كتاب Design Rules for Actuators in Active Mechanical Systems

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Design Rules for Actuators in Active Mechanical Systems
Oriol Gomis-Bellmunt
Lucio Flavio Campanile

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Contents
Part I Introductory Remarks
1 Actuator Principles and Classification 3
1.1 Actuator Principles . 5
1.1.1 Electromagnetic Actuators 5
1.1.2 Fluid Power Actuators 11
1.1.3 Piezoelectric Actuators . 13
1.1.4 Thermal Shape Memory Alloy Actuators 20
1.1.5 Other Actuators . 22
1.2 Solid-State versus Conventional Actuation . 25
References . 27
2 Actuator Design Analysis . 29
2.1 Nature and Objectives of Actuator Design Analysis 29
2.2 Performance Indexes 33
2.3 Design Parameters 36
2.3.1 Geometrical Factors 37
2.3.2 Aspect Ratios . 40
2.3.3 Filling Factors . 41
2.4 Output Quantities 43
2.4.1 Output Quantities Expression 43
2.4.2 Steady-State Analysis 45
2.5 Thresholds 48
2.6 Maximum Target Quantity for a Given Size . 50
2.6.1 Output Mechanical Quantities Maximization . 51
2.6.2 Other Quantities . 53
2.7 Scalability 54
2.8 Dimensional Analysis . 55
2.8.1 The Buckingham Pi Theorem 55
2.8.2 Non-Dimensional Numbers 59
2.9 Validation . 61
xiiixiv Contents
2.9.1 Prototype Construction . 61
2.9.2 Industrial Actuators 61
2.9.3 Simulation 62
2.10 Considerations on Actuators Dynamics 71
2.10.1 Dynamical Analysis 71
2.10.2 Control System 73
References . 78
Part II Conventional Actuators
3 Design Analysis of Solenoid Actuators 81
3.1 Design Parameters 81
3.2 Output Quantities 82
3.3 Thresholds 84
3.4 Maximum Output Quantities . 86
3.5 Scalability 90
3.6 Dimensional Analysis . 92
3.7 Finite Element Analysis . 94
3.8 Comparison with Industrial Actuators . 96
3.9 Dynamics . 102
3.9.1 System Modeling 102
3.9.2 Open Loop Simulation 103
3.9.3 Control Design 103
3.9.4 Closed Loop Simulation 105
References . 109
4 Design Analysis of Moving Coil Actuators 111
4.1 Design Parameters 111
4.2 Output Quantities 111
4.3 Thresholds 114
4.4 Maximum Output Quantities . 114
4.5 Scalability 116
4.6 Dimensional Analysis . 116
4.7 Finite Element Analysis . 118
4.8 Comparison with Industrial Actuators . 120
4.9 Dynamics . 120
4.9.1 System Modeling 120
4.9.2 Control Design 126
4.9.3 Closed Loop Simulation 127
References . 131
5 Design Analysis of Hydraulic Actuators 133
5.1 Design Parameters 133
5.2 Force-Stroke and Work-Stroke Characteristic . 133
5.3 Thresholds 135
5.4 Maximum Force, Stroke and Work 136Contents xv
5.4.1 Forward Motion . 136
5.4.2 Backward Motion 136
5.4.3 Considering Forward and Backward Motion 138
5.4.4 Stroke and Work . 139
5.5 Scalability 141
5.6 Dimensional Analysis . 141
5.7 Industrial Actuators . 141
5.8 Dynamics . 142
5.8.1 System Modeling 143
5.8.2 Open Loop Simulation 145
References . 153
Part III Solid-State Actuators
6 Design Principles for Linear, Axial Solid-State Actuators . 157
6.1 Complexity Levels in Modeling Solid-State Actuators 157
6.2 Limits and Advantages of a Linear Theory of Solid-State
Actuation Based on Prescribed Induced Strain 158
6.3 Theory of Single-Stroke Linear Solid-State Actuators 159
6.3.1 Definitions and Symbols 159
6.3.2 Free Stroke and Blocking Force 164
6.3.3 Actuator Coupled with a Linear Elastic Structure 165
6.3.4 Activation Boundary . 167
6.3.5 Strength Boundary . 168
6.3.6 Stroke Work 168
6.3.7 Hybrid Actuators 174
6.4 Design Principles and Rules 176
6.4.1 Actuator Performance as a Function of Geometry . 176
6.4.2 The Stiffness-Matching Paradigm 181
6.4.3 Design of Hybrid Actuators . 183
6.4.4 Solid-state Actuator in a Compliant Frame . 183
