Index

Note: Page numbers followed by f indicate figures, t indicate tables and b indicate boxes.

A

Abe, 16
ABS braking, 385–394
Adhesion, 79–80
Aerodynamic drag, 514
Aligning stiffness, 93–94, 153, 228
Aligning stiffness, definition, 5–6
Aligning torque, definition, 3
Aligning torque, steady state, 4, 88, 228–230
Axes system, 4–5, 62–63
Axle characteristics, 7, 12, 36–37, 40
Axle cornering stiffness, 9–12
Axle side force, 11

B

Badalamenti and Doyle, 478
Bakker, 165, 168, 171
Bayer, 506–507
Bayle, 165, 171–173
Belt distortion, 75, 128
Belt dynamics, 271, 404–405, 445
Belt segments, 583
Bernard, 82, 89–90
Berritta, 506–507
Berzeri, 426
Biral, 507
Brake lever arm, 460–462
Breuer, 506–507
Brockman and Braisted, 458–459
Bruni, 455
Brush model, 82, 84, 88, 90–127, 406–426
Böhm, 88–90

C

Calspan flat track test stand, 204, 569
Camber reduction factor, 126–127
Camber stiffness, 77, 156
Capsize mode, 531
Carcass compliance, 82–85, 126, 349–351, 382, 621
Carcass distortion, 75
Caster length (trail), 9, 300, 312, 511
Center of gravity, 22–23, 306–309, 533, 540, 550
Characteristic equation, 29–30, 290, 321–322
Characteristics, cf. tire characteristics
Characteristic speed, 25–26
Cheli, 455
Clark, 458
Cleat, 487–493
Coefficient of friction, 5–6, 82, 131–132, 176
Combined slip with Fx as input, 163–165
Composite slip, 175
Conicity, 79, 129–131, 191–196
Constitutive relations, 453–462
Contact center, 62–63, 200
Contact length, 95–96, 153–154, 281, 624
Contact patch mass, 350, 387, 400–401
Contact patch slip model, 406–444, 587, 588f
Contact width, 116
Cornering force, cf. side force
Cornering on uneven road, 58, 214
Cornering stiffness, 5–6, 93–94, 223–224
loss (side force), 359
string model, 215–240, 258–268
vs normal load, 2, 5, 143–144, 168
Cornering stiffness, definition, 5–6
Cossalter, 507
Critical speed, 25, 28, 55, 144–145, 531, 548
Cross section, 64–65, 75, 199–200, 510
Curvature factor, 166–167
Cutoff frequency, 233–237

D

Damping:
motorcycle steer, 524
shimmy, 291–292
tire, 454
vehicle handling, 28
Davis, 478–479
Deflections (tire), 63, 84
Delft dynamic brake and cleat rig, 463–464, 574f
Delft flat plank, 491, 498f, 572
Delft pendulum test stand, 464–465, 465f, 474, 574–575
Delft-Tire, 588
Delft tire test trailer, 462–463, 466
Delft University of Technology, 362, 404, 462–463, 572
Delft yaw oscillation test rig, 464–466, 575–576
Differential equations:
- with carcass compliance, 415–417
contact patch, 396, 407, 409, 415
single contact point, 312, 355
string approximations, 253–255
Dijks, 178–179
Dugoff, 82

E

Effective inputs, 404–405, 475–476
Effective road plane height/slope, 476, 478–487, 493–497
Effective rolling radius, 63, 69, 77, 156, 201, 344, 348, 367–370, 459, 461–462, 487–493, 498–499, 618
Effective rolling radius, def., 3–4, 63
Eigenvalues:
motorcycle, 529, 531
vehicle handling, 28
Eindhoven University of Technology, 572, 586–587
Eldik Thieme, van, xiv, 568, 572
Empirical model, 82
Equations of motion:
braked wheel system, 382
car-trailer, 53–57
contact patch mass, 428, 449
motorcycle, 520–529
rigid belt, 446
shimmy, 294
steering vibrations, 381
vehicle handling, 16–17, 19–21, 31–32

