200 ms.

Efficiency of Pneumatic Devices

Semi-rotary and Linear Actuators 27

Level of hit of intake valve Position of the Piston [cm]

Intake Exhaust

Fig. (3.4). Control of the original Truglia motor. Position of the piston (cm), intake and exhaust valve control signals, Time (s).

In its original version, the Truglia motor is characterized by two main defaults. First, the opening of the inlet valve occurs before the piston reaches its Upper Dead Center (UDC). The time position of the UDC is at t=0.2 s. The early opening causes a negative transient of the torque, as can be seen in Fig. (3.5). The pressure in the cylinder of the original Truglia motor is represented in Fig. (3.6), with an inlet pressure of 16 bar.

Fig. (3.5). Torque developed by one cylinder of the original Truglia motor (Nm), Time (s).

28 Semi-rotary and Linear Actuators

Alfred Rufer

Fig. (3.6). Pressure in the cylinder of the original Truglia motor (N/m2), Time (s).

A first modification of the inlet angle to a position corresponding to the UDC can improve the behaviour of the motor, as can be shown in Figs. (3.7) and (3.8).

Fig. (3.7). Pressure in the cylinder with delayed inlet angle to the position at the UDC (N/m2), Time (s).

Efficiency of Pneumatic Devices

Semi-rotary and Linear Actuators 29

The result of this modification on the developed torque is shown in Fig. (3.8). The negative component of the torque has disappeared.

Fig. (3.8). Torque developed with an inlet angle corresponding to the UDC (Nm), Time (s).

The role of the anti-return valve in the cylinder-head of the Truglia motor is illustrated in Fig. (3.9), where the torque developed with an inlet pressure of P1 = 10 bar is shown. The volumetric expansion factor of the cylinder is given by the ratio of the volume V1 (at the limit of the constant pressure displacement work) and the volume V2 (reached after complete expansion at the Bottom Dead Centre (BDC).

Fig. (3.9). Torque developed with an inlet pressure of 10 bar and limited at zero thanks to an anti-return valve (Nm), Time (s).

30 Semi-rotary and Linear Actuators

Alfred Rufer

With a value of 16 for the expansion factor, the lower value of the pressure after expansion would reach the value of: P2 = P1/16 = 10/16 = 0.62 bar This value is under the value of the ambient pressure (present at the lower side of the piston) and would produce a negative value of the torque. The anti-return valve avoids the pressure to come under the value of the atmospheric pressure Fig. (3.10).

Fig. (3.10). Pressure in the cylinder with an inlet pressure of 10 bar and with the presence of an anti-return valve. (N/m2), Time (s).

1.2. Expansion in a Separated Chamber with Sequential Strokes (The MDI Motor) The principle of combining the constant pressure work and the expansion in the same volume makes the control of the valves more complicated and asks for good accuracy. In a different concept, an additional expansion cylinder is coupled to the displacement cylinder through a specific mechanism able to produce a succession of intake and expansion according to a defined sequence. The principle of the MDI motor is represented in a simplified way in Fig. (3.11), where the displacement/expansion cycle is decomposed in four steps noted as:

Efficiency of Pneumatic Devices

Semi-rotary and Linear Actuators 31

A: Filling of the main cylinder with air at constant pressure Pin B: Expansion due to an air transfer from V1 to V1 +V2 C: Exhaust and; D: return to the initial state. V1 A

Reservoir

Filling V1

B

D

V1 C V2 Exhaust V1 --> 0 V2 --> 0

Expansion from V1 to V1+V2

Fig. (3.11). Principle of the MDI motor with « active chamber ».

The complex movements of the two pistons according to an adapted sequence are realized by using a specific mechanism. Fig. (3.12) shows the coupling mechanism and the two pistons of an MDI motor [21].

Fig. (3.12). The two pistons of the MDI motor with its coupling mechanism (Courtesy MDI).

32 Semi-rotary and Linear Actuators

Alfred Rufer

The mechanism illustrated in Fig. (3.12) imposes the sequential movement of the two pistons according to the diagram given in Fig. (3.13). One can see that the intake stroke of the first piston (load piston in the diagram) is ahead of the expansion stroke of the second piston, while the exhaust phase of the motor occurs when the two pistons move simultaneously upwards to their Upper Dead Centers (PMH in the diagram).

Fig. (3.13). Movements of the two pistons (sequential strokes) (Courtesy MDI).

The main advantage of using the sequential stroke principle is that the system of control valves of the motor is simplified. Effectively, no transfer valve is represented in Fig. (3.12); only intake and an exhaust valves are needed. The air transfer from V1 to V1+V2 is automatically achieved by the dynamics of the pistons. 1.3. Expansion in a Separated Chamber with Reciprocating Strokes The principle of the expansion in a separated chamber with reciprocating strokes is represented in Fig. (3.14). The two cylinders are of the double acting type and are coupled to a crankshaft with 180° shifted pins. The alternative movements of the pistons can generate strokes of displacement at constant pressure during intake into the small cylinder, as well as an expansion of the air during the transfer from the small cylinder to the larger one in the following stroke. This principle can be applied to linear cylinders (Chapter 5), but also to coupled vane-type rotary actuators, as will be explained in Chapter 4.

Efficiency of Pneumatic Devices

Semi-rotary and Linear Actuators 33

V1a

V1b

V2a

V2b

Fig. (3.14). Principle of the expansion in a separated chamber with reciprocating strokes.

34

Semi-rotary and Linear Actuators, 2023, 34-74

CHAPTER 4

Coupling Two Rotary-Type Actuators Abstract: This chapter presents the first example of the combination of two actuators of different volumes with which the principle of adding an expansion work can be realized. The two semi-rotary actuators are mechanically coupled and describe an oscillatory motion. Then the oscillatory motion is transmitted to an electric generator through a so-called motion rectifier. The structure of the new system is presented with the control valves and control circuitry. The different variables of the system as pressure, torques, and mechanical work are calculated by simulation. The efficiency of the new system is calculated and compared with the efficiency of a single actuator without expansion. The principle of adding an expansion work with semi-rotary actuators is then presented but with one actuator only where the expansion occurs in the same and unique chamber. Efficiency, torque waveform and produced mechanical work are presented, as well the control circuits. The power reversibility of a system using semi-rotary actuators is addressed, and a solution with a crankshaft is studied.

Keywords: Adiabatic and Isothermal Expansion, Expansion Work, Power Reversibility, Semi-rotary Actuators, Torques. 1. CONTEXT AND MOTIVATION In the introduction (Chapter 1), the System Gallino was introduced. This airpowered diving lamp uses one rotary actuator for pneumatic to mechanical conversion. As was described, a so-called motion rectifier transforms the alternating movement of the actuator into a unidirectional rotative motion, driving an electric generator. The general principle is maintained in this chapter, but in order to improve the energetic efficiency, a second actuator of the same type but with a larger volumetry is directly coupled to the original one. The chambers of the vane-type machines are moving in a synchronous tandem operation. 1.1. Structure of the System Fig. (4.1) shows the global scheme of the proposed new system. As pneumatic to mechanical converters, vane type rotary actuators are used [21]. Such actuators Alfred Rufer All rights reserved-© 2023 Bentham Science Publishers

Coupling Two Rotary-Type Actuators

Semi-rotary and Linear Actuators 35

have an alternating rotary movement of 270°. In this concept, the two actuators are directly coupled, and their alternating movement is transformed into a fully rotating one using a mechanical motion rectifier, as will be described more in details in Section 4.1.3 After rectification, the output shaft is coupled to an electrical generator. V2b

V1b

Not inverting

M2 r1

M1 P2

AX1

FW1

r2

Inverting

FW1

Gen

P2

Pin

AX2

90 90

V1a

V2a Anti-return valves

Free-wheeling clk.-w.

Free-wheeling c. clk.-w.

Fig. (4.1). The concept of the compressed air driven generator.

The two vane-type rotary actuators have two active chambers each, corresponding to the volumes V1a and V1b, respectively V2a and V2b. The chambers V1a and V1b are fed alternatively by the input compressed air, and they produce torque contributions alternatively according to the two clockwise and anti-clockwise motions. 1.2. The Mechanical Motion Rectifier The wing-rotors of both actuators are mounted synchronously on the same shaft AX1 Fig. (4.1). This shaft transmits its alternating motion via two one-way (antireturn) roller clutches coupled to an inverting and a non-inverting gear to an output shaft AX2, resulting into a unidirectional full rotative motion [15]. From this output shaft, the motion goes to the electric generator via another multiplying gear. This additional gear is foreseen for an adaptation of the slow motion of the actuators to a sufficiently high rotational speed of the generator.

36 Semi-rotary and Linear Actuators

Alfred Rufer

1.3. Operating Principle The chambers V2a and V2b are fed from the exhaust air of the chambers of the first actuator. Volume V2a receives the exhaust air of the V1b chamber during the clockwise motion, and the volume V2b that-one of the V1a chamber during the anticlockwise one. Because of the different volumes of the chambers of the first and second actuators, the air-transfer from the chambers of the first actuator to thatones of the second-one corresponds to a real expansion of the transferred air, allowing so to recover a significant part of the internal energy of the compressed air. In the studied example, the volume ratio of the two actuators is chosen as V2/V1 = 3. The schematics of the system with its control circuits are represented in Fig. (4.2).

V2b

V1b

Motion Retifier

Gen

V1a V2a Xtr_ab

Xexh_b

Xtr_ba

Xexh_a

Xin_a

Xin_b X16b

+12 V

+12 V

Sign gen

220 VAC

0V

0V O°

Fig. (4.2). Control valves and control circuits of the system.

For the control of the different airflows, 6 valves are needed. First, the air is controlled between the supply reservoir and the chambers of the small actuator

Coupling Two Rotary-Type Actuators

Semi-rotary and Linear Actuators 37

(Xin_a and Xin_b). The control of the transfer of the air from V1a to V2b, respectively V1b to V2a, is controlled by the two transfer valves (Xtr_ab, Xtr_ba). Finally, the exhaust of the expanded air is released by the two exhaust valves (Xexh_a, Xexh_b). The diagram of Fig. (4.2) also shows the presence of two antireturn valves at the level of the air transfer lines. The purpose of these anti-return valves was explained in Chapter 3.1.1 with the example of the Truglia motor. In this example, the alternating frequency of the actuators is imposed by an external frequency generator. 2. SIMULATION OF THE SYSTEM In the next paragraphs, the system with two actuators is simulated in a simplified form. The motion of the two coupled devices is imposed and the six valves are controlled accordingly. The intake, transfers and exhaust phases last over the complete half-cycles, meaning from 0° to 270° in the clockwise motion and from 270° to 0° in the anti-clockwise one. The oscillation frequency is chosen as 1 Hz, or 0.5 s for each half period. The evolution of the volumes of the chambers of the actuators is indicated in Fig. (4.3a and b). Fig. (4.3a) shows the volumes of the two complementary chambers V1a and V2b, during the two half-periods (0 to 0.5s clockwise and 0.5 to 1s anticlockwise). Fig. (4.3b) shows the evolution of the two other chambers (V1b and V2a) for the same cycle. In addition, the yellow curve represents the equivalent expansion volume of the interconnected chambers V1b+V2a. During the first halfcycle, this last evolution corresponds to a real expansion, but in the second halfcycle, the volume decrease does not have any significant contribution to the torque, the exhaust valve being open. 2.1. Parameters of the System The principal parameters of the actuators can be read from [5], and they are given in a summarized form in Table 4.1. Table 4.1. Parameters of the two coupled actuators. Actuator type

CRB1-63

CRB1-100

Volume of chambers

118 cm

376 cm3

Torque (10bar)

22 Nm

75 Nm

Radius r

r1=0.025 m

r2=0.038 m

Surface of wing

S1=10 cm

S2=21 cm2

3

2

38 Semi-rotary and Linear Actuators

Alfred Rufer

a)

b) Fig. (4.3). Evolution of the volumes of the two actuators (cm3). Time (s). a) Volumes V1a and V2b. b) Volumes V1b, V2a and V1b+V2a

Coupling Two Rotary-Type Actuators

Semi-rotary and Linear Actuators 39

2.2. The Pressure Variation During the Expansion The pressure in the chambers of the small device is constant during the intake phases and corresponds to the value of the supply pressure. In the simulation, this value is chosen as 10 bar. Then, the air is expanded during the transfer from the chambers of the small device to the chambers of the larger one. The expansion of the air is supposed to be of the adiabatic type. The resulting pressure P2 in the chambers takes the value of: J

P2

§ V1max · Pin ¨ ¨ V  V ¸¸ © 1a ,b 2b,a ¹

with ɀ = 1.4

(4.1)

This expansion pressure appears simultaneously in the volumes V2a and V1b (first half-cycle) and in V2b and V1a (second half-cycle) as long as the c-w and a-c-w motions are not completed. At the end of the two motions, the volume ratio is equal to 118/376 = 0.31, and the corresponding pressure ratio becomes Pin/P2 = 0.19 according to rel. 4.1. In Fig. (4.4), the pressure P2 in the expansion volume V1b+V2a is represented (blue curve), together with the pressure in the inlet chamber of the first actuator (Pin) (red). While Pin is not changing during the motion of the wing, the pressure P2 is decreasing according to rel. 4.1.

Fig. (4.4). Pressures Pin (red) and P2 (blue) during the first half of the cycle (clockwise motion) (N/m2), Time (s).