6.4.5 The Actuator’s Own Stiffness as a Design Requirement 190
6.4.6 Coupled Design of Actuator and Host Structure . 192
6.4.7 Simultaneous Optimization of Actuator Position and
Geometry . 194
6.5 Extension to the Dynamic Case . 195
6.5.1 Work Produced by a Solid-State Actuator in Cyclic
Operation . 195
6.5.2 Maximum Cycle Work and Power Output 198
6.5.3 Design Principles and Rules for the Dynamic Case 200
References . 200
Index . 203List of Figures
1.1 Example industrial system. Press transfer system in sheet-metal
working. Courtesy of Bosch Rexroth AG . 4
1.2 Usual block diagram of a mechatronic system 4
1.3 Industrial DC motor. Courtesy of BEI Kimco Magnetics . 7
1.4 Industrial solenoid actuators. Courtesy of NSF Controls Ltd 8
1.5 Industrial moving coil actuators. Courtesy of BEI Kimco Magnetics . 9
1.6 Example hydraulic cylinder. Courtesy of Bosch Rexroth AG . 12
1.7 Hydraulic cylinder parts. Courtesy of Bosch Rexroth AG 12
1.8 Example pneumatic cylinder. Courtesy of Bosch Rexroth AG . 13
1.9 Sample piezoelectric actuators. Courtesy of Noliac . 14
1.10 Sample piezoelectric actuators. Courtesy of Cedrat . 15
1.11 Axes and deformation directions . 15
1.12 Different deformation modes: (a) longitudinal mode, (b) transverse
mode, (c) shear mode 16
1.13 Equivalent circuit of a piezoelectric element excited at high frequency 17
1.14 Displacement-force curves 18
1.15 Shape memory alloy actuator used in medical applications. It
consists in a tissue spreader used in open heart surgery. Courtesy of
Memory Metalle GmbH 21
1.16 Shape memory alloy parts. Courtesy of Memory Metalle GmbH 22
1.17 Comb actuator by Ando et al. [1] 23
1.18 Magnetostrictive actuator concept. Courtesy of ETREMA Products,
Inc 24
1.19 Ultrasonic magnetostrictive actuator. Courtesy of ETREMA
Products, Inc 24
2.1 Actuator design procedure 32
2.2 Maximum stress versus maximum strain for different classes of
actuators (Data extracted from [5]) . 34
2.3 Maximum frequency versus maximum strain for different classes
of actuators (Data extracted from [5]) . 35
xviixviii List of Figures
2.4 Maximum frequency versus maximum stress for different classes
of actuators (Data extracted from [5]) . 35
2.5 Maximum volumetric power density versus maximum strain for
different classes of actuators (Data extracted from [5]) 37
2.6 Maximum mass power density versus maximum strain for different
classes of actuators (Data extracted from [5]) 37
2.7 Maximum volumetric power density versus maximum strain times
maximum stress for different classes of actuators (Data extracted
from [5]) . 38
2.8 Resolution versus maximum strain for different classes of actuators
(Data extracted from [5]) . 38
2.9 Efficiency versus maximum mass power density for different
classes of actuators (Data extracted from [5]) 39
2.10 Pipe analyzed in Example 2.2 . 40
2.11 Coil wiring scheme employed in the k f f calculation developed in
(2.9) 42
2.12 Coil wiring scheme employed in the k f f calculation developed in
(2.11) . 42
2.13 Comparison of the ?i parameters of the different exposed conductor
configurations 43
2.14 Sketch of the system under analysis in Example 2.3 . 44
2.15 Cube force characteristic of Example 2.3 45
2.16 Capacitive actuator of Example 2.4 . 46
2.17 Force-stroke curve of Example 2.4 . 47
2.18 Work-stroke curve of Example 2.4 . 47
2.19 Force-stroke curve equilibrium points of Example 2.5 . 48
2.20 BH saturation curve of Example 2.7 50
2.21 Design factor of Example 2.9 . 53
2.22 Force per cross section performance as a function of the parameter ? 55
2.23 Typical screen of a finite analysis software (COMSOL by
COMSOL AB) of the example of the permanent magnet and the