F

Fancher, 82
Finite Element Model, 478
Forissier, 171
Four wheel steer, 35f
Frank, 88
Frequency response:
align. torque (SWIFT), 236
- and approximations, 243f
braked wheel, 109–110
lateral force (SWIFT), 237
longitudinal force (single point), 372–373
longitudinal force (SWIFT), 394, 408f, 410f
steering vibrations, 379–385
string model, 224–225
string with approx. dynamics, 272
SWIFT (zero belt mass), 410–411
vehicle handling, 32
Freudenstein, 88–90, 139–140
Fritz, 214
Fromm, 88, 288
FTire, 405, 582–586

G

Geometric filtering, 475
Gillespie, 16
Gipser, xv, 84, 405, 478, 582, 586
Goncharenko, 256
Gong, 478
Gough, 476
Green function, 84
Growth (centrifugal), 440, 618
Guan, Dihua, 84
Guntur, 390–391
Guo, 84, 89–90
Gyroscopic couple, 218, 269–271, 288, 294, 297–300, 306–309, 348–349, 533

H

Handling curve, 36, 556–557
Handling diagram, 36f, 38, 557f, 559–560
Handling experiments, 598
Hasegawa, 506–507
Ho and Hall, 214
HSRI (UMTRI), 82
Human rider model, 506
Hurwitz stability criterium, 55, 290
Hysteresis, 366–367

I

Iffelsberger, 506–507
Inclination angle, cf. camber angle
Influence function, 84
Instability:
divergent, 28, 56, 290, 292, 296–297
oscillatory, 2, 55–57, 292, 312

J

Jagt, van der, 198, 206, 349–350, 386, 394, 438–441
Jansen, xiv, 507
Jianmin, 366–367, 624
Julien, 88

K

Karlsruhe University of Technology, 569–572
Katayama, 507
Keldysh, 241, 256–257
Kluiters, 214, 241, 249–250
Kobiki, 468
Kooijman, 507
Kortüm, 16

L

Laerman, 214
Lafon, 171
Lagrange’s equations, 17
Lateral acceleration response, 34
Lateral c.g. offset (motorcycle), 550
Lateral force, cf. side force
Lateral slip, 67
Lateral slip stiffness, cf. cornering
stiffness
Lateral stiffness
standing tire, 228, 231
suspension, 288
Limebeer, 506–507
Limit-cycle, 287–288, 320–322
Lippmann, 476
Loaded radius, 198, 201, 448, 457, 461–462, 618
Load transfer, 7, 9, 514–515
Load variations, 277–281, 410
Longitudinal force, 3–4, 157, 179, 181, 366–378
Longitudinal force, definition, 3–4
Longitudinal slip, 97–100, 406–410
Longitudinal slip, definition, 3–4, 63–65, 70, 97–100
Longitudinal slip stiffness, 6, 99–100, 156, 387, 409, 617–618
Longitudinal slip stiffness, definition, 5–6
Lugner, xiv, 16

M

Magic Formula, cosine version, 170f, 171
Magic Formula motorcyc., 176, 565
Magic Formula Tire Model, 165–206, 565
Magic Formula with turn slip, 183–188
Maneuvering, 52f, 507
Mastinu, 84
MATLAB, 611
Meier-Dörnberg, 214
Meijaard, 507
MF-Tire, 588
Michelin, 165, 168f, 171
Milliken, xvi, 16, 51, 53, 150–152
Milliken Research Associates, 51
Mitschke, 16, 458
Modes of vibration, 309–310, 454, 563–564
Moment method, 51–53
Moreland, 214, 241, 256–258
Motorcycle dynamics, 505–566
Motorcycle tire force/ and moment, 202–206
Mousseau, 478
MTS Flat Trac III, 203f, 206
MTS Flat Trac Roadway Simulator, 53, 53f

