89,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Hydrostatic Transmissions and Actuators takes a pedagogical approach and begins with an overview of the subject, providing basic definitions and introducing fundamental concepts. Hydrostatic transmissions and hydrostatic actuators are then examined in more detail with coverage of pumps and motors, hydrostatic solutions to single-rod actuators, energy management and efficiency and dynamic response. Consideration is also given to current and emerging applications of hydrostatic transmissions and actuators in automobiles, mobile equipment, wind turbines, wave energy harvesting and airplanes. End of chapter exercises and real world industrial examples are included throughout and a companion website hosting a solution manual is also available.
Hydrostatic Transmissions and Actuators is an up to date and comprehensive textbook suitable for courses on fluid power systems and technology, and mechatronics systems design.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 574
Veröffentlichungsjahr: 2015
Ähnliche
Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
For Whom This Book Has Been Written
Book Organization
Acknowledgements
About the Companion Website
Chapter 1: Introduction to Power Transmission
1.1 Transmission Ratio
1.2 Mechanical Transmissions
1.3 Hydraulic Transmissions
1.4 Hydrostatic Transmissions
1.5 Hydromechanical Power-Split Transmissions
1.6 Mechanical and Hydrostatic Actuators
Exercises
References
Chapter 2: Fundamentals of Fluid Flows in Hydrostatic Transmissions
2.1 Fluid Properties
2.2 Fluid Flow in Hydraulic Circuits
Exercises
References
Chapter 3: Hydrostatic Pumps and Motors
3.1 Hydrostatic and Hydrodynamic Pumps and Motors
3.2 Hydrostatic Machine Output
3.3 Hydrostatic Pump and Motor Types
3.4 Energy Losses at Steady-State Operation
3.5 Modelling Pump and Motor Efficiencies
Exercises
References
Chapter 4: Basic Hydrostatic Transmission Design
4.1 General Considerations
4.2 Hydrostatic Transmission Efficiency
4.3 Transmission Output
4.4 Steady-State Design Applications
4.5 External Leakages and Charge Circuit
4.6 Heat Losses and Cooling
Exercises
References
Chapter 5: Dynamic Analysis of Hydrostatic Transmissions
5.1 Introduction
5.2 Modelling and Simulation
Exercises
References
Chapter 6: Hydrostatic Actuators
6.1 Introductory Concepts
6.2 Hydrostatic Actuator Circuits
6.3 Common Pressure Rail and Hydraulic Transformers
Exercises
References
Chapter 7: Dynamic Analysis of Hydrostatic Actuators
7.1 Introduction
7.2 Mathematical Model
7.3 Case Study
Exercises
References
Chapter 8: Practical Applications
8.1 Infinitely Variable Transmissions in Vehicles
8.2 Heavy Mobile Equipment
8.3 Hybrid Vehicles
8.4 Wind Turbines
8.5 Wave Energy Extraction
8.6 Aeronautical Applications
References
Appendix A: Hydraulic Symbols
Appendix B: Mathematics Review
B.1 The
Nabla
Operator ()
B.2 Ordinary Differential Equations (ODEs)
References
Appendix C: Fluid Dynamics Equations
C.1 Introduction
C.2 Fluid Stresses and Distortion Rates
C.3 Differential Fluid Dynamics Equations
C.4 Control Volume Analysis
References
Index
End User License Agreement
Pages
xiii
xiv
xv
xvii
xix
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
Guide
Cover
Table of Contents
Begin Reading
List of Illustrations
Chapter 1: Introduction to Power Transmission
Figure 1.1 Typical situation requiring a power transmission
Figure 1.2 Classification of power transmissions according to the transmission ratio
Figure 1.3 Train of friction discs
Figure 1.4 Schematic representation of a two-speed sequential gearbox
Figure 1.5 Sequential gearbox
Figure 1.6 Schematic representation of a planetary gearbox
Figure 1.7 In-line planetary gear reducer 3:1-10:1 | AE series (courtesy of Apex Dynamics, USA)
Figure 1.8 Two engaging gears (only one tooth profile per gear is shown)
Figure 1.9 Basic continuously variable transmission
Figure 1.10 Transmission ratio in a mechanical IVT
Figure 1.11 Schematic representation of a toroidal CVT
Figure 1.12 Toroidal power-split IVT [7]
Figure 1.13 Combination of a toroidal CVT and a gearbox
Figure 1.14 Continuously variable transmission with conic pulleys: (a) Case 1 – and (b) Case 2 –
Figure 1.15 Variable diameter CVT (courtesy of Jatco Ltd)
Figure 1.16 Schematic representation of a hydraulic transmission
Figure 1.17 Torque converter: (a) schematic diagram and (b) exploded view (courtesy of BD Diesel Performance)
Figure 1.18 Operational principle of hydrostatic pumps and motors (left: pump and right: motor)
Figure 1.19 External gear-type hydrostatic pump (courtesy of Parker-Hannifin Corp.)
