Dynamic Stability Analysis of Cages in High-Speed Oil-Lubricated Angular Contact Ball Bearings

To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.

Air flow patterns and noise analysis inside high speed angular contact ball bearings

The vortex formed around the rolling ball and the high pressure region formed around the ball-raceway contact zone are the principle factors that barricades the lubricant entering the bearing cavity, and further causes improper lubrication. The investigation of the air phase flow inside the bearing cavity is essential for the optimization of the oil-air two-phase lubrication method. With the revolutionary reference frame describing the bearing motion, a highly precise air phase flow model inside the angular contact ball bearing cavity was build up. Comprehensive factors such as bearing revolution, ball rotation, and cage structure were considered to investigate the influences on the air phase flow and heat transfer efficiency. The aerodynamic noise was also analyzed. The result shows that the ball spinning leads to the pressure rise and uneven pressure distribution. The air phase velocity, pressure and cage heat transfer efficiency increase as the revolving speed increases. The operating noise is largely due to the impact of the high speed external flow on the bearing. When the center of the oil-air outlet fixes near the inner ring, the aerodynamic noise is reduced. The position near the inner ring on the bigger axial side is the ideal position to fix the lubricating device for the angular contact ball bearing.

Quasi Dynamic Calculation of Local Stiffness of Angular Contact Ball Bearings

In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness.

Bifurcation of Periodic Motion of Rigid Rotor System Supported by Angular Contact Ball Bearings

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.

Dynamic Analysis of Flexible Cage of High-speed Angular Contact Ball Bearing

A dynamics formula was established for the flexible cage of high-speed angular contact ball bearing. A modified Craig-Bampton component mode synthetic method was used to establish the formula with regard to the flexibility of cage and based on a dynamic analysis of angular contact ball bearing,and a rigid-flexible multi-body dynamic analysis program was developed using ADAMS,which is verified by a computation example of Gupta. The results show that it's not likely to keep the rotation smoothness of cage when the ratio of pocket clearance to guiding clearance and the ratio of radial load to axial load become too large or too small. By comparison,the flexible cage runs more smoothly than the rigid cage.

Skidding and spinning investigation for dry-lubricated angular contact ball bearing under combined loads

Sliding and spinning behaviors significantly affect the performance of rolling bearings,especially for dry-lubricated bearings,micro and macro sliding may lead to increased wear of the solid lubricating film.A unified rolling contact tribology analytical model is proposed for dry-lubricated angular contact ball bearings(ACBBs)considering the extreme conditions including high combined loads and rolling contact effects.A comprehensive solution framework is proposed to ensure the robustness of the model under different loading conditions.Equilibrium equations are solved to study the effects of friction coefficients,rotating speeds,and combined loads on the skidding and spinning characteristics of the ACBB.The results show that the rolling contact effects and combined loads significantly affect the skidding and spinning performance of the ACBB.Further analysis reveals that the skidding mechanism is related to the interaction between ball kinematical motion and traction forces.The developed analytical model is proved to more accurately predict the bearing kinematical and tribological behavior as it discards the raceway control hypothesis and considers the macro/micro-slipping,creepage,and self-spinning motions of the ball,which is validated using both the existing pure axial loading dry-lubricated ACBB model and the classical Jones–Harris model.The study would provide some guidance for the structure and lubrication design of dry-lubricated ACBBs.

Starved lubrication analysis of angular contact ball bearing based on a multi-degree-of-freedom tribo-dynamic model

When the oil supply is not adequate to maintain the ideal lubrication,angular contact ball bearing will enter into the starved lubrication regime resulting in the potential performance degradation and consequently the severe failures.To study the effects of starved lubrication on the performance of angular contact ball bearing,this paper first proposes a multi-degree-of-freedom(DOF)tribo-dynamic model by introducing five-DOF inner ring,six-DOF balls,and six-DOF cage.The model considers the starved lubrication in the ball-raceway contact and the full multi-body interactions between the bearing components.With different ball-raceway starvation degrees being analyzed,the effects of starved lubrication on the bearing tribo-dynamic performance are first revealed.By comparison,it is found that the oil film thickness,the skidding performance,and the traction forces in the ball-raceway contact are significantly influenced by the starvation degrees.It is also found that the starvation-induced change of the ball-pocket contact force is dramatical under combined loads,and the maximum contact force under this load condition increases with the increasing starvation degrees.

