Bearing Dynamic Coefficients Calculation
Bearing dynamic coefficients are the effective stiffness and damping coefficients of the bearing when the rotor is at its equilibrium position. For a sufficiently loaded bearing, the rotor will in steady state take an eccentric equilibrium position in the bearing to support the static loads. It then does a small amplitude whirl about this equilibrium position due to the dynamic loads on the rotor such as eccentricity, misalignment, and so on. A dynamic coefficient approximation works well if the static load on the rotor is much larger than the dynamic loads. If dynamic loads is comparable to the static load or the bearing is lightly loaded, the rotor undergoes a large amplitude whirl without any well-defined equilibrium position. In such a case, the nonlinearity of the bearing forces must be accounted for in order to accurately predict the dynamics of the rotor.
Determination of the dynamic coefficients of the bearing is done at the equilibrium position of the journal for the given static load. The change in the net bearing reaction forces as the bearing equilibrium position is disturbed is then obtained. There are two fundamentally different approaches that can be used: infinitesimal perturbation and finite perturbation.
Infinitesimal Perturbation
Perturbed differential equations in terms of new pressure perturbation degrees of freedom are obtained by considering the derivative of the Reynolds equation with respect to the equilibrium position perturbation. Bearing dynamic coefficients are expressed in terms of the new pressure perturbation degrees of freedom.
This is the method used in the Rotordynamics Module.
Finite Perturbation
Reynolds equation is solved for two conditions, first at the equilibrium state and then by considering a finite perturbation to the equilibrium position. The difference in the net reaction force in the bearing with respect to the perturbation gives the corresponding coefficients. In this approach, perturbation amplitudes should be small enough to get the accurate results. Typical perturbation values used are
0.01
C
for displacement and
0.01
Ω
C
for velocity.