Figure 1.20 Pressure rise in the pump–motor conduit
Figure 1.21 Two different ways of controlling the pump output flow: (a) variable-speed prime mover and (b) variable-displacement pump
Figure 1.22 Pump output flow and displacement
Figure 1.23 Pump output flow and variable prime mover speed
Figure 1.24 Motor output flow and displacement
Figure 1.25 Pressure in a hydrostatic transmission with a variable-displacement motor
Figure 1.26 Pressure relief valve: (a) picture, (b) operational principle and (c) ISO representation
Figure 1.27 Pressure overshoot attenuation using relief valves
Figure 1.28 ISO Representation of the hydrostatic transmission shown in Figure 1.27
Figure 1.29 Charge circuit in a hydrostatic transmission
Figure 1.30 Check valve (spring loaded and standard): (a) picture, (b) operational principles and (c) ISO representations
Figure 1.31 ISO representation of a hydrostatic transmission with charge circuit
Figure 1.32 Schematics of typical accumulators: (a) weight-loaded accumulator, (b) spring-loaded accumulator and (c) gas-loaded membrane (diaphragm) accumulator
Figure 1.33 Oil pressure,
p
, as a function of time during the accumulator discharge
Figure 1.34 Gas-loaded membrane accumulator: (a) picture, (b) operational principle and (c) ISO representation of the corresponding hydraulic circuit
Figure 1.35 Energy storage (a) and regeneration (b) using hydraulic accumulators
Figure 1.36 Classification of hydrostatic drives
Figure 1.37 Transmission ratio for a variable-displacement pump and fixed-displacement motor transmission
Figure 1.38 Power, speed and torque output for a variable-displacement pump and fixed-displacement motor transmission for a constant load at the motor
Figure 1.39 Transmission ratio for a fixed-displacement pump and variable-displacement motor transmission
Figure 1.40 Power, speed and torque output for a fixed-displacement pump and variable-displacement motor transmission
Figure 1.41 Transmission ratio for a variable-displacement motor and variable-displacement pump transmission
Figure 1.42 Compact unit transmission configurations and picture of a Z-shaped hydrostatic transmission (courtesy of Danfoss Power Solutions)
Figure 1.43 Closed-circuit transmission
Figure 1.44 Open-circuit hydrostatic transmission
Figure 1.45 Counterbalance valve as a means of decelerating the motor
Figure 1.46 Power flow in a hydrostatic transmission
Figure 1.47 Power flow in a typical HMT
Figure 1.48 Typical architectures for an (a) input-coupled HMT, (b) output-coupled HMT and (c) compound-type HMT
Figure 1.49 Input-coupled transmission
Figure 1.50 Forces acting on the sun gear shaft and the planet gear
Figure 1.51 Power relation in a 100% efficient input-coupled HMT
Figure 1.52 Energy flow (regions A and B in Figure 1.51): (a) region A, (b) region B and (c) lockup point
Figure 1.53 Energy flow (region C in Figure 1.51): (a) 0 <
R
T
< R
TL
and (b)
R
T
→ 0
+
Figure 1.54 Energy flow (region D in Figure 1.51): (a)
R
T
→ 0
−
and (b)
R
T
< 0
Figure 1.55 Simple mechanical actuator
Figure 1.56 A screw-type mechanical actuator
Figure 1.57 Displacement-controlled and electrohydrostatic actuators: (a) displacement-controlled actuator and (b) electrohydrostatic actuator
Figure 1.58 Example of a valve-controlled actuator
Figure 1.59 ISO representation of the hydraulic circuit shown in Figure 1.58
Figure 1.60 Double-rod hydrostatic actuator
Figure 1.61 Two-cylinder actuator system
Figure 1.62 Two-speed gearbox
Figure 1.63 Dual-motor circuit
Chapter 2: Fundamentals of Fluid Flows in Hydrostatic Transmissions
Figure 2.1 Viscous flow between two plates caused by fluid dragging
Figure 2.2 Effect of the oil viscosity on the pump performance
Figure 2.3 Mass of fluid under compression
Figure 2.4 Presence of air and volumetric deformation in hydraulic conduits
Figure 2.5 Effective bulk modulus as a function of the gauge pressure in the presence of entrapped air for different percentages of
V
G
/
V
Figure 2.6 Thick-walled tube under internal pressure
Figure 2.7 Volumetric dilatation as a function of the inner pressure for different nominal diameters (DNs) of hydraulic hoses (reproduced courtesy of Contitech AG)
Figure 2.8 Accumulator in the circuit
Figure 2.9 Effective bulk modulus in the presence of a hydraulic accumulator
Figure 2.10 Force transmission in a conduit for an incompressible fluid (a) and a compressible fluid (b)
Figure 2.11 Compressibility flowrate
Figure 2.12 Laminar (a) and turbulent (b) flows between two parallel plates
Figure 2.13 Laminar flow inside a cylindrical conduit
Figure 2.14 Orifice flow
Figure 2.15 Vane pump model
Figure 2.16 Difference between a flow developed between infinitely parallel plates (a) and a flow developed between limited parallel plates (b)
Figure 2.17 Fluidic friction
Figure 2.18 Flow between two concentric cylinders
Figure 2.19 Leakage in a hydraulic cylinder
Chapter 3: Hydrostatic Pumps and Motors
Figure 3.1 Single-piston hydrostatic pump: (a) output port open and (b) output port closed
Figure 3.2 Typical hydrodynamic pump: (a) output port open and (b) output port closed
Figure 3.3 Single-piston hydrostatic motor
:
(a) unlocked shaft and (b) locked shaft
Figure 3.4 Hydrodynamic motor (turbine): (a) unlocked shaft and (b) locked shaft
Figure 3.5 Variable-displacement pump at (a) maximum and (b) minimum displacement
Figure 3.6 Single-piston pump: (a) suction and (b) discharge
Figure 3.7 (a) Displacement chamber flow and (b) output flow
Figure 3.8 Three piston pumps operating in parallel
Figure 3.9 Displacement chamber flow (a) and output flow (b) for the three-piston pump illustrated in Figure 3.8
Figure 3.10 Output flow for five and six pistons in parallel
Figure 3.11 Influence of leakages on the output flow
Figure 3.12 Influence of fluid compressibility on the output flow
Figure 3.13 Operation with an (a) inviscid and incompressible fluid in contrast with a (b) viscous and compressible fluid
Figure 3.14 Single-piston motor: (a) motoring mode and (b) discharge mode
Figure 3.15 Geometry details of the crank-and-piston mechanism
Figure 3.16 Torque output as a function of the crank angle for a complete revolution (single piston)
Figure 3.17 Torque output as a function of the crank angle for a complete revolution (multiple pistons)
Figure 3.18 Schematic representation (a) and picture (b) of a radial piston pump (part b is a courtesy of Bosch-Rexroth Corp.)