levitating ball . 64
2.24 Example element mesh using COMSOL by COMSOL AB. It can
be noted that the permanent magnet and the ball are finer meshed
that the surrounding air . 65
2.25 Post-processing of the solved examples. The streamlines show the
magnetic flux flow 66
2.26 Post-processing of the solved examples. The ball colors and arrows
show the different Maxwell tensor stresses in the ball . 67
2.27 Post-processing of the solved examples. The slices show the
different values of magnetic flux density 68
2.28 Post-processing of the solved examples. The isosurface show the
different surfaces having the same magnetic flux density . 69
2.29 Obtained FEA results for the permanent magnet and ball system of
Example 2.15 . 70List of Figures xix
2.30 Comparison of the different polynomials proposed to model the
force-displacement curve of Example 2.15 70
2.31 Real part of the poles of (2.70) 72
2.32 Imaginary part of the poles of (2.70) 73
2.33 Dynamic step response of the system with different ? and ?0 = 10
rad/s 74
2.34 Bode plot of the system for different ? and ?0 = 10 rad/s 75
2.35 Typical open loop control block diagram of a mechatronic system 75
2.36 Typical closed loop control block diagram of a mechatronic system . 76
3.1 Solenoid actuator sketch 81
3.2 Force-displacement curves for the solenoid actuator . 83
3.3 Work-displacement curves for the solenoid actuator . 84
3.4 Force-displacement curves for elastic and constant loads . 85
3.5 Solenoid force design factor depending on kr1 and kr3 with
kl2 = 0.5 and ? = 0.7 . 88
3.6 Solenoid force design factor depending on ? and kr1 with kl2 = 0.5
and kr3 = 0.78 88
3.7 Solenoid force design factor depending on ? and kr3 with kl2 = 0.5
and kr1 = 0.29 89
3.8 Solenoid force design factor depending on kl2 and kr1 with ? = 0.7
and kr1 = 0.29 89
3.9 Solenoid work design factor depending on kr1 and kr3 with
kl2 = 0.75 and ? = 1.01 . 90
3.10 Solenoid work design factor depending on ? and kr1 with
kl2 = 0.75 and kr3 = 0.86 . 90
3.11 Solenoid work design factor depending on ? and kr3 with
kl2 = 0.75 and kr1 = 0.39 91
3.12 Solenoid work design factor depending on kl2 and kr1 with
? = 1.01 and kr1 = 0.39 . 91
3.13 Solenoid force scalability for different ? coefficients in the Nusselt
number expression 92
3.14 Geometry of the actuator analyzed with COMSOL 95
3.15 Finite element mesh of the actuator analyzed with COMSOL . 97
3.16 Flux densities and Maxwell tensor stresses in the analyzed actuator 98
3.17 Detail of the airgap flux densities and Maxwell tensor stresses in
the analyzed actuator 99
3.18 Datasheet of an industrial solenoid actuator. Courtesy of NSF
Controls Ltd 100
3.19 Industrial electromagnetic actuator force-area comparison . 101
3.20 Industrial electromagnetic actuator work-volume comparison . 101
3.21 Simulated solenoid actuator scheme 103
3.22 Position response of the solenoid actuator to an open loop simulation 104
3.23 Speed, current and force response of the solenoid actuator to an
open loop simulation . 104xx List of Figures
3.24 Position-speed curve response of the solenoid actuator to an open
loop simulation . 105
3.25 Simulated solenoid actuator scheme 106
3.26 Solenoid actuator response tracking a rectangular reference 106
3.27 Speed, current and force of the solenoid actuator tracking a
rectangular reference . 107
3.28 Solenoid actuator response tracking a triangular reference 107
3.29 Speed, current and force of the solenoid actuator tracking a
triangular reference 108
3.30 Solenoid actuator response tracking a sinusoidal reference . 108
3.31 Speed, current and force of the solenoid actuator tracking a
