Surface Roughness Effects on Vortex Torque of Air Supported Gyroscope

In order to improve the drift precision of air supported gyroscope, effects of surface roughness magnitude and direction on vortex torque of air supported gyroscope are studied. Based on Christensenʹs rough surface stochastic model and consistency transformation method, Reynolds equation of air supported gyroscope containing surface roughness information is established. Also effects of mathematical models of main machining errors on vortex torque are established. By using finite element method, the Reynolds equation is solved numerically and the vortex torque in the presence of machining errors and surface roughness is calculated. The results show that surface roughness of slit has a significant effect on vortex torque. Transverse surface roughness makes vortex torque greater, while longitudinal surface roughness makes vortex torque smaller. The maximal difference approaches 11.4% during the range analyzed in this article. However surface roughness of journal influences vortex torque insignificantly. The research is of great significance for designing and manufacturing air supported gyroscope and predicting its performance.