Figure 3.19 Schematic representation (a) and picture (b) of a radial piston motor with an eccentric shaft (part b is a courtesy of Bosch-Rexroth Corp.)
Figure 3.20 Schematic representation (a) and picture (b) of a radial piston motor with an outer stroke ring (courtesy of Bosch-Rexroth Corp.)
Figure 3.21 Axial piston arrangement of the cylinders
Figure 3.22 Schematic representation and picture (courtesy of Parker-Hannifin Corp.) of a swashplate pump
Figure 3.23 Port plate (a) and commutation loss (b)
Figure 3.24 Forces acting on the swashplate pump piston
Figure 3.25 Schematic representation of the swashplate motor
Figure 3.26 Schematic representation (a) and picture (b) of a typical bent-axis motor (part b is a courtesy of Danfoss Power Solutions)
Figure 3.27 Forces acting on the bent-axis motor piston
Figure 3.28 Schematic representation (a) and picture (b) of a floating-cup pump (part b is a courtesy of Innas B.V.)
Figure 3.29 External gear pump
Figure 3.30 Torque generation on an external gear motor
Figure 3.31 Gerotor pump
Figure 3.32 Gerotor motor
Figure 3.33 Vane pump
Figure 3.34 Vane motor
Figure 3.35 Schematic representation of a digital displacement pump
Figure 3.36 Example of a digitally controlled output flow
Figure 3.37 Digital output flow control
Figure 3.38 Energy balance in a generic hydrostatic motor (a) and pump (b)
Figure 3.39 Typical volumetric efficiency curves: (a) bent-axis pump/motor (reproduced courtesy of Parker-Hannifin Corp.); (b, c) axial piston pump and motor (reproduced courtesy of Danfoss Power Solutions)
Figure 3.40 Input flow as a function of the angular speed for an external gear motor (reproduced courtesy of Bosch-Rexroth Corp.)
Figure 3.41 Overall efficiency level curves for the Sauer-Danfoss series 40 axial piston pump (reproduced courtesy of Danfoss Power Solutions)
Figure 3.42 Typical volumetric efficiency curves for a hydrostatic pump/motor
Figure 3.43 Linear interpolation of based on the relative pressure differential
Figure 3.44 Data selection on the volumetric efficiency curves for the Sauer-Danfoss series 40 (a) pump and (b) motor
Figure 3.45 Comparison between the constant coefficient model (solid curves) and the experimental data (dashed curves) for (a) pumps and (b) motors
Figure 3.46 Extrapolated efficiency curves and comparison between the theoretical model (solid curves) and the experimental data (dashed curves) for (a) pumps and (b) motors
Figure 3.47 Extrapolation of the volumetric efficiency values for low relative speeds of the (a) pump and the (b) motor
Figure 3.48 Data selection on the overall efficiency curves for the pump and motor represented in Figure 3.39(b) and (c), respectively
Figure 3.49 Comparison between the theoretical overall efficiency (solid curves) and the experimental data (dotted curves) for (a) pumps and (b) motors
Figure 3.50 Comparison between the theoretical overall efficiency (solid curves) and the experimental data (dotted curves) for pumps
Figure 3.51 Mechanical efficiencies for the (a) pumps and the (b) motors represented by Figure 3.39(a) and (b)
Figure 3.52 Single piston on an inclined surface
Figure 3.53 Single-piston pump
Chapter 4: Basic Hydrostatic Transmission Design
Figure 4.1 Motor speed control using the (a) pump displacement and the (b) motor displacement
Figure 4.2 Mechanical and volumetric losses in a hydrostatic transmission
Figure 4.3 Flows in a typical hydrostatic transmission
Figure 4.4 Typical ways to connect a pump and a motor in a transmission: (a) metal tubes and (b) flexible hoses (only one branch of the circuit is shown)
Figure 4.5 Typical tube fitting
Figure 4.6 Typical hose fitting
Figure 4.7 Typical quick-disconnect coupling (a) disconnected socket and plug, (b) connected coupling and (c) picture
Figure 4.8 Typical pressure drop chart for a quick coupling with an ½ in. inner diameter (reproduced courtesy of RYCO Hydraulics Pty. Ltd.)