精密轴系低温动态摩擦力矩波动分析及优化策略

精密轴系作为机械设备旋转支承核心,其动态摩擦力矩及平稳性直接影响整机功耗及运转精度,尤其在低温环境下,由于温度对润滑油黏度、零件尺寸和配合关系的影响,精密轴系更易出现动态摩擦力矩异常波动。针对某精密轴系低温环境下批次性动态摩擦力矩异常波动现象进行了主因素分析,通过ADAMS平台建立仿真模型,分析了引导间隙、兜孔间隙对保持架动态特性的影响。结合拆解数据,指出兜孔间隙不合理引发的兜孔磨损是造成精密轴系动态摩擦力矩异常波动的原因,通过数理统计对保持架参数进行优化,兜孔间隙与引导间隙之比为0.70~0.85时,该精密轴系低温下运转稳定。

石墨烯纳米颗粒参数对角接触球轴承油气润滑特性的影响

为探究高速旋转状态下油气负载石墨烯润滑特性,以B7003C轴承为研究对象,通过有限元软件建立其三相润滑流场的数值模型,考虑石墨烯纳米颗粒参数对润滑的影响,观察润滑油和石墨烯纳米颗粒在轴承腔内的分布和变化,结果表明:轴承腔内石墨烯润滑油的体积随时间延长而增大,一段时间后润滑油总体积与分布状态在轴承腔内随时间脉动循环;石墨烯质量分数增加改变了基础油的润湿性,增大了相同工况下轴承腔内油的含量,进而改善了轴承润滑状态;石墨烯纳米颗粒在轴承腔内的运动轨迹和分布与其粒径尺寸有关,小粒径石墨烯扩散速度更快,主要参与钢球与内沟道润滑,更易从轴承腔入油口一侧溢出;大粒径石墨烯主要参与钢球与外沟道润滑,更易从油气入口侧进入轴承腔内参与润滑。

喷嘴位置对轴承腔内油气润滑两相流的影响

基于气液两相流理论,采用多重坐标系法构建角接触球轴承数值计算模型,分析不同喷嘴位置和转速下轴承腔内油相体积分数、保持架表面及轴承内外圈的油气分布特性。结果表明:在轴承低转速下,正面供油时轴承腔内油相体积分数及其周向分布的波动大于背面供油;正面供油时保持架下表面会产生润滑油的积聚,造成润滑油无法及时通过出口排出,而背面供油时润滑油在保持架表面的油相分布更均匀;正面供油时内圈左面油相体积分数较高,外圈油相分布变化较大,而背面供油时内圈右面、中间面及外圈中间面油相体积分数较高。不同转速下喷嘴位置对腔内油相分布的影响也不同,低转速下正面供油时腔内油相体积分数更高,高转速下喷嘴位置对轴承腔内油相分布的影响较小,润滑油在轴承腔内分布较为均匀,保持架下侧未见明显的润滑油积聚。

含石墨烯油气润滑的角接触球轴承腔热流数值分析

为更有效地降低大功率高速电主轴用高速角接触球轴承腔温度,对含石墨烯的油气润滑影响轴承腔热流特性的规律进行分析。基于流体力学守恒方程,建立了高速角接触球轴承腔体内压缩气体、润滑油和石墨烯颗粒形成的气液固三相流热流分析数学模型。通过数值模拟分析了不同速度压缩气体状态下油气通道中的石墨烯润滑油环状流形成条件、轴承腔内石墨烯润滑油流场速度,以及石墨烯颗粒分布与轴承腔温度场的关系。结果表明,石墨烯润滑油速度与压缩气体速度之比为1∶10时,油气通道中会形成石墨烯润滑油环状流,使高速角接触球轴承腔具有良好的润滑效果;高速运转工况下,轴承腔内石墨烯的分布状态同时受离心力与滚珠高速自旋的影响,而且石墨烯颗粒分布越密集,该区域的温度越低;石墨烯润滑油在滚珠与内圈接触区域流速越大,表面换热系数越高,该区域散热越快,为石墨烯油气润滑更好地降低高速角接触球轴承温度、保障轴承正常工作提供了理论依据。

