A Novel Numerical Approach to Calculate the Nonlinear Film Force of Squeeze Film Dampers

Squeeze film dampers (SFD) demonstrate excellent performance dissipating mechanical energy for rotating machinery. Many researchers employ an approximate analytical solution to solve the stiffness and damping of SFD. The low accuracy of the approximate analytical method limits its application due to too many assumptions. The manuscript develops a novel numerical approach to solve the nonlinear film force of SFD effciently and accurately. First, this study establishes the mathematical Reynolds equation of SFD and simplifies it into difference equations by the numerical difference method. Then the equations are transformed into a linear equation set through a numerical strategy, and the film pressure distribution is solved by QR factorization. The numerical method is validated by comparing it with the approximate analytical approach. Furthermore, the dynamic responses of a rotor-SFD system acquired by the proposed approach and the analytical approximation manifest that the accuracy of the novel numerical approach is higher than the analytical solution, especially when the system is in a non-synchronous vibration state.