Analysis of aerostatic spindle radial vibration error based on microscale nonlinear dynamic characteristics

This paper presents a method of predicting the radial rotary error of an aerostatic spindle based on the microscale-effect to investigate the influence of gas film fluctuation on the rotation accuracy of the aerostatic spindle. First, the gas bearing of the spindle is simplified as a spring-damping system with two degrees of freedom perpendicular to each other. Additionally, the aerostatic spindle bearing-rotor system is established by considering the forced vibration and deflection vibration of the rotor. Subsequently, the microscale-effect is introduced into the dynamic model of the gas film flow, and the dynamic Reynolds equation of the gas film is established in the microscale. Moreover, the nonlinear dynamic stiffness and dynamic damping coefficient are obtained by the perturbation method. The nonlinear dynamic parameters in the microscale are introduced into the dynamic model of the bearing-rotor system and all the vibration errors are obtained. By comparison with the conventional case, it is found that the spindle gyration error increased and that the response delay occurred when the microscale-effect is considered. Moreover, the influence of the supply pressure and speed on the vibration of the spindle is also analyzed. An experiment measuring the spindle rotation error is carried out. The experimental results reveal that the prediction method of the nonlinear spindle rotation error in the microscale is more accurate, and that the errors are 5.8% and 9.6%