变双曲圆弧齿线圆柱齿轮传动几何特性分析

摘要

According to the processing principle of cylindrical gear with variable hyperbolic circular-arc-tooth-trace (VH-CATT) and the deduced tooth surface equation of the gear,the range of parameters was determined.Based on the obtained tooth surface equation and the differential geo-metry,the calculation method of the principal curvature of concave and convex gear of VH-CATT was obtained.Based on the principle of spatial meshing,the relative velocity of gear teeth on meshing point at an input angular velocity was calculated.According to the calculated method of the curvature of the tooth surface and the relative velocity,the formula for calculating the sliding ratio of VH-CATT pair was derived.Setting a certain VH-CATT design parameters for example,principal curvature,induced curvature and sliding ratio were calculated and their change trends were analyzed.Sliding ratios under different design parameters were obtained,as the reference of analysis and optimization for gear design.Analysis res-ults showed that for the VH-CATT pair,the greater the modulus,tooth number ratio and tooth trace radius,the smaller the range of sliding ratio of gears is,and the abrasion in working process would be more uniform.Gear pair with larger modulus,smaller tooth number ratio,greater tooth trace radius has better performance in wear process.The quantitative relationship between sliding ratio and wear of VH-CATT was established,which provides reference for the calculation of gear wear.%根据变双曲圆弧齿线圆柱齿轮的加工原理与推导得到的齿面方程,确定方程各相关参数的取值范围,基于得到的齿面方程,依据微分几何,得到变双曲圆弧齿线圆柱齿轮凹、凸面主曲率的计算方法;基于空间啮合原理,计算齿轮副在某一输入角速度下两齿面啮合点处的相对运动速度;根据已得到的齿面曲率、相对运动速度计算方法,推导变双曲圆弧齿线圆柱齿轮副滑动率的计算公式.最后,以某一确定设计参数的变双曲圆弧齿线圆柱齿轮副作为算例,计算其主曲率、诱导法曲率和滑动率,分析其变化趋势;并计算不同设计参数下的滑动率,分析设计参数对其影响,以此作为分析该齿轮副设计及优化的参考.结果表明:对变双曲圆弧齿线圆柱齿轮来说,模数越大,齿数比越小,齿线半径越大,则滑动率的变化范围越小,齿轮副在运转过程中的磨损更均匀;就磨损而言,大模数、小齿数比、大齿线半径的齿轮具有更好的性能.建立变双曲圆弧齿线圆柱齿轮副滑动率与磨损之间的量化关系,反映出其正相关关系,为齿轮磨损量的计算提供参考.