点接触共轭渐开线蜗杆副啮合理论及性能分析

任雯; 李杰; 王天羽; 李海涛

doi:10.13700/j.bh.1001-5965.2022.0778

点接触共轭渐开线蜗杆副啮合理论及性能分析

doi: 10.13700/j.bh.1001-5965.2022.0778

任雯¹,
李杰^{1, 2},
王天羽^{1, 2},
李海涛^{1, 2, ,}

1.
中国农业大学工学院，北京 100083
2.
中国农业大学机械工程训练中心，北京 100083

基金项目: 直升机传动技术国家重点实验室基金(HTL-O-19G02)

详细信息

通讯作者:
E-mail：h.li@cau.edu.cn

中图分类号: TH132.4
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- 被引次数: 0
出版历程
- 收稿日期: 2022-09-14
- 录用日期: 2022-11-04
- 网络出版日期: 2023-01-10
- 整期出版日期: 2024-10-31

Meshing theory and performance analysis of point-contact conjugate involute worm gear pair

REN Wen¹,
LI Jie^{1, 2},
WANG Tianyu^{1, 2},
LI Haitao^{1, 2
, ,}

1.
College of Engineering，China Agricultural University，Beijing 100083，China
2.
Mechanical Engineering Training Center，China Agricultural University，Beijing 100083，China

Funds: Fund of National Key Laboratory of Science and Technology on Helicopter Transmission (HTL-O-19G02)

More Information

Corresponding author: E-mail：h.li@cau.edu.cn

摘要

摘要:
点接触共轭渐开线蜗杆传动可以降低蜗杆副对制造、装配等误差的敏感性，并能保证传动精度。基于微分几何和齿轮啮合原理，构建了含有制造和安装误差的点接触共轭渐开线蜗杆传动数学模型，研究了螺旋角、模数、压力角等主要设计参数对啮合性能的影响规律，并进行了传动副对制造和安装误差敏感性的研究。通过仿真实验验证了接触区的分布情况。研究结果表明，含有制造和安装误差时，传动副的瞬时传动比恒定；选取适中的螺旋角、较小的模数及较小的压力角会增大接触区的面积，提高传动副的重合度；传动副对制造和安装误差均不敏感，但应尽量减小或避免制造和安装轴交角造成的误差。通过仿真分析得到接触区和重合度与理论计算结果一致，验证了所提理论的正确性。
- 点接触 /
- 共轭 /
- 渐开线蜗杆 /
- 啮合性能 /
- 误差分析
Abstract:
Point-contact conjugate involute worm drive can reduce the sensitivity of the worm gear pair to manufacturing and assembly errors and ensure transmission accuracy. On the basis of differential geometry and gear meshing theory, this paper constructed a mathematical model of point-contact conjugate involute worm drive containing manufacturing and assembly errors, studied the influence of main design parameters such as helix angle, modulus, and pressure angle on the meshing performance, and analyzed the sensitivity of the worm gear pair to manufacturing and assembly errors. Finally, the distribution of the contact area was verified through simulation. The results show that the instantaneous drive ratio of the worm gear pair remains constant with manufacturing and assembly errors. The selection of a moderate helix angle, a small modulus, and a small pressure angle will increase the contact area and raise the contact ratio of the worm gear pair. The worm gear pair is insensitive to manufacturing and assembly errors, but the manufacturing and assembly errors of crossed axis angle should be minimized or avoided. The contact area and contact ratio obtained from the simulation analysis agree with the theoretical calculations, verifying the correctness of the theory.
- point contact /
- conjugate /
- involute worm /
- meshing performance /
- error analysis

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图 1 双自由度展成渐开线蜗杆坐标系

Figure 1. Coordinate system of generation of involute worm with two degrees of freedom

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图 2 单自由度展成蜗轮坐标系

Figure 2. Coordinate system of generation of worm gear with single degree of freedom

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图 3 点接触共轭渐开线蜗杆副坐标系

Figure 3. Coordinate system of point-contact conjugate involute worm gear pair

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图 4 接触迹线与接触区随螺旋角的变化情况

Figure 4. Variation of contact line and area with helix angle

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图 5 螺旋角对椭圆长轴和重合度的影响

Figure 5. Influence of helix angle on major axis of ellipse and contact ratio

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图 6 接触迹线与接触区随模数的变化情况

Figure 6. Variation of contact line and area with modulus

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图 7 模数对椭圆长轴和重合度的影响

Figure 7. Influence of modulus on major axis of ellipse and contact ratio

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图 8 接触迹线与接触区随压力角的变化情况

Figure 8. Variation of contact line and area with pressure angle

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图 9 压力角对椭圆长轴和重合度的影响

Figure 9. Influence of pressure angle on major axis of ellipse and contact ratio

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图 10 接触迹线随中心距误差的变化情况

Figure 10. Variation of contact line with center distance error

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图 11 接触迹线随轴交角误差的变化情况

Figure 11. Variation of contact line with crossed axis angle error

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图 12 接触迹线随轴向移动误差的变化情况

Figure 12. Variation of contact line with axial movement error

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图 13 误差对椭圆长半轴的影响

Figure 13. Influence of error on major axis of ellipse

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图 14 点接触共轭渐开线蜗杆副三维模型

Figure 14. Three-dimensional model of point-contact conjugate involute worm gear pair

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图 15 蜗轮齿面接触压强及状态

Figure 15. Contact pressure and state of worm gear tooth surface

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图 16 安装误差对蜗轮齿面压强的影响

Figure 16. Influence of error on pressure of worm gear tooth surface

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表 1 螺旋角几何参数

Table 1. Geometric parameters of helix angle

算例	螺旋角β₂/（°）
算例Ⅰ-A	3.0
算例Ⅰ-B	3.6
算例Ⅰ-C	4.2
算例Ⅰ-D	4.8

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表 2 模数几何参数

Table 2. Geometric parameters of modulus

算例	端面模数m_t2/ mm
算例Ⅱ-A	2.7
算例Ⅱ-B	3.0
算例Ⅱ-C	3.3
算例Ⅱ-D	3.6

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表 3 压力角几何参数

Table 3. Geometric parameters of pressure angle

算例	压力角α_n/（°）
算例Ⅲ-A	18.5
算例Ⅲ-B	20.0
算例Ⅲ-C	21.5
算例Ⅲ-D	23.0

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表 4 误差几何参数

Table 4. Geometric parameters of errors

参数	误差值	参数	误差值
∆a₁₄/mm	±0.4	∆Σ₁₄/(°)	±0.8
∆a₂₃/mm	±0.4	∆Σ₂₃/(°)	±0.8
∆a₁₂/mm	±0.4	∆Σ₁₂/(°)	±0.8
∆b₁₄/mm	±0.4	∆c₁₄/mm	±0.4
∆b₂₃/mm	±0.4	∆c₂₃/mm	±0.4
∆c₁/mm	±0.4	∆c₂/mm	±0.4

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