滚动轴承旋转精度测量实验设计

为提升“新工科”专业人才培养质量,满足行业对毕业生解决复杂工程问题能力的要求,以滚动轴承旋转精度测量为例,设计一项包含理论建模、测量数据研究、软件开发的工程实验。基于角接触球轴承旋转精度检测时的接触关系,建立径向跳动值和轴向跳动值计算解析模型。选取9个均布位置检测轴承套圈设计参数,利用傅里叶级数对测量数据进行轮廓拟合,设计旋转精度计算流程并进行编程计算,得出旋转精度变化规律。计算与测试结果一致,遵循国家标准开展实验,与工程问题无缝衔接,实施过程具有创新性,强化实验对人才培养的支撑作用。

考虑内、外圈复合故障的角接触球轴承振动特性研究

为描述考虑内、外圈复合故障角接触球轴承的振动特性,建立了角接触球轴承内、外圈复合故障时变位移激励模型;基于非线性Hertz接触理论,建立了角接触球轴承时变刚度模型;提出了考虑内、外圈复合故障的角接触球轴承动力学计算方法,研究了不同参数和工况条件下复合故障轴承的振动响应规律。研究结果表明:随着故障尺寸和轴承载荷的增大,复合故障轴承的振动特征频率不变,但其幅值增大;随着轴承转速的增大,复合故障轴承的振动特征频率及其幅值均增大;故障位置的变化将对复合故障轴承的振动特征产生很大影响,故障处越接近承载区,轴承的负载越大,振动特征越明显。

联合载荷作用下精密轴系角接触球轴承钢球与保持架动力学行为分析

针对联合载荷作用下精密轴系角接触球轴承钢球与保持架的相互作用行为,基于滚动轴承动力学理论建立了精密轴系动力学分析模型,分析了转速、载荷、轴承结构参数对钢球与保持架动力学行为的影响,并通过保持架转速试验验证了模型的准确性,结果表明:力矩载荷对钢球与保持架动力学行为的影响程度较径向载荷明显;在径向载荷作用下,当转速小于40000 r/min时钢球与保持架的作用力随轴向预紧力增大而增大,当转速大于40000 r/min时钢球与保持架的作用力随轴向预紧力增大先减小后增大;在力矩载荷作用下,钢球与保持架的作用力随着力矩载荷的增大先增大再减小而后急剧增大;增大保持架兜孔间隙与外沟曲率半径系数有利于减小钢球与保持架的作用力。

角接触球轴承内圈织构设计及对油气润滑两相流的影响

针对角接触球轴承油气润滑中内圈润滑油含量少和保持性差的问题,提出在轴承内圈滚道设计圆凹坑形表面织构的润滑增效方法。基于气液两相流模型和多重参考系方法,建立内圈织构化角接触球轴承腔内油气两相流数值分析模型,分析内圈织构对轴承油气两相流动及润滑增效的影响。结果表明:织构化轴承可以显著提高润滑油在内圈的保持量,同时改善轴承腔内润滑油分布不均的状况;在微织构附近油气两相流动更不规则,所产生的压力梯度和速度梯度有利于提高气液两相膜的承载力;随着轴承转速的升高,内圈织构润滑增效效果相对减弱;随着供油量的增加,内圈织构润滑增效效果更加显著。

表面局部缺陷角接触球轴承弹流润滑性能研究

根据高速角接触球轴承自旋的运动特征,同时考虑轴承高速摩擦生热的影响,建立了表面具有局部缺陷的角接触球轴承弹流润滑模型。采用多重网格法获得弹流润滑各参数数值解,同时计算出轴承油膜刚度。研究了自旋、热效应和表面局部缺陷对球轴承弹流润滑性能的影响规律,计算结果表明:考虑自旋条件时,轴承的油膜厚度减小、压力增大,油膜刚度增大;随着轴承温度升高,轴承油膜厚度减小,油膜压力和油膜刚度增大;当润滑油流经轴承表面局部缺陷时,缺陷区域轴承润滑油油膜厚度增大,油膜压力减小,而非缺陷区域轴承最小油膜厚度减小,最大油膜压力增大,油膜刚度增大。

Influences of preload on the friction and wear properties of high-speed instrument angular contact ball bearings

