A Tolerance Mathematical Model Based on Fractal Theory for Tolerance Analysis of Gear

摘要

For effectively making the tolerance analysis of gear, it is necessary to build a suitable tolerance mathematical model, which can not only clearly express the characteristics of each type of variation but also meet the requirement of tolerance analysis. Due to the complexity of tooth flank, the previous tolerance modeling approaches used to simplify the variation models of tooth flank. For building more reasonable model and improving the quality of gear tolerance analysis, fractal theory is employed in this paper. Based on this model, the mathematical models of pitch deviation and eccentricity deviation are also built. Then the tolerance mathematical model for spur gear is obtained. Furthermore, the ETCA (Error Tooth Contact Analysis) method is proposed to analyze the effects of different deviations on transmission error based on the above model. Finally, a gear tolerance analysis method based on Monte Carlo simulation is discussed and an example is analyzed by taking transmission error as functional requirement parameter. The paper provides a valuable reference for improving the quality of gear tolerance analysis and tooth flank's contact and dynamic analysis.