The aim of the book is to give an up-to-date review of rotor dynamics, dealing with basic topics as well as a number of specialized topics usually available only in journal articles. Part I deals with the classical topics of rotor dynamics, the dynamic behavior of linear, steady state rotating machines; simple models as well systems with many degrees of freedom obtained from finite element models. Part II, advanced rotor dynamics deals with some specialized topics on rotors, bearings, discs and blades. The accompanying CD-ROM includes a simplified version of the DYNROT code and two short videos.
Author(s): Giancarlo Genta
Series: Mechanical Engineering Series
Edition: 1
Publisher: Springer
Year: 2005
Language: English
Pages: 674
Contents......Page 14
Preface......Page 8
Symbols......Page 21
1 Introduction......Page 25
1.1 Linear rotordynamics......Page 28
1.1.1 Equation of motion......Page 29
1.1.2 Rotating systems......Page 30
1.1.3 Complex coordinates......Page 31
1.1.4 Free vibration......Page 33
1.1.5 Forced response......Page 47
1.2 Nonlinear rotordynamics......Page 53
1.3 Nonstationary rotordynamics......Page 54
1.4 Time domain versus frequency domain......Page 55
I. Basic topics......Page 57
2.1 Undamped Jeffcott rotor......Page 58
2.2 Complex coordinates in rotordynamics......Page 69
2.3 Jeffcott rotor with shaft bow......Page 72
2.4 Jeffcott rotor with viscous damping......Page 74
2.5 Jeffcott rotor with structural damping......Page 93
2.6 Jeffcott rotor with nonsynchronous damping......Page 100
2.7 Effect of the compliance of the bearings......Page 103
2.8 Rotating coordinates......Page 108
2.9 Stability in the supercritical field......Page 112
2.10 Drag torque at constant speed......Page 113
3 Model with four degrees of freedom: Gyroscopic effect......Page 115
3.1 Generalized coordinates and equations of motion......Page 116
3.2 Uncoupled gyroscopic system......Page 125
3.3 Free whirling of the coupled, undamped system......Page 129
3.4 Response to unbalance and shaft bow......Page 139
3.5 Frequency response......Page 142
3.6 Unbalance response: modal computation......Page 143
3.7 Modal uncoupling of gyroscopic systems......Page 145
4 Discrete multi-degrees-of-freedom rotors......Page 161
4.1 Transfer matrices approach: the Myklestadt-Prohl method......Page 163
4.2 Lumped parameters stiffness method......Page 177
4.3 The finite element method......Page 178
4.4 Real versus complex coordinates......Page 192
4.5 Fixed versus rotating coordinates......Page 194
4.6 Complex state-space equations......Page 195
4.8 Critical-speed computation......Page 196
4.9 Computation of the unbalance response......Page 198
4.10 Plotting the Campbell diagram and the roots locus......Page 199
4.11 Reduction of the number of degrees of freedom......Page 205
5.1 The Euler-Bernoulli vibrating beam......Page 223
5.2 Other boundary conditions......Page 231
5.3 Effect of the moments of inertia: Timoshenko beam......Page 235
5.4 Dynamic stiffness matrix......Page 241
6 Anisotropy of rotors or supports......Page 249
6.1 Isotropic rotors on anisotropic supports......Page 250
6.2 Nonisotropic rotors on isotropic supports......Page 268
7.1 Torsional free vibration......Page 286
7.2 Forced vibrations......Page 296
7.3 Torsional critical speeds......Page 300
7.4 Axial vibration......Page 301
8 Rotor-bearings interaction......Page 302
8.1 Rigid-body and flexural modes......Page 303
8.2 Linearization of the characteristics of the bearings......Page 305
8.3 Rolling elements bearings......Page 312
8.4 Fluid film bearings......Page 319
8.5 Magnetic bearings......Page 337
8.6 Bearing alignment in multibearing rotors......Page 348
II. Advanced topics......Page 350
9.1 Nonisotropic Jeffcott rotor......Page 351
9.2 Equation of motion for an anisotropic machine with many degrees of freedom......Page 359
10 Nonlinear rotordynamics......Page 367
10.1 Nonlinear isotropic Jeffcott rotor......Page 368
10.2 Nonlinear isotropic Jeffcott rotor running on nonsymmetric supports......Page 388
10.3 Nonlinear anisotropic Jeffcott rotor running on symmetric supports......Page 394
10.4 Systems with many degrees of freedom......Page 397
11.1 Nonstationary linear Jeffcott rotor......Page 406
11.2 Nonstationary general Jeffcott rotor......Page 416
11.3 Nonstationary rotor with four degrees of freedom......Page 420
11.4 Generic, torsionally stiff, multi-degrees-of-freedom system......Page 423
11.5 Blade loss......Page 425
12 Dynamic behavior of free rotors......Page 431
12.1 Single rigid-body rotor......Page 432
12.2 Large amplitude whirling of a linearily constrained rigid rotor......Page 449
12.3 Twin rigid-bodies free rotor......Page 457
12.4 Multibody free rotors......Page 474
13 Dynamics of rotating beams and blades......Page 482
13.1 Rotating pendulum......Page 483
13.2 Rotating pendulum constrained to oscillate in a plane......Page 487
13.3 Spring-loaded rotating pendulum......Page 489
13.4 Rotating string......Page 490
13.5 Dynamics of a row of rotating pendulums......Page 501
13.6 Interaction between the dynamics of the blades and the dynamics of the shaft......Page 526
14.1 Rotating membranes......Page 533
14.2 Rotating circular plate......Page 538
14.3 Disc-shaft interaction (modes with m = 0 or m = 1)......Page 541
14.4 Uncoupled modes (modes with m ≥ 2)......Page 543
14.5 Vibration of rotating circular rings......Page 544
14.6 Vibration of thin-walled, rotating cylinders......Page 554
14.7 Instability of rotating cylinders partially filled with liquid......Page 555
15 Three-dimensional modeling of rotors......Page 557
15.1 Symmetry of the rotor......Page 558
15.2 Simplified FEM elements for thin bladed-discs modeling......Page 564
15.3 General finite element discretization......Page 574
15.4 Equation of motion in the inertial frame......Page 583
15.5 Axi-symmetrical annular elements......Page 585
15.6 Axi-symmetrical shell element......Page 590
16 Dynamics of controlled rotors......Page 597
16.1 Open-loop equations of motion......Page 598
16.2 Closed-loop equations of motion......Page 600
16.3 Rigid rotor on magnetic linearized bearings......Page 608
16.4 Modal control of rotors......Page 622
A.1 Equation of motion......Page 630
A.1.1 Associated eigenproblem......Page 631
A.1.2 Free response......Page 634
A.1.3 Forced response......Page 635
A.1.4 State-space representation......Page 636
A.1.5 Frequency response......Page 637
A.2 Rotating systems......Page 638
A.2.1 Real coordinates......Page 639
A.3 Circulatory and noncirculatory coupling......Page 640
B. An outline on rotor balancing......Page 644
B.1 Rigid rotors......Page 645
B.2 Flexible rotors......Page 648
B.2.1 Modal balancing......Page 649
B.2.2 Influence coefficients method......Page 652
C. Rotordynamics videos......Page 657
D. DYNROT LIGHT rotordynamics code......Page 659
E. Books on rotordynamics......Page 661
References......Page 663
C......Page 669
I......Page 670
R......Page 671
W......Page 672
