Research on dynamics of cylindrical roller bearing with circular pockets considering conformal contact
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摘要:
针对接触廓形高度密合的滚子-兜孔圆弧面、滚子-兜孔端面、滚子-挡边等协调接触副，基于Winkler弹性基础模型，提出一种协调接触建模方法，然后结合牛顿-欧拉动力学理论，提出考虑协调接触的圆兜孔圆柱滚子轴承的六自由度动力学建模方法，通过与文献结果和实验数据对比，验证了建模方法的有效性，在此基础上仿真研究了保持架质量偏心和内外圈角度不对中对保持架打滑/涡动、滚子打滑/偏歪斜、滚子-兜孔碰撞以及滚子-挡边碰撞的影响，结果表明：保持架质量径向偏心会加剧保持架和滚子的打滑，但有助于提高保持架涡动的稳定性，而轴向偏心会引起滚子的偏歪斜，当轴向偏心与径向偏心叠加时，滚子与兜孔、挡边更易产生边缘碰撞；内外圈角度不对中也容易引起滚子的偏歪斜，以及滚子与兜孔、挡边的边缘碰撞，但可明显降低保持架和滚子的打滑。
Abstract:For the conformal contact pairs such as the roller-circular surface of the pocket, the roller-end face of the pocket, and the roller-rib with highly close contact profiles, based on the Winkler's elastic foundation model, a conformal contact modeling method was proposed; by combining the conformal contact modeling method with the Newton-Euler's dynamics theory, the six degree-of-freedom dynamics modeling method of the bearing with circular pockets considering conformal contact was proposed; and by comparing with both the reference results and the experiment data, the proposed dynamics modeling method was validated. On this basis, influences of both the mass eccentricity of the cage and the angle misalignment of the inner and outer rings on the cage slip/whirl, the roller slip/skew/tilt, the roller-cage collision and the roller-rib collision were studied by use of dynamics simulation. The results showed that the radial mass eccentricity of the cage could aggravate the cage slip and the roller slip, but contributed to improve the cage whirl stability, and the axial mass eccentricity may cause the roller skew/tilt; when the axial mass eccentricity was combined with the radial mass eccentricity, the roller-pocket peripheral collision and the roller-rib peripheral collision easily appeared. Secondly, the angle misalignment of the inner and outer rings was more likely to cause the roller skew/tilt, and the roller-pocket peripheral collision and the roller-rib peripheral collision, but it can significantly reduce the cage slip and the roller slip.
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图 3 滚子-兜孔面Winkler干接触模型
Figure 3. Winkler model of dry contact of roller-pocket surface
图 18 不同偏心下保持架涡动轨迹及速度偏差比
Figure 18. Whirl orbit and standard deviation ratio of mass center translational speed of cage under different eccentricities
图 20 不同偏心下滚子自转打滑率曲线
Figure 20. Roller rotational slip rate curves under different eccentricities
图 23 不同偏心下兜孔圆弧面与滚子的最大干接触力分布
Figure 23. Maximum dry contact force distribution of roller-circular surface of pocket under different eccentricities
图 24 保持架偏心下兜孔端面与滚子端面的最小间隙分布
Figure 24. End face minimum clearance distribution of pocket-roller under cage eccentricity
图 25 保持架偏心下内圈挡边与滚子端面的最小间隙分布
Figure 25. End face minimum clearance distribution of rib-roller under cage eccentricity
图 26 不同偏转方向下保持架涡动轨迹及速度偏差比
Figure 26. Whirl orbit and standard deviation ratio of mass center translational speed of cage under different deflection directions
图 27 不同偏转方向下保持架打滑率曲线
Figure 27. Cage slip rate curves under different deflection directions
图 28 不同偏转方向下滚子自转打滑率曲线
Figure 28. Roller rotational slip rate curves under different deflection directions
图 29 不同偏转方向下滚子歪斜曲线
Figure 29. Roller skew curves under different deflection directions
图 30 不同偏转方向下滚子偏斜曲线
Figure 30. Roller tilt curves under different deflection directions
图 31 套圈偏转下兜孔圆弧面与滚子的最大干接触力分布
Figure 31. Maximum dry contact force distribution of roller-circular surface of pocket under ring deflection
图 32 套圈偏转下兜孔端面与滚子端面的最小间隙分布
Figure 32. End face minimum clearance distribution of pocket-roller under ring deflection
图 33 套圈偏转下内圈挡边与滚子端面的最小间隙分布
Figure 33. End face minimum clearance distribution of rib-roller under ring deflection
表 1 轴承几何参数、材料及工况
Table 1. Bearing geometry, material and operating conditions
参数 数值及说明 几何参数 轴承型号 NU2330EM1 轴承内径/mm 165 几何 滚子数 14 参数 滚子长度/mm 74.6 滚子半径/mm 22.5 径向游隙/mm 0.08 兜孔间隙/mm 0.36/滚子引导 挡边轴向侧隙/mm 0.015 材料 滚子及套圈 钢 保持架 黄铜 工况 内圈转速/（r/min） 1000 径向载荷/kN 50 
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表 2 轴承几何参数
Table 2. Bearing geometry
参数 数值 滚子数 13 轴承内径/mm 35 轴承外径/mm 72 内滚道直径/mm 44 外滚道直径/mm 63.82 径向游隙/mm 0.02 挡边轴向侧隙/mm 0.015 保持架内径/mm 48.5 保持架外径/mm 59 兜孔间隙/mm 0.1 兜孔轴向侧隙/mm 0.015 滚子直径/mm 10 滚子长度/有效长度/mm 11/7.2
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表 3 轴承材料
Table 3. Bearing material
元件 材料 材料特性 密度/ （kg/m3） 弹性模量/GPa 泊松比 滚子 钢 7820 207 0.28 套圈 钢 7820 207 0.28 保持架 黄铜 8600 106 0.32
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