sinusoidal reference . 109
4.1 Moving coil actuator sketch . 112
4.2 Moving coil actuator reluctances . 113
4.3 Moving coil design factor depending on ? and kr1 with kr3 = 0.94
and kl1 = kl4 = 0.5 115
4.4 Moving coil work modified design factor depending on kr1 and kl4
with kl1 = 0.5 and ? = 1.1 . 116
4.5 Geometry of the actuator analyzed with COMSOL 119
4.6 Finite element mesh of the actuator analyzed with COMSOL . 121
4.7 Flux densities of the analyzed actuator 122
4.8 Flux densities and Maxwell tensor stresses in the analyzed actuator 123
4.9 Datasheet of an industrial moving coil actuator. Courtesy of BEI
Kimco Magnetics . 124
4.10 Industrial electromagnetic actuator force-area comparison . 125
4.11 Industrial electromagnetic actuator work-volume comparison . 125
4.12 Simulated moving coil actuator scheme . 127
4.13 Moving coil actuator response tracking a rectangular reference . 128
4.14 Speed, current and force of the moving coil actuator tracking a
rectangular reference . 128
4.15 Moving coil actuator response tracking a triangular reference . 129
4.16 Speed, current and force of the moving coil actuator tracking a
triangular reference 129
4.17 Moving coil actuator response tracking a sinusoidal reference 130
4.18 Speed, current and force of the moving coil actuator tracking a
sinusoidal reference . 130
5.1 Hydraulic actuator . 134
5.2 Geometry of a hydraulic actuator 134
5.3 Forward force design factor . 136
5.4 Backward force design factor, ? = 1 . 138
5.5 Forward-backward averaged force design factor, ? = 1 139
5.6 Forward work design factor . 140List of Figures xxi
5.7 Comparison between the input to output diameter ratio existing in
industrial actuators and the results of the present work . 142
5.8 Industrial hydraulic actuator force-area performance 143
5.9 Simulated hydraulic actuator scheme . 145
5.10 Position and speed response of the hydraulic actuator to an open
loop simulation. Simulation 1 . 146
5.11 Transient of the position and speed response. Simulation 1 . 147
5.12 Mass flow and pressure response of the hydraulic actuator to an
open loop simulation. Simulation 1 . 148
5.13 Pressure-flow curve response of the hydraulic actuator to an open
loop simulation. Simulation 1 . 149
5.14 Position and speed response of the hydraulic actuator to an open
loop simulation. Simulation 2 . 150
5.15 Transient of the position and speed response. Simulation 2 . 151
5.16 Mass flow and pressure response of the hydraulic actuator to an
open loop simulation. Simulation 2 . 152
5.17 Pressure-flow curve response of the hydraulic actuator to an open
loop simulation. Simulation 2 . 153
6.1 Actuator force and stroke . 159
6.2 Symbols for (a) ideal force generator , (b) ideal stroke generator
and (c) linear elastic spring . 161
6.3 Circuits representing (a) a serial arrangement of an ideal stroke
generator and a spring between two rigid walls and (b) a parallel
arrangement of the same two components, with one end fixed 162
6.4 Drawings of the mechanical systems of Figure 6.3, in the same
order, (a) a serial arrangement of an ideal stroke generator and a
spring between two rigid walls and (b) a parallel arrangement of
the same two components, with one end fixed 162
6.5 Spring element with (a) stroke and force indications, (b) ideal
stroke and (c) force generators with integrated sensors . 163
6.6 Circuits representing (a) an induced-force actuator and (b) an
induced-stroke actuator . 163
6.7 Symbol for an induced-stroke actuator 164
6.8 Actuator (a) in open-loop configuration and (b) in shorted
configuration . 165