Figure 4.9 Equivalent length ratio for conduits at 90° bends
Figure 4.10 Views of the M25PV pump (a) and M25MF motor (b) showing the input and output ports A and B (courtesy of Danfoss Power Solutions)
Figure 4.11 Details of a 7/8-14 SAE J514 O-ring tube-case male fitting (courtesy of HY-LOK Corporation)
Figure 4.12 Example of metal tube lines in a hydrostatic transmission
Figure 4.13 Conduit efficiency of the circuit shown in Figure 4.12 as a function of the flow,
q
c
, for some selected pressure differentials
Figure 4.14 Pump and motor connected by long flexible hoses
Figure 4.15 Conduit efficiency as a function of the flow,
q
c
, for some selected pressure differentials considering a 20 m long hose connection
Figure 4.16 Conduit efficiency as a function of the flow,
q
c
, for some selected pressure differentials using quick-disconnecting hoses
Figure 4.17 Hydrostatic transmission applied to an elevator
Figure 4.18 Effect of the volumetric losses on the output speed (rpm) at 170 bar (
D
p
in cm
3
/rev)
Figure 4.19 Overall efficiencies of the pump, motor and transmission at 170 bar as a function of the pump displacement,
D
p
(cm
3
/rev)
Figure 4.20 Input torque,
T
p
(Nm), as a function of the pump displacement,
D
p
(cm
3
/rev)
Figure 4.21 Power at the pump and motor, (kW), as a function of the pump displacement,
D
p
(cm
3
/rev)
Figure 4.22 Transmission efficiency for (a) different pressure differentials and a constant prime mover speed and (b) different prime mover speeds and a constant pressure differential
Figure 4.23 Variable input speed/constant output speed transmission
Figure 4.24 Input torque,
T
p
(Nm), and speed, ω
p
(rpm), as a function of the input power, (kW)
Figure 4.25 Input speed,
ω
p
(rpm) as a function of the motor displacement,
D
m
(cm
3
/rev) for different volumetric efficiencies
Figure 4.26 Conduit flow,
q
c
(l/min), as a function of the motor displacement,
D
m
(cm
3
/rev), for different volumetric efficiencies
Figure 4.27 Transmission efficiencies η
C
, η
p
, η
m
and η
HT
as a function of the motor displacement,
D
m
(cm
3
/rev)
Figure 4.28 Variation of the overall efficiency of the transmission, η
HT
, with the motor displacement,
D
m
(cm
3
/rev) for different conduit efficiencies
Figure 4.29 Volumetric and mechanical efficiencies of the motor, η
v
m
and η
m
m
, as a function of the displacement,
D
m
(cm
3
/rev)
Figure 4.30 Power output, (kW), as a function of the motor displacement,
D
m
(cm
3
/rev) for different transmission efficiencies
Figure 4.31 Charge pump displacement,
D
cp
(cm
3
/rev) as a function of the main pump displacement,
D
p
(cm
3
/rev), for the elevator in Case Study 1
Figure 4.32 Typical hydrostatic transmission (courtesy of Danfoss Power Solutions)
Figure 4.33 Ratio between the heat losses and the power input relative to (a) Case Study 1 and (b) Case Study 2 (
D
p
and
D
m
in cm
3
/rev)
Figure 4.34 Ratio between the heat losses and the maximum power input relative to (a) Case Study 1 and (b) Case Study 2 (
D
p
and
D
m
in cm
3
/rev)
Figure 4.35 Hydrostatic transmission equipped with a flushing valve module (LF)
Figure 4.36 Pump and motor displacement variation in time
Chapter 5: Dynamic Analysis of Hydrostatic Transmissions
Figure 5.1 Hydraulic motor connected to a load
Figure 5.2 Typical behaviours of the pressure differential during a transient
Figure 5.3 Acceleration valves in the circuit
Figure 5.4 Phase angle of the
i
th piston in an axial piston pump
Figure 5.5 Instantaneous angular speed and pressure differential in a typical hydraulic motor connected to a hydrostatic pump
Figure 5.6 Pressure and speed in circuit with a compressible fluid
Figure 5.7 Speed and pressure versus time: (a) undamped mode and (b) damped mode
Figure 5.8 Periodic input signal and resonance
Figure 5.9 Beating
Figure 5.10 Schematic representation of a (a) passive mass–spring damper and an (b) active piezoelectric damper
Figure 5.11 Simplified transmission model
Figure 5.12 Volumetric circuit flows
Figure 5.13 Variation of the coefficient
K
(l/(min bar)) with the motor speed,
ω
m
(rpm)
Figure 5.14 Pressure differential (bar) and motor speed (rpm) as functions of time
Figure 5.15 Pressure differential (bar) and motor speed (rpm) as functions of time (undamped case)
Figure 5.16 Effect of damping factor on the pressure differential (bar) and motor speed (rpm)
Figure 5.17 Influence of the load's inertia on the motor speed (rpm) and pressure differential between conduits (bar)
Figure 5.18 Pressure differential (bar) and motor speed (rpm) considering a 50% reduction in the effective bulk modulus
Figure 5.19 Pump flow versus time
Figure 5.20 Output flow for a constant pump speed and a variable number of cylinders
Figure 5.21 Pressure differential (a) and motor speed (b) for different values of the constant
h
