Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

作     者：ZHANG Jun GUO Fan 

作者机构：School of Mechanical Engineering Anhui University of Technology 

出 版 物：《Chinese Journal of Mechanical Engineering》 (中国机械工程学报（英文版）)

年 卷 期：2015年第28卷第6期

页      面：1194-1203页

核心收录：

学科分类：07[理学] 08[工学] 080203[工学-机械设计及理论] 070102[理学-计算数学] 0802[工学-机械工程] 0701[理学-数学] 080201[工学-机械制造及其自动化] 

基　　金：Supported by National Natural Science Foundation of China(Grant No.51375013) Anhui Provincial Natural Science Foundation of China(Grant No.1208085ME64) 

主　　题：tooth modification helical planetary gears response surface method Monte Carlo simulation 

摘      要：Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.