A recursive method for determining long-period mesh stiffness of cylindrical gears considering real tooth surface deviations

A recursive method is proposed for determining long-period time-varying mesh stiffness (TVMS) of cylindrical gears, considering real tooth surface deviations. Due to variations in the real deviations of each gear tooth and the presence of hunting tooth pairs, the superposition of contact point deviations between the driving and driven gears results in a long period for the TVMS. A long-period recursive model of contact point deviation superposition is developed based on even mesh technique and tooth surface measurement technique. This model considers the matching relationships of contact elements and the forward and backward recursion relationships of each contact element over a long period. Furthermore, a loaded tooth contact analysis (LTCA) model with long-period superposition deviations is established, and a double-layer iterative algorithm is devised to solve for long-period TVMS and transmission error (TE). The validity of the proposed method is confirmed through tooth surface measurements and TE experiments. The effects of load, deviation superposition, and deviation size on long-period TVMS are investigated. Finally, the main frequency components in the TVMS spectrum that may cause low-frequency vibrations in gears are identified.