Figure 5.22 Variation of the motor speed with time: (a) resonant and (b) non-resonant case
Figure 5.23 Circuit without energy losses: (a) resonant and (b) non-resonant case
Figure 5.24 Beating phenomenon
Chapter 6: Hydrostatic Actuators
Figure 6.1 Sign convention (a) and quadrant operation (b) for a single-rod cylinder
Figure 6.2 Pump-cylinder connection in a double-rod hydrostatic actuator
Figure 6.3 Unmatched flows in a single-rod hydrostatic actuator
Figure 6.4 Dual-pump, open-circuit, displacement-controlled actuator
Figure 6.5 Operation in the first and second quadrants
Figure 6.6 Operation in the third and fourth quadrants
Figure 6.7 Dual-pump, closed-circuit, displacement-controlled actuator
Figure 6.8 Operation in the first and second quadrants
Figure 6.9 Operation in the third and fourth quadrants
Figure 6.10 Dual-pump electrohydrostatic actuator with accumulators: (a) cylinder extension and (b) cylinder retraction
Figure 6.11 Operation in the first and the third quadrants
Figure 6.12 Operation in the second and fourth quadrants
Figure 6.13 Circuit with a hydraulic transformer: (a) cylinder extension and (b) cylinder retraction
Figure 6.14 Operation in the first and second quadrants
Figure 6.15 Operation in the second and fourth quadrants
Figure 6.16 Circuit correction to account for external leakages (use of a variable-displacement pump in the hydraulic transformer)
Figure 6.17 Single-pump circuit with a directional valve: (a) cylinder extension and (b) cylinder retraction
Figure 6.18 Operation in the first and third quadrants
Figure 6.19 Operation in the second quadrant: (a) incorrect circuit configuration and (b) correct circuit configuration
Figure 6.20 Operation in the fourth quadrant: (a) incorrect circuit configuration and (b) correct circuit configuration
Figure 6.21 Single-pump circuit with pilot-operated check valves
Figure 6.22 Operation in the first quadrant
Figure 6.23 Operation in the third quadrant
Figure 6.24 Operation in the second quadrant
Figure 6.25 Operation in the fourth quadrant
Figure 6.26 Single-pump circuit with pilot-operated check valves and an accumulator
Figure 6.27 Operation in the first and second quadrants (accumulator discharge)
Figure 6.28 Operation in the third and fourth quadrants (accumulator charge)
Figure 6.29 Two cylinders sharing one charge pump
Figure 6.30 Single-pump circuit with inline check valves
Figure 6.31 Operation in the first and third quadrants
Figure 6.32 Operation in the second quadrant
Figure 6.33 Operation in the fourth quadrant
Figure 6.34 Energy storage circuit
Figure 6.35 Operation of the energy storage circuit: (a) storage, (b) and (c) regeneration, (d) discharge
Figure 6.36 Bypass mode operation
Figure 6.37 Regenerative displacement-controlled actuator with pilot-operated check valves
Figure 6.38 Operation in the first and third quadrants
Figure 6.39 Operation in the second and fourth quadrants
Figure 6.40 Energy reuse in the first and third quadrants
Figure 6.41 Operation in the second and fourth quadrants of a regenerative actuator with a directional valve
Figure 6.42 Holding a force
F
against an obstacle during the first quadrant
Figure 6.43 Double-rod actuator
Figure 6.44 Operation in the first quadrant
Figure 6.45 Operation in the second quadrant
Figure 6.46 Common pressure rail concept in a pneumatic circuit
Figure 6.47 Common pressure rail
Figure 6.48 Common pressure rail with valve-controlled actuators
Figure 6.49 Operation in the first quadrant of a cylinder connected to the pressure rails by means of a dual-pump hydraulic transformer
Figure 6.50 Cylinder control with a conventional (two-quadrant) hydraulic transformer operating in the first and third quadrants
Figure 6.51 Cylinder control with a conventional hydraulic transformer operating in the second and fourth quadrants
Figure 6.52 (a) Innas IHT prototype (courtesy of Innas B.V.); (b) IHT symbol in comparison with the conventional hydraulic transformer symbol; (c) cylinder control in a CPR
Chapter 7: Dynamic Analysis of Hydrostatic Actuators
Figure 7.1 Single-rod displacement-controlled actuator
Figure 7.2 Volumetric circuit flows
Figure 7.3 Forces acting on a single-rod hydraulic cylinder
Figure 7.4 Coulomb friction as a function of the cylinder speed
Figure 7.5 Static and slip friction between dry surfaces
Figure 7.6 Viscous friction as a function of the cylinder speed
Figure 7.7 Combined dry, viscous and Stribeck friction
Figure 7.8 Friction model for the hydraulic cylinder
Figure 7.9 Friction force versus cylinder speed
Figure 7.10 Piloted check valve: (a) partially-open during normal operation and (b) fully open during pilot operation
Figure 7.11 Cross-cut of a Bosch-Rexroth SL-type piloted check valve, series 6X (courtesy of Bosch-Rexroth Corp.)
Figure 7.12 Typical pressure versus flow curve in piloted operational mode (reproduced courtesy of Bosch-Rexroth Corp.)
