不同预载机制和过盈量下角接触球轴承的动力学特性

李震; 王青山; 王瑞华; 秦斌

doi:10.13224/j.cnki.jasp.20220334

不同预载机制和过盈量下角接触球轴承的动力学特性

doi: 10.13224/j.cnki.jasp.20220334

李震^1,,
王青山^1,*, ,,
王瑞华¹,
秦斌²

1.
中南大学机电工程学院，长沙 410012
2.
中南大学交通运输工程学院，长沙 410015

基金项目: 国家自然科学基金（52075554）

详细信息

作者简介:
李震（1996-），男，博士生，主要从事轴承转子系统研究

通讯作者:
王青山（1989-），男，副教授、博士生导师，博士，主要从事机械结构振动噪声研究。E-mail：qingshanwang@csu.edu.cn

中图分类号: V229⁺.2
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-13
- 网络出版日期: 2023-07-07

Dynamic characteristics of angular contact ball bearings under different preloading mechanisms and interference amount

LI Zhen^1
,,
WANG Qingshan^{1,*
, ,},
WANG Ruihua¹,
QIN Bin²

1.
College of Mechanical and Electrical Engineering， Central South University，Changsha 410012，China
2.
School of Traffic and Transportation Engineering， Central South University，Changsha 410015，China

摘要

摘要:
基于Hertz弹性接触理论和无滚道控制理论，建立了不同预载机制下五自由度角接触球轴承拟静力学分析模型，采用牛顿拉夫逊法对已建立的模型进行数值求解，探究预载机制和过盈量对角接触球轴承动力学特性的影响。通过将已建立模型求解接触角和轴承刚度结果与已有文献结果进行对比，验证模型的有效性。分别探究了过盈量对内外圈装配压力和滚道接触变形量的影响以及过盈量和预载机制对轴承刚度的影响。结果表明：随过盈量增加，内外圈装配压力增加，初始接触角减小；随着过盈量增加，轴承径向刚度增加，轴向刚度和角刚度减小；与定压预紧相比，定位预紧能够提高轴承刚度；探究转速对接触变形和装配压力的影响，确定了松脱旋转速度约为40 000 r/min。
- 过盈量 /
- 预载机制 /
- 牛顿拉夫逊 /
- 轴承刚度 /
- 接触角
Abstract:
Based on Hertz elastic contact theory and raceless control theory, a quasi-static analysis model of angular contact ball bearings with five degrees of freedom under different preloading mechanisms was established. Newton Raphson method was used to numerically solve the established model for exploring the influences of preloading mechanisms and interference amount on the dynamic characteristics of angular contact ball bearings. The effectiveness of the model was verified by comparing the results of contact angle and bearing stiffness of the established model with those of existing literature. The influences of the interference amount on the assembly pressure of the inner and outer rings and the contact deformation of the raceway as well as the influences of the interference amount and the preloading mechanisms on the bearing stiffness were explored. The results showed that with the increase of interference, the assembly pressure of inner and outer rings decreased and the initial contact angle decreased; with the increase of interference, the radial stiffness of the bearing increased, while the axial stiffness and angular stiffness decreased; compared with constant pressure preloading, positioning preloading can improve the bearing stiffness; ghe influence of rotation speed on contact deformation and assembly pressure was investigated, and the release rotation speed was determined to be about 40000 r/min.
- interference amount /
- preloading mechanism /
- Newton Raphson /
- bearing stiffness /
- contact angle

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图 1 圆环过盈配合示意图

Figure 1. Diagram of ring interference fit

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图 2 角接触球轴承过盈配合示意图

Figure 2. Interference fit of angular contact ball bearing

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图 3 角接触球轴承几何模型

Figure 3. Geometric model of angular contact ball bearing

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图 4 滚珠周向分布示意图

Figure 4. Schematic diagram of ball circumferential distribution

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图 5 第j个滚珠的受力分析

Figure 5. Force analysis of the jth ball

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图 6 轴承模型求解流程图

Figure 6. Flow chart of bearing model solution

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图 7 轴承内外圈接触角的对比结果

Figure 7. Comparison results of inner and outer ring contact angle of bearing

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图 8 轴承刚度的对比结果

Figure 8. Comparison results of bearing stiffness

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图 9 过盈量对内圈装配应力和滚道接触变形量的影响

Figure 9. Influence of interference amount on inner ring assembly stress and raceway contact deformation

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图 10 过盈量对外圈装配应力和滚道接触变形量的影响

Figure 10. Influence of interference amount on outer ring assembly stress and raceway contact deformation

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图 11 过盈量对轴承初始接触角的影响

Figure 11. Influence of interference amount on initial contact angle of bearing

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图 12 不同预载机制下实际轴向载荷和位移的变化趋势

Figure 12. Variation trends of actual axial load and displacement under different preloading mechanisms

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图 13 旋转速度对径向变形以及实际装配压力的影响

Figure 13. Influence of rotating speed on radial deformation and actual assembly pressure

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图 14 过盈量和预载机制对轴承轴向刚度的影响

Figure 14. Influence of interference amount and preload mechanism on axial stiffness of bearing

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图 15 过盈量和预载机制对轴承径向刚度的影响

Figure 15. Influence of interference amount and preload mechanism on radial stiffness of bearing

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图 16 过盈量和预载机制对轴承角刚度的影响

Figure 16. Influence of interference amount and preload mechanism on angle stiffness of bearing

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表 1 FAG B7014AC轴承参数

Table 1. Bearing parameters of FAG B7014AC

参数	数值
弹性模量E/10⁵ （N/mm²）	2.06
泊松比ν	0.3
滚珠密度ρ/（kg/m³）	7850
滚珠直径d/mm	12.5
内圈滚道曲率半径r_i/mm	6.54
外圈滚道曲率半径r_o/mm	6.54
内圈滚道接触直径d₂/mm	77
外圈滚道接触直径d₃/mm	102
滚珠个数N	19

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表 2 SKF EEB3-2Z轴承参数

Table 2. Bearing parameters of SKF EEB3-2Z

参数	数值
弹性模量E/10⁵ （N/mm²）	2.06
泊松比ν	0.3
滚珠密度ρ/（kg/m³）	7850
滚珠直径d/mm	3.969
内圈滚道曲率半径r_i/mm	2.064
外圈滚道曲率半径r_o/mm	2.064
内圈滚道接触直径d₂/mm	13.06
外圈滚道接触直径d₃/mm	18.21
滚珠个数N	7

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表 3 B7008C相关材料参数

Table 3. Material parameters of B7008C

参数	材料	弹性模量/ 10⁵ （N/mm²）	泊松比ν	密度 / （kg/m³）
转轴	TC4	1.1	0.3	4510
轴承	9Cr18	2.06	0.3	7850
轴承座	TC4	1.1	0.3	4510

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表 4 B7008C轴承参数

Table 4. Bearing parameters of B7008C

参数	数值
转轴和轴承过盈配合直径d₁/mm	40
轴承和轴承座过盈配合直径d₄/mm	68
轴承座外径d₅/mm	∞
滚珠直径d/mm	7.144
内圈滚道曲率半径r_i/mm	4.0
外圈滚道曲率半径r_o/mm	3.79
内圈滚道接触直径d₂/mm	46.838
外圈滚道接触直径d₃/mm	61.176
滚珠个数N	19

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