40 Semi-rotary and Linear Actuators

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2.3. From the Pressure to the Torque Fig. (4.5) represents the evolution of the torque contributions of the first actuator during the first stroke (clockwise motion) occurring in the first half-period. These torque contributions are related to both sides of the wing. The V1a-side surface S1a is multiplied by the pressure Pin to obtain the acting force. Further, this force is multiplied by the corresponding radius r1 to get the M1a torque component. The effective surface and related radius are given in Table 4.1. This contribution is represented in red in Fig. (4.5). The V1b-side surface S1b is multiplied by the pressure P2 and further by the same radius r1 to obtain the M1b torque component (blue curve in Fig. (4.5)). M1 is obtained by subtraction of both components. This torque is represented in yellow in Fig. (4.5). The contribution of the second actuator in the first stroke (clockwise motion) is represented in red in Fig. (4.6) (M2). This torque results from the V2a-side contribution (effect of P2, P2 being the absolute pressure) and the V2b-side, where the pressure is equal to the atmospheric pressure. On the same figure, the torque contribution M1 of the first actuator is represented again (blue curve). Then, the total torque Mtot during the first half-period (yellow curve) is shown.

Fig. (4.5). Torque contributions of the first actuator (Nm), Time (s).

In Figs. (4.7) and (4.8), the torque contributions of the two actuators during the second half-period are represented. The waveforms are identical to that-ones of

Coupling Two Rotary-Type Actuators

Semi-rotary and Linear Actuators 41

Figs. (4.5) and (4.6). The positive sign of these torques for the second half period indicates that they are defined at the output of the motion rectifier.

Fig. (4.6). Torque contributions of the two actuators and total torque during the first half-period (Nm), Time (s).

Fig. (4.7). Torque contributions of the first actuator during the second half-period (Nm), Time (s).

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Alfred Rufer

Fig. (4.8). Torque contributions of the two actuators and total torque during the second half-period.

Finally, Fig. (4.9) shows the total torque during one complete period. Its average value is also represented.

Fig. (4.9). Total torque produced over one complete period (output of the motion rectifier).

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Semi-rotary and Linear Actuators 43

2.4. The Effect of the Anti-Return Valve When the inlet pressure of the cascaded actuators is below a critical level corresponding to the value of the atmospheric pressure multiplied by the pressure ratio of the expansion, the torque developed by the second actuator becomes negative (braking). In order to avoid this effect, the connecting line between the two exchanging volumes (for example, V1b and V2a during the clockwise motion) is equipped with an anti-return valve (Figs. 4.1 and 4.2). This anti-return valve allows the suction of air from the surrounding into the chamber where the pressure has reached the atmospheric level. This inlet of air at ambient temperature has additionally the role of warming up the chamber after the expansion. Fig. (4.10) shows the torque developed by the system with an inlet pressure equal to 2 bar.

a)

b)

Fig. (4.10). Torque developed by the system with an inlet pressure of 2 bar (Nm). a) Total torque and average value b) Torque contributions in the first half-period: M1 (blue), M2 (red) Total torque (yellow).

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2.5. Exhaust Temperature The expansions of the air in the two pairs of changing volumes, namely V1b+V2a in the first half-period and V1a+V2b in the second one, are producing a significant decrease in the temperature. In adiabatic conditions, this decrease is given by rel. 4.2. T2

T1

J 1

V2 / V1

with J = 1.4

(4.2)

The evolution of the temperature of the two expansion volumes is represented in Fig. (4.11). The curve represents the temperature of both expansion volumes, alternatively in the first half-period, respectively in the second one. The temperature is given in Kelvin (absolute temperature). In each volume, the temperature’s initial value is the atmospheric temperature (20°C or 293 K). The end-value after the expansions is equal to -88°C or 184 K. In the real case, the temperature does not reach this low value, due to the fact the actuator’s body and rotating wing are exchanging some heat with the air.

Fig. (4.11). Temperature decrease caused by the expansions.

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Semi-rotary and Linear Actuators 45

3. EFFICIENCY CONSIDERATIONS 3.1. Efficiency of the Coupled Actuators From the curves of Fig. (4.9), the output power, respectively, the mechanical energy produced by the two coupled actuators, can be evaluated. For this evaluation, the angular velocity of the rectified motion is calculated. During the 1second period of the pneumatic actuators, an angle of 270° is run in both directions. After the motion rectification, the output angle is equal to:

Mout

2 ˜ Mactuator

2 ˜ 270q 540q

(4.3)

The resulting angular velocity becomes:

Zout

2 ˜S

540 1 360 1s

2 ˜ S ˜1.5rad / s 9.42rad / s

(4.4)

Then, multiplying the angular velocity by the average value of the torque gives the average output power:

Pout

Zout ˜ M tot

av

9.42rad / s ˜ 40.5 Nm 381W

(4.5)

The transmitted mechanical energy becomes: Wout

Pout ˜ T

381W ˜1s 381J

(4.6)

The efficiency of the enhanced converter (two cascaded actuators) is calculated on the base of the produced mechanical work and the injected enthalpy into the system, namely: Kconv

Wout

+ in

Wout U  Pin ˜ 'V

(4.7)

U is the thermodynamic content of the injected air under pressure and is calculated as the energy needed for the compression into a volume V1 of the

46 Semi-rotary and Linear Actuators

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equivalent mass of air from the atmospheric pressure to the value of Pin, V1 being the filled volume of the first actuator during the total period.

U

Ecomp

§ P P · Pin ˜V1 ¨ ln in  1  atm ¸ Pin ¹ © Patm

(4.8)

The detailed calculation of rel. (4.8) is given in Appendix 1. Numerically, and considering the two half-cycles, U becomes: U

Ecomp

1bar · § 10bar 10 ˜105 N / m2 ˜ 2 ˜ 0.000118m3 ¨ ln 1  ¸ 331J 10bar ¹ © 1bar

Pin ˜ 'V

10 ˜105 N / m2 ˜ 0.000236m3

(4.9) (4.10)

236 J

The efficiency becomes: Kconv

Wout

+ in

381J 331J  236 J

(4.11)

0.67

This value corresponds to the enhanced efficiency of the actuator-based conversion where the transferred air is additionally expanded in a second chamber. This value can be compared to the poor efficiency of a system without additional expansion. In such a single actuator, the torque produced corresponds to: M1

M1th  M1atm

25.05 Nm  2.4 Nm

22.65 Nm

(4.12)

The corresponding efficiency becomes: Kconv

Wout _ single

+ in

M 1 ˜ Mout U  Pin ˜ 'V

22.65 Nm ˜ 9.42rad 331J  236 J

0.376

(4.13)

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Semi-rotary and Linear Actuators 47

3.2. Isothermal or Adiabatic The expansion of the air in the converter has been simulated in the previous sections under adiabatic conditions. It is well known that the expansion of the air being realized in isothermal conditions presents a higher performance. Even if the practical realization of an expansion system with isothermal conditions is very hard to achieve [5, 18, 24], this study tries to evaluate the efficiency performance of the system where such conditions would be given. In Fig. (4.12), the torque produced by the system with the two actuators operated in cascade as described in Fig. (4.1) is given. The blue curve is identical to the curve represented in Fig. (4.9) and corresponds to adiabatic expansion. Its average value is also represented (around 40.5 Nm). The red curve represents the torque developed in a similar system with isothermal conditions. Its average value is also given (46.3 Nm).

Fig. (4.12). Torque and average value under isothermal and adiabatic conditions.

The efficiency of the system with isothermal conditions is calculated on the base of the new average torque according to rel. 4.14:

Pout

Zout ˜ M tot

av

9.42rad / s ˜ 46.3Nm 436W

The efficiency calculated over one cycle (1s) becomes:

(4.14)

48 Semi-rotary and Linear Actuators

Kconv

Alfred Rufer

Wout

+ in

436 J 331J  236 J

(4.15)

0.76

In comparison to the result given in rel. 4.11 (0.67), the efficiency under isothermal conditions brings an increase of a factor 0.76/0.67 = 1.13 or 13%. Referred to the performance of a single actuator without expansion, the new system with an additional expansion volume in adiabatic conditions has a performance of: 0.67/0.375 = 1.78 or an increase of 78% Considering the same reference of the classical actuator, the new system with an additional expansion chamber in isothermal conditions has a performance of: 0.76/0.375 = 2.02 or an increase of 102%. 4.3.3 Considering the Friction in the Actuators To get a more realistic value of the conversion efficiency, the friction torque of the pneumatic actuators must be introduced. The identification of the friction torque has been described in [23]. According to these results, the value of the Coulomb friction torque alone is considered. For a general case, the friction torque is supposed to be equal to 10% of the rated torque of the actuator. For the single actuator, the effective torque is given by: M 1e

M 1  M 1 fric

0.9 ˜ 22.65 Nm

20.38 Nm

(4.16)

Then, taking into account the friction, the efficiency becomes: Kconv

Wout _ single_eff

+ in

M1e ˜ Mout U  Pin ˜ 'V

20.38 Nm ˜ 9.42rad 331J  236 J

0.338

(4.17)

For the cascaded actuators, the effective torque is equal to the average torque minus the friction of both individual actuators:

Coupling Two Rotary-Type Actuators

M tote

Semi-rotary and Linear Actuators 49

M totav  M fric _1  M fric _ 2

(4.18)

40.5 Nm  0.1˜ 22 Nm  0.1˜ 75 Nm 30.8Nm Poute

Zout ˜ M tot

e

9.42rad / s ˜ 30.8 Nm

290W

(4.19)

Finally, the efficiency becomes for the 1s cycle: Kconv

e

Woute

+ in

290 J 331J  236 J

0.51

(4.20)

4. EXPERIMENTAL SET-UP In Fig. (4.13), a small experimental set-up is represented. On the left side of the figure, the electrical generator of the output is represented. On the right side, the prime mover composed of the two cascaded angular actuators can be shown. On top of them, the electromagnetic distribution valves are mounted. In the middle of the figure, the motion rectifier can be seen. This part can be observed with more details in Fig. (4.14). The two cascaded angular actuators are shown in Fig. (4.15).

Fig. (4.13). The small power demonstration system.

Fig. (4.14). Details of the motion rectifier.

50 Semi-rotary and Linear Actuators

Alfred Rufer

Fig. (4.15). The two cascaded angular actuators.

A second demonstrator has been realized with parameters corresponding to the simulated system. In Figs. (4.16) and (4.17), the complete assembly can be seen.

Fig. (4.16). The second demonstrator.

Fig. (4.17). The components of the second demonstrator.

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Semi-rotary and Linear Actuators 51

At the left side of the figures, the two angular actuators are coupled. Then, in the middle, the motion rectifier can be seen with its inverting gear train and its noninverting train realized with a tooth-belt. This motion rectifier has additionally an output multiplication gear in order to increase the rotational speed of the electric generator. The motion rectifier is shown with more details in Fig. (4.18a and b).

Fig. (4.18). Details of the motion rectifier.

The electrical generator is on the right side of the photos.

Fig. (4.19). The original system developed by Gianfranco Gallino (courtesy G. Gallino).

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5. DISPLACEMENT AND EXPANSION WORK IN ONE SINGLE ACTUATOR 5.1. Basic Principle In Section 3.1, the principle of realizing the displacement work and the expansion work in the same cylinder has been introduced. Section 3.1.1 has described more in detail the properties of the Truglia motor as an example of such a system. This principle can be applied to a motor based on double effect rotating actuators as were used in the previous paragraphs of this chapter. For the rotating actuator, the displacement work corresponds to an intake phase under constant pressure, for a volume value comprised between zero and V1. After this first phase, the intake valve is closed and the air under pressure is expanded while the vane continues its motion up to the end position. The expanded air occupies then the total volume of chamber V2. To reach the same energetic performance as for the system with two cascaded actuators, the full volume of the single actuator (V2) must have the same value as the volume of the larger actuator of the cascade. The volume V1 of the intake phase is equal to the volume of the small cylinder of the cascade. For the displacement work at constant pressure and for the expansion work in the same actuator, two angles are defined for one chamber, for example, for the a side of the rotating vane, namely the intake angle Φ_int_a, and the expansion angle Φ_exp_a as indicated in Fig. (4.20).

V2b

)_int_a V2a

Fig. (4.20). Intake and expansion angles.

)_exp_a

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Semi-rotary and Linear Actuators 53

These angles are obtained from angular sensors, as shown in Fig. (4.21). The intake phase at constant pressure begins at the origin of the stroke at the aside of the actuator. Then the intake and the related work at constant pressure lasts over the defined angle Φ_int_a. During this phase, the intake valve at this side (a) is open, and the exhaust valve of the opposite side (b) is also open. For the double effect rotary actuator, 4 valves are needed, two for the intakes and two for the exhausts. The principle of adding a non-return valve for each chamber remains (see sec. 4.2.4). The different valves are represented in Fig. (4.21).

V2b Motion Retifier

Gen

V2a Xexh_b

Xexh_a

Xin_a

+12 V

Xin_b

X_int_a & &

220 VAC

S R

X_int_b X_exh_b

X_exh_a

0V

Fig. (4.21). The complete system of one rotary actuator with displacement and expansion work in the same device.

After the intake, an expansion phase lasts for the remaining angle of the stroke Φ_exh_a. During this phase, the intake valve is closed in order to initiate the expansion. The exhaust valve at the opposite side is kept open up to the end of the stroke.

54 Semi-rotary and Linear Actuators

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5.2. Closed Loop Operation of the Semi-Rotary Actuator For the system with cascaded actuators, as represented in Fig. (4.2), the oscillating frequency is controlled “open-loop” and adapted to the rotation frequency of the generator in such a way that the clockwise and anti-clockwise motions follow one another without pause. For the single actuator with integrated displacement and expansion, the angular position of the vane and the control of the valves must be imposed in a synchronous manner. For this purpose, a 4-channel sensor with a double disk is proposed. The sensor and control system are represented in Fig. (4.22), together with the sequential diagram of the signals. In this representation, the sensor is specially designed for a 270° angular actuator. X_b_270

X_a_270 X_b_0_90

X_a_0_90

X_a_0_90

X_int_a

&

X_b_0_90

&

X_b_270

S R

X_a_270

X_int_b X_exh_b X_exh_a

X_a_0_90 X_a_270 X_b_0_90 X_b_270 X_exh_a X_exh_b X_int_a X_int_b 0°

90° Clockwise

0° 90° 270° 180° (270°) (0°) (90°) Anti-clockwise

Fig. (4.22). 4-channel position sensor and generation of the control signals for the valves.