Figure 7.13 Pump output flow
Figure 7.14 Numerical results for the first and fourth quadrants: (a) pump flow,
q
p
, (b) cylinder displacement,
x
, (c) cylinder speed,
v
, (d) pressure in line 1–2,
p
12
, (e) and (f) pressure in line 3–4,
p
34
Figure 7.16 Piloted check-valve flows
Figure 7.15 Numerical results for the second and third quadrants: (a) pump flow,
q
p
, (b) cylinder displacement,
x
, (c) cylinder speed,
v
, (d) pressure in line 1–2,
p
12
, (e) pressure in line 3–4,
p
34
, and (f) piloted check-valve flows,
q
v1
and
q
v2
Figure 7.17 Viscous force between a stationary and a moving plate
Figure 7.18 Viscous force in a cylinder
Figure 7.19 Simplified version of a double-rod actuator
Chapter 8: Practical Applications
Figure 8.1 Schematics of a typical rear-driven vehicle
Figure 8.2 Typical (a) torque and power curves and (b) specific fuel consumption for an internal combustion engine
Figure 8.3 Hydraulic bucket lift: cabin and engine are mounted on a rotary platform (a), and hydraulic motor M is connected to the wheel (b)
Figure 8.4 Wheel loader
Figure 8.5 Hydraulic excavator
Figure 8.6 Hydraulic circuit for a mini-excavator
Figure 8.7 Circuit using hydraulic transformers
Figure 8.8 Hydraulic truck equipped with an energy-regenerative hydrostatic transmission (courtesy of UPS – United Parcel Service)
Figure 8.9 Artemis BMW 350i prototype: (a) dual motor assembly and (b) high-pressure accumulator (courtesy of Artemis Intelligent Power Ltd)
Figure 8.10 Series electric hybrid schematics
Figure 8.11 Parallel electric hybrid schematics
Figure 8.12 Series hydraulic hybrid schematics
Figure 8.13 Parallel hydraulic hybrid schematics
Figure 8.14 Simple series hybrid circuit
Figure 8.15 Operation in normal traction mode: (a) forward, (b) stop, (c) reverse
Figure 8.16 Energy storage modes: (a) energy storage (vehicle stopped), (b) regenerative braking
Figure 8.17 Regeneration mode
Figure 8.18 Dual-pump hydraulic transformers connected to a hydraulic motor with (a) clockwise rotation and (b) counter-clockwise rotation
Figure 8.19 Equivalence between the IHT and the conventional design
Figure 8.20 Innas hybrid scheme
Figure 8.21 Energy flow in an Innas hybrid vehicle
Figure 8.22 An asynchronous electric motor (courtesy of ABB motors)
Figure 8.23 Magnetic field produced by an electric current in a solenoid
Figure 8.24 Rotating magnetic field in a typical stator
Figure 8.25 Asynchronous electric motor: (a) general schematics and (b) rotating coil detail
Figure 8.26 Simple three-phase synchronous generator
Figure 8.27 Permanent magnet synchronous generator (courtesy of The Switch)
Figure 8.28 Power flow in a wind power generator
Figure 8.29 Schematics of the Delft Offshore Turbine
Figure 8.30 A hydrostatic transmission turbine (courtesy of Artemis Intelligent Power Ltd)
Figure 8.31 Wave converter in operation
Figure 8.32 Wave energy extraction
Figure 8.33 Circuit with flow rectifier
Figure 8.34 Circuit operation: (a) buoy ascending; (b) buoy descending
Figure 8.35 Aerodynamic surfaces on a Boeing 767 and details of the elevator and rudder control [37]
Figure 8.36 (a) Compact electrohydrostatic actuator used in the (b) Airbus A380 aeroplane
Figure 8.37 Typical circuit for an aileron EHA
Appendix B: Mathematics Review
Figure B.1 Solutions to the second-order homogeneous ODE with constant coefficients
Figure B.2 Example of a discontinuous function at
t
= 0
Figure B.3 Block diagram representation of a linear differential equation
Appendix C: Fluid Dynamics Equations
Figure C.1 Particle tracking on a flow
Figure C.2 Equilibrium of forces in a fluid element in the
x
-direction
Figure C.3 Strain state of a fluid element in the plane
xy
. (a) Elongation, (b) shearing
Figure C.4 Infinitesimal control volume and mass balance along the
x
-axis
Figure C.5 Force balance in a fluid element in the
x
-direction
Figure C.6 Cartesian and cylindrical coordinates
Figure C.7 Flow through a control volume
Figure C.8 Elementary flow through the area
dS
Figure C.9 Work done by an elementary force,
d
F
, on a moving system
Figure C.10 Ideal flow through a hypothetical tube
List of Tables
Chapter 1: Introduction to Power Transmission
Table 1.1 Transmission ratio range for the power-split transmission
Table 1.2 Non-standard prime mover hydraulic symbols
Chapter 2: Fundamentals of Fluid Flows in Hydrostatic Transmissions
Table 2.1 Absolute and kinematic viscosity units
Table 2.2 ISO viscosity classification of hydraulic fluids
Table 2.3 Standard dimensions and bulk moduli for steel metal tubes
Chapter 3: Hydrostatic Pumps and Motors
Table 3.1 Possible operations for the second cylinder
Table 3.2 Digital displacement sequence for the pump represented in Figure 3.36
Table 3.3 Danfoss series 40 pumps and motors
Table 3.4 Nodal values of the overall efficiencies (Figure 3.48)
Table 3.5 Overall efficiency models for the pumps and motors represented in Figure 3.39
Chapter 4: Basic Hydrostatic Transmission Design
Table 4.1 Typical wall thicknesses (in.) for a seamless stainless steel tube as a function of the outer diameter OD (in.) and (maximum) inner pressure (psi)
Table 4.2 Danfoss series 40 pumps
Table 4.3 Danfoss series 40 motors
Chapter 7: Dynamic Analysis of Hydrostatic Actuators
Table 7.1 Typical experimental data for the friction coefficients and cylinder dimensions [5]
Table 7.2 Data used in the simulations
Table 7.3 Extension and retraction periods used in our simulations
Table 7.4 Values of the parameters
i
and
j
in Eq. (7.39)
Chapter 8: Practical Applications
Table 8.1 Fuel economy improvement for hybrid SUV prototypes (gasoline engine)
Appendix B: Mathematics Review
Table B.1 Some selected Laplace transforms
Hydrostatic Transmissions and Actuators
Operation, Modelling and Applications
Gustavo Koury Costa
Department of Mechanics–Federal Institute of Education, Science and Technology, Recife, Pernambuco, Brazil
Nariman Sepehri
Department of Mechanical Engineering–University of Manitoba, Winnipeg, Manitoba, Canada
This edition first published 2015
© 2015 John Wiley & Sons, Ltd
Registered office
John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.
