Sun Yuantao, Li Yingcheng, Gu Caohang, Zhang Qing, Chen Kaige
School of Mechanical Engineering, Tongji University, No. 4800 Caoan Road, Shanghai, 201804, China.
Sci Rep. 2025 Jul 8;15(1):24537. doi: 10.1038/s41598-025-09419-8.
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.
磨损是小模数齿轮的主要失效模式。受安装误差、公差等级和侧向间隙的影响，磨损过程具有随机性和缓慢时变特性，导致其可靠性随时间变化，不同精度等级的要求会给设计和使用带来巨大挑战。为解决这一问题，本文提出一种基于维纳过程的小模数齿轮动态可靠性模型，并通过分析可靠性变化规律预测小模数齿轮的剩余寿命。首先，数值模拟结果表明小模数齿轮的磨损过程符合带漂移系数的维纳过程，并采用回归模型分析齿廓各位置的磨损情况。其次，通过整合基本维纳过程模型，利用福克 - 普朗克 - 柯尔莫哥洛夫（FPK）方程建立齿轮磨损的动态可靠性模型。第三，考虑各种精度等级，求解不同精度要求下磨损的动态可靠性，分析其可靠性规律并计算剩余寿命，在考虑精度等级的同时优化小模数齿轮的设计参数。这有利于小模数齿轮的设计和选型，从而提高其可靠性和使用寿命。