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Semi-rotary and Linear Actuators 55

The actuator runs in clockwise and anti-clockwise motions over the maximum angular excursion (270°). The clockwise and anticlockwise motions follow a pseudo set-value signal generated by a bi-stable SR flip-flop. This toggle switch is set to “1” at the end of the anti-clockwise (return) motion by the signal x_b_270. It is reset to “0” when the rotor reaches its end position in the clockwise motion (x_a_270 signal for reset). The 90° sectors of the sensor’s disks produce the signals x_a_0_90 and x_b_0_90, which impose the duration of the intake in each chamber. The respective control signals for the intake valves are generated by a combination of the x_a_0_90 and x_b_0_90 signals and the respective true and inverse pseudo set-value signals given by the RS flip-flop. The exhaust valves are directly controlled by the true (x_exh_b) and inverse (x_exh_a) signals of the pseudo set-value. The two detectors for the end-of-stroke, which generate the set and reset signals for the RS flip-flop, can be placed in a short advanced angular position to allow an inversion of the angular velocity of the rotor with air-injection in the opposite chamber before the vane hits the end-of-stroke blockers. 5.3. Torque Generated in Adiabatic and Isothermal Conditions The torque produced in this single actuator system is characterized by a segment with constant torque during the intake phase. Then, the torque decreases according to the relation that takes into account the variation of the volume. Fig. (4.23) shows in a simplified simulation the curves of the generated torque over a full period, namely a clockwise stroke followed by an anti-clockwise stroke. The curves show the expansion in adiabatic as in isothermal conditions. In the same figure, the values of the torque averages are also represented. A comparison with the curves of the torques of a system with cascaded actuators described in the first sections of this chapter. Fig. (4.23b) shows that the energetic performances (e.g., the efficiency) of the two systems are identical. Effectively, the torque averages are of the same values. When the torque average values are identical, the superposed torque ripple is, however, much more pronounced in the system with one actuator only. A more accurate and detailed simulation of the single actuator with its sensors, control signals and closed loop operation will be presented in the next section.

56 Semi-rotary and Linear Actuators

Alfred Rufer

a)

b) Fig. (4.23). a) Torque produced in a system based on one actuator only with displacement and expansion work in the same device (Nm). b) Torque produced with a double actuator system (Nm).

6. SIMULATION OF THE SINGLE ACTUATOR SYSTEM WITH SENSORS AND CLOSED LOOP CONTROL The simulation of the system represented in Fig. (4.21) with sensors, control signals and the closed loop operation will take into account the real operation of the motion rectifier described at paragraph 4.1.2 For this purpose, the mechanical model given in Fig. (4.24) will be used. In this model, the first integration block represents the movement of the wing-rotor of the actuator alone. At its input side, a factor K1 is used to characterize the inertia of this rotor. The action of the motion rectifier corresponds to limiting the speed of the rotor to the value of the

Coupling Two Rotary-Type Actuators

Semi-rotary and Linear Actuators 57

rotational speed of the output shaft. This value is set as a constant (Omega) in order to simplify the simulation. This parameter could be simulated separately as another mechanical integrator, as represented with a dotted line in the lower left side of the figure. The limitation function is given through a simple limiting block where the upper limit (Omega) and the lower one (-Omega) are directly imposed. As a result, the speed of the rotor appears at the output of the limiting block. In reality the angular velocity of the rotor cannot overtake that of the output shaft (Omega), and the output of the first integrator must be controlled with an antireset wind-up circuit. This circuit comprises a subtraction block that compares the output and the input of the limitation block. The output of the comparator is fed back to the input with a factor K2.

Torque (therm.)

+

K1

Rotor speed

1 s

1 s

Rotor position

+ K2

1 s

Omega

-1

Fig. (4.24). Mechanical model of the rotor and motion rectifier.

Then, the position of the rotor is simulated with a second integrator. The output quantity corresponds to the rotor position. From the position of the rotor, the signals produced by the sensors are generated, as well as the control signals for the valves. The computation of the control signals is realized according to the description in Fig. (4.22). Sensors signals and control signals are represented in Fig. (4.25). In Fig. (4.26), the speed of the rotor and its position are represented. The angular speed of the rotor is limited through the parameter Omega set to 6.28 rad/s. One can see that the rotor speed jumps from a positive value (°Omega) to a negative one (-Omega) with a specific slope, corresponding to the inertia of the rotor alone.

58 Semi-rotary and Linear Actuators

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X_a_270

X_b_270

X_int_a

X_int_b

X_exh_b

X_exh:a

Fig. (4.25). Signals from the sensors and control signals. Horizontal axis: Time, (s).

Fig. (4.26). Rotor speed (blue, (rad/s)) and rotor position (red, (rad)).

The position of the rotor is controlled by the RS flip flop, as represented in Fig. (4.21), which acts as a kind of two-point controller. The rotation angle swings up and down from nearly zero and 4.71 rad. These values correspond to the end-ofstrokes positions of the 270° actuator. From the angular position of the rotor, the volumes of both chambers (a and b) can be easily calculated. They are represented in Fig. (4.27).

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Semi-rotary and Linear Actuators 59

Fig. (4.27). Volumes of the two chambers of the actuator (cm3). Side a (blue) and side b (red).

Combining the variables representing the volumes and the control signals of the valves, the pressure in each chamber can be calculated. On the curves of Fig. (4.28), one can clearly distinguish the flat segments at the beginning of the clockwise and anti-clockwise strokes, corresponding to the intake under constant pressure. These segments are followed by the expansion curves when the intake valves are closed. In this simulation, the expansion is considered in adiabatic conditions. At the end of the expansion, the rotor has reached its end-position and returns in the opposite direction. In this phase, the exhaust valves are opened and the atmospheric pressure appears in the chambers.

Fig. (4.28). Pressures in the chambers (N/m2), (upper curve a-chamber, lower curve b-chamber), Time (s).

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From the pressures in the chambers and the surface of the wing, the forces acting on both sides of the wing are calculated, as well as the generated torque, considering the radius of the force’s action. The torque produced through the pressure in the chambers is represented in Fig. (4.29) (red curve). This torque produces the motion of the rotor shown in the blue curve of the figure. This curve corresponds to the speed of the rotor, which is limited in both directions through the motion rectifier, which drives the generator at a constant speed of 6.28 rad/s.

Fig. (4.29). Torque applied to the rotor (red, (Nm)) and rotor speed (blue, rad/s)), Time (s).

Between the clockwise and anti-clockwise motions, the rotor undergoes a speedreversal. During this reversal, the roller-clutches of the free-wheeling devices in the motion rectifier are inactive, and no torque is transmitted to the output-shaft. This can be observed on the curve of Fig. (4.30), where the torque effectively transmitted to the output of the rectifier is shown. By the change from a positive value to a negative value of the torque, one can see a zero segment of the duration of the speed reversal.

Fig. (4.30). Torque transmitted to the output of the motion rectifier (Nm).

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Semi-rotary and Linear Actuators 61

Finally, the mechanical power at the output of the motion rectifier is represented Fig. (4.31). The instantaneous value of the power (blue curve) corresponds to the value of the transmitted torque multiplied by the value of the rotational speed. In the figure, the average value of the power is also represented.

Fig. (4.31). Mechanical power (W) and average at the output of the motion rectifier, Time (s).

7. EXPERIMENTAL SET-UP 7.1. The 180° Actuator The experimental setup is realized with one 180° actuator, as represented in Fig. (4.32). The alternating movement is transformed into a unidirectional rotation through the same motion rectifier as in Section 4.4.

V2b V2a

Fig. (4.32). The 180° actuator.

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7.2. Control Circuits The control circuit for the inlet and exhaust valves is represented in Fig. (4.33). The same principle as for the 270° actuator is used. A SR flip-flop and the AND combinations for the intake valves are realized with 12V CMOS logic circuits. 7.3. Sensor System for the 180° Actuator The sensor system uses four proximity detectors activated by two rotating sections of ferromagnetic material. Fig. (4.34) illustrates the sensor system where the detectors are placed at 180° positions. The sectors which activate the intake valves cover 60° angles, leading to a volume ration for the expansion of factor ¼. 4013

X_b_270

+12V DC

14

2 5 3 4

1 2

8 9 150: 11 10

13

S

2 1

12

R

&

5

3

&

4

IRF 610 120:

X_int_a

6

13

7

X_a_270

4011

14

12

&

IRF 610

9

11

&

150:

10

X_int_b

120:

8 7

IRF 610

X_exh_b

120:

X_a_0_90 150:

X_exh_a IRF 610 120: X_b_0_90 150:

+12V DC

230V AC

0V DC

Fig. (4.33). Control circuits with logic functions and amplifiers for the valves.

7.4. The Complete Assembly The complete assembly is shown in Fig. (4.35). The 180° actuator is on the right side. In the middle of the figure, is the motion rectifier, and on the left side, is the electric generator. Between the actuator and the motion rectifier, the sensor system with its four detectors and the rotor with its activating sectors.

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Semi-rotary and Linear Actuators 63

60° Start at 0° open intake a open exh. b

X_int_a

X_a_180

X_b_180 60°

X_int_b

X_int_a

X_a_180

X_b_180

X_int_b

X_int_a

X_a_180

X_b_180

Rotation of 60° close intake a

After rot. of 180°(-) Reset flip flop open exh. a open intake b

X_int_b

Fig. (4.34). Sensor system for a 180° actuator with 60° intake angle.

Fig. (4.35). Pneumatic drive with a single actuator (180°).

7.5. Measurements Fig. (4.37) shows the evolution of the pressure in the two chambers of the single actxref refuator with integrated expansion. These curves correspond to the theoretical curves which were simulated (Fig. 4.28) but show some differences mainly due to the limited performances of valves and tubing. The different phases are indicated: Intake, expand and exhaust.

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Fig. (4.36). Details of the single actuator system a) actuator with valves, b) control electronics, c) sensor system

Fig. (4.37). PPressures in the chambers a: upper curve b: lower curve. Time: 20 ms/div, Pressure: 5 bar/div.

For the intake phase, the pressure in the chambers does not establish instantaneously, but rises according to an exponential form, mainly caused by the small section of the tubes and of the valves. Then, the expansion phase lasts over a reduced time and a reduced expansion ratio. This is due to delays of the control valves, as can be shown in Fig. (4.38). The period of one cycle is 150ms.

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Semi-rotary and Linear Actuators 65

The left picture of Fig. (4.38) shows the relation between the sensor signal “End of stroke” of chamber b and the pressure in chamber a. Before the sensor signal rises, chamber a is in its exhaust phase. The pressure is not at the level of the atmospheric pressure but takes the value of a pressure difference DPexh caused by the exhaust flow of the air through the small valve and tubing. After the delay time DTint, the intake valve is opened.

Fig. (4.38). Control signals and pressure in the chamber. Left/upper curve: End of stroke signal from the sensor (5V/div), Left/lower curve: Pressure in the corresponding chamber (5 bar/div), Right/upper curve: Sensor signal for the length of the intake (5V/div), Right/lower curve: Pressure in the corresponding chamber (5bar/div).

Due to this delay, the rotor of the actuator hits its end of stroke stop after DTmech instead of being braked pneumatically by the opening of the intake valve of the chamber a. While the rotor is blocked at its stop, the exhaust flow goes to zero and the pressure decreases from DPexh to the atmospheric level. Then, after DTint, the intake valve a opens and the pressure rises during the new intake phase. In the right picture of Fig. (4.38), the relation between the sensor signal giving the length of the intake and the pressure in the corresponding chamber is represented. The sensor signal rises at a “length angle” which is the symmetric one before the end of the stroke position. The signal X_int_a for real length of the intake for the corresponding chamber is activated through the SR flip flop as represented in Fig. (4.33) (logic “and” function). A time delay DTexp appears between the falling edge of the sensor signal and the real beginning of the expansion. This is due to the slow response of the valve especially by closing. The delayed expansion causes a reduction of the expansion factor.

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These records illustrate the limits of the realized demonstrator and the need to use fast control valves for such an application [11]. Additionally, the section of the valves and of the pipes must be chosen as large as possible, allowing fast filling and exhaust of the chambers of the actuator. 8. THE REVERSIBILITY OF THE SYSTEM BASED ON SEMI-ROTARY ACTUATORS In the general context of energy storage with compressed air, it would be of the highest interest to use the same apparatus for the compression and for the expansion of the air. The different systems described hereabove, from the Gallino system to the drive using cascaded semi-rotary actuators, the pneumatic devices are used for the expansion only. But it would be interesting to use the same devices for the compression of the air. In fact, the industrial components which are used are designed as actuators, and their sealing components do not allow to work in the compression mode. Let us suppose that some solution exists for designing those actuators for the compression mode. But the coupling element between the pneumatic actuator and the rotating generator being a motion rectifier which cannot transmit a reverse power flow, a new solution must be found if the actuators must work as compressors. 8.1. The Crankshaft and Piston Rod System Instead of the Motion Rectifier It is clear from the beginning that actuators working over an angle of 270° cannot be driven from an oscillating mechanical element itself set in movement by a rotating crankshaft. In Fig. (4.39), a new configuration is represented with a motor and an actuator operating as a pump. The actuator is still of a semi-rotary type but has oscillations over an angle of 90°. In order to benefit from a sufficient volumetric power density, a double vane type actuator is chosen.

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Semi-rotary and Linear Actuators 67

Motor

Actuator (pump) B

I0

I$

2 ˜l / 2

l

2 ˜l

V

H Fig. (4.39). Rotating machine driving a semi-rotary vane-type actuator.

