Calculation of time-varying backlash for an involute spur gear pair

Abstract

Backlash plays a significant role in gear design and geared dynamics analysis. This study aims to establish a model of the time-varying backlash for a standard involute spur gear pair. The elastic deformations, thermal deformations and film thickness deformation at the meshing point are considered in this model. Asperity and fluid loads are included in film thickness. A time-varying backlash model with contact ratio is developed according to the force analysis at the meshing point. The contributions and effects of the various deformations on the backlash are analyzed. The effects of rotation speed, torque load and tooth surface temperature on the time-varying backlash are studied. Results show that the influence of various parameters on the backlash cannot be ignored. The time-varying backlash is less affected by elastic deformation and oil film thickness deformation, and is greatly affected by the thermal deformation. The time-varying backlash increases with the increase of torque load and the decreases of rotation speed and tooth surface temperature. Tooth surface temperature is validated experimentally due to its importance in the established model.