For starved-oil or solid lubrication of high-speed instrument angular contact ball bearings, friction heating and wear are the main reasons of bearing failures. This paper presents a dynamic wear simulation model to investigate the impacts of different preload methods and the changes of preload caused by wear on bearing wear life. The integral value QV of stress and sliding velocity in the contact ellipses between a ball and the inner and outer races determines friction heating and wear. The changes of QV with the friction coefficient and the wear volume under constantforce preload and fixed-position preload are analyzed. Results show that under the same initial preload, the QV decreases with an increase of the friction coefficient for both preload methods, and the latter is slightly larger. The wear of the ball and the race is equivalent to the ball diameter reduction.The QV of constant-force preload is almost not changed with a decrease of the ball diameter, but for fixed-position preload, the value decreases firstly and then increases substantially due to insufficient preload, and slipping occurs, the ball diameter is reduced by 0.025%, while the preload is reduced by 60.33%. An estimation of the bearing wear life under different preload methods requires a consideration of the changes in the wear rate of bearing parts.

分步精超角接触球轴承外圈沟道工艺试验研究

为提高角接触球轴承外圈沟道精超的加工精度及加工效率,基于沟道表面在精超加工过程中的变化特点,对轴承外圈的精超加工部分进行深入研究,细分为粗精超、精超两步,采用正交试验法来对每一步加工参数进行优化,将优化得出的结果和常规的一步精超试验结果作对比分析,试验结果表明:相较于常规的一步精超,采用分步精超能够将轴承超精加工精度提高10.42%,并且超精加工时间减少2s,说明分步精超的加工精度及加工效率均要高于常规的一步精超。

考虑圆度误差的角接触球轴承温升特性研究

以往有关于轴承温升特性的研究多注重轴承温升以及圆度误差对轴承振动的影响,其中圆度误差对轴承温升影响的文献较少,且研究对象多针对的是低速、轻载轴承的温升。为此,建立了考虑圆度误差、轴承预紧力、离心效应、热力耦合等影响的角接触球轴承热-力耦合模型,研究了轴承沟道圆度误差对轴承温升的影响规律。首先,以轴承拟动力学、弹流润滑理论、传热学理论和基尔霍夫能量守恒定律为基础,建立了考虑圆度误差、轴承预紧力、离心效应、热力耦合等影响的角接触球轴承热-力耦合模型;然后,利用模型分析了不同工况条件、圆度误差对轴承温升特性影响;最后,将模型计算结果与试验结果进行了比较,验证了角接触球轴承热-力耦合模型的合理性。研究结果表明:模型计算结果和实验结果相比,最大相对误差为5.37%;随着圆度误差阶次的增加,轴承温度呈现波动性变化,且随着转速的增加,波动趋势愈加显著;随着润滑油温度的升高,温度波动逐渐减小;当圆度误差的阶次等于球数n/2±2(n=1,2,3…)时,轴承外圈温度比不考虑圆度误差时要低,因此将圆度误差控制在特定阶次内能有效降低轴承温升,从而提高工作效率;轴承外圈温度的波动性与外圈圆度误差的幅值成正比,为轴承设计提供了重要参考;外圈温度与沟道圆度误差阶次之间呈周期性变化,并与钢球的个数形成映射关系,当圆度误差阶次等于球数的(2 n-1)/4倍(n=1,2,3…)时,轴承外圈温度达到最高;当圆度误差阶次等于球数的n/2倍(n=1,2,3…)时,轴承外圈温度最低,这一规律可为轴承的优化提供具体参考方向。

变载荷作用下的角接触球轴承动力学分析

为研究球轴承在变载荷作用下的动力学行为,建立了角接触球轴承的动力学模型,并在不同的载荷谱下进行了角接触球轴承的动力学计算,对比了不同载荷谱作用下球与内外圈的接触角和接触载荷以及球的自转角速度和公转角速度随时间的变化。结果表明:载荷瞬时变化产生的冲击会导致球与内外圈的接触载荷和接触角发生突变,且变化幅度与冲击载荷大小相关;在受载荷冲击后,球的自转角速度和公转角速度也会发生突变,并且随轴承的转动,球的自转角速度和公转角速度会最终达到一个稳定值;载荷变化幅度越大,变化频率越快,轴承运动的变化幅度就越大。