Dynamics of Machinery I

1. Rotor-bearing systems 1 1.1 Evolution of rotating machinery 1 1.2 Rotor-bearing dynamics 22 1.3 Rotor precession 24 1.4 Modeling the rotor 26 1.5 Evolution of rotor design philosophy 29 1.6 Historical perspective 32 2. Simple rotors in rigid bearings 39 2.1 Simple rotor models 39 2.2 Symmetric undamped rotors 40 2.2.1 Equations of motion 41 2.2.2 Steady state response 43 2.3 Damped symmetric rotors 46 2.3.1 Effect of viscous external damping 47 2.3.2 Effect of viscous internal damping 54 2.3.3 Combined external and internal damping 62 2.3.4 Gravity loading 65 2.3.5 Effect of shaft bow 66 2.3.6 Rotor precession in rigid bearings 67 2.4 Undamped asymmetric rotors 68 2.4.1 Reference frames 69 2.4.2 Inertia torques on a spinning disc 69 2.4.3 Equations of motion for elastically supported discs 72 2.4.4 Natural frequencies of precession 75 2.4.5 Response to harmonic excitation 81 2.4.6 Campbell diagrams 87 2.4.7 Effect of gyroscopic torque on critical speeds 97 2.4.8 Remarks on the precession of asymmetric rotors 98 3. Simple rotors in flexible bearings 101 3.1 Symmetric rotors in flexible bearings 101 3.1.1 Effect of bearing flexibility 102 3.1.2 Effect of external damping 109 3.1.3 Effect of external and internal damping 117 3.1 4 Effect of bearing damping 119 3.1.5 Combined effect of bearing damping and shaft mass 131 3.2 Symmetric rotors in fluid film bearings 3.2.1 Unbalance response 136 3.2.2 Stability of precession motion 142 3.3 Asymmetric rotors in flexible bearings 145 3.3.1 Equations of motion 145 3.3.2 Natural frequencies of precession 148 3.3.3 Unbalance response 152 3.3.4 Effect of bearing damping 156 3.3.5 Mixed modes of precession 158 3.4 Simulation examples 168 4. Rotor dynamic analysis 207 4.1 Undamped critical speeds 207 4.1.1 Effect of support flexibility 207 4.1.2 Critical speed map 209 4.1.3 Influence of stator inertia 217 4.2 Damped critical speeds 4.2.1 Linear bearing models 219 4.2.2 Equations of damped motion 220 4.2.3 Eigenvalue problem of damped rotor systems 220 4.2.4 Campbell diagrams 222 4.2.5 Orbits and precession mode shapes 223 4.3 Peak response critical speeds 224 4.4 Stability analysis 227 4.5 Simulation examples 231 4.6 Planar modes of precession 273 Index 283