The oscillations of the actuator are driven by a connecting rod coupled to a crankshaft element which rotates on the engine shaft. The motion of the actuator requires a crankshaft whose crank pin describes, along the horizontal axis, the same displacement as the lever coupled to the actuator. A lever of length l moves horizontally over a distance of 1.41 (root of 2) times the length l. The radius of gyration of the crankpin will therefore be 1.41 * l / 2. The motor axis is placed on the height V referred to the position of the rotating axis of the actuator. This value corresponds to the projection of l for an angle of 45° relative to the vertical axis (midpoint of the stroke of 90°). The engine is placed in its horizontal position at a distance of 1.5 to 2 times the horizontal displacement H of the lever attachment on the connecting rod. The length of the connecting rod is equal to this distance. In the realized example, the length of the lever is defined as L = 5 cm. The horizontal displacement of the connecting rod attachment on the lever is then H =

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1.41 * 5cm = 7.07 cm The crankshaft gyration radius is then r=3.535 cm The length of the connecting rod becomes B = 10 cm A demonstration system made with wood/metal elements is represented in Fig. (4.40).

Fig. (4.40). Demonstration system of the rotating machine driving a semi-rotary vane-type actuator operated as a pump.

8.2. The Question of the Inertia of the Oscillating Vane-Rotor The semi-rotary actuators driving the motion rectifier, as described in the previous examples, pose a problem related to the inertia of their rotor while inverting their motion. The motion rectifier does not allow to recover this kinetic energy due to the presence of the free-wheeling devices. As a consequence, the kinetic energy of the rotor is dissipated during the choc at the end of the stroke if no special measure is taken. For the system where the control of the valves is done on the basis of signals from the position sensors of the rotor of the actuator, a principle of “intake

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Semi-rotary and Linear Actuators 69

anticipation” can be realized in which the rotor is braked pneumatically by the early opening of the intake valve of the opposite side before reaching the end of the stroke. The kinetic energy is then absorbed by the intake channel of the next stroke. The system using a crankshaft and connecting rod instead of the motion rectifier naturally recovers the momentum of the alternating rotor. Indeed, the action of the connecting rod on the crankshaft transmits torque to the rotating part when the angular position is favorable. This effort is transformed into a rotational movement. The kinetic energy of the parts in alternating motion is transmitted and then recovered from the rotating inertia. 8.3. Combining the Operations of Compression and Expansion of SemiRotating Actuators The connecting rod-lever system shown in Figs. (4.39 and 4.40) operates without problems when movement is imposed by the motor axis, that is, through its crankpin, which periodically describes a continuous circle. The movement of the crankpin forces the angular actuator to move 90 ° back and forth. For a transfer of power in the reverse direction, that is to say, for an operation where the rotation of the motor axis would be imposed by the angular actuator through its lever and the connecting rod, there are angular positions of the motor axis for which no torque can be transmitted. These angles correspond to what are called the top and bottom dead centers of the crankshaft (ϕM = 0 ° and ϕM = 180 °). These dead points correspond to the extreme left and right positions in the diagram in Figure 4.39. They also correspond to the extreme positions of the actuator (ϕA = 0 ° and ϕA = 90 °). Reversibility of movement and torque generation without dead centers can be achieved by combining two actuators, the latter being coupled to the motor/generator shaft by crankshaft pins offset from each other by 90 °. Such a system has been produced as a model, as shown in Fig. (4.41). For this system, the axes of the two actuators with their levers are visible in the upper part of the figure. The engine axis and the crankshaft with its crankpins offset by 90 ° is visible in the lower part of the figure. Finally, a complete system with motor/generator and the two 90°actuators can be seen in Fig. (4.42). On the right side of the figure are the control valves. They are of the 5/2 type and are electrically controlled from two position sensors giving 90° shifted signals referred to as the crankshaft.

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Fig. (4.41). Model for the reversible system.

Fig. (4.42). Reversible system with two actuators coupled to the rotating machine with two 90° shifted crankpins.

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Semi-rotary and Linear Actuators 71

Fig. (4.43) gives the functional diagram of the system with its control and sensors. X_0

X_90

Fig. (4.43). Reversible system with two 90° shifted actuators.

8.4. Experimentation with a Vane-Type Actuator Operating as a Compression Machine A vane-type actuator has been coupled to an electric motor for its operation as a compression-machine. The system realized corresponds to the schematic representation of Fig. (4.39) and is represented in Fig. (4.44). The pneumatic components used for this demonstrator are represented in Fig. (4.45). The valves used in this system are simple anti-return valves.

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Fig. (4.44). Drive of the semi-rotary actuators for the compression mode.

Fig. (4.45). Schematic diagram of the system operated in compression mode.

The demonstrator has shown very poor performance in the compression mode, mainly due to the quality of the sealings of the vanes, which are not designed for this mode. Additional experimentation has been done in order to verify that the poor performance is not due to the anti-return valves (pressure drop in the forward direction, related to the low operating pressure). For this experimentation, the control of the airflow from the chambers to the reservoir has been realized with active solenoid valves, controlled by a position sensor coupled to the oscillating rotor.

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Semi-rotary and Linear Actuators 73

Also, for this additional experiment, the result was very bad and confirmed that angular actuators are not intended for air compression. 8.5. Reducing the Footprint of the Reversible System The realization of a reversible system on the base of a crankshaft and piston rod system, as described in the previous sections, is characterized by a larger footprint than the system using a motion rectifier. From the diagram of Fig. (4.39), it is evident that the actuator and the electric machine must be placed at a specific distance one from the other and cannot be operated on the same axis as was the case for the system with a motion rectifier. One mechanical solution, however, can be imagined where the rotor of the electric motor and the rotor of the semi-rotating actuator can be placed in the same vertical plane reducing the footprint of the system in the perpendicular direction to the motor axis. A demonstrator model and a schematic diagram are represented in Figs. (4.46 and 4.47). From these representations, one can observe the presence of two half-rods, the one transmitting the horizontal movement away from the motor axis, and the second bringing the movement back to the actuator axis. The coupling node between the two half-rods is supported by an additional lever which oscillates in parallel to the lever of the actuator.

Fig. (4.46). Demonstrator model for the reduction of the footprint.

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Axis of the actuator

Fig. (4.47). Mechanism for the reduction of the footprint.

DISCLOSURE Part of this chapter has previously been published in A High Efficiency Pneumatic Drive System Using Vane-Type Semi-Rotary Actuators, in Facta universitatis-series: Electronics and Energetics, in 2021, vol. 34, no. 3, pp. 415433.

Semi-rotary and Linear Actuators, 2023, 75-109

75

CHAPTER 5

The Pneumatic Motor with Linear Cylinders Abstract: A pneumatic motor is studied where the pneumatic actuators consist of linear cylinders. This mechanical principle based on the use of a crankshaft and piston rods has the inherent property of being reversible. For this system, the same principle of adding expansion work with an additional volume is applied as it was in the previous chapter for semi-rotary actuators. The mechanical behavior of the crankshaft and piston rod is described, and the following pneumatic displacement and expansion work is simulated. Two different architectures are simulated, namely, first, a system with pistons operating in phase and second, with alternating pistons. The energy efficiency of the new motor is calculated and compared with the efficiency of a system using a single linear cylinder. Further, the principle of realizing the expansion work in the same cylinder as for the displacement work is applied to the motor with linear cylinders. The torque, power and converted work are presented with the simulation results. The study is completed with the presentation of a physical demonstrator system.

Keywords: Adiabatic expansion, Alternating piston-rods, Energy efficiency, Expansion work, In-phase piston rods, Linear cylinders, Pneumatic motor, Torques. 1. BASIC PRINCIPLE A pneumatic motor can be realized on the basis of a linear piston/cylinder component. In such a system, the linear movement of the piston is converted into rotational motion using a conventional crankshaft and connecting rod. Based on the previous descriptions of principles used to increase energetic efficiency, a pneumatic motor concept using two linear cylinders is described. In this concept, the linear cylinder pistons are connected to a classical crankshaft with crankshaft pins shifted at 180°. This concept belongs to the previously defined category of motors with expansion in an additional chamber and reciprocating strokes (Section 3.1.3). Alfred Rufer All rights reserved-© 2023 Bentham Science Publishers

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In section 5.2, the dynamics of the piston/crankshaft assembly are given, with relations to calculate the torque and the lateral reaction force. In section 5.3 of this chapter, a simple pneumatic motor is described where the cylinder works according to the classical principles of pneumatic devices, namely with only a succession of sequences with constant pressure displacement work. The typical variables are simulated as the dynamics of the piston/crankshaft assembly and the developed torque. The energetic performance of this elementary motor is also evaluated. In section 5.4, a pneumatic motor with enhanced efficiency will be described where an additional expansion chamber is coupled to the first single piston system. Pressures, forces and torques will be simulated. Finally the energetic performance will be calculated and compared to the performance of the single cylinder system. An experimental system is also realized. 2. OPERATING PRINCIPLE OF THE MOTOR WITHOUT EXPANSION A double acting linear cylinder is used as prime mover Fig. ( 5.1). The two working chambers are filled alternatively with compressed air. Each filling stroke is characterized by its displacement work with a constant force exerted by the piston. Before entering the reversal motion, where the force is then exerted by the opposite chamber, the air of the first chamber is released to the ambient, losing its energetic content bound to the pressure. The corresponding energy loss factor or equivalent efficiency has been presented in Chapter 2.3.2.

V16a

V16b

V16a

V16b

Fig. (5.1). Reciprocating cylinder with crankshaft and connecting rod (top view and side view).

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Semi-rotary and Linear Actuators 77

2.1. Mathematical Description of the Piston/Crankshaft Assembly In Fig. (5.2), the piston is represented with the connecting rod and the crankshaft. The parameters are indicated as r, the radius of the crankshaft, l the length of the connecting rod, and Φ the angle of rotation of the crankshaft. The diameter of the piston, d and its position x are also indicated.

d l

x

I

r

Fig. (5.2). Piston, crankshaft and connecting rod.

The position of the piston is given through rel. (5.1): x

r(1  cos M ) 

O 2

r sin 2 M

(5.1)

Where the connecting rod ratio λ is used and is defined as:

O

r l

(5.2)

The velocity of the piston is given by: v

Z ˜ r ˜ sin M (1  O cos M )

(5.3)

In the simulation process, the torque developed by the motor is calculated through the indirect calculation of the power. If the force exerted on the piston is given by:

Fp

p˜A

(5.4)

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The mechanical power is defined by the product of the force by the piston’s velocity:

Pow Fp ˜ v

(5.5)

The torque is obtained by the division of the power by the angular velocity ω:

Mmot Pow / Z

(5.6)

A direct calculation of the torque is, however, possible with the extended model represented in Fig. (5.3). The force on the connecting rod Fs, the tangential force Ft and the reaction force Fn are also defined.

Fig. (5.3). Force diagram for torque calculation.

The torque on the crankshaft is given by rel. 5.7:

M mot Ft ˜ r

(5.7)

The tangent force Ft is given by:

Ft Fs cos(S / 2  (E  M ))

(5.8)

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Semi-rotary and Linear Actuators 79

The force transmitted through the connecting rod Fs is calculated with the help of the piston force Fp and the angle beta:

Fs

Fp

(5.9)

cos E

This angle is given by rel. (5.10):

§r · arc sin ¨ ˜ sin M ¸ ©l ¹

E

(5.10)

The perpendicular reaction Fn is defined as per (5.11):

Fn

Fs sin E

Fp cos E

sin E

(5.11)

2.2. Simulation of a Motor with one Double Acting Cylinder A pneumatic motor is simulated where a double acting cylinder is used. The dimensions of the cylinder are: Diameter d=16mm The stroke is given by twice the radius of the crankshaft, namely: Xa = 2*r =20mm The motor is running with a constant rotational speed, namely Ω = 31.4 rad/s First, the position of the piston is represented in Fig. (5.4a). The simulation lasts over two periods. Then, the velocity of the piston is shown in Fig. (5.4b). The curve shows the typical form due to the specific connecting rod ratio.

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Fig. (5.4a). Position of the piston (m) versus time (s).

Fig. (5.4b). Velocity of the piston (m/s) versus time (s).

The cylinder is fed with compressed air at a pressure of 10 bar. The air is brought alternately to the left and to the right sides of the piston. The control valves are activated at the top and bottom dead centres. These points correspond to angles of 0° and 180°. The 16 mm diameter of the piston corresponds to a surface of:

A

S d2 4

201  mm 2  or  201˜106 m 2

(5.12)

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Semi-rotary and Linear Actuators 81

The force caused by the air pressure is:

F A ˜ p 201˜106 m2 ˜10 ˜105 N / m2 201N

(5.13)

On the opposite side of the piston, the atmospheric pressure causes a counter force of 20.1N, and the total force exerted on the piston becomes:

Ftot 201N  20.1N 180.9N

(5.14)

The total force is represented in Fig. (5.5).

Fig. (5.5). Force on the 16 mm piston (no expansion) (N) Time (s).

The calculation of the torque applied to the crankshaft is done using the instantaneous value of the power. This quantity can be calculated through:

P Ftot ˜ v

(5.15)

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The evolution of the power is shown in Fig. (5.6).

Fig. (5.6). Power developed by the 16 mm piston (W), Time (s).

Then the torque follows as:

M tot

P

Z

and is represented in Fig. (5.7).

Fig. (5.7). Torque produced by the 16 mm piston (no expansion) (Nm), Time (s).

(5.16)

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Semi-rotary and Linear Actuators 83

2.3. Energetic Efficiency The energetic efficiency of the motor is evaluated by calculation of the ratio of the mechanical energy obtained at the output to the enthalpy injected at the input of the pneumatic actuator. The transmitted mechanical energy is obtained from the simulation curve of Fig. (5.8). It corresponds to the time integral of the instantaneous power according to rel. 5.17. The final value of the converted energy is equal to 14.46 J.

