高速重载弧齿锥齿轮齿面多目标优化设计

任鸿飞; 王三民; 陈鹏; 张旭阳; 张全清

doi:10.13433/j.cnki.1003-8728.20220185

高速重载弧齿锥齿轮齿面多目标优化设计

doi: 10.13433/j.cnki.1003-8728.20220185

1.
西北工业大学机电学院，西安　710072

详细信息

作者简介:
任鸿飞，硕士研究生，905973622@qq.com

通讯作者:
王三民，教授，博士生导师，wangsami@nwpu.edu.cn

中图分类号: V232.8
计量
- 文章访问数: 65
- HTML全文浏览量: 41
- PDF下载量: 13
- 被引次数: 0
出版历程
- 收稿日期: 2021-12-14
- 网络出版日期: 2024-03-08
- 刊出日期: 2024-02-01

Multi-objective Optimal Design of Tooth Surface of High Speed and Heavy Load Spiral Bevel Gears

1.
School of Mechanical Engineering, Northwestern Polytechnical University, Xi′an 710072, China

摘要

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。
- 弧齿锥齿轮 /
- 重合度 /
- 传动误差 /
- 多目标优化 /
- NSGA-II算法
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.
- spiral bevel gears /
- contact ratio /
- transmission error /
- multi-objective optimization /
- NSGA-II algorithm

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图 1 抛物线型传动误差曲线

Figure 1. Parabolic transmission error curve

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图 2 NSGA-II流程

Figure 2. Flowchart of NSGA-II

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图 3 Pareto近似前沿

Figure 3. Pareto approximate frontier

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图 4 优化前2阶参数对应的TCA结果

Figure 4. TCA results corresponding to the second-order parameters before optimization

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图 5 优化后2阶参数对应的TCA结果

Figure 5. TCA results corresponding to the second-order parameters after optimization

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图 6 优化前2阶参数对应的LTCA结果

Figure 6. LTCA results corresponding to the second-order parameters before optimization

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图 7 优化后2阶参数对应的LTCA结果

Figure 7. LTCA results corresponding to the second-order parameters after optimization

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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

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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

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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

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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

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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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