外圈偏斜对润滑下预紧球轴承刚度特性影响

孙敏杰; 赵利锋; 张涛

doi:10.13224/j.cnki.jasp.20240293

外圈偏斜对润滑下预紧球轴承刚度特性影响

doi: 10.13224/j.cnki.jasp.20240293

孙敏杰^{1, 2,},
赵利锋^{1, 2},
张涛^{1, 2}

1.
上海集优机械有限公司轴承技术中心，上海 201108
2.
上海天安轴承有限公司，上海 201108

基金项目: 上海市青年科技启明星计划扬帆专项资助项目（23YF1444100）

详细信息

作者简介:
孙敏杰（1996-），男，工程师，硕士，主要从事滚动轴承力学研究。E-mail：1178854928@qq.com

中图分类号: V232；TH133.33
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- 被引次数: 0
出版历程
- 收稿日期: 2024-05-08
- 网络出版日期: 2025-10-16

Influences of outerring misalignment on stiffness characteristics of lubricated and preloaded ball bearing

SUN Minjie^{1, 2
,},
ZHAO Lifeng^{1, 2},
ZHANG Tao^{1, 2}

1.
Department of Bearing Technology Center，Shanghai PRIME Machinery Company，Limited，Shanghai 201108，China
2.
Shanghai Tian An Bearing Company，Limited，Shanghai 201108，China

摘要

摘要:
为了研究轴承外圈偏斜安装误差对润滑下预紧球轴承支承刚度的影响，通过推导轴承外圈偏斜下套圈与钢球的几何变形与受力关系式，提出了一种油膜影响的轴承刚度矩阵解析算法，并结合考虑球滚道脱离接触的拟静力学改进算法与球轴承-主轴系统刚度迭代算法，建立了外圈偏斜下包含润滑油膜的预紧球轴承刚度计算方法。结合具体算例表明：定压预紧下较大的轴承外圈偏斜使滚动体与内圈出现非接触区。润滑的作用减小了滚动体与套圈的接触角，并增大滚动体与套圈的接触力，且润滑对定压下最大偏斜接触角的影响更显著，对定位下最大偏斜接触力的影响更显著。定压预紧下考虑润滑作用后在外圈偏斜不大时轴承的刚度被削弱，但在较大的外圈偏斜下刚度反而接近甚至比干接触时更大。在定位预紧下润滑油膜增大了轴承的支承刚度，且随转速的上升而逐渐增大，随着外圈偏斜的增大而逐渐增大。
- 球轴承 /
- 外圈偏斜 /
- 油膜厚度 /
- 刚度特性 /
- 非线性接触
Abstract:
In order to investigate effects of outering misalignment on the contact and stiffness characteristics of lubricated and preloaded ball bearing, the geometry and force equilibrium relationship for ball bearing with outering misalignment was established and a new method was proposed for computation of the stiffness matrix considering lubrication. Combined with ball-raceway separation condition and ball-bearing-spindle iteration method, a stiffness matrix of preloaded ball bearing with certain outerring misalignment in a lubricated bearing-spindle system was analyzed. The results showed that the non-contact area between the ball and the inner ring occurred under constant force preload with a large outering misalignment. When lubrication was considered, the max. contact angle was reduced notably in constant force preload while the max. contact force was increased significantly in fixed position preload with certain outerring misalignment. Under constant force preload, lubrication weakened the stiffness of the bearing when the outerring misalignment was small while increased the stiffness with a large outerring misalignment. Under the fixed position preload, the stiffness of the bearing increased gradually with the increase of the rotational speed as well as outerring misalignment.
- ball bearing /
- outerring misalignment /
- film thickness /
- stiffness characteristic /
- non-linear contact

HTML

图 1 轴承剖视

Figure 1. Section view of bearing

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图 2 第j个滚动体与套圈截面剖视

Figure 2. Section view of jth ball and bearing ring

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图 3 第j个滚动体与套圈趋近量

Figure 3. Mutual approach of jth ball and bearing ring

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图 4 球滚道变形位移几何关系

Figure 4. Geometrical relation of ball center and raceway

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图 5 球轴承支承的主轴系统

Figure 5. Spindle system supported by ball bearing

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图 6 计算流程图

Figure 6. Flow chart of calculation

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图 7 外圈偏斜下轴承附加载荷对比

Figure 7. Comparison of additional force caused by outerring misalignment

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图 8 不同模型的接触力与趋近量

Figure 8. Contact force and mutual approach with different models

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图 9 定压预紧下外圈偏斜误差对轴承受力的影响

Figure 9. Contact force considering outerring misalignment under constant force

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图 10 定压预紧下外圈偏斜误差对轴承接触角的影响

Figure 10. Contact angle considering outerring misalignment under constant force

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图 11 定压预紧下外圈偏斜误差对轴承刚度的影响

Figure 11. Bearing stiffness considering outerring misalignment under constant force

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图 12 定压预紧下外圈偏斜误差与转速对轴承刚度的影响

Figure 12. Bearing stiffness considering outerring misalignment with different speeds under constant force

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图 13 定位预紧下外圈偏斜误差对轴承受力的影响

Figure 13. Contact force considering outerring misalignment under fix position

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图 14 定位预紧下外圈偏斜误差对轴承接触角的影响

Figure 14. Contact angle considering outerring misalignment under fix position

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图 15 定位预紧下外圈偏斜误差对轴承刚度的影响

Figure 15. Bearing stiffness considering outerring misalignment under fix position

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图 16 定位预紧下外圈偏斜误差与转速对轴承刚度的影响

Figure 16. Bearing stiffness considering outerring misalignment with different speeds under fix position

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表 1 轴承结构参数

Table 1. Bearing structure parameters

参数	数值或说明
参数	1号球轴承	2号球轴承
支承点位置l/mm	50	450
滚动体数目N_ball	8	8
滚动体直径D_w /mm	13.494	13.494
内圈沟曲率半径r_i /mm	7.017	7.017
外圈沟曲率半径r_o/mm	7.017	7.017
径向游隙$ {p_{\text{d}}} $/μm	36.8	36.8
等效初始接触角$ {\alpha _0} $/（°）	15	15
预紧力$ {F_{{\text{pre}}}} $/N	固定	定压500
节圆直径d_m/mm	57.5	57.5

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