Applications of unconstrained minimization methods to the dynamic analysis of air-lubricated bearings

This study deals with the procedure to estimate the stiffness and damping of air-lubricated bearings under dynamic conditions. Unconstrained minimization methods were used in the nonlinear least squares (NLS) analysis to obtain the dynamic parameters of simulated noisy data with small signal-to-noise ratios (SNR). In the analysis the contaminating noise, either uniform or norma(lv distributed noise, was scaled to give a known SNR and added to a simulated noise-free data. Even with poor initial-guess in the NLS as demonstrated in this study, both simplex and Powell's methods reach minimal variance with far fewer searching steps than those of the lattice and Hooke's methods. In the example of experimental study, the effect of an arbitrary data truncation point on the parameter estimation can be minimized in the fitting process by adding additional parameter-phase angle. The result shows good agreement between experimentally determined stiffness and theoretical prediction. This study provides a general procedure for dynamic analysis of air-lubricated bearings from noisy experimental mental measurements.