点接触直齿轮副的构建及接触分析

谯禹娟; 彭帅; 汪海涛; 张炳正

doi:10.13224/j.cnki.jasp.20240759

点接触直齿轮副的构建及接触分析

doi: 10.13224/j.cnki.jasp.20240759

谯禹娟^1,,
彭帅^{1, 2,*, ,},
汪海涛¹,
张炳正¹

1.
重庆文理学院智能制造工程学院/汽车工程学院，重庆 402160
2.
重庆城市职业学院工业机器人运维重庆市高校工程中心，重庆 402160

基金项目: 重庆市教委科学技术研究项目（KJQN202301316）；工业机器人运维重庆市高校工程中心开放基金（YWZX20220004）；重庆市研究生科研创新项目（CYS240777）

详细信息

作者简介:
谯禹娟（2000-），女，硕士生，主要从事精密齿轮传动研究。E-mail：202316015020@stu.cqwu.edu.cn

通讯作者:
彭帅（1988-），男，副教授，博士，主要从事智能制造、精密齿轮传动研究。E-mail：shuaipeng@cqwu.edu.cn

中图分类号: V219；TH132.429
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出版历程
- 收稿日期: 2024-11-10
- 网络出版日期: 2025-01-09

Construction and contact analysis of point-contact spur gear pairs

1.
School of Intelligent Manufacturing Engineering/School of Automotive Engineering，Chongqing University of Arts and Sciences，Chongqing 402160，China
2.
Opening Project of Engineering Research Center of Chongqing Education Commission of China in Running and Maintenance of Robots，Chongqing City Vocational College，Chongqing 402160，China

摘要

摘要:
针对齿轮因轴线误差出现的非正常啮合问题，提出一种点接触直齿轮副的构建方法。在虚拟辅助渐开线齿轮齿面两端选取两点，通过一条光滑曲线连接两点作为主动轮的接触迹线，求解得到与之相啮合的配对接触迹线，最后将法截面齿廓沿两接触迹线扫掠构建出两齿轮齿面。在MATLAB和UG中设置具体参数并分别建立点接触直齿轮副几何及实体模型，对比分析点接触直齿轮副齿轮正常啮合与非正常啮合时的接触形状以及接触应力。结果表明：两齿面在啮合时始终沿各自接触迹线运动保持点接触条件，其啮合点始终在理论啮合线上，且实体模型的接触过程与理论啮合仿真过程相吻合；齿轮副在非正常啮合下的啮合点仍呈椭圆状分布，其应力值与正常啮合时的应力值相差约为18.09%。
- 点接触 /
- 渐开线 /
- 直齿轮 /
- 边缘接触 /
- 接触特性
Abstract:
In order to solve the problem of abnormal meshing of gears due to axis error, a construction method of point-contact spur gear pair was proposed. By selecting two points at both ends of the tooth surface of the virtual auxiliary involute gear, a smooth curve was obtained to connect the two points as the meshing trajectory of the driving wheel, and a curve meshing with the meshing trajectory was solved. Then, the tooth surfaces of the two gears were constructed by the tooth profile sweeping along two meshing trajectories. By setting specific parameters, geometric and solid models of point-contact spur gear pairs were established in MATLAB and UG respectively, and the contact shape and contact stress of the point-contact spur gear pairs were compared and analyzed during normal and abnormal meshing conditions. The results showed that the two tooth planes kept the point contact state along their respective meshing trajectories during meshing, the meshing points were on the theoretical meshing line, and the contact process of the solid model was consistent with the theoretical meshing simulation process. The meshing points of the gear pair were still elliptically distributed in the abnormal meshing state, and the difference between the stress value and the stress value of the normal meshing was about 18.09%.
- point contact /
- involute /
- spur gear /
- edge contact /
- contact characteristic

HTML

图 1 渐开线齿轮接触迹线移动方式

Figure 1. Way involute gear contact line moves

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图 2 构建步骤

Figure 2. Construction steps

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图 3 空间坐标系

Figure 3. Spatial coordinate system

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图 4 接触迹线选取

Figure 4. Contact trace selection

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图 5 接触迹线线性关系

Figure 5. Linear relationship of contact trace

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图 6 曲面构建

Figure 6. Surface construction

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图 7 圆弧齿廓构建

Figure 7. Construction of circular arc tooth profile

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图 8 点接触直齿轮副

Figure 8. Point-contact spur gear pair

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图 9 啮合仿真

Figure 9. Mesh simulation

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图 10 运动仿真

Figure 10. Motion simulation

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图 11 几何示意图

Figure 11. Geometric diagram

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图 12 接触区域有限元网格

Figure 12. Finite element mesh of contact area

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图 13 约束及扭矩设置

Figure 13. Constraint and torque setting

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图 14 正常啮合下的应力

Figure 14. Stress under normal meshing

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图 15 轴线误差示意图

Figure 15. Illustration of axis errors

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图 16 非正常啮合下的应力

Figure 16. Stress under abnormal meshing

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表 1 齿轮副参数

Table 1. Gear pair parameters

参数	数值
模数/mm	4
齿轮1齿数	20
齿轮2齿数	20
齿宽/mm	40
上偏移量/mm	2
下偏移量/mm	3.5
分度圆半径/mm	50
分度圆压力角/（°）	20
齿廓圆弧半径/mm	15
齿根高半径/mm	43
齿顶高半径/mm	36

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