Dynamic characteristics and fatigue life analysis of U-shaped pocket cylindrical roller bearings
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摘要:
针对航空发动机圆柱滚子轴承保持架打滑、摩擦生热及疲劳破坏的问题，提出一种U形兜孔圆柱滚子轴承，并对其保持架打滑、摩擦力矩及疲劳寿命展开研究。基于Hertz接触理论、流体润滑理论、轴承动力学理论，建立U形兜孔圆柱滚子轴承刚柔耦合动力学仿真模型；基于Miner线性累计损伤理论，建立保持架疲劳寿命模型，在此基础上，研究了轴承结构参数对保持架打滑、摩擦力矩及疲劳寿命的影响规律，并运用响应面法与NSGA-Ⅱ（nondominated sorting genetic algorithm Ⅱ）相结合对轴承结构参数进行优化，对比分析优化前后的轴承保持架打滑率及摩擦力矩。结果表明：轴承结构参数对轴承性能影响显著，在相同工况下，不同轴承结构参数组合对应的保持架打滑率和轴承摩擦力矩最大差值分别达到了3.65%和
1203 N·mm；在不同工况下，优化后的轴承保持架打滑率最大降低了4.74%，轴承摩擦力矩最大减少了548 N·mm；与普通轴承相比，在不同工况下，优化后的轴承均表现出更低的保持架打滑率和摩擦力矩。Abstract:A U-shaped pocket cylindrical roller bearing was proposed to solve the problems of sliding, frictional heating and fatigue failure of cylindrical roller bearing retainer of aero-engine. The sliding, frictional moment and fatigue life of the retainer were analyzed. A rigid-flexible coupling dynamics simulation model of U-shaped pocket cylindrical roller bearings was subsequently established, leveraging Hertz contact, fluid lubrication, and bearing dynamics theories; Based on the Miner linear cumulative damage theory, the fatigue life model of the retainer was established. Based on this, the influences of the bearing structure parameters on the slip, friction moment and fatigue life of the retainer were studied. The response surface method and NSGA-Ⅱ (nondominated sorting genetic algorithm Ⅱ) were combined to optimize the bearing structure parameters. The slip rate and friction moment of the bearing retainer before and after optimization were compared and analyzed. The results showed that the bearing structure parameters had a significant impact on the bearing performance. Under the same working condition, the maximum difference between the cage slip rate and the bearing friction moment corresponding to different bearing structure parameter combinations reached 3.65% and
1203 N·mm, respectively; under different working conditions, the maximum sliding rate of the optimized bearing retainer was reduced by 4.74%, and the maximum friction moment of the bearing was reduced by 548 N·mm; the optimised bearings showed lower cage slip and friction torques than the plain bearings under different operating conditions. -
图 1 U形兜孔圆柱滚子轴承结构示意图
Figure 1. Schematic diagram of U-shaped pocket hole cylindrical roller bearing structure
图 3 U形兜孔圆柱滚子轴承刚柔耦合动力学仿真模型
Figure 3. Rigid flexible coupling dynamic simulation model of U-shaped pocket hole cylindrical roller bearing
图 6 滚子槽深对轴承摩擦力矩的影响
Figure 6. Effect of roller groove depth on bearing frictional torque
图 10 滚子槽宽对轴承摩擦力矩的影响
Figure 10. Effect of roller groove width on bearing friction torque
图 14 滚子槽深对保持架最大动应力的影响
Figure 14. Effect of roller groove depth on the maximum dynamic stress of the cage
图 15 滚子槽深对保持架应力幅值-循环次数的影响
Figure 15. Effect of roller groove depth on cage stress amplitude-number of cycles
图 17 滚子个数对保持架最大动应力的影响
Figure 17. Effect of the number of rollers on the maximum dynamic stress of the cage
图 18 滚子个数对保持架应力幅值-循环次数的影响
Figure 18. Effect of the number of rollers on the stress amplitude-cycle number of the cage
图 20 滚子槽宽对保持架最大动应力的影响
Figure 20. Effect of roller groove width on the maximum dynamic stress of the cage
图 21 滚子槽宽对保持架应力幅值-循环次数的影响
Figure 21. Effect of roller groove width on cage stress amplitude-number of cycles
图 23 间隙比对保持架最大动应力的影响
