Design and analysis of modified cylindrical gears with a higher-order transmission error

• Gears with higher order polynomial function of transmission error (H-TE) is described to reduce vibration and noise.
• The coefficients of H-TE is determined by minimizing amplitude of loaded transmission error (ALTE) under applied load.
• A reverse TCA for the derivation of coefficients of additional rotation and deviations of the pinion are developed.
• The relationships between ALTE and effective contact ratios are investigated.
• Wave form and amplitude of transmission error under multi-load are discussed.

A design of tooth surface modifications for cylindrical gears that are provided with a controllable higher order polynomial function of transmission error (H-TE) are proposed to reduce vibration and noise, and the procedures for creating mathematical models of the tooth surfaces are described. Firstly, the polynomial coefficients of H-TE curve as well as processing parameters for rack generating pinion tooth surface can be individually determined based on TCA and LTCA by optimizing the aim of minimum amplitude of loaded transmission error (ALTE) of drive gears by using the particle swarm optimization (PSO). Secondly, the deviations of pinion tooth surface with H-TE from the theoretical one are derived according to the rack movement parameters. Thirdly, a numerical simulation of example based on spur gears and helical gears with different order transmission error are performed, which prove that the actual contact ratio and the effective contact ratios are the valid indices and the gear drive with H-TE has the lowest ALTE. The proposed gear drives are proved numerically to be able to reproduce the H-TE function and the effective contact ratios are the valid indices of LTE.