N

Natural frequencies:
shimmy, 309f, 310f
steering vibration, 309–310, 315f
tire in-plane, 371–372, 468t
tire out-of-plane, 271, 468, 468t
vehicle handling, 30
Neutral steer, 25
Neutral steer point, 24
Nishimi, 507
Non-dimensionalisation, 552
Non-holonomic constraint, 523
Non-lagging part, 496–497, 517
Non-linear system, 517–520, 555–563
Non-steady state, 211–286
Nonuniformity, 366–378
Normal deflect., 200, 456f, 494
Normal force, 456–458, 494
Nyquist plot:
and approximations, 247f
- with gyroscopic couple, 270
string model, 215–240
string with approx. dynamics, 274
SWIFT (with zero belt mass), 431
tire measurements, 239f, 245f

O

Oertel, xv, 405, 478, 578–582
Olley, 288
Optimization, 589
Out of roundness, 370, 372–373
Oversteer, 25, 40
Overturning couple, 182, 196–201, 198f, 198t, 206, 452

P

Pacejka, 565, 586–587
Parameter assessment, 463, 466, 469, 483, 589
Parameters Mag.F../SWIFT, 613–625
Parking maneuver, 436–444
Path curvature, 24, 171, 183, 189f, 422, 541, 548–549
Pevsner, 16
Phase plane, 46f
Physical model, 82, 85, 420, 426, 582
Plöchl, xvi
Ply-steer, 75, 129–131, 191–196
Pneumatic trail, definition, 5–6
Point of intersection, 62–63
Pothole response (SWIFT), 503–504
Pressure distribution, 82–84, 89, 92
Pure slip, 5

R

Radial stiffness, 478–480
Radt, 16, 150–152
Regression technique, 168
Reimpell, 178–179, 198, 456–457
Relaxation length:
- with carcass compl., 398f
contact patch model, 416f
motorcycle tire, 531, 533
vs normal load, 517
single pt. model, 251–252, 329
string model, 226f, 230f, 236
string with tread elements, 258, 260–261, 283
vehicle handling, 22
Residual stiffness, 404–405, 405f, 435, 466
Residual torque, 156, 164–165, 195
Response successive steps, 452f, 472f, 473f
Response to cleats (SWIFT), 487–493, 499
Response to load var., 277–281, 349, 365f
Rider robot, 507, 536
Rigid ring, 444, 454, 474
Rigid wheel, 296–297, 484f
Rise time, 31
RMOD-K, 405, 578–582
Road camber, 487
Road experiments, 462–463, 483, 582–583
Road unevenness, 389–390, 475–504
Rogers, 213, 249
Roll angle motorcycle, 540, 543–544
Roll axis, 8, 611
Rolling resist. moment, 63–64, 89, 182, 459–462
Rolling resistance, 371–372, 458–462, 616
Roll steer/camber, 13–14, 21–22
Rotation transformation, 511–512
Ruijs, 507, 536