Fig. (5.8). Energy transmitted from the 16 mm piston (J), Time (s). t

³ P(t)dt

Wout

(5.17)

0

Wout

14.46 J

The efficiency is calculated through rel. (5.18): Kconv

Wout

+ in

Wout U  Pin ˜ 'V

(5.18)

U is the thermodynamic content of the injected air under pressure and is calculated as the energy needed for the compression into V1 of the equivalent mass of air from the atmospheric pressure to the value of Pin, V1 being the filled volume of the actuator during the total duration of the simulation (2 periods).

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The fully expanded volume of one chamber of the 16 mm piston system is: d2

V16 _ max

S 4

˜ 2r (0.016)2

U

Ecomp

S 4

˜ 0.02 4.02 ˜106 m3

§ P P · Pin ˜V1 ¨ ln in  1  atm ¸ Pin ¹ © Patm

(5.19)

(5.20)

Numerically, and considering the two complete cycles (ϕ =0…4π), U becomes: U

1bar · § 10bar Ecomp 10 ˜105 N / m2 ˜ 4 ˜ 4.02 ˜106 m3 ¨ ln 1 ¸ 22.5 J 10bar ¹ © 1bar

Pin ˜ 'V

10 ˜105 N / m2 ˜ 4 ˜ 4.02 ˜106 m3 16 J

(5.21)

(5.22)

The efficiency becomes: Kconv

Wout

+ in

14.46 J 16 J  22.55 J

0.375

(5.23)

3. A PNEUMATIC MOTOR WITH ENHANCED EFFICIENCY – ADDING AN EXPANSION CHAMBER WITH RECIPROCATING STROKES Fig. (5.9) shows the pneumatic motor with enhanced efficiency. In addition to the first cylinder, a second one is coupled to the crankshaft. The two cylinders are moving in phase opposition. They have different sizes but have the same stroke. They are working in a cascaded way, in a similar manner as was described in Chapter 4 for the angular actuators. In the studied system, the cylinders have diameters of 16mm and 32mm. The stroke of both actuators is equal to 20mm. Factor two of the diameter of the cylinders imposes a ratio of four concerning the volumes. The volume of the 16 mm cylinder is equal to: V16 _ max

d2

S 4

˜ 2r (0.016)2

S 4

˜ 0.02 4.02 ˜106 m3

(5.24)

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Semi-rotary and Linear Actuators 85

V32a

V32b

V16a

V16b

Fig. (5.9). Pneumatic motor with additional expansion chamber.

And the volume of the 32 mm cylinder is: V32 _ max

d2

S 4

˜ 2r

(0.032)2

S 4

˜ 0.02 16.08 ˜106 m3

(5.25)

The operating cycle is defined by the following steps: 1) Filling of the small volume (V16a for 0° to 180°, respectively V16b for 180° to 360°). 2) Transfer from the small volume (V16a for 180° to 360°, respectively 16b for 0° to 180°) into the larger one (V32a, respectively V32b).

The crankshaft with its crankpins placed at 0° and 180° defines the alternations between fillings and transfers. The control signals for the valves are generated from a position sensor. The pressure in the cylinders is constant during the fillings and varies during the transfer from the small volumes to the larger ones. The pressure changes are defined according to an adiabatic expansion curve given by rel. 5.26.

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P2

§V · P1 ¨ 1 ¸ © V2 ¹

(5.26)

The different volumes of the cascaded cylinders are indicated in the schematic representation of Fig. (5.9). 3.1. Simulation Results The behaviour of a pneumatic motor with two complementary cylinders is simulated. First, the position and velocity of the two pistons are simulated. The changes in the pressures in the respective cylinders are also calculated. Then, the torque contributions of the small and of the larger cylinders are represented. Based on the produced output power and on the enthalpy injected in the system, the energetic performance is calculated. 3.2. Position and Velocity of the two Pistons First the positions of the two alternating pistons are represented in Fig. (5.10), and their velocity in Fig. (5.11).

Fig. (5.10). Positions of the two cylinders (m), Time (s).

3.3. Contributions of the 16 mm Piston The pressure level in the chambers of the first cylinder is imposed from the air supply during the first half period (the filling). Then, the pressure is given by the expansion of the air into the second cylinder. The pressures in the alternating chambers of the 16 mm cylinder are represented in Fig. (5.12).

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Semi-rotary and Linear Actuators 87

Fig. (5.11). Velocity of the two pistons (m/s), Time (s).

From the pressures in the volumes of the first cylinder, the corresponding force is calculated according:

F

A˜p

(5.27)

Fig. (5.12). Pressures in the chambers of the 16 mm cylinder (cascaded cylinders), (N/m2), Time (s).

The curves of the forces in the left volume (16a) and in the right volume (16b) are represented in Fig. (5.13). These forces are represented according to a convention of the normal axis to the surfaces of the piston. These forces are positive.

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Fig. (5.13). Forces exerted on the two sides of the 16 mm piston (N), Time (s).

The resulting force of the 16 mm cylinder is represented in Fig. (5.14). In this representation, the resulting force on the piston shows its direction. It is positive in the first half period (movement from left to the right), and negative in the other direction (180°-360°, movement from the right to the left).

Fig. (5.14). Resulting force exerted by the 16 mm piston (N), Time (s).

The resulting force is then multiplied by the piston’s velocity to obtain the instant value or the mechanical power. This power concerns only the contribution of the 16mm piston.

P

v˜F

(5.28)

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Semi-rotary and Linear Actuators 89

The corresponding curve is shown in Fig. (5.15).

Fig. (5.15). Power developed by the 16 mm piston (W), Time (s).

The developed mechanical power of the 16 mm piston on the crankshaft is then divided by the angular speed, leading to the profile of the torque.

M16 P / Z The corresponding curve is represented in Fig. (5.16).

Fig. (5.16). Torque developed by the 16 mm piston (Nm), Time (s).

(5.29)

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3.4. Contributions of the Second Piston Fig. (5.17) shows the evolution of the pressure in the volumes of the second cylinder (the 32mm cylinder). The first curve shows the pressure in the left side chamber V32a, where the pressure is equal to the atmospheric pressure during the first half period (0°-180°). This phase of the sequence corresponds to the exhaust phase, where the expanded mass of air is released into the atmosphere. During this phase, the piston moves from right to left, while the 16mm piston moves from left to right.

Fig. (5.17). Pressures in the chambers of the 32 mm cylinder (N/m2), Time (s).

During the second half period (180°-360°), the pressure decreases from the level of the filling (10*105 N/m2), down to the level of 1.43*105 N/m2. This corresponds to an adiabatic expansion with a volume ratio of ¼. The second curve shows the pressure in the right chamber of this cylinder (V32b). The phases of exhaust and of expansion alternate all 180°, but are in opposite angular positions in reference to the left side chamber. One can note the different evolutions of the expansions in the left and in the right chambers, this is due to the different evolution of the position of the piston in the first and second half periods. This is related to the not identical speed profile of the pistons with the specific ratio of the radius of the crankshaft to the length of the connecting rod. In Fig. (5.18), the forces on the left and right sides of the 32mm piston are represented. In these curves, the influence of the atmospheric pressure during the exhaust phases is taken into account.

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Semi-rotary and Linear Actuators 91

Fig. (5.18). Forces exerted on the 32 mm piston (N), Time (s).

For the calculation of the torque contribution of this cylinder, the same method as for the first cylinder is used, namely a calculation through the piston’s power. The power curve of the 32 mm piston is shown in Fig. (5.19).

P

v˜F

(5.30)

Fig. (5.19). Power curve of the 32 mm piston (W), Time (s).

From the power curve, the torque is calculated:

M32 P / Z

(5.31)

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The evolution of the torque M32 is represented in Fig. (5.20).

Fig. (5.20). Torque contribution of the 32 mm piston (Nm), Time (s).

3.5. Total Torque of the Motor The total torque of the motor composed of the two contributions from each cylinder is calculated as:

Mtot M16  M32 The evolution of the total torque is given in Fig. (5.21).

Fig. (5.21). Evolution of the total torque. (Nm), Time (s).

(5.32)

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Semi-rotary and Linear Actuators 93

The torque represented in Fig. (5.21) shows no identic contributions in the first and second half periods. This is due to the specific evolution of the pistons and their related speed in the two half periods. This corresponds to a system where the pistons are 180° phase shifted and where the same sides of the cylinders (left and right) are cascaded for the expansion. 4. SYSTEM WITH PISTONS IN PHASE AND CROSS CONNECTED EXPANSION WAYS For the mechanical coupling of the two cylinders, another possibility exists in changing the position of the pins on the crankshaft for a synchronous evolution of both pistons (same phase position). To obtain a similar expansion of the air, cross connected exchange lines between the cylinders must be chosen for the transfer of the air. This solution is called the zero angle shifted pistons. The corresponding diagram is shown in Fig. (5.22). For the system with pistons in phase and cross connection of the expansion ways, the two torque contributions are calculated (16 mm piston and 32 mm piston).

V32a

V32b

V16a

V16b

Fig. (5.22). System with pistons in phase and cross connected expansion ways.

4.1. Contributions of the Small Cylinder The torque contribution of the small cylinder (16 mm cylinder) is represented in Fig. (5.23), and the torque contribution of the 32 mm cylinder is represented in Fig. (5.24).

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Fig. (5.23). Torque contribution of the 16 mm piston (in phase pistons and cross connection) (Nm), Time (s).

Fig. (5.24). Torque contribution of the 32 mm piston (in phase pistons and cross connection) (Nm), Time (s).

The curve in Fig. (5.24) shows an evolution of the torque that is of similar amplitude in the first and second half periods. The marked difference in the maximum amplitudes that was typical of the system with 180° shifted pistons (Fig. (5.16) in section 5.4.3) is no more present. 4.2. Contributions of the Larger Cylinder The torque contribution of the larger cylinder (the 32 mm cylinder) is represented in Fig. (5.24). This time, the difference in the amplitudes of the maximum torque in the first and second periods is marked.

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Semi-rotary and Linear Actuators 95

4.3. Total Torque of the Motor The total torque developed by the motor with synchronous pistons is represented in Fig. (5.25). The curve shows less modulation as in the case of the motor with reciprocating pistons. To show the difference between both systems, the two curves are superposed in Fig. (5.26).

Fig. (5.25). Total torque of the system with zero phase shift of the pistons (Nm), Time (s).

Fig. (5.26). Comparison of the total torques of the two systems (0° and 180° shifted pistons) (Nm), Time (s).

5. ENERGY CONVERTED AND CALCULATION OF THE EFFICIENCY 5.1. Converted Energy The mechanical energy at the output of the pneumatic motor is calculated by the integration of the power as was already done for the single cylinder. The curve showing the converted energy during the complete cycle (2 periods) is shown in Fig. (5.27).

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Fig. (5.27). Converted energy (J), Time (s).

The energy amounts converted by the two systems, as described in sections 5.4 and 5.5, are represented in superposition in Fig. (5.28). The final values of the converted energy over the two periods are identic and reach the final value of 26.75 J.

Fig. (5.28). Superposed curves of the converted energy by the two systems (0° and 180° shifted pistons) (J), Time (s).

5.2. Efficiency of the System with Expansion The efficiency of the system with expansion is calculated on the basis of the produced mechanical work and the injected enthalpy into the system. In fact, this enthalpy is identic to the enthalpy injected in the cylinder of the first motor (one cylinder only) as was described in section 5.3.1, rel. (5.20). The transmitted mechanical energy is equal to 26.75 J, as was described in the previous section.

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Semi-rotary and Linear Actuators 97

Wout 26.75J

(5.33)

U is the thermodynamic content of the injected air under pressure and is calculated as the energy needed for the compression into V1 of the equivalent mass of air from the atmospheric pressure to the value of Pin, V1 being the filled volume of the first actuator during the total running period (0° to 4π).

U

Ecomp

§ P P · Pin ˜ V1 ¨ ln in  1  atm ¸ Pin ¹ © Patm

(5.34)

Numerically, and considering the two complete cycles (ϕ =0…4π), U becomes: U

Ecomp

1bar · § 10bar 10 ˜105 N / m2 ˜ 4 ˜ 4.02 ˜106 m3 ¨ ln 1 ¸ 10bar ¹ © 1bar

Pin ˜ 'V 10 ˜105 N / m2 ˜ 4 ˜ 4.02 ˜106 m3 16 J

22.5 J (5.35)

(5.36)

The efficiency becomes:

Kconv

Wout + in

26.75 J 16 J  22.55 J

0.693

(5.37)

6. COMPARISON OF THE MECHANICAL WORK The mechanical work obtained at the output of the two systems, namely the single cylinder motor and the motor with cascaded cylinders with expansion, is represented in Fig. (5.29) for comparison. The figure shows that the energy converted by adding an expansion chamber can be nearly doubled. This is fully compatible with the energy efficiencies calculated for the two systems (rel. 5.17 and rel. 5.33). 7. EXPERIMENTAL SET-UP An experimental set-up of a system with 180° shifted crankshaft pins is realized. The pneumatic cylinders are 16 mm and 32 mm in diameter, respectively. The stroke is equal to 20 mm. The system is controlled by a position sensor mounted

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on the rotating shaft. The air valves are controlled according to the sequential diagram of Fig. (5.30). The whole system with its control electronics is represented schematically in Fig. (5.31).

Fig. (5.29). Comparison of the converted energies (J), Time (s).

O°

18O°

X_contr X16a X16b X_tr_a X_tr_b X_exh_a X_exh_b

Fig. (5.30). Control sequence of the pneumatic valves.

36O°

The Pneumatic Motor with Linear Cylinders

Semi-rotary and Linear Actuators 99 Xexh_b Xexh_a

V32a

V32b Xtr_b

Xtr_a

V16a

V16b X16b

X16a

+12 V X_contr 220 VAC

0V

Fig. (5.31). Pneumatic motor assembly with control of the pneumatic valves.

Fig. (5.32). Experimental set-up with two cylinders.

Fig. (5.33). Experimental set-up (front view with crankshaft).

