دانلود کتاب Dynamics of Machinery II

فهرست مطالب :

5. Finite element analysis of rotor-bearing systems 1
5.1 Rotor component models 1
5.2 Kinematics of rigid body precession 3
5.2.1 Main reference frames 3
5.2.2 Rigid-body precession 3
5.2.3 Small rotations of the spin axis 4
5.3 Equations of motion for rotor components 7
5.3.1 Thin disks 7
5.3.2 Uniform shaft elements 13
5.3.3 Bearings and seals 31
5.3.4 Flexible couplings 35
5.4 System equations of motion 36
5.4.1 Second order configuration space form 37
5.4.2 First order state space form 40
5.5 Eigenvalue analysis 40
5.5.1 Right and left eigenvectors 41
5.5.2 Reduction to the standard eigenvalue problem 42
5.5.3 Campbell and stability diagrams 43
5.6 Unbalance response 47
5.6.1 Modal analysis solution 47
5.6.2 Spectral analysis solution 48
5.7 Kinematics of elliptic motion 49
5.7.1 Elliptic orbits 49
5.7.2 Decomposition into forward and backward circular motions 52
5.7.3 Variable angular speed along the ellipse 54
5.8 Model order reduction 56
iv
DYNAMICS OF MACHINERY
5.8.1 Model condensation 56
5.8.2 Model substructuring 62
5.8.3 Stepwise model reduction methods 68
References 76
6. Fluid film bearings and seals 77
6.1 Fluid film bearings 77
6.2 Static characteristics of journal bearings 78
6.2.1 Geometry of a plain cylindrical bearing 79
6.2.2 Equilibrium position of journal center in bearing 80
6.3 Dynamic coefficients of journal bearings 83
6.4 Reynolds equation and its boundary conditions 84
6.4.1 General assumptions 86
6.4.2 Reynolds’ equation 87
6.4.3 Boundary conditions for the fluid film pressure field 89
6.5 Analytical solutions of Reynolds’equation 90
6.5.1 Short bearing (Ocvirk) solution 90
6.5.2 Infinitely long bearing (Sommerfeld) solution 99
6.5.3 Finite-length cavitated bearing (Moes) solution 99
6.6 Physical significance of the bearing coefficients 103
6.7 Bearing temperature 107
6.7.1 Approximate bearing temperature 108
6.7.2 Viscosity-temperature relationship 109
6.8 Common fluid film journal bearings 112
6.8.1 Plain journal bearings 112
6.8.2 Axial groove bearings 112
6.8.3 Pressure dam bearings 114
6.8.4 Offset halves bearings 116
6.8.5 Multilobe bearings 117
6.8.6 Tilting pad journal bearings 124
6.8.7 Rayleigh step journal bearings 128
6.8.8 Floating ring bearings 129
6.9 Squeeze film dampers 130
6.9.1 Basic principle 130
CONTENTS
6.9.2 SFD design configurations 132
6.9.3 Squeeze film stiffness and damping coefficients 133
6.9.4 Design of a squeeze film damper 135
6.10 Annular liquid seals 137
6.10.1 Hydrostatic reaction. Lomakin effect 138
6.10.2 Rotordynamic coefficients 139
6.10.3 Final remarks on seals 146
6.11 Annular gas seals 147
6.12 Floating contact seals 150
6.12.1 Design characteristics 151
6.12.2 Seal ring lockup 154
6.12.3 Locked-up oil seal rotordynamic coefficients 155
References 159
7. Instability of rotors 161
7.1 Whirling of rotating shafts 161
7.2 Instability due to rotating damping 164
7.2.1 Planar rotor model 165
7.2.2 Qualitative effect of damping 166
7.2.3 Whirl speeds of rotor with rotating damping 168
7.2.4 Quantitative effects of damping 172
173
7.3.1 Oil-whirl and oil-whip phenomena 174
7.3 Whirl in hydrodynamic bearings
7.3.2 Half frequency whirl 176
7.3.3 Onset speed of instability 178
7.3.4 Crandall’s explanation of journal bearing instability 179
7.3.5 Stability of linear systems 187
7.3.6 Instability of a simple rigid rotor 189
7.3.7 Instability of a simple flexible rotor 194
7.3.8 Instability of complex flexible rotors 199
7.4 Interaction with fluid flow forces 199
7.4.1 Steam whirl 199
7.4.2 Impeller-diffuser interaction 201

v
vi


DYNAMICS OF MACHINERY
7.5 Dry friction backward whirl 203
7.5.1 Rotor-stator rubbing 203
7.5.2 Dry friction whirl 204
7.6 Instability due to asymmetric factors 206
7.6.1 Parametric excitation 207
7.6.2 Shaft anisotropy 207
7.6.3 Asymmetric inertias 219
7.6.4 Finite element analysis of asymmetric rotors 226
References 229
Index 233