受载齿轮副啮入冲击激励计算方法

王承登; 何泽银; 杨震; 伍宏建; 刘威

doi:10.13224/j.cnki.jasp.20220383

受载齿轮副啮入冲击激励计算方法

doi: 10.13224/j.cnki.jasp.20220383

王承登^1,,
何泽银^{1, 2,*, ,},
杨震³,
伍宏建¹,
刘威¹

1.
重庆交通大学机电与车辆工程学院，重庆 400074
2.
重庆大学机械传动国家重点实验室，重庆 400030
3.
重庆齿轮箱有限责任公司技术中心，重庆 402263

基金项目: 国家自然科学基金（52005066）；重庆市自然科学基金（cstc2021jcyj-msxmX0562）

详细信息

作者简介:
王承登（1997-），男，助理工程师，硕士，主要研究方向为齿轮传动及振动噪声控制。E-mail：wcd2678691332@163.com

通讯作者:
何泽银（1985-），男，教授，博士，主要研究方向为振动噪声与控制。E-mail：zeyin_he@126.com

中图分类号: V232.8；TH132.41
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出版历程
- 收稿日期: 2022-05-29
- 网络出版日期: 2023-10-25

Calculation method of meshing impact excitation of loaded gear pair

WANG Chengdeng^1
,,
HE Zeyin^{1, 2,*
, ,},
YANG Zhen³,
WU Hongjian¹,
LIU Wei¹

1.
School of Mechanical and Vehicle Engineering， Chongqing Jiaotong University，Chongqing 400074，China
2.
State Key Laboratory of Mechanical Transmission， Chongqing University，Chongqing 400030，China
3.
Technology Center，Chongqing Gearbox Company Limited，Chongqing 402263，China

摘要

摘要:
针对目前理论不能准确计算受载齿轮啮入冲击时间的问题，提出一种基于圆柱碰撞理论与接触动力学理论的受载齿轮副啮入冲击激励计算方法，准确计算受载齿轮啮入冲击时间与冲击力。建立受载变形下的渐开线齿轮啮入冲击数学模型，应用反转法计算出线外啮合点的精确位置，基于圆柱碰撞理论求得齿对啮入冲击力。同时在所建立的啮入冲击数学模型上，准确计算冲击时间，并与现有计算方法进行对比分析。而后根据齿轮运行真实工况，对航空机匣齿轮副进行动态接触有限元分析，提取冲击时间与冲击力，并与理论进行对比。结果表明：计算模型的啮入冲击时间误差在15%以内，最大啮入冲击力误差小于10%，故该冲击激励计算方法能对冲击时间与最大啮入冲击力进行准确快速求解。
- 冲击时间 /
- 啮入冲击 /
- 线外接触 /
- 圆柱碰撞 /
- 动态接触
Abstract:
In view of the problem that the current theory can not accurately calculate the meshing impact time of loaded gear, a calculation method of meshing impact excitation of loaded gear pair based on cylindrical collision theory and contact dynamics theory was proposed to accurately calculate the meshing impact time and impact force of loaded gear. The mathematical model of meshing impact of involute gear under load and deformation was established. The exact position of the outer meshing point of the line was calculated by the inversion method, and the meshing impact force of the tooth pair was obtained based on the cylindrical collision theory. At the same time, on the basis of the established mathematical model of meshing impact, the impact time was accurately calculated and compared with the existing calculation methods. Then, according to the actual working condition of the gear, the dynamic contact finite element analysis of the gear pair of the aircraft gearbox was carried out, while the impact time and impact force were extracted, and compared with the theory. The results showed that the error of the meshing impact time of the calculation model was within 15%, and the error of the maximum meshing impact force was less than 10%. Therefore, the impact excitation calculation method can accurately and quickly solve the impact time and the maximum meshing impact force.
- impact time /
- meshing impact /
- off line contact /
- cylindrical collision /
- dynamic contact

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图 1 啮入冲击理论

Figure 1. Meshing impact theory

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图 2 等效圆柱碰撞

Figure 2. Equivalent cylinder collision

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图 3 啮入冲击点位置

Figure 3. Position of meshing impact point

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图 4 啮合冲击数学模型

Figure 4. Mathematical model of meshing impact

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图 5 等效圆柱碰撞模型

Figure 5. Equivalent cylinder collision model

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图 6 冲击时间段

Figure 6. Impact time period

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图 7 啮入冲击力

Figure 7. Meshing impact force

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图 8 最大啮合冲击力随转矩变化规律

Figure 8. Variation law of maximum meshing impact force with torque

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图 9 最大啮合冲击力随转速变化规律

Figure 9. Variation law of maximum meshing impact force with rotating speed

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图 10 最大啮合冲击力随齿宽变化规律

Figure 10. Variation law of maximum meshing impact force with tooth width

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图 11 齿顶修形

Figure 11. Gear addendum modification

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图 12 修行后冲击点

Figure 12. Impact point after gear modification

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图 13 最大啮合冲击力随修形变化规律

Figure 13. Variation law of maximum meshing impact force with modification

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图 14 齿廓误差

Figure 14. Error of gear profile

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图 15 最大啮合冲击力随齿廓总误差变化规律

Figure 15. Variation law of maximum meshing impact force with total error of tooth profile

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图 16 有限元法流程图

Figure 16. Flow chart of finite element method

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图 17 动态接触有限元模型

Figure 17. Dynamic contact finite element model

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图 18 加载后从动轮角速度曲线

Figure 18. Angular velocity curve of driven wheel after loading

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图 19 动态啮合力

Figure 19. Dynamic meshing force

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图 20 单对轮齿接触力

Figure 20. Single tooth contact force

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表 1 两冲击时间计算方法对比

Table 1. Comparison of two impact time calculation methods

转速/（r/min） t_s/μs t_c/μs t_a/μs

1000（n₁） 36.3 215 1666.7
10000（n₂） 33.2 7.34 166.7
100000（n₃） 2500 0.245 16.7

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表 2 齿轮副几何参数

Table 2. Geometric parameters of gear pair

参数主动轮从动轮

齿数Z 36 21
模数m/mm 3
压力角α/（°） 20
齿宽b/mm 16
中心距a/mm 85.5
齿顶高系数h_a 1
顶隙系数c 0.25

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