Multi-objective Optimal Design of Tooth Surface of High Speed and Heavy Load Spiral Bevel Gears
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摘要: 以提高弧齿锥齿轮强度性能和减振降噪为出发点,基于TCA(Tooth contact analysis)、LTCA(Load tooth contact analysis)及局部综合法建立高重合度与低啮合转换处传动误差幅值的齿面多目标优化设计模型;利用带精英策略非支配排序遗传算法(NSGA-II)优化3个齿面2阶接触参数,根据目标函数重要程度从Pareto最优解集中选择最终优化解。结果表明:给定工况下,优化后的2阶参数使得弧齿锥齿轮副重合度增加了16.69%,啮合转换处传动误差幅值降低了87.33%;同时承载传动误差均值、齿面接触应力均值与大小轮齿根弯曲应力均值分别降低了11.82%、0.25%、12.32%和13.61%,改善了齿轮副的强度性能和啮合性能,实现了减振降噪的效果。Abstract: To improve the strength performance of spiral bevel gears and reduce vibration and noise, a multi-objective optimization design model for tooth surfaces of spiral bevel gears was established by using the tooth contact analysis (TCA), load tooth contact analysis (LTCA) and local synthesis method to increase the contact ratio and reduce the transmission error amplitude at the transition of meshing; the non-dominated sorting genetic algorithm with elite strategy NSGA-II was used to optimize three second-order the contact parameters of the tooth surfaces, and the optimized solution was selected from the Pareto optimal solution set according to the importance of the objective function. The results showed that, under the given conditions, the optimized second-order parameters increased the contact ratio of the spiral bevel gear pair by 16.69%, and reduced the transmission error amplitude at the meshing conversion by 87.33%; meanwhile, the average load transmission error, the average tooth surface contact stress and the average tooth root bending stress of the large and small gears were reduced by 11.82%, 0.25%, 12.32% and 13.61% respectively, which improved the strength performance and meshing performance of the gear pair, and achieved the effect of the vibration and noise reduction.
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表 1 齿轮坯基本参数
Table 1. Basic parameters of gear blank
参数 小轮 大轮 齿数 28 73 大端模数/mm 3.85 3.85 齿宽/mm 40 40 压力角/(°) 20 20 中点螺旋角/(°) 30 30 轴交角/(°) 70 70 旋向 左旋 右旋 表 2 NSGA-II相关参数设置
Table 2. NSGA-II related parameter setting
参数 数值 种群规模 200 变异概率 0.1 交叉概率 0.9 表 3 优化前后2阶接触参数
Table 3. Second-order contact parameters before and after optimization
参数 优化前 优化后 接触迹线与根锥夹角$ \eta /(^\circ ) $ 60 30.377 传动比1阶导数$ {m'_{21}} $ −0.008 −0.001 接触椭圆长半轴与齿宽之比 0.18 0.15016 表 4 优化前后目标函数计算结果
Table 4. Calculation results of objective function before and after optimization
参数 优化前 优化后 重合度 1.458 1.75 啮合转换处传动误差幅值/(″) 11.130 1.410 表 5 优化前后各接触特征响应
Table 5. Contact characteristics response before and after optimization
参数 优化前 优化后 承载传动误差均值/(″) −83.2911 −70.4445 齿面接触应力均值/MPa 1411.322 1407.748 大轮齿根弯曲应力均值/MPa 328.440 287.963 小轮齿根弯曲应力均值/MPa 321.891 278.068 -
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