Figure 23. Effect of clearance ratio on maximum dynamic stress of cage
图 24 间隙比对保持架应力幅值-循环次数的影响
Figure 24. Effect of clearance ratio on stress amplitude-cycle number of cages
图 27 优化前后轴承打滑率对比
Figure 27. Comparison of bearing slip rate before and after optimization
图 28 优化前后轴承摩擦力矩对比
Figure 28. Comparison of bearing friction moment before and after optimization
图 31 不同内圈转速下试验轴承打滑率
Figure 31. Test bearing slippage rate under different rotational speeds of inner ring
图 32 不同内圈转速下试验轴承外圈温度（径向载荷为
2000 N）Figure 32. Temperature of the outer ring of the test bearing under different rotational speeds of inner ring （radial load of
2000 N）
图 33 不同内圈转速下试验轴承外圈温度（径向载荷为
2500 N）Figure 33. Temperature of the outer ring of the test bearing under different rotational speeds of inner ring （radial load of
2500 N）
图 34 不同内圈转速下试验轴承外圈温度（径向载荷为
3000 N）Figure 34. Temperature of the outer ring of the test bearing under different rotational speeds of inner ring （radial load of
3000 N）
图 35 不同内圈转速下试验轴承外圈温度（径向载荷为
3500 N）Figure 35. Temperature of the outer ring of the test bearing under different rotational speeds of inner ring （radial load of
3500 N）参数 数值 轴承外径/mm 125 轴承内径/mm 70 节圆直径/mm 98.5 径向游隙/mm 0.05 滚子直径/mm 15 滚子长度/mm 22 额定转速/（r/min） 6000 极限转速/（r/min） 6300 额定动载荷/kN 180 额定静载荷/kN 193 
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表 2 轴承的结构参数
Table 2. Structural parameters of bearings
参数 数值 保持架内径/mm 60 保持架外径/mm 79.66 轴承内径/mm 40 轴承外径/mm 90 轴承宽度/mm 23 滚子直径/mm 14 滚子长度/mm 15 额定转速/（r/min） 20000 极限转速/（r/min） 25000 额定动载荷/kN 62 额定静载荷/kN 52
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表 3 轴承的材料参数
Table 3. Material characteristics parameters of bearings
部件 密度/10−6 （kg/mm3） 弹性模量/105 （N/mm2） 泊松比 保持架 7.46× 1.1 0.3 内圈 7.85 2.07 0.29 外圈 7.85 2.07 0.29 滚子 7.85 2.07 0.29
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表 4 润滑油主要参数
Table 4. Main parameters of the lubricant
参数 数值 密度/10−7 （kg/mm3） 8.6 黏压系数/10−8 （1/Pa） 1.28 动力黏度/10−2 （Pa·s） 3.3
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表 5 设计变量参数
Table 5. Parameters of design variables
因素 水平 −1 0 1 滚子槽深H/mm 2 2.75 3.5 滚子个数B 10 14 18 滚子槽宽D/mm 2 3.5 5 间隙比G 0.4 0.8 1.2
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表 6 响应面试验设计及仿真结果
Table 6. Response surface test design and simulation results
序号 H/mm B D/mm G Sc//% Mc/（N·mm） 1 2 10 3.5 0.8 15.57 1772 2 3.5 10 3.5 0.8 13.14 1377 3 2 18 3.5 0.8 15.85 1933 4 3.5 18 3.5 0.8 13.4 1538 $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ 24 2.75 18 3.5 1.2 14.85 2096 25 2.75 14 3.5 0.8 14.13 1285 26 2.75 14 3.5 0.8 14.11 1279 27 2.75 14 3.5 0.8 14.09 1289
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表 7 回归模型的相关系数
Table 7. Correlation coefficients of regression models
相关系数 打滑率 摩擦力矩 R2 0.9912 0.9959 $R_{\text{adj}}^{2} $ 0.9699 0.9911 $R_{\text{pre}}^{2} $ 0.9298 0.9765
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表 8 方差分析结果
Table 8. Analysis of variance results
参数 打滑率 摩擦力矩 F值 P值 F值 P值 H 43.84 < 0.0001 15.26 0.0021 B 6.1 0.0295 2.54 0.1373 D 9.64 0.0091 10.65 0.0068 G 34.13 < 0.0001 23.58 0.0004 H2 8.46 < 0.0001 0.4885 0.4979 B2 0.7027 0.4183 3.58 0.0828 D2 0.4863 0.4989 0.3680 0.5554 G2 2.38 0.1488 34.44 < 0.0001
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表 9 优化后轴承结构参数
Table 9. Optimized bearing structure parameters
mm 参数 数值 保持架内径 60 保持架外径 79.66 滚子槽深 3 滚子个数 10 滚子槽宽 3.5
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