S

Sakai, 90, 126–127
Savkoor, 88
Scaling factors, 178–179
Schlippe,von, 213, 221, 241, 287–288
Schmeitz, xv, 478, 485–487, 589–591
Segel, 6–7, 16, 82, 213, 215, 221, 345–346
Self aligning torque, cf. aligning torque
Self-excited oscillations, 287–288
Separatrix, 47–48, 323–324
Shang, Jin, 84
Shape factor, 166
Sharp, xiv, 84, 506–507
Sharpness factor, 168f
Shimmy, 288, 317–320
Side force, 4, 88, 92, 172, 184–185, 277–286, 473f
Side force, definition, 2
Side force steer, 9–10
Side slip, definition, 2
Side walls, 87–88, 95–96
Sign convention, 3, 63, 609
Similarity modelling method, 161–162
Single point approximations
enhanced m.., 349, 397, 400–401
fully non-linear, 353
linear, 252, 289–290, 329
semi-non-linear, 335–336, 395, 400
Single track vehicle, 611
Singular point, 38–39, 45
Sliding region, 80, 93–94, 102–103, 118–119
Sliding velocity, 74, 79
Slip angle, 20, 92, 513
Slip angle, definition, 2, 4, 67
Slip components, 67
Slip point, 63, 97–98, 346–347
Slip radius, 63
Slip ratio, cf. longitudinal slip
Smiley, 213, 241, 248–249
Speed of revolution, 66
Speed of rolling, angular, 65, 69–70
Speed of rolling, linear, 65, 70, 97–98
Spin (slip), 67, 184, 332, 436
Stability:
car-trailer, 53–57
motorcycle, 529–538
vehicle handling, 16–58
Stability boundary, 40, 56f, 302t, 303–305, 312
Standing waves, 458–459
Standstill (stop, start), 334, 394–401, 436
State space, 323–324
Steady-state cornering, 24–27, 35–49, 539–564
Steady-state response:
string model, 215–240
vehicle handling, 16, 32
Steer angle, 21, 537–538, 542
Steer compliance, 7, 9–10
Steering vibrations, 379–385
Steer stiffness, 291–292, 297
Steer torque, 195, 551–552, 560–561
Stepan, 291–292
Step response (tire):
measured, 238, 339–343
motorcycle, 529–538
single point model, 330
string model, 225–232
and approximations, 242f, 243f
SWIFT (zero belt mass), 410–411
vehicle handling, 587
Strackerjan, 214, 271
Straight tangent approx., 215, 241, 250–251
String model, 215–240, 258–268, 277–281
String with tread elements, 258–268, 277–281
Suspension compliance, 300, 383
Synchronous oscillation, 325–328
System of axes, cf. axes system

T

Takahashi, 214, 277, 338, 361–362, 364, 506–507
Tandem rear axle, 43
Tandem ‘cam’ technique, 485–486
Teerhuis, 507
Test facilities, 463–466, 567–576
Tire characteristics (steady-state):
brush model, 90–127, 117f, 119f
brush model, camber, 120f
brush model, spin, 119–120
example, 3–7
Magic Formula, 165–206
Magic Formula motor cycle, 207f
Magic Formula with turn slip, 183–184
measured, 82, 616
nondimensionalised, 151f
similarity method, 150–165
spin, turn slip, 138
string with tread elements, 258–268
tread simulation model, 128–140
Tire dynamics, 271, 444–462
Tire inertia, 268–276, 404, 621
Tire models, 81–85
Tire pull, 195–196
TNO-Automotive, xiv–xv, 176–177, 196, 404, 568
Toe angle, 9
Torsional stiffness:
motorcycle, 535–536
standing tire, 228, 237
Trailer, 53–57
Trajectory, 145–146
Transfer function:
string model, 228
string with tread elements, 258
Transient slip values, 392, 396
Transient tire behaviour, 385
Tread compliance, 130
Tread simulation model, 128–140
Tread width effect, 344, 431
Truck, 43, 139, 327
TU-Delft, xiv, 165, 232f, 339–343, 568
Turning, 112–127
Turn slip, 68, 70, 112–113, 138, 183–188, 228, 231
Turn slip stiffness, 228, 231

U

UMTRI, 6–7, 572
Unbalance, 325–327
Understeer, 24–25, 541, 548
Understeer at braking, 49–50

V

Vehicle handling, 16–58
Vehicle handling experiments, 611
Vehicle model, 7–8, 8f, 16–17
Vehicle slip angle response, 31–32
Vehicle stability, cf. stability
Volvo, 165
Vries, de, 171, 175–176, 464–466, 518

W

Wavelength, 212, 363, 386, 403–474
Weave mode, 529
Weighting function, 171–173, 184
Weir, 507
Wet road, 6–7, 155
Wheel lock, 140–147
Whipple, 506
Willumeit, 84
Wind-up oscillations, 397–400
Winkler, 43
Wisselman, 506–507
Wobble mode, 531

Y

Yaw velocity response, 22–23

Z

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