The right of the authors to be identified as the authors of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.
Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: While the publisher and authors have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the authors shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought
Library of Congress Cataloging-in-Publication Data
Costa, Gustavo K.
Hydrostatic transmissions and actuators / Gustavo K. Costa, Department of Mechanics Federal Institute of Education, Science and Technology, Recife, Pernambuco, Brazil, Nariman Sepehri, Department of Mechanical Engineering--University of Manitoba, Winnipeg, Manitoba, Canada.
pages cm
Includes bibliographical references and index.
ISBN 978-1-118-81879-4 (hardback)
1. Oil hydraulic machinery. 2. Fluid power technology. 3. Hydrostatics. 4. Power transmission. 5. Actuators. I. Sepehri, Nariman. II. Title.
TJ843.C67 2015
620.1′06–dc23
2015022962
A catalogue record for this book is available from the British Library.
ISBN: 9781118818794
To Flávia Maria, my beloved wife
Gustavo Koury Costa
To Aresh, Parisa and Anoush, the joys of my life
Nariman Sepehri
Preface
The need for transmitting mechanical power has always been present in many fields of engineering. Take, for example an automobile where power must be transferred either from the engine to the wheels or from the driver's foot to the wheels during braking. This book focuses on two specific power transfer situations: (a) transmission between two rotating shafts, and (b) transmission between a rotating shaft and a hydraulic actuator. The power-conveying medium, in both cases, is a hydraulic fluid.
For Whom This Book Has Been Written
This book has been written for undergraduate students but will also be useful to practical engineers and junior graduate students who need to have introductory knowledge on the subject of hydrostatic power transmissions and actuation. The pre-requisites for the reader are minimal; no more than a little knowledge about power hydraulics and a basic understanding of calculus and physics are necessary. The book has been constructed in such a way that students do not need to refer other sources of information to understand the text. Every effort has been made to derive most of the equations found in the text. Only a few of the many formulas found in the book do not have a formal development because of either the degree of complexity involved or their straightforward nature. To help solidifying the concepts, we have also included a list of exercises at the end of most chapters.
Book Organization
The book is organized in a way that caters to different audiences with varied backgrounds. For students who do not have a strong foundation in fluid power, this book is best read from cover to cover. On the other hand, a practical engineer who wants to learn how to calculate the efficiency of hydrostatic transmissions, can go straight to Chapters 3 and 4. However, we have made every attempt to follow a logical and progressive way of exposing the theme, having in mind the students who will read the book from the first chapter to the last chapter. In that sense, we have followed an approach whereby the reader obtains a complete overview of the subject matter in the first chapter. And then in subsequent chapters, details are provided so that when the reader arrives to the end of the book, he or she will have acquired a solid and concise knowledge of the exposed themes.
In terms of the subjects explored in each chapter, there is a clear division following the overall exposition given in Chapter 1. From Chapter 2 to Chapter 5, we focus on power transmissions between rotating shafts (hydrostatic transmissions). Chapters 6 and 7 concentrate on hydrostatic actuators. Finally, Chapter 8 focuses on conventional and new applications of both hydrostatic transmissions and actuators.
To ensure practicality, most of the examples in the book use catalogue data from manufacturers. While great care has been taken in the reproduction of illustrations and/or information taken from manufacturers, inadvertent typographical errors or omissions may have occurred. In some particular cases where catalogue data are unavailable, or when it is not strictly necessary to provide this data, we follow a purely theoretical approach in presenting the concepts. The overall idea behind using real catalogue data is to introduce the students to real-world applications as they work through the examples of the book.
In what follows, we briefly describe the subjects covered in every chapter of this book.
Chapter 1 presents an introduction to hydrostatic transmissions and actuators. Since applications now using mechanical power transmissions constitute a potential field for hydrostatic transmission usage, we review the subject of mechanical transmissions first. Hydraulic components are gradually introduced in this chapter.
Chapter 2 reviews some basic definitions and concepts about hydraulics, such as fluid compressibility and viscosity, pressure losses and internal flows in hydraulic circuits.
