Title Page
Copyright Page
Preface
Table of Contents
Symbols
Chapter 1 Introduction
1.1 Linear rotordynamics
1.1.1 Equation of motion
1.1.2 Rotating systems
1.1.3 Complex coordinates
1.1.4 Free vibration
1.1.5 Forced response
1.2 Nonlinear rotordynamics
1.3 Nonstationary rotordynamics
1.4 Time domain versus frequency domain
Part I
Basic topics
Chapter 2 Jeffcott rotor
2.1 Undamped Jeff
cott rotor
2.1.1 Equations of motion
2.2.1 Free whirling
2.2.2 Unbalance response
2.3 Jeffcott
rotor with shaft bow
2.4 Jeffcott
rotor with viscous damping
2.4.1 Equations of motion
2.4.2 Some considerations on rotating damping
2.4.3 Free whirling
2.4.4 Unbalance response
2.4.5 Response to a static force constant in time
2.4.6 Shaft bow
2.4.7 Frequency response
2.5 Jeffcott
rotor with structural damping
2.5.1 Equation of motion
2.5.2 Free whirling
2.5.3 Mixed damping
2.5.4 Unbalance response
2.5.5 Dependence of the loss factor on frequency
2.6 Jeffcott
rotor with nonsynchronous damping
2.7 Effect
of the compliance of the bearings
2.7.1 Unbalance response
2.7.2 Free whirling
2.8 Rotating coordinates
2.9 Stability in the supercritical field
2.10 Drag torque at constant speed
Chapter 3 Model with four degrees of freedom:Gyroscopic effect
3.1 Generalized coordinates and equations ofmotion
3.1.1 Kinematics
3.1.2 Equations of motion in real
coordinates
3.1.3 Equations of motion in complex coordinates
3.1.4 Static and couple unbalance
3.2 Uncoupled gyroscopic system
3.2.1 Complex coordinates
3.2.2 Real coordinates
3.3 Free whirling of the coupled, undamped system
3.4 Response to unbalance and shaft bow
3.5 Frequency response
3.6 Unbalance response: modal computation
3.7 Modal uncoupling of gyroscopic systems
3.7.1 Configuration-space approach
3.7.2 State-space, com
plex-coordinates approach
Chapter 4 Discrete multi-degrees-of-freedomrotors
4.1 Transfer matrices approach: theMyklestadt-Prohl method
4.1.1 Undamped systems
4.1.2 Damped systems
4.2 Lumped parameters stiffness method
4.3 The finite element method
4.3.1 Timoshenko beam element for rotordynamic analysis
4.3.2 Mass element
4.3.3 Spring element
4.3.4 Assembling the structure
4.3.5 Constraining the structure
4.3.6 Damping matrices
4.3.7 Transfer matrices methods and the FEM
4.4 Real versus complex coordinates
4.5 Fixed versus rotating coordinates
4.6 Complex state-space equations
4.7 Static solution
4.8 Critical-speed computation
4.9 Computation of the unbalance response
4.10 Plotting the Campbell diagram and the rootslocus
4.11 Reduction of the number of degrees offreedom
4.11.1 Nodal reduction techniques
4.11.2 Modal reduction
4.11.3 Component mode synthesis
Chapter 5 Continuous systems: Transmissionshafts
5.1 The Euler-Bernoulli vibrating beam
5.2 Other boundary conditions
5.3 Effect
of the moments of inertia: Timoshenkobeam
5.4 Dynamic stiffness matrix
Chapter 6
Anisotropy of rotors or supports
6.1 Isotropic rotors on anisotropic supports
6.1.1 Jeffcott
rotor on nonisotropic supports
6.1.2 Effect
of damping
6.1.3 System with many degrees of freedom
6.2 Nonisotropic rotors on isotropic supports
6.2.1 Nonisotropic Jeffcott
rotor
6.2.2 Effect
of damping
6.2.3 Response to a static force
Chapter 7
Torsional and axial dynamics
7.1 Torsional free vibration
7.1.1 Lumped parameters approach
7.1.2 Consistent parameters approach
7.1.3 Geared systems
7.2 Forced vibrations
7.3 Torsional critical speeds
7.4 Axial vibration
Chapter 8
Rotor-bearings interaction
8.1 Rigid-body and flexural modes
8.2 Linearization of the characteristics of thebearings
8.3 Rolling elements bearings
8.4 Fluid film bearings
8.4.1 Forces exerted by the oil film on the journal instationary conditions
8.4.2 Linearized dynamics of the bearing
8.4.3 Stability problems linked with the use of lubricatedbearings
8.4.4 Effect
of seals, clearances, and dampers
8.5 Magnetic bearings
8.6 Bearing alignment in multibearing rotors
Part II
Advanced topics
Chapter 9
Anisotropy of rotors and supports
