Geometric contact characteristics and sensitivity analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gear with error theory considered

计及误差理论的变双曲圆弧齿线圆柱齿轮几何接触特性及敏感性分析

¹ School of Mechanical & Electronical Engineering, Lanzhou University of Technology, Lanzhou 730050, China
² R & D Center of Sichuan Jian'an Industry Co., Ltd, Yaan 625100, China

Received: 16 August 2021

Abstract

Gear transmission characteristics are the most important research contents in gear transmission, and contact characteristics are important factors that affect gear transmission performance. The establishment of tooth surface contact analysis (TCA) model of a gear pair plays a guiding role in analyzing its contact characteristics. The rotary surface equation of the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear cutter is obtained with the large cutter forming principle, and the mathematical model of the gear tooth surface is established based on the gear meshing conditions. With the influence of installation error on gear contact performance considered, a TCA model with installation error was established. The influence of different installation errors and different design parameters on the geometric contact characteristics and sensitivity of the gear pair is analyzed. The analysis results show that the central distance error may affect the contact ratio of the VH-CATT cylindrical gear pair and that the shaft parallelism error has a great influence on its transmission characteristics, greatly changing the size and position of the gear pair contact area. The design parameters also affect the size and location of the contact area to various degrees.

摘要

齿轮传动特性是齿轮传动中最为重要的研究内容之一, 而接触特性是影响齿轮传动性能的重要因素, 齿面接触分析(TCA)模型的建立对分析齿轮副接触特性具有指导作用。通过大刀盘成形原理得到变双曲圆弧齿线圆柱齿轮刀具回转面方程, 基于齿轮啮合条件建立了该齿轮的齿面数学模型。考虑安装误差对齿轮接触性能的影响, 建立了含有安装误差的TCA模型, 分析了不同安装误差和设计参数对齿轮副几何接触特性及敏感性的影响。结果表明: 中心距误差会对变双曲圆弧齿线圆柱齿轮副重合度产生影响; 平行度误差对其传动特性影响很大, 极大程度上改变了齿轮副接触区域的大小和位置; 设计参数对齿轮接触区域大小及位置也会造成不同程度的影响。