Analysis and verification of the quasi-dynamic model for the three-point contact ball bearing
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摘要:
为定量预测与规避双半内圈角接触球轴承三点接触现象，降低轴承异常磨损风险，采用牛顿-欧拉矢量力学方法，结合该轴承结构与受载特点，对双半内圈角接触球轴承内部元件相对位置与速度关系进行了描述，综合考虑轴承各元件相互作用力、运动惯性力、陀螺力矩以及润滑油对轴承元件施加的流体拖动力与挤压力，建立了考虑三点接触情况的双半内圈角接触球轴承拟动态性能分析模型，并完成轴承非线性方程组求解算法优化，且通过与国外成熟软件计算结果和保持架转速试验结果对比，验证了所建立模型的准确性，研究表明，所建立的双半内圈角接触球轴承分析方法对内部接触角分布和应力分布的预测误差小于12%，对于最大接触应力的预测误差小于2%，且对接触痕迹的预测较为准确，对于保持架实际转速的预测误差小于10%，可用于双半内圈角接触球轴承设计优化。
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关键词:
- 双半内圈角接触球轴承 /
- 三点接触特性 /
- 接触应力 /
- 接触痕迹 /
- 保持架转速试验.
Abstract:In order to predict the three-point contact phenomenon and reduce the risk of abnormal wear, with the help of Newton-Euler vectorial mechanics, combining with the force and structure features, relative location and velocity relationship of internal element of the arched inner race ball bearing were described, the force of bearing parts, inertia force, gyroscopic torque, fluid drag force and extrusion force were considered in process of the arched inner race ball bearing quasi-dynamic modeling considering the three-point contact condition, the optimization of algorithm for solving nonlinear equations of the model was completed, and the accuracy of the model was validated by comparing with foreign mature software and test of the cage rotational speed. The results indicated that the proposed model had a maximum error of 12% for contact angle and contact stress distribution, and a maximum error of 2% for maximum contact stress, and also had high precision for the contact traces prediction, at the same time, the model had a maximum error of 10% for the cage rotational speed by the test validation, so that the model can be used for improving optimization design of the arched inner race ball bearing.
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图 12 通过Masta计算的内圈接触痕迹图
Figure 12. Diagram of contact traces of the inner ring by Masta
图 13 通过本文模型计算的内圈接触痕迹图
Figure 13. Diagram of contact traces of the inner ring by the model in this paper
图 14 通过Masta计算的外圈接触痕迹图
Figure 14. Diagram of contact traces of the outer ring by Masta
图 15 通过本文模型计算的外圈接触痕迹图
Figure 15. Diagram of contact traces of the outer ring by the model in this paper
图 16 转速为20000 r/min时接触应力计算结果图
Figure 16. Diagram of calculation result of contact stress at rotational speed 20000 r/min
图 17 转速为20000 r/min时接触应力计算相对误差图
Figure 17. Diagram of the relative error of contact stress calculation at rotational speed 20000 r/min
图 18 转速为10000 r/min时接触应力计算结果图
Figure 18. Diagram of calculation result of contact stress at 10000 r/min
图 19 转速为10000 r/min时接触应力计算相对误差图
Figure 19. Diagram of the relative error of contact stress calculation at rotational speed 10000 r/min
图 21 当内圈转速为15500 r/min时保持架转速对比图
Figure 21. Diagram of cage rotational speed comparison when inner ring rotational speed is 15500 r/min
图 22 当内圈转速为14400 r/min时保持架转速对比图
Figure 22. Diagram of cage rotational speed comparison when inner ring rotational speed is 14400 r/min
表 1 轴承主要参数
Table 1. Main design parameters of bearing
参数 数值 节圆直径/mm 140 轴承内径/mm 100 轴承外径/mm 180 滚珠直径/mm 19.05 滚珠数目 18 垫片角/（°） 20 初始接触角/（°） 25 内圈沟曲率系数 0.54 外圈沟曲率系数 0.52 保持架内径/mm 130.1 保持架外径/mm 146.3 
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表 2 轴承材料参数
Table 2. Material parameters of bearing
参数 数值 密度/（kg/m3） 7800 泊松比 0.3 弹性模量/GPa 209
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表 3 轴承工况
Table 3. Working condition of bearing
参数 数值 内圈转速/（r/min） 20000 径向载荷/N 6000 轴向载荷/N 1112
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表 4 试验轴承结构参数
Table 4. Main parameters of tested bearing
参数 数值 节圆直径/mm 165 轴承内径/mm 130 轴承外径/mm 200 滚珠直径/mm 24.606 滚珠个数 17 垫片角/（°） 25 初始接触角/（°） 25 内圈沟曲率系数 0.525 外圈沟曲率系数 0.515 引导间隙/mm 0.6 兜孔间隙/mm 1.594 引导方式 外引导
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