9.1 Nonisotropic Jeffcott
rotor
9.2 Equation of motion for an anisotropic machinewith many degrees of freedom
Chapter 10 Nonlinear rotordynamics
10.1 Nonlinear isotropic Jeffcott
rotor
10.1.1 Equation of motion
10.1.2 Unbalance response -
circular whirling
10.2 Nonlinear isotropic Jeffcott
rotor running onnonsymmetric supports
10.3 Nonlinear anisotropic Jeffcott
rotor runningon symmetric supports
10.4 Systems with many degrees of freedom
Chapter 11
Nonstationary rotordynamics
11.1 Nonstationary linear Jeffcott
rotor
11.1.1 Equations of motion
11.1.2 Torsionally stiffirotor
with imposed acceleration
11.1.3 Torsionally stiffrotor
with imposed torque
11.1.4 Torsionally compliant rotor: small torsional vibrationswith imposed acceleration
11.2 Nonstationary general Jeffcott
rotor
11.3 Nonstationary rotor with four degrees offreedom
11.4 Generic, torsionally stiff,
multi-degrees-of-freedom system
11.5 Blade loss
Chapter 12
Dynamic behavior of free rotors
12.1.1 General considerations
12.1.2 Equations of motion
12.2 Large amplitude whirling of a linearilyconstrained rigid rotor
12.3 Twin rigid-bodies free rotor
12.3.1 Linearized approach
12.3.2 Nonlinear approach
12.4 Multibody free rotors
Chapter 13
Dynamics of rotating beams andblades
13.1 Rotating pendulum
13.2 Rotating pendulum constrained to oscillate ina plane
13.3 Spring-loaded rotating pendulum
13.4 Rotating string
13.4.1 Rotating string constrained to oscillate in a plane
13.4.2 Rotating beam
13.5 Dynamics of a row of rotating pendulums
13.5.1 Pendulums on a rigid support
13.5.2 In-plane oscillations of pendulums on elastic supports
13.5.3 Spring-loaded pendulums on elastic supports
13.5.4 Damped pendulums on elastic supports
13.5.5 Out-of-plane oscillations of pendulums on elasticsupports
13.6 Interaction between the dynamics of theblades and the dynamics of the shaft
Chapter 14
Dynamics of rotating discs and rings
14.1 Rotating membranes
14.2 Rotating circular plate
14.3 Disc-shaft interaction (modes with m=0 or m=1)
14.4 Uncoupled modes (modes with m>2)
14.5 Vibration of rotating circular rings
14.5.1 Out-of plane flexural vibrations
14.6 Vibration of thin-walled, rotating cylinders
14.7 Instability of rotating cylinders partially filledwith liquid
Chapter 15
Three-dimensional modeling of rotors
15.1 Symmetry of the rotor
15.2 Simplified FEM elements for thin bladed-discsmodeling
15.2.1 Kinematics
15.2.2 Shape functions
15.2.3 Kinetic and potential energy
15.2.4 Element matrices
15.3 General finite element discretization
15.3.1 Kinematics of the deformation of a rotating body
15.3.2 Kinetic energy
15.3.3 Potential energy
15.4 Equation of motion in the inertial frame
15.4.1 Velocity
15.4.2 Kinetic energy
15.4.3 Equations of motion of the element
15.5 Axi-symmetrical annular elements
15.5.1 Shape functions
15.5.2 Kinetic and potential energy
15.5.3 Equations of motion
15.6 Axi-symmetrical shell element
15.6.1 Brick elements
Chapter 16
Dynamics of controlled rotors
16.1 Open-loop equations of motion
16.1.1 Real coordinates
16.1.2 Complex coordinates
16.2 Closed-loop equations of motion
16.2.1 Ideal proportional control
16.2.2 Ideal PID control
16.2.3 Dynamics of the control system
16.3 Rigid rotor on magnetic linearized bearings
16.3.1 Equations of motion
16.3.2 Symmetrical system
16.3.3 Nonsymmetrical system
16.3.4 Geometric re-colocation
16.4 Modal control of rotors
Appendix A
Vectors, matrices, and equations ofmotion
A.1 Equation of motion
A.1.1 Associated eigenproblem
A.1.2 Free response
A.1.3 Forced response
A.1.4 State-space representation
A.1.5 Frequency response
A.2 Rotating systems
A.2.1 Real coordinates
A.2.2 Complex coordinates
A.3 Circulatory and noncirculatory coupling
Appendix B
An outline on rotor balancing
B.1 Rigid rotors
B.2 Flexible rotors
B.2.1 Modal balancing
B.2.2 Influence coefficients method
Appendix C
Rotordynamics videos
Appendix D
DYNROT LIGHT rotordynamicscode
Appendix E
Books on rotordynamics
References
Index