Ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法

Design of Multi-Objective Tooth Optimization for Hypoid Gear with Ease-off Topological Modification

为了提高汽车驱动桥综合传动性能,提出基于ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法。预置传动误差参数及抛物线修形参数设计小轮法向ease-off曲面,小轮修形齿面表示为大轮的共轭齿面叠加ease-off曲面。结合齿面接触分析(TCA)、齿面承载接触分析(LTCA)方法及齿轮摩擦理论最新进展,得到接触线离散点的滑动速度、啮合承载变形、载荷分布及局部摩擦系数,进而确定齿面瞬时啮合效率和Block闪温。以承载传动误差幅值(ALTE)最小、齿面闪温最小和平均啮合效率最大进行多目标优化,获得最佳修形齿面,并分析齿面滑动速度与综合曲率半径的变化及重合度对啮合性能的影响。算例表明:最优ease-off修形齿面在啮入、啮出端有足够的抛物线传动误差,可有效减小ALTE并降低安装误差的敏感性;在整个齿高方向有一定的齿廓修形且接触迹线角较小时,齿轮副则有较大重合度,且齿顶、齿根载荷向节线附近集中,而节线附近的滑动速度较小,导致接触线平均摩擦系数下降,因此,啮合效率增加,齿面闪温下降;齿面适配量过大时,接触线载荷增加,摩擦功耗增大,啮合效率减小。

A design approach of multi-objective tooth optimization for hypoid gears with ease-off topological modification is proposed to improve comprehensive meshing performances of automobile drive axle. Firstly, the modified pinion is represented by a sum of two vector functions that determine the conjugate tooth of gear and the pinion normal ease-off surfaces, respectively, and are expressed by both predesigned transmission error function and tooth profile modification curves. Secondly, based on tooth contact analysis (TCA), loaded tooth contact analysis (LTCA) and the latest friction theory of gear, the bearing deformations, sliding velocity, distribution of loads and local friction coefficient of the discrete points on contact line of gears are obtained, and the instantaneous meshing efficiency and Block flash temperature are further determined. Thirdly, the best ease-off surfaces are obtained by solving a multi-objective optimization problem with minimal amplitude of loaded transmission error (ALTE), minimal instantaneous flash temperature and maximal average meshing efficiency. Moreover, the distribution of sliding velocity, the radius of curvature on tooth, and the influences of contact ratio on meshing performances are explored. Numerical results show that the best ease-off modification has enough parabola transmission errors at the meshing start and the meshing end, which can effectively reduce the sensitivity of installation error and ALTE. In addition, profile modification and small inclination of contact path contribute to a greater contact ratio, and the loads at top and root concentrate near the pitch line, while the sliding speed near the pitch line is smaller, as a result the meshing efficiency increases and the flash temperature decreases. However, when the tooth surface mismatch is too large, the loads and friction power consumption will increase, and the meshing efficiency will decrease.