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8. DISPLACEMENT WORK AND EXPANSION WORK IN THE SAME CYLINDER 8.1. Basic Principle In Section 3.1, the principle of realizing the displacement work and the expansion work in the same cylinder has been introduced. Section 3.1.1 has described more in detail the properties of the Truglia motor as an example of such a system. This principle can be applied to a motor based on double effect linear cylinders, as used in the previous paragraphs of this chapter. 8.2. Asymmetrical Evolution of the Piston and Design of the Intake Angles An interesting property of such a motor is given by the asymmetric evolution of the piston in its descending and ascending motions. The asymmetric evolution can be observed on the curve of the piston’s velocity, as shown in Fig. (5.34). Especially, the rise of the speed in the first quarter of the period is faster than the rise in the third quarter.

Fig. (5.34). Evolution of the speed of the piston in the linear cylinder. (m/s), Time (s).

The difference between the ascending and descending strokes will be considered for the calculation of the corresponding angles of the crankshaft in relation to the positions of the pistons for an identic intake volume in ascending and descending modes. The study of the system given in this section is based on a cylinder having the same parameters as the larger one of the double cylinder system of the previous sections. The displacement work is also adjusted to the value as in the previous

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Semi-rotary and Linear Actuators 101

system, with a corresponding volume being equal to one-fourth of the volume of the larger cylinder. As a result, the displacement work as well as the expansion work of the motor with displacement/expansion in the same cylinder will be theoretically identical. The consumption of air from the pressurized reservoir is also identical to the consumption of the double cylinder system. The displacement work of the descending stroke is defined in addition to the value of the pressure and the piston’s surface, through the length of the displacement as indicated with the parameter xint_a in Fig. (5.35). For a cylinder having a maximal stroke of 20mm, the displacement length must be chosen as 5mm (1/4 of the maximal stroke).

Iint_a xint_a

xint_b

xint_b0

Iint_b

Fig. (5.35). Lengths of the displacements in descending and ascending motions.

The displacement work of the ascending stroke is defined through the length of the displacement as indicated with the parameter xint_b in Fig. (5.35). This parameter is chosen as identic to the displacement length xint_a of the descending stroke.

xint_ b

xint_ a

1 ˜ 20mm 4

0.005m

(5.38)

For the use of the same formalism as indicated in Fig. (5.2) and in rel. 5.1, the parameter xint_b0 is introduced (Fig. 5.35). From rel. 5.1, the lengths of the displacements are defined as:

xint_b0 xstroke _ max  xint_ b 0.020m  0.005m 0.015m

102 Semi-rotary and Linear Actuators

x int_ a

x int_ b0

r(1  cos Mint_ a ) 

Alfred Rufer

O 2

r sin 2 Mint_ a

r(1  cos Mint_ b0 ) 

O 2

r sin 2 Mint_ b0

(5.39)

(5.40)

The values of the rotation angles of the crankshaft ϕint_a and ϕint_b0 to move the piston up to the positions of xint_a and xint_b0 are obtained through successive approximations using the relations 5.39 and 5.40, namely:

Mint_ a 53.5q

(5.41)

Mint_b0 247.5q

(5.42)

These angles correspond to the position of the crankshaft where the intake valves are closed, respectively, where the expansion work begins in the chambers. To design the real intake angles for the descending and ascending strokes, the following angles for the openings of the intake valves are given:

Mint_ a _ open 0q

(5.43)

Mint_b_ open 180q

(5.44)

The real intake angles become:

Mint_ a 53.5q Mint_b Mint_b0  180q 247.5q  180q 67.5q

(5.45) (5.46)

The difference between these two values is in relation to the asymmetrical motion in the descending and ascending strokes, as described in the beginning of this section.

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Semi-rotary and Linear Actuators 103

For the exhaust of the expanded air, the openings and closings of the exhaust valves are:

Mexh_ a _ open 180q

(5.47)

Mexh_ a _close 360q

(5.48)

Mexh_b_ open 0q(or360q)

(5.49)

Mexh_b_close 180q

(5.50)

8.3. Control of the Valves From the definitions of the previous paragraph, the control sequences of the intake and exhaust valves can be defined. The evolution of the signals is represented in Fig. (5.36). The signal names are explicit.

intake_a exhaust_a Intake_b exhaust_b

Fig. (5.36). Control signals for the intake and exhaust valves Time (s).

From the sequence diagram of Fig. (5.36), three independent position sensors are needed. The first is controlling the intake valve at side a of the piston:

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(5.51)

Intake_a = Xin_a

The second sensor directly controls the intake valve at the b side of the piston (5.52)

Intake_b = xin_b

For the two exhaust valves, only one sensor is needed. Its signal (zeropi) changes at 180°. The control signals are generated according: ________

exhaust _ a

exhaust _b

zeropi

(5.53) (5.54)

zeropi

Fig. (5.37) shows the elements of the sensor system. The sensors can be, for example, of the ferromagnetic type, reacting to the presence of a ferromagnetic surface (black sectors on the rotating disks). Xin_a

Xin_b

Fig. (5.37). Position sensors for the control of the intake and exhaust valves.

zeropi

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Semi-rotary and Linear Actuators 105

A global schematic diagram of the system with its control and position sensors is given in Fig. (5.38). Xexh_b Xexh_a

V32a

V32b Xint_b

Xint_a

Xin_b

Xin_a +12 V zeropi 220 VAC

0V

Fig. (5.38). Schematic diagram of the system with control and sensors.

8.4. Evolution of the Volumes of the Chambers The evolution of the volumes of each chamber (a and b side of the piston) is represented in Figs. (5.39) and (5.40). The curves show the same asymmetry of the rate of change of both volumes.

Fig. (5.39). Evolution of the volume of chamber a (m3), Time (s).

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Fig. (5.40). Evolution of the volume of chamber b (m3), Time (s).

8.5. Force Exerted on the Piston The force exerted on the piston is given by the pressure multiplied by the piston’s surface. In Fig. (5.41), the total force is represented as the sum of different components: ●

●

●

Force on the a-side of the piston given by the pressure during intake and expansion Force on the b-side of the piston given by the pressure during intake and expansion Forces on the a and b-sides of the piston given by the atmospheric pressure during the exhaust

Fig. (5.41). Total force exerted on the piston (N), Time (s).

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Semi-rotary and Linear Actuators 107

The force is positive during the first half-period (motion from left to the right), and is negative during the second half-period (motion from the right to the left). It is easy to understand the constant value of the force during the intake, when the pressure is constant, and the typical decrease during expansion. 8.6. Torque and Power With the goal to evaluate the waveform of the torque, the same method as in the previous sections is used, namely the indirect calculation through the instantaneous value of power. This value is the product of the force multiplied by the piston’s velocity and is represented in Fig. (5.42). This representation shows different values of the maxima of the power during the descending and ascending strokes. This difference is caused by the different velocities of the piston, even if the value of the force is the same during both intakes.

Fig. (5.42). Mechanical power transmitted to the crankshaft (W), Time (s).

The value of the torque is then obtained by dividing the power by the angular velocity of the crankshaft. The corresponding curve is given in Fig. (5.43).

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Fig. (5.43). Torque produced by the motor (Nm), Time (s).

8.7. Mechanical Work Produced The mechanical work produced is obtained by the integration of the power over the two periods. The corresponding curve is given in Fig. (5.44). The final value of the produced work is 26.85 J. This value corresponds to the work produced by the system using two cylinders described in Sec. 5.6.1, (Fig. 5.28). A small difference is observed (26.75J instead of 26.85J) due to the precision of the simulation. The two systems must theoretically produce the same amount of work because they are characterized both by a displacement at constant pressure over the same volume, followed by an expansion of the same amount of air with an identic volume ratio. The pointed shape of the torque of the system with one cylinder (Fig. 5.43) can be the reason for the small difference obtained in the simulation. DISCLOSURE Part of this chapter has previously been published in A High Efficiency Pneumatic Motor Based on DoubleActing Linear Cylinders, in World Wide Journal of Multidisciplinary Research and Development, in 2021, vol. 7, no. 1, pp. 25-36.

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Semi-rotary and Linear Actuators 109

Fig. (5.44). Mechanical work produced by the system with displacement and expansion in the same cylinder (J), Time (s).

110

Semi-rotary and Linear Actuators, 2023, 110-131

CHAPTER 6

Linear Pneumatic Cylinder Reduced Air Consumption

Assembly

with

Abstract: The method of adding expansion work to pneumatic actuators is studied for classical linear cylinders. The operating principle of new cylinder assemblies is presented. A first simulation set illustrates the performance of the new assembly and tries to define the parameters of a single cylinder which produces the same mechanical performance. Acceleration, speed and reached position within a given time are the conditions for the comparison. Then, the air consumption of both compared systems is calculated. With an experimental set-up, a parasitic effect is observed, which consists of a pre-expansion transient due to parasitic dead volumes related to the tubing and internal volumes of the valves. A second assembly is realized with larger volumetry in order to observe the dependency of the parasitic effect from the size of the cylinders. For the control, a system with simpler control valves is also studied. .

Keywords: Adiabatic expansion, Cylinder assemblies, Dead volumes, Energetic performance, Energy efficiency, Expansion work, Linear cylinders. 1. INRODUCTION In Chapters 3, 4 and 5, different systems using pneumatic actuators have been analysed and discussed, especially from the point of view of energetic efficiency. The principle of combining two types of production of mechanical work has been applied, namely the production of so-called displacement work under constant pressure and expansion work realized through the variation of the active volume. The production of this expansion work has been realized with air transfer from a first volume to a second one of larger dimensions, or simply by controlling the intake valve of one volume. 1.1. New Cylinder Assemblies In the present chapter, the same principle of recovering the thermodynamic content of the pressurized air is applied to linear cylinders, where in addition to the simple displacement work produced in a conventional cylinder, the air is addiAlfred Rufer All rights reserved-© 2023 Bentham Science Publishers

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Semi-rotary and Linear Actuators 111

tionally expanded in a supplementary pneumatic chamber system, allowing to recover a significant part of the injected enthalpy [25]. Fig. (6.1) shows one of the possible arrangements of the new assembly, where the displacement work is produced by a central cylinder and where the expansion of the air is done within three peripheral cylinders mechanically coupled to the central one. In such an arrangement, the volumetric ratio of the expansion is equal to 3.

Fig. (6.1). One of the possible arrangements of the proposed cylinder assembly.

The system illustrated in Fig. (6.1) is studied, and its performance is compared with a single cylinder producing the same work. Fig. (6.2) gives a front view and a side view of the proposed system, while Fig. (6.2b) shows the single cylinder with compatible mechanical interface elements.

Fig. (6.2). Proposed system a) Front and side view, b) single cylinder with a compatible interface.

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The cylinder assembly with one central and three peripheral cylinders is represented in Fig. (6.2) is only one of the possibilities of coupling cylinders for realizing the additional expansion work. Three other solutions are represented in Fig. (6.3).

Fig. (6.3). Different configurations of coupled cylinder-assemblies.

In Fig. (6.3a), central cylinder is used for the displacement work and two lateral cylinders assume the function of producing expansion work. In Fig. (6.5), the small cylinder produces the displacement work while the parallel running larger cylinder produces the additional expansion work. In Fig. (6.3), a similar assembly is shown, but where the two cylinders are placed on the same axis. In this configuration, no torsional effort is produced. One of the two coaxially running cylinders must be of the double rod type.

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Semi-rotary and Linear Actuators 113

2. OPERATING PRINCIPLE AND CONTROL The proposed system is studied in its execution as an assembly of individual cylinders, as represented in Figs. (6.1) and (6.2). The chambers of the central cylinder are fed from the air reservoir under constant pressure. Then the air is transferred into the chambers of the three other cylinders running in parallel. As represented in the diagram of Fig. (6.4a), two intake valves, Vina and Vinb, are feeding the chambers of the first cylinder. The transfer of the air from the first cylinder to the three others is controlled through the two transfer valves, Vtra and Vtrb. Finally, after the expansion, the air at the final expansion pressure is released into the external atmosphere through two exhaust valves Vexha and Vexhb. The sequences of operation are defined according to the diagram of Fig. (6.4c). V1b

V1a Vina

Vina

Vinb

Vtrb

Vtra Vtrb

Vtra

Vexhb

Vexha

Vexha

Vexhb V2a

a)

Vinb

V2b

b)

c)

Fig. (6.4). Model and control of the system.

The simulation of the system is considering a simplified model where the three parallel running cylinders are represented by one cylinder of three times larger volume (Fig. 6.4b).

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3. THE PRESSURE VARIATION DURING THE EXPANSION The expansion of the air is supposed to be of the adiabatic type, and the resulting pressure P2 in the chambers V2a (first half-cycle) and V2b (second half-cycle) and of the respective feeding chambers V1b and V1a takes the value of: J

P2

§ V1max · Pin ¨ ¨ V  V ¸¸ © 1a ,b 2b,a ¹

with ɀ = 1.4

(6.1)

At the end of the two motions, the volume ratio is equal to 1/3, and the corresponding pressure ratio becomes Pin/P2 = 0.21 according to rel. (6.1). The produced mechanical work by the proposed system must be evaluated as a contribution of four main components, namely the forces generated by the intake pressure on the surfaces of the first piston and the forces generated by the expansion and exhaust pressure on the surfaces of the first and second one. An analytic calculation of the sum of these four components is not realistic due to the fact that the expansion pressure depends on the position of the pistons, which further is the result of the double integration of the global force (force to speed, speed to position). For the evaluation of the mechanical performance of the system, but also for the estimation of all internal variables, the way of simulation is chosen. 4. SIMULATION OF THE PROPOSED SYSTEM The new cylinder assembly is modelled according to the schematic representation of Fig. (6.4b). This model is composed of a first cylinder assuming the function of the intake and production of a constant pressure mechanical work. A second equivalent cylinder is used for the modelling of the expansion function and the related expansion work. From the sum of the produced components of the forces, the speed V of the output rod is calculated by integration. From the speed, the position X is calculated through further integration (Fig. 6.5). The four components of the produced force, namely the a- and b-side contributions of both cylinders, are calculated in dependency of the pressure in the chambers. These pressures depend on the variable volumes of each chamber which are estimated in dependency of the position of the output rod and of the intake air pressure Pin. In the functional diagram of Fig. (6.5), the output power is also calculated as also the produced mechanical work.

