弧齿锥齿轮基本参数优化设计

Optimal design of basic parameters of spiral bevel gears

为改善因传统机械式机床加工运动受限而采用局部共轭接触造成的齿面接触区域小的现状,同时为提升齿面接触性能,提出了一种弧齿锥齿轮基本参数优化设计方法。基于齿轮副全齿面接触的实现方法,以齿轮基本参数为优化变量、排除啮合界限线和根切界限线(以下简称为“2类界限线”)及防止齿顶变尖为约束条件,建立了以传动润滑性能综合参数和齿面瞬时接触线总长度最大为目标的齿面接触性能多目标优化数学模型。引入更加适合模型本身的现代多目标骨干粒子群算法求解最优基本参数。以一个具体的弧齿锥齿轮为研究对象,对比基本参数优化设计前后齿面的接触性能指标。数值仿真结果表明,优化后2类界限线分布于工作齿面区域外,表征润滑性能的综合参数的最小值和表征承载能力的齿面瞬时接触线总长度的最小值都有明显提升。有限元模型仿真结果表明,优化后工作齿面无干涉且呈全齿面接触。该研究提供了一种快速可行的弧齿锥齿轮基本参数最优设计方法,为弧齿锥齿轮的优化设计提供了参考。

An optimal design method of basic parameters of spiral bevel gears was proposed to improve the situation of little contact area caused by local conjugate contact due to the limited machining of the traditional machine tools,and the contact performance of the tooth surface.Based on the realization method of gear pair fulltooth contact,a multi-objective optimization mathematical model of tooth contact performance was established with the gear basic parameters as the optimization variable,eliminating meshing limit line and root cutting limit line(referred to as"two class limit lines")and preventing the addendum becoming sharp as the constraint conditions,aiming at maximizing the lubrication performance comprehensive parameter and total length of instantaneous contact line on the tooth surface.The modern bare-bones multi-objective particle swarm optimization algorithm which was more suitable for the model was used to solve the optimal basic parameters.A spiral bevel gears with specific parameters was taken as the research object,and the contact performance indexes of the tooth surface before and after the optimal design of the basic parameters were compared.The numerical simulation results showed that the two class limit lines were distributed outside the working flank of tooth surface,both the minimum value of the comprehensive parameters characterizing the lubrication performance and total length of instantaneous contact line on the tooth surface characterizing the carrying performance were significantly improved,and the simulation results of finite element model showed that the optimized working tooth surface contacted fully without interference.The study provides a fast and feasible method to obtain the optimal basic parameters of spiral bevel gears,which provides a reference for the optimal design of spiral bevel gears.