Dynamic modelling of angular contact ball bearings with local defects under EHL considering impact force
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摘要:
为详细地分析具有局部缺陷的角接触球轴承(ACBBs)的运行状态，针对传统模型未考虑轴承润滑及缺陷引起的冲击力问题，建立ACBBs在弹流润滑(EHL)条件下考虑冲击力的局部缺陷ACBBs动力学模型。建立考虑自旋的缺陷轴承弹流润滑模型，计算出缺陷轴承的油膜厚度及油膜刚度，再提出ACBBs局部缺陷时变位移激励模型和时变刚度模型，在此基础上建立与缺陷尺寸及轴承转速有关的瞬时冲击力函数；基于Hertz接触理论和冲击力函数，提出外圈具有局部缺陷ACBBs动力学计算方法；研究具有故障的角接触球轴承振动特性，并通过实验验证，分析了不同参数对轴承动力学响应的影响规律。计算结果表明：轴承在润滑条件下，冲击力对轴承的振动影响明显减弱；随着缺陷尺寸和载荷的增大，轴承故障特征的频率均不变，但其幅值增大；随着轴承转速的增大，轴承故障特征频率及其幅值均增大，为滚动轴承的故障诊断和维护提供了有力依据。
Abstract:In order to precisely analyze the operating status of angular contact ball bearings (ACBBs) with local defects and response to the impact force caused by bearing lubrication and defects in the traditional model, a dynamic model of ACBBs with local defects considering impact force under elastohydrodynamic lubrication (EHL) conditions was proposed. Firstly, an EHL model for defective bearings considering spin was established, and the oil film thickness and oil film stiffness of the defective bearings were calculated. Time-varying displacement excitation model and time-varying stiffness model for local defects in ACBBs were presented. On this basis, an instantaneous impact force function related to defect size and bearing speed was established. Secondly, based on Hertz contact theory and impact force function, a dynamic calculation method for ACBBs with local defects on the outer ring was proposed. Finally, the vibration characteristics of ball bearings with faults were investigated, and the influence of different parameters on the dynamic response of the bearings was analyzed through experiments. The calculation results show that under lubrication conditions, the impact force on the vibration of the bearing is significantly weakened. With the increase in defect size and load, the frequency of bearing fault characteristics remains unchanged, but its amplitude increases. As the bearing speed increases, the characteristic frequency and amplitude of bearing faults increase, providing a powerful basis for fault diagnosis and maintenance of rolling bearings.
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图 6 滚动体与故障边缘碰撞简化图
Figure 6. Simplified diagram of collision between rolling element and fault edge
图 10 滚动体陷入矩形缺陷时的位移
Figure 10. Displacement of rolling element when trapped in a rectangular defect
图 11 瞬时冲击力与缺陷角度和转速之间的关系
Figure 11. Relationship among instantaneous impact force, defect angle, and rotational speed
图 15 瞬时冲击力与缺陷跨度角之间的关系
Figure 15. Relationship between instantaneous impact force and defect span angle
图 16 不同缺陷跨度角的振动幅值变化趋势
Figure 16. Variation trend of vibration amplitude for different defect span angles
图 17 不同缺陷跨度角时外圈的振动响应
Figure 17. Vibration response of outer ring at different defect span angles
图 18 ∆φfa=0.6°，不同转速对轴承振动幅值的影响
Figure 18. Effect of different rotational speeds on bearing vibration amplitude when ∆φfa=0.6°
图 19 ∆φfa=0.8°，不同转速对轴承振动幅值的影响
Figure 19. Effect of different rotational speeds on bearing vibration amplitude when ∆φfa=0.8°
图 20 ∆φfa=1°，不同转速对轴承振动幅值的影响
Figure 20. Effect of different rotational speeds on bearing vibration amplitude when ∆φfa=1°
图 21 载荷对轴承外圈故障振动响应的影响
Figure 21. Effect of load on vibration response of outer ring fault of bearing
表 1 弹流润滑参数
Table 1. EHL parameter values
动力黏度
η/（Pa·s）润滑油密度
ρ0/（kg·m−3）黏压系数
α/（m2·N−1）环境温度/
℃标准大气压
p0/Pa0.05 0.91 1.2×10−8 25 1.01×105 
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表 2 各参数取值范围
Table 2. Range of values for each parameter
参数 取值 k 1～9.5 ub/（m·s−1） 1～40 w/N 200～104 G 2500 ～5000 W 3.23×10−4～1.94×10−3 U 1.68×10−11～6.74×10−10 Ωs 0～4.41×10−11
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参数 数值 内圈直径di/mm 30 外圈直径do/mm 62 滚动体直径db/mm 9.525 滚动体个数Z/个 12 轴承宽度D/mm 16 初始接触角α0/（°） 25 弹性模量E/Pa 2.1×1011 泊松比 0.3
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表 4 转速、缺陷角度对冲击力的影响
Table 4. Effect of rotational speed and defect angle on impact force
转速n/（r·min−1） 缺陷角度∆φfa/（°） 冲击力Fimp/N 1200 0.6 3.917 1200 0.8 6.284 1200 1 13.44 1500 0.6 21.56 1500 0.8 24.25 1500 1 38.67
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