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foundation natural frequencies. These forces can be constant or variable with impulse loadings. The effect of these forces on the rotor-bearing system can be great. Piping strains can cause major misalignment problems and unwanted forces on the bearings. Operation of reciprocating machinery in the same area can cause foundation forces and unduly excite the rotor of a turbomachine.
Forces generated by rotor motion. These forces can be classified intotwo categories: (1) forces due to mechanical and material properties， and (2) forces caused by various loadings of the system. The forces from mechanical and material properties are unbalanced and are caused by a lack of homo-geneity inmaterials， rotorbow， and elastic hysterisis of the rotor. The forces caused by loadings of the system are viscous and hydrodynamic forces in therotor-bearingsystem， and various blade loading forces， which vary in the operational range of the unit.
Forces applied to a rotor. Rotor-applied forces can be due to drivetorques， couplings，gears， misalignment， and axial forces from piston andthrust unbalance. They can be destructive， and they often result in the total destruction of a machine.
Rotor .earing System Instabilities
Instabilities in rotor-bearing systems may be the result of different forcingmechanisms. Ehrich， Gunter，Alford， and others have done considerable work to identify these instabilities. One can divide these instabilities into two general yet distinctly different categories: (1) the forced or resonant instability dependent on outside mechanisms in frequency of oscillations;
.able 5-2 Forces Acting on Rotor .earing Systems
Source of Force Description Application
1.  Forces transmittedConstant， Constant linear acceleration.to foundations，casing， unidirectional force or bearing pedestals.Constantforce， Rotation in gravitational or
rotational magnetic field.Variable， Impressed cyclic ground
unidirectional or foundation-motion.
Impulsive forces Airblast，explosion，
Random forces  or earthquake. Nearby
unbalanced machinery. Blows， impact.
2.  Forces generated Rotating unbalance:Present in all rotating machinery. by rotor motion. residual， or bent shaft.
Coriolis forces  Motion around curve of varying radius. Space applications. Rotary-coordinated analyses.
Elastic hysteresis  Property of rotormaterial， which
of rotorappears when rotor is cyclicallydeformed inbending， torsionally or axially.
Coulomb friction  Construction damping arising from relative motion between shrunkfitted assemblies. Dry-friction bearing whirl.
Fluid friction  Viscous shear of bearings. Fluid entrainment in turbomachinery. Windage.
Hydrodynamicforces， Bearing load capacity. static. Volute pressure forces.
Hydrodynamicforces，  Bearing stiffness and damping
dynamic. properties.
Dissimilar elastic beam  Rotors with differing rotor lateral
Stiffness reaction forces  stiffnesses. Slottedrotors，
electricalmachinery， Keyway. Abrupt speed change conditions Gyroscopic moments Significant in high-speed flexible rotors with discs.
3.  Applied to rotor Drive torque Accelerating or constant-speed operation Cyclic forces Internal combustion engine torque and force components.
Oscillating torques  Misaligned couplings. Propellers. Fans. Internal combustion engine drive.
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Source of Force  Description Transient torques Heavy applied rotor force Gravity Magnetic field: stationary or rotating Axial forces  Application Gears with indexing or positioning errors. Drive gear forces. Misaligned 3-or-more rotor-bearing assembly. Nonvertical machines. Nonspatial applications. Rotating electrical machinery. Turbomachine balance pistonCyclic forces frompropeller， or fan. Self-excited bearing forces. Pneumatic hammer 
　
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