Dynamic reliability modeling and analysis of small modulus gear wear based on the Wiener process

Wear is the main failure mode of small modulus gear. Due to the influence of the installation error, tolerance grade and lateral clearance, the wear process has randomness and slow time-varying characteristics, which leads to its reliability changing with time, and the requirements of different precision grades will bring great challenges for design and use. To solve this problem, this paper proposes a dynamic reliability model for small modulus gears based on Wiener process, and predicts the residual life of small modulus gear by analyzing the change rule of reliability. Firstly, the numerical simulation results demonstrate that the wear process of the small modulus gear conforms to the Wiener process with a drift coefficient, and the regression model is used to analyze the wear at each position of the tooth profile. Secondly, by integrating the basic Wiener process model, a dynamic reliability model for gear wear is established using the Fokker-Planck-Kolmogorov (FPK) equation. Thirdly, considering various precision grades, the dynamic reliability of wear under different accuracy requirements is solved, the rule of its reliability is analyzed and the residual life is calculated to optimize the design parameters of the small modulus gear while considering the precision grades. This is beneficial for the design and selection of small modulus gears, thereby improving their reliability and service life.