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Semi-rotary and Linear Actuators 115

Control

Pin

Cylinder 1

x force a-side force b-side

-

+ force a-side force b-side

1/s

work

+

+

Cylinder 2

power

1/m

1/s

V

1/s

X

+ pressure

xJ

V1/V2

Fig. (6.5). Functional diagram of the simulation. Table 6.1. Parameters of the single cylinder. Diameter

0.012 [m]

Stroke

0.020 [m]

Operating pressure

5 bar

4.1. Simulation Results According to the set of parameters given in Table 6.1, the internal and external variables of the system are calculated. The simulation results are given for a complete round-trip cycle of the cylinders. This cycle can be divided into four sectors as represented in Fig. (6.6). A corresponds to the motion of the rod from left to right, B illustrates the stop at the right end of stroke, C corresponds to the return stroke from right to left, and D illustrates the stop at the left end of the stroke. The different sectors are related to the position of the mobile part. This position is given as a time function in Fig. (6.9). Fig. (6.6) shows the evolution of the pressure in chambers V1a and in V1b. In reality, the simulated curves represent the pressure in the exchange lines between the first and the second equivalent cylinders, downstream of the intake valves. The upper values of the curves correspond to the intake pressure (5 bar in the simulated case), and the lower values show the value of the pressure after the expansion (rel. (6.1)). The translation time of the rod is 0.08 s, while the stop time is 0.42 s.

116 Semi-rotary and Linear Actuators

A

B

C

Alfred Rufer

D

A:

Intake V1a Expand V1b

B:

Stop right

to

the

C:

Expand V1a Intake V1b

D

Stop to the left

Fig. (6.6). Evolution of the pressures (N/m2).

The pressures indicated in Fig. (6.6), together with the values of the pressures in the intake, exchange and exhaust ways, produce a global acceleration force as represented in Fig. (6.7). The blue curve in Fig. (6.7) represents the force of the new system with expansion (F1). The two other curves represent the forces of a single cylinder without expansion. These curves will be used for the evaluation of the reduction of air consumption. Their role and significance will be explained in section 6.5. The force exerted on the mobile part of the parallel connected piston rods produces an acceleration and brings this part on a determined velocity. The corresponding curves are shown in Fig. (6.8). The velocity (speed) S1 corresponds to the force F1 of Fig. (6.7). The speed S2 to the force F2 and the speed S3 to the force F3. From the curves of the velocity Fig. (6.8), the position reached by the mobile part is also simulated. The curves can be seen in Fig. (6.9). The curve P1 corresponds to the cylinder assembly with expansion. The mobile equipment starts at position zero and reaches the end of the stroke at the value of 0.020 m. The sequences of the movement (A, B, C, D) are the same as explained in Fig. (6.6).

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Semi-rotary and Linear Actuators 117

F1:

Force of the cylinder assembly (with expansion)

F2:

Force of a single cylinder without expansion producing the average value of F1

F3:

Force of a single cylinder for an identic action as F1

Fig. (6.7). Forces produced in the cylinders (N).

Fig. (6.8). Velocity of the mobile part (m/s).

S1:

Speed of the cylinder assembly (with expansion)

S2:

Speed of a single cylinder without expansion produced by F2 (average of F1)

S3:

Speed of a single cylinder produced by F3

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P1:

Position of the cylinder assembly (with expansion)

P2:

Position of a single cylinder without expansion produced by F2

P3:

Position of a single cylinder produced by F3

Fig. (6.9). Position of the mobile equipment (m).

The simulation further calculates the mechanical power transmitted to the mobile part. This variable corresponds to the product of the speed by the accelerating force. The curve of the power is represented in Fig. (6.10). Then from the transferred power, the produced mechanical work is calculated by a simple integral. The curve is given in Fig. (6.11).

Fig. (6.10). Power dissipated by the mobile equipment (W).

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Semi-rotary and Linear Actuators 119

Fig. (6.11). Energy (work) transferred to the mobile equipment (J).

5. EFFICIENCY OF THE NEW ASSEMBLY The efficiency of the new assembly is calculated on the base of the produced mechanical work and the injected enthalpy into the system. From Fig. (6.11), the produced work by the moving part during the first stroke is:

Wout= 0.5 * 2.915 J

(6.2)

The energy efficiency is calculated as in rel. (4.7): Kconv

Wout

+ in

Wout U  Pin ˜ 'V

(6.3)

U is the thermodynamic content of the injected air under pressure and is calculated as the energy needed for the compression into a volume V1 of the equivalent mass of air from the atmospheric pressure to the value of Pin, V1 being the filled volume of the first actuator. V1=2.262*10-6 m3

120 Semi-rotary and Linear Actuators

U

Ecomp

Alfred Rufer

§ P P · Pin ˜ V1 ¨ ln in  1  atm ¸ Pin ¹ © Patm

(6.4)

1bar · § 5bar 5 ˜105 N / m 2 ˜ 0.00000226m3 ¨ ln 1  ¸ 0.91J 5bar ¹ © 1bar

Pin ˜ 'V

5 ˜105 N / m 2 ˜ 0.00000226m3 1.13J

(6.5)

Finally, and according to rel. (6.3) the efficiency becomes:

Kconv

Wout

+ in

0.5 ˜ 2.91J 1.13J  0.91J

0.713

(6.6)

5.1. Comparison of Performance The value of efficiency given through rel. (6.6) characterizes the efficiency of the new proposed system. It is now interesting to compare this value with the efficiency of a classical cylinder operated without expansion and producing the same mechanical work. A first attempt is to simulate the dynamics of the same load driven by a cylinder producing the average value of the force of the new system. The value of the intake pressure and the maximum length of the stroke is the same. From Fig. (7) (F2), Fig. (8) (S2) and Fig. (9) (P2), the simulation shows that this force does not produce the same mechanical work. This force is produced by a cylinder whose diameter (0.01665 m) is calculated in function of the value of the constant average force to be produced under the same pressure (87.09 N) applied for the same duration as the traveling time measured for the new system (0.08 s). The curve P2 in Fig. (6.9) shows that the maximum length (0.020 m) of the stroke is not reached. From Fig. 8, one can observe that the force F2 produces the same velocity as the new system (see S1 and S2 in Fig. (6.8)). By a successive iteration process, it is possible to determine the amplitude of a constant force (superior to F2) that produces the same displacement of the load at the same time as for the new system. The value of this force is 104.0621 N (F3 in Fig. (6.7), S3 in Fig. (6.8) and P3 in Fig. (6.9)).

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Semi-rotary and Linear Actuators 121

From the value of F3, the diameter of the equivalent single cylinder can be calculated as: 4˜ F S˜p

deq

4 ˜104.06 N S ˜ 4 ˜105 N / m2

0.0182m

(6.7)

The value of 4*105 for the pressure in rel. (6.7) takes into account the action of the atmospheric pressure on the rear side of the piston. The intake volume of the single cylinder becomes:

V1s

S ˜d2 4

˜l

S ˜  0.0182m

2

4

˜ 0.02m 5.2 ˜106 m3

(6.8)

The energy content of this intake volume is calculated as given by rel. (6.4) § P P · Pin ˜V1s ¨ ln in  1  atm ¸ Pin ¹ © Patm 1bar · § 5bar 5 ˜105 N / m 2 ˜ 0.0000052m3 ¨ ln 1 ¸ 5bar ¹ © 1bar U

Ecomp

2.1J

(6.9)

The associated displacement work is Pin ˜ 'V

5 ˜105 N / m 2 ˜ 0.0000052m3

2.6 J

(6.10)

The efficiency of the single cylinder becomes Kconv

Wout

+ in

0.5 ˜ 2.91J 2.6 J  2.1J

0.309

(6.11)

The reduction of consumption of air is defined as the ratio of the two intake volumes

122 Semi-rotary and Linear Actuators

kred

V1 V1s

Alfred Rufer

2.26 ˜106 m3 5.20 ˜106 m3

0.43

(6.12)

6. EXPERIMENTAL SET-UP An experimental set-up has been realized according to the arrangement represented in Fig. (6.1). Four cylinders are connected mechanically at their stator side as at the side of the moving piston rods. The central cylinder has the role of the intake and production of constant pressure displacement work. The schematic representation of the cylinders and control system is given in Fig. (6.4a). Fig. (6.12) shows the realized system.

Fig. (6.12). Views of the realized set-up.

6.1. The Parasitic Effect of the Dead Volumes The distribution of the air through the different inlet-, transfer- and exhaust-valves and through the connecting tubes between the different cylinders affects the system with dead volumes. These volumes were not considered in the ideal simulation and calculation of the performance and of the theoretic value of efficiency. In the recording of the pressures of Fig. (6.13), the change-over from constant pressure displacement work and stop at the left end (A+B with reference to Fig. (6.6) to expansion work (C) is affected by an abrupt variation of the pressure. This transient phenomenon can be explained through the simplified model represented in Fig. (6.14). In this model, there are two dead volumes represented, namely V1p, which is a model of the volumes of the tubing between the intake valve, the chamber of the first cylinder V1, and the transfer valve Vtra. A second dead volume

Linear Pneumatic Cylinder Assembly

Semi-rotary and Linear Actuators 123

V2p represents the tubing between the transfer valve Vtra and the chamber of the second cylinder, V2. In reality, this second cylinder is composed of three individual small cylinders, which makes the connections more complex.

Fig. (6.13). Abrupt variation of the pressure (2.5*10-5 N/m2 per div.), Time (200ms/div).

V1p

V1

Vina

Vtra

V2p

V2

Fig. (6.14). Simplified model of the system with dead volumes.

At the instant of the change-over where the transient occurs, the pistons have reached their end-of-stroke position at the left side. The intake valve is closed. The intake pressure has been established inside the fully deployed first cylinder and in the dead volume V1p. Then, the transfer valve opens in order to start the filling of the volume of the second cylinder V2 when the pistons move in the opposite direction. At the instant of the opening of the transfer valve, the downstream volume is not equal to zero as if the piston has not moved, but the air under pressure in V1 and V1p inrushes into the dead volume V2p. As a result, the

124 Semi-rotary and Linear Actuators

Alfred Rufer

initial pressure of the expansion stroke is not equal to P1 but is changed to P1’ due to a pre-expansion. The value of P1’ is governed by a relation of an adiabatic expansion: J

§ V1  V1 p · P1 ' P1 ¨ ¨ V1  V1 p  V2 p ¸¸ © ¹

(6.13)

The volume of the chamber of the first cylinder V1 is 2.26 cm3, while the dead volume V1p is 1.47 cm3. The dead volume V2p is 1.66 cm3. As a consequence, after the opening of the transfer valve Vtr, the initial pressure level in the V1 + V2 volume for expansion is: 1.4

§ · 2.26cm3  1.47cm3 P1 ' 5bar ¨ 3 3 3 ¸ © 2.26cm  1.47cm  1.66cm ¹

0.597 ˜ 5bar

2.98bar

(6.14)

The negative effect of the pre-expansion is particularly significant in the case of the realized demonstrator due to the small volume of the cylinders versus the value of the dead volumes. Additionally, the assumption of an adiabatic preexpansion should also be questioned. The final value of the pressure after pre-expansion and expansion becomes: 1.4

§ 2.26cm3  1.47cm3  1.66cm3 · P2 ' 2.98bar ¨ 3 3 3 ¸ © 3 ˜ 2.26cm  1.47cm  1.66cm ¹

0.54 ˜ 2.98bar 1.25bar

The final pressure of the idealized system (without dead volumes) was calculated according rel. (6.1). With an initial value of the pressure of 5 bar, the final value of the pressure of the idealized system was: 1.4

P2

§1· Pin ¨ ¸ © 3¹

5bar ˜ 0.21 1.07bar

Linear Pneumatic Cylinder Assembly

Semi-rotary and Linear Actuators 125

6.2. A System with Greater Volumes In the previous example, the effect of the dead volumes has been shown. In the studied system, the dead volumes are in the same order of magnitude as the active volumes of the cylinders. This is due to the small volume of the chosen cylinders (2.26 cm3) but also to the complex piping of the three peripheral cylinders. In order to get an example with less effect on the dead volumes, longer cylinders with 100 mm stroke are chosen instead of the 20 mm of the previous example. Additionally, a system with only two lateral cylinders is chosen, where the tubing system becomes simpler. The diameter of the central cylinder where the displacement work is produced is chosen as 12mm. The diameter of the lateral cylinders where the expansion work is produced is chosen as 16mm (Fig. 6.15). The data of the cylinders are given in Table 6.2.

Fig. (6.15). Cylinder assembly with 100 mm stroke actuators. Table 6.2. The data of the cylinders. Cylinder type

Bore size

Pressure area (push)

Pressure area (pull)

Stroke

PB12-100

12 mm

113 mm

93.4 mm

100 mm

PB16-100

16 mm

201 mm

181 mm

100 mm

2 2

2

2

126 Semi-rotary and Linear Actuators

Alfred Rufer

The cylinder assembly with valves and tubing is represented in Fig. (6.16). Air in Vina

Vinb

Vtra

Vexhb

Vexha

ON/OFF

Vtrb

a)

b)

Fig. (6.16). Cylinder assembly with 100 mm stroke actuators.