Chapter 3 focuses on hydrostatic pumps and motors. After exploring the fundamental aspects of pumps and motors in general, a succinct description of some representative models is given. The definition of efficiency takes up a considerable portion of the chapter, given its importance in hydrostatic transmissions. We also explore the basics of digital displacement and floating cup technologies.
Chapter 4 explores the steady-state operation of hydrostatic transmissions. After reading this chapter, the student will be able to create a basic design of a typical hydrostatic transmission.
Chapter 5 complements the steady-state analysis of hydrostatic transmissions carried out in Chapter 4 by exploring the transient regime. In this chapter, the student has the chance to study the oil compressibility effects, introduced in Chapter 2, that occur when the hydrostatic transmission is subject to dynamic loads.
Chapter 6 focuses on the theme of hydrostatic and electrohydrostatic actuators. Several circuit designs are described in detail. The chapter closes with a description of the common pressure rail technology and its relation with hydraulic transformers.
Chapter 7 introduces the dynamic analysis of hydrostatic actuators. A nonlinear analysis is carried out, and the equations describing the model are solved numerically.
Chapter 8 puts together current and potential applications of hydrostatic transmissions and actuators. Each application is described in detail, so that students can have a good knowledge of the benefits and drawbacks of the hydrostatic technology in every case.
Appendix A lists the several ISO hydraulic symbols used in the book.
Appendix B contains the necessary mathematical tools for a complete understanding of the book. Special emphasis is given to the solution of second-order linear differential equations, where the method of the Laplace transform is briefly presented.
Appendix C reviews the basics of fluid dynamics with a special emphasis on the Navier–Stokes equations, which are developed in detail. For students who are not familiar with the theme, this appendix constitutes a sufficient basis for the subjects covered in the book.
Some examples given in this book require a numerical solution. In this case, the reader can find the source code for the corresponding computer programs written in Scilab script language1www.wiley.com/go/costa/hydrostatic. The parts of the book for which a computer script is available have been marked with the download icon .
We have done our best to make the text as clear and rich as possible to the student, and it is our most sincere desire that this book contributes to the understanding and the development of this very important field of fluid power engineering.
1
Scilab is a free programming environment available at
http://www.scilab.org
(April 2014).
Acknowledgements
Primarily, the authors wish to thank the reviewers for their comments during the preparation of this book as they have definitely impacted its quality. This book was conceived during the postdoctoral studies of Gustavo Koury Costa, in the Fluid Power and Telerobotics Research Laboratory at the University of Manitoba, Canada. In this aspect, he is grateful for the support of the University of Manitoba for the post-doctoral position offering and the Federal Institute of Science and Technology of Pernambuco (Brazil) which, together with the Capes Foundation (Brazil), provided the financial aid during his stay in Winnipeg. He also acknowledges the help of Maria Auxiliadora Nicolato from Capes, for her assistance during his stay in Canada; Luciana Lima Monteiro, for her friendship and for the promptness to help with the necessary paperwork in Brazil; Robert and Madeline Blanchard for their warm welcome and support; Paulo Lyra and Carlos Alberto Brayner for helping with the post-doctoral application; and Arthur Fraser, who did not hesitate to fly from Scotland to Winnipeg to visit. Last but not least, he acknowledges the support of the colleagues from the Department of Mechanics of his home institution, who agreed to take over his classes while he was away.
Nariman Sepehri is grateful to the University of Manitoba for providing the infrastructure, Natural Sciences and Engineering Research Council of Canada (NSERC) for providing continuous support of his research in fluid power systems and controls, and all his past and present graduate students from whom he always receives considerable help and education. Finally, both authors are grateful to Shari Klassen of the University of Manitoba for her editorial work and comments on the writing style of this book.
Gustavo Koury Costa
Nariman Sepehri
August 2015
About the Companion Website
This book's companion website www.wiley.com/go/costa/hydrostatic provides you with additional resources to further your understanding, including:
A solutions manual
Scilab scripts
Links to useful web resources
Chapter 1Introduction to Power Transmission
The term power transmission refers to a collection of devices assembled to transmit power from one physical point to another. In this chapter, we describe the most common types of power transmissions and introduce the subject of hydrostatic transmissions and actuators. This chapter is divided into six parts:
Mechanical transmissions
Hydrodynamic transmissions
Hydrostatic transmissions
Hydromechanical transmissions
Mechanical actuators
Hydrostatic actuators
It is important to mention that there are other types of power transmissions. For example, an electricity gridline is a type of power transmission – from the generator to the final user. However, when mechanical energy is involved (kinetic and potential), the aforementioned types are the most representative.
The majority of this chapter deals with the topic ‘transmissions’, with a smaller portion dedicated to ‘actuators’, as actuators can be seen as a special type of hydrostatic transmission where the motor is replaced by a hydraulic cylinder. We start with a basic concept common to both mechanical and hydrostatic transmissions: the transmission ratio.
1.1 Transmission Ratio
1.1.1 Generalities
Figure 1.1 illustrates a typical situation where a power transmission can be applied. The input shaft is rotating with an angular speed and is connected to a prime mover (such as an electric motor or an engine) whose output power is . We connect the input shaft to an output (driven) shaft that must rotate at an angular speed . The angular speed of the driven shaft may be greater or lesser than the angular speed of the input shaft or even have an opposite direction in relation to the input shaft's angular speed.
Figure 1.1 Typical situation requiring a power transmission
