Tooth friction force and transmission error of spur gears due to sliding friction

This study investigated the tooth friction force and transmission error (TE) of spur gears due to sliding friction under quasi-static condition. The sliding velocity and friction force of spur gears and mesh compliance during meshing were calculated. The load–deformation relations between the tooth normal load, tooth errors, and mesh compliance, and moment equilibrium equation, including friction force, were derived. The friction force, tooth load, and TE of unmodified and linear tip-relief modified spur gears were analyzed by using the derived equations. Results indicated that the friction force, tooth load, and TE increased during approach and decreased in recess regardless of tooth modification, particularly in the single-mesh region. Friction caused larger peak-to-peak change of TE than that without friction. Xu's friction coefficient generated smooth TE and tooth load transitions near the pitch point, and BK's friction coefficient remained approximately constant, except for the sharp increase in tooth load and TE near the pitch point.