6.9 Actuator coupled with a linear elastic structure 166
6.10 Characteristic curves of (a) an actuator and (b) of a linear spring in
the respective Fu-planes. (c) Interaction of both curves in the same
Fu-plane (F=actuator force) 166
6.11 Interaction of the characteristic curves of actuator and structure (a)
for ks ka and (b) for ks ka 166xxii List of Figures
6.12 (a) Actuator characteristic curves for different values of the induced
strain. (b) Activation boundary. The shaded area represents the
operation domain of the actuator when coupled with a passive
structure without pre-stress . 167
6.13 (a) Typical strength boundary of a piezoelectric stack actuator. (b)
Operation domain (shaded area) as defined by the strength and the
activation boundaries 168
6.14 (a) Mechanical work performed by the actuator while interfaced
with a passive structure without pre-stress. (b) Work produced
against linear structures of different stiffness; stiffness matching
condition (thick line, dark shaded area) . 171
6.15 Maximum effective stroke work against a linear structure
without pre-stress while considering the strength boundaries: (a)
Passive strength boundary, (b) active strength boundary, without
intersection with the stiffness matching path and (c) active strength
boundary intersecting the stiffness matching path . 172
6.16 Graphs of (a) an actuator working against a constant load, (b)
coupled with a structure with pre-strain and (c) coupled with a
structure with pre-stress or loaded by an external constant force . 172
6.17 Mechanical work performed by the actuator (a) against a constant
load and (b) against a structure with pre-strain . 173
6.18 Hybrid actuator in simple serial arrangement, (a) open-loop and (b)
shorted 175
6.19 Hybrid actuator in simple parallel arrangement, (a) open-loop and
(b) shorted . 176
6.20 Graph of a solid-state actuator integrated into a compliant mechanism177
6.21 (a) Host structure characteristic with working point and
characteristics of actuators providing the required output quantities.
(b) Characteristic of the optimal actuator according to the stiffness
matching principle. (c) Extension to the case of a general load 182
6.22 The fish-mouth actuator 185
6.23 The fish-mouth actuator spring as a two-degrees-of-freedom system . 185
6.24 Graph of the hybrid solid-state actuator with (a) open-loop output,
(b) shorted input and (c) general loading 188
6.25 The elliptical region of the fish-mouth actuator spring . 189
6.26 Design of a hinge less trailing-edge flap . 194
6.27 Design space graphs for the hinge less trailing-edge flap . 194
6.28 (a) Family of elliptical trajectories for an oscillating host system
and (b) trajectory described for a given oscillating induced stroke . 197List of Tables
1.1 Resistivity of different materials . 10
1.2 Magnetic permeability of different materials . 10
1.3 Piezoelectric material relevant parameters . 19
1.4 Piezoelectric material properties [27] . 19
1.5 Main applications of piezoelectric devices . 21
1.6 Magnetostrictive maximum strain. Data from [17] 23
2.1 Actuator drive input quantities for different actuator technologies . 44
2.2 Actuator limiting quantities . 49
2.3 Force-position data obtained using FEA . 65
3.1 Solenoid actuator dimensional analysis quantities . 93
3.2 Dimension matrix for the solenoid force analysis . 93
4.1 Moving coil actuator dimensional analysis quantities 117
4.2 Dimension matrix for the moving coil force analysis 117
5.1 Hydraulic actuator dimensional force analysis quantities . 141
5.2 Hydraulic actuator dimensional work analysis quantities

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