The pressure levels of the pre-expansion and expansion are calculated on the base of the schematic representation of Fig. (6.17). In this representation, the lengths of the pipes are indicated (in mm). The symbol M is used for the representation of the pressure sensor. A fictive additional dead volume A is also represented for the estimation of the pressure levels to be compared with the pressure recordings. Vina 80

M

30

90

40 35

A 40

Vtra

50

40 30

A 40

80 40

M

Vexha

Fig. (6.17). Schematic representation of the cylinder assembly.

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Semi-rotary and Linear Actuators 127

The system represented in Fig. (6.17) corresponds to an experimental set-up where only the push-side of the first cylinder is fed, and where the expansion of the air is realized at the pull sides of the lateral actuators. The feeding pressure P1 corresponds to an absolute pressure of 6 bar (relative pressure measured = 5 bar). From the recordings of Fig. (6.18), one can see that a pre-expansion due to the dead volumes occurs. The pressure after pre-expansion is of 4.4 bar (absolute).

P1

P1'

P2'

Fig. (6.18). Pressure recordings (1*10-5 N/m2 per div.), Time (200ms/div).

The dead volumes, according to the representation of Fig. (6.12), are calculated as the sum of the volumes of the tubing and of the additional volumes A. A represents the internal volumes of the valves and of the pressure sensors. With an internal section of the tubes of:

Sint

V1P

 2.5mm

2

S 4

4.9mm 2

4.9mm 2 (30mm  80mm  90mm  40mm  35mm)  A 1340mm3  A 1.34cm3  A

V2 P

4.9mm 2 (50mm  30mm  40mm  40mm  40mm  40mm  40mm  80mm)  A 1560mm3  A 1.56cm3  A

(6.16)

(6.17)

(6.18)

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Alfred Rufer

The additional dead volume A is calculated according rel. (6.21): J

' 1

P

§ V12  V1P · ¨ ¸ ˜ P1 © V12  V1P  V2 P ¹

1.4

11.3  1.34  A § · ¨ ¸ ˜ P1     11.3 1.34 A 1.56 A © ¹

(6.19)

Where V12 is the volume of the fully expanded chamber (push side) of the 12mm cylinder. V16 is the volume of the fully expanded chamber (push side) of the 16 mm cylinder. Further,

1.4

11.3  1.34  A § · ¨ ¸ © 11.3  1.34  A  1.56  A ¹

P1' P1

(6.20)

With P1’ = 4.4bar and P1 =6 bar,

1.4

0.73

11.3  1.34  A § · 0.798 ¨ ¸ © 11.3  1.34  A  1.56  A ¹

(6.21)

The additional dead volume becomes

A 2.16cm3 The calculation of the pressure P2’ after expansion into the two lateral cylinders is then done J

' 2

P

§ V12  V1P  V2 P · ' ¨ ¸ ˜ P1 © 2 ˜V16  V1P  V2 P ¹

1.1

§ 11.3  1.34  A  1.56  A · ¨ ¸ ˜ 4.4bar 1.72bar (6.22) © 2 ˜18.1  1.34  A  1.56  A ¹

The exponent γ =1.1 is chosen in relation with the cooling inside of the tubes and cylinders during the air transfer and expansion.

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Semi-rotary and Linear Actuators 129

6.3. Control with a Simplified Tubing and Valve System (Supposed less dead volumes) – using 5/2-way Valves The connection between the different cylinders and valves, according to the scheme given in Figs. (6.4a) and (6.16b), is very complex. The number of valves and tube sections is the main cause of the dead volume leading to the preexpansion phenomenon. Instead of the use of six 2 port valves, namely 2 intake, 2 transfer and 2 exhaust valves, the control of the proposed system can be realized using so-called 5/2-way valves. The corresponding system with these valves is represented in Fig. (6.19). The distribution of the air for the push and pull side of the first cylinder is realized through the valve represented on the top left side of the picture. Then, the transfer of the air from the push side (respectively, pull side) of the first cylinder to the pull side (respectively, push side) of the second one is realized by the two other distribution valves. These valves are controlling alternately the transfer and exhaust phase to and from the second cylinder. The upper scheme of Fig. (19) shows the state of the valves and air path for the pull stroke, while the lower diagram shows the state of the valves and path for the pull stroke.

Air in

Air out

Air out

Air in

Air out

Fig. (6.19). Control with 5/2 way valves.

Air out

130 Semi-rotary and Linear Actuators

Alfred Rufer

6.4. Experiment with the 100 mm Assembly The diagrams of Fig. (6.20) represent a system assembly with single sided feeding of the cylinders. As was already described in the experiment of Fig. (6.17), the push side of the first cylinder is filled with constant pressure while the pull side of the second receives the air transferred from the first one (expansion). The pressure in the first cylinder is measured (M1) as well as the pressure in the second one, downstream of the valves. A1

M1

A3

M2

Air in

A2

Air out

A1

M1

A3

M2

Air in

A2

Air out

Fig. (6.20). Simplified system and control with 5/2 way valves.

Fig. (6.21). The experimental set-up with 5/2 way valves.

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Semi-rotary and Linear Actuators 131

From the curves of Fig. (6.21), one can see that the phenomenon of the preexpansion due to the dead volumes is still present.

Fig. (6.22). Pressures in the experiment with 5/2 way valves (1*10-5 N/m2 / div), Time (200ms/div).

DISCLOSURE Part of this chapter has previously been published in Revisiting the Industrial Pneumatic Technology—An Innovative Development for an Increased Energetic Efficiency, in ASME Open Journal of Engineering, in 2022, 011018.

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CHAPTER 7

The Effect of the Dead Volumes and Pre-Expansion on the Produced Work Abstract: In Chapter 6, the parasitic effect of pre-expansion due to the presence of dead volumes has been observed. This effect will now be analyzed in more detail in this chapter. Especially the influence of this pre-expansion on the total produced mechanical work is calculated. Different pre-expansion factors are considered and the mechanical work of an ideal system without pre-expansion will be compared with the reduced mechanical work of a cylinder assembly affected by pre-expansion.

Keywords: Dead Volumes, Pre-expansion, Pre-expansion Factor, Torque Reduction. 1. INTRODUCTION The experimental results realized with linear cylinders and described in Chapter 6 have revealed the parasitic effect of the pre-expansion due to the presence of dead volumes. This effect is inherent to all systems where pressured air is intended to be transferred from one volume to another. The systems described in Chapters 4, 5 and 6 have been simulated in ideal conditions where no dead volumes have been considered. Typically, the evolution of the pressure during the expansion phase, as illustrated in Fig. (4.4), shows that the initial value of pressure P2 of the expansion process corresponds to the value of the intake pressure Pin of the air in the small chamber established during the previous stroke. The absence of discontinuity in the pressure by the changeover from filling to expanding is due to the condition that the interconnection of the volumes V1b and V2a results in V1b+V2a, as represented in Fig. (4.3b). In practice, the interconnection of the volumes must be modelled taking into account the dead volumes as represented in Fig. (6.14) and (6.17). The pre-expansion phenomenon observed with the small cylinders in the previous chapter can be characterized by the ratio of the pressure after the opening of the transfer valve to the initial value of the pressure upstream of this valve before its Alfred Rufer All rights reserved-© 2023 Bentham Science Publishers

The Effect of the Dead Volumes

Semi-rotary and Linear Actuators 133

opening (P1 to P1’ in Fig. (6.18)). This ratio of the pressure discontinuity is called the pre-expansion factor. In the next sections, the pre-expansion and its effect on the developed torque will be simulated. The considered system corresponds to the system described in Chapter 4, namely the system with coupled semi-rotary actuators. But the evolution of the volumes of the complementary smaller and larger chambers of this system is identical to the evolution of the coupled chambers of the systems using linear cylinders. First, the discontinuity of the pressure will be shown in Section 7.1.1 In this simulation, the intake pressure and the parameters of the devices of the system of Chapter 4 are considered. This will allow to make a comparison of an ideal system with a system with dead volumes. The comparison will be done on the base of the different torques produced by the ideal and non-ideal system models, and for two different values of the pre-expansion factor. A pre-expansion factor of 0.6 characterises the system simulated in Section 7.1.2 and a value of 0.8 characterises the system simulated in Section 7.1.3. 1.1. Discontinuity of the Pressure The discontinuity of the pressure illustrating the pre-expansion due to dead volumes is represented in Fig. (7.1). The initial (filling) pressure is 10 bar, and the pre-expansion factor is equal to 0.6 The expansion process is conditioned by the same parameters as for the example of Chapter 4.

Fig (7.1). Pressure discontinuity due to pre-expansion X: Time (s) (similar to Fig. 4.3 to 4.9) Y: Pressure (bar).

134 Semi-rotary and Linear Actuators

Alfred Rufer

1.2. Torques Developed with a Pre-Expansion Factor of 0.6 Fig. (7.2) illustrates the torque contributions of both sides of the wing of the first (small) actuator during the second half period. The curves of an ideal system without pre-expansion are represented for comparison with the curves of a system with pre-expansion. The curves of the system without pre-expansion are identic to the curves simulated in Chapter 4.

Fig. (7.2). Torque contributions of the first (small) actuator (Nm).

In Fig. (7.3), the torque contributions of the first (smaller) and second (larger) actuators are represented. The curves show the phenomenon in the second halfperiod. The curves of a system with and without pre-expansion are represented.

The Effect of the Dead Volumes

Semi-rotary and Linear Actuators 135

Fig. (7.3). Torques developed by the two actuators without and with pre-expansion (Nm).

Fig. (7.4) illustrates the total torque (output of the motion rectifier) of the system without and with pre-expansion. For the evaluation of the increase in the performance due to the additional expansion chamber, the torque of the original actuator without expansion is also represented (22.5 Nm).

Fig. (7.4). Total torque and average torque of a system without and with pre-expansion and torque of the original actuator without expansion (22.5 Nm).

136 Semi-rotary and Linear Actuators

Alfred Rufer

1.3. Comparison of Energetic Performances The curves of the developed torques and their average values are used for the evaluation of the energetic performance of the different systems. The calculation is made for the semi-rotary actuator and assembly, but the method can be applied to systems using linear devices. In Table 7.1, the different values of the torque averages of the different systems are summarised. Four different cases are considered where the air consumption or, in other words the injected enthalpies are the same. The first case is the small actuator alone without expansion. Then, the assembly with an additional expansion device is considered under the ideal conditions without dead volumes. The two other cases give the torque averages developed by the same assembly but with consideration of the pre-expansion due to the dead volumes. Two values of the pre-expansion factor are indicated, namely 0.6 and 0.8. Table 7.1. Torques produced by different systems. System

Pre-expansion Factor

Single actuator without expansion

Torque Average 22.5 Nm

Assembly with expansion ideal model

1

40.5 Nm

Assembly with consideration of dead volume

0.8

35.6 Nm

Assembly with consideration of dead volume

0.6

31 Nm

In Section 4.3, the energetic performance has been defined in the form of an equivalent conversion efficiency as the ratio of the produced mechanical work to the injected enthalpy.

Kconv

Wout

+ in

Wout U  Pin ˜ 'V

(7.1)

The injected enthalpy into all four systems has the same value and has been evaluated as:

+ in U  Pin ˜ 'V

complete cycle.

331J  236 J

567 J

for the first actuator and for a

The mechanical work is calculated as:

Wout

M AV ˜ Mout ,

jout = 9.42 rad for a complete cycle of the 270° actuator

The Effect of the Dead Volumes

Semi-rotary and Linear Actuators 137

The indicated values in Table 7.2 reflect very well the advantage of cascading two actuators of different volumes in order to recover the thermodynamic energy content of the injected air under pressure. The poor value of the efficiency of a single actuator without expansion is also a relevant indication of the inherent low efficiency of classical pneumatic devices. Table 7.2. Energy efficiency of the different systems. System

Pre-expansion factor

Single actuator without expansion

hconv 0.376

Assembly with expansion ideal model

1

0.67

Assembly with consideration of dead volume

0.8

0.59

Assembly with consideration of dead volume

0.6

0.51

The considered values for the pre-expansion factor (0.6 and 0.8) concern small actuators where the dead volume of the control and tubing cannot be neglected compared to the active volume of the device itself. For larger actuators, the preexpansion phenomenon should not reduce the pressure significantly, and the performance should be similar to the performance calculated with the ideal model.

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CHAPTER 8

Application Example: A Pneumatic Driven Hydrogen Compressor with Increased Efficiency Abstract: In this chapter, an application example is studied where the energetic efficiency of a pneumatically driven device is of importance. The chosen example consists of an air-driven gas booster used as a Hydrogen compressor in a refuel station for H2 driven cars. The needed force for the driving of the compression cylinders is calculated, and a new pneumatic motor based on the principle of adding expansion work is proposed. The new motor is designed for sufficient effort for moving the mobile equipment under the maximum compression force. The air consumption of the new system is calculated, and finally, the air savings in comparison to a classical air-driven booster. The simulation is completed with a dynamic part showing the dynamic performance in terms of velocity and time to reach the final position of the pistons

Keywords: Air-driven gas-booster, Design, Dynamic simulation, Energetic efficiency, Saving of air. 1. INTRODUCTION In many domains of gas pressurization, but specifically for the refueling stations for hydrogen powered vehicles, so-called gas-boosters are used. These gasboosters are driven by a central double acting pneumatic motor. In this chapter, an air driven hydrogen compressor is studied, and a new approach is presented based on the principles described in Chapters 4 and 5. This can significantly improve the energy efficiency of the compression stations, or in other terms, can significantly reduce the consumption of compressed air for an identic output performance. A schematic representation of a hydrogen refilling station is given in Fig. (8.1) where hydrogen is produced from an electrolyser, fed from photovoltaic panels. The high-pressure compression stage based on a gas-booster is also represented. In this example, the air compressor, which provides the activation fluid of the gas booster, is also powered by renewable power sources. Alfred Rufer All rights reserved-© 2023 Bentham Science Publishers

A Pneumatic Driven Hydrogen Compressor

Semi-rotary and Linear Actuators 139

Booster

Electrolyser H2

Rectifier

H2 P2

P1