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.

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.

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.

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。

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。

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。

Impact of lubricant traction coefficient on cage's dynamic characteristics in high-speed angular contact ball bearing

In this paper,the formulas of elasto-hydrodynamic traction coefficients of three Chinese aviation lubricating oils,4109,4106 and 4050,were obtained by a great number of elastohydrodynamic traction tests.The nonlinear dynamics differential equations of high-speed angular contact ball bearing were built on the basis of dynamic theory of rolling bearings and solved by Gear Stiff（GSTIFF） integer algorithm with variable step.The impact of lubricant traction coefficient on cage＇s dynamic characteristics in high-speed angular contact ball bearing was investigated,and Poincare map was used to analyze the impact of three types of aviation lubricating oils on the dynamic response of cage＇s mass center.And then,the period of dynamic response of cage＇s mass center and the slip ratio of cage were used to assess the stability of cage under various working conditions.The results of this paper provide the theoretical basis for the selection and application of aviation lubricating oil.

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。

热力耦合作用的双半内圈角接触球轴承热特性

针对航空发动机高速重载双半内圈角接触球轴承运行中生热问题,基于滚动轴承动力学以及传热学理论,考虑轴承热变形以及润滑油的作用,建立热力耦合作用的双半内圈角接触球轴承动力学分析模型。采用预估-校正的GSTIFF变步长积分算法求解动力学方程组,分析了工况参数和结构参数对轴承热特性的影响,结果表明:考虑热力耦合的轴承动力学模型更接近试验结果;内、外圈温度受转速以及轴向力的影响较大,轴向力对内、外圈温差的影响较大;内圈沟曲率半径系数对轴承温度的影响较大,当内圈沟曲率半径系数为0.532时内、外圈温差最小,外圈沟曲率半径系数和垫片厚度对轴承温度的影响较小。

弹流润滑影响下的轴承耦合缺陷动力学建模研究

针对传统动力学模型未考虑弹流润滑的影响以及深沟球轴承多点缺陷理论参考较少的问题。基于非线性Hertz接触理论与时变位移激励函数,建立了弹流润滑影响下的具有耦合缺陷的深沟球轴承二自由度动力学模型。通过对比缺陷轴承实验信号与数值仿真信号的幅频信息,验证了动力学模型的准确性。并依据此模型分析了缺陷宽度、径向载荷、转速对油膜参数、典型时域特征参数的影响。分析表明:随着缺陷宽度、径向载荷的增大,有量纲指标峰值、均方根值与无量纲指标峭度因子、脉冲因子均呈现增大趋势;随着转速的增大,峰值、均方根值与峭度因子、脉冲因子呈现相反的趋势;随着径向载荷、转速的增大,油膜参数也呈现相反的趋势。

基于Fluent的高速角接触球轴承润滑脂动态分布

以脂润滑高速角接触球轴承为研究对象,建立润滑脂流动仿真模型,根据轴承实际运转工况设置模型速度、温度等边界条件,通过拟合常温至高温条件下的润滑脂黏度模型参数,建立全温域范围赫-巴黏度模型来描述润滑脂非牛顿流体特性,采用CFD软件Fluent进行仿真试验,并分析轴承在不同转速、温度和填脂量下的润滑脂分布。结果表明:在一定的填脂量下,随着转速提高润滑脂在轴承腔内分布更均匀,且在保持架转动方向的两侧分布更多,而内圈润滑脂量逐渐减少,转移到保持架和外圈;相对于常温,在高温下润滑脂流动性更高,向离心方向扩散的特征更为明显,这是内圈更易磨损的原因之一;在润滑脂填充比例为19.8%~29.7%的范围内,随着填脂量提高,润滑脂分布状态更好。

薄壁四点接触球轴承-腕部关节系统接触动力学分析

在机器人实际工况中,针对含有薄壁四点接触球轴承的机器人腕部关节系统的运动稳定性问题,对腕部系统模型进行了简化设计和仿真研究。在考虑薄壁结构的弹性变形和动态接触作用耦合影响的基础上,建立了刚柔耦合工业机器人腕部关节系统模型,分析了不同受载工况和正反转驱动下的变形规律和动态特性。首先,基于多体动力学和Hertz接触理论,设计了包含薄壁四点接触球轴承和中空轴及基座的腕部关节系统刚柔耦合接触动力学仿真模型;然后,考虑薄壁中空轴、基座、轴承套圈和保持架的结构弹性变形、钢球和套圈滚道、保持架的动态接触作用,研究了机器人腕部关节系统两种实际工况对保持架和钢球角速度、保持架和薄壁基座振动位移、钢球与套圈的动态接触力的影响;最后,计算分析了两种工况下腕部关节系统的动态载荷规律和振动响应特性。研究结果表明:在相对较大的径向载荷作用下,保持架和钢球会出现打滑现象,速度呈现周期波动,保持架和基座具有更好的运动稳定性,其薄壁轴承内部载荷降低,主副接触对均承担联合载荷,轴承内部载荷稳定性也更好。该仿真模型及结果可以为薄壁腕部关节系统的动力学分析与设计提供参考。

保持架兜孔形状对高速角接触球轴承保持架动态性能的影响分析

分别建立了方柱形、圆柱形和球形兜孔保持架的角接触球轴承动力学数值仿真模型,试验结果验证了模型的准确性。对三种不同兜孔形状的保持架在不同间隙比下进行了分析,结果表明:球形兜孔保持架运动稳定性显著优于方柱形和圆柱形兜孔保持架,而在间隙比小于1时,圆柱形兜孔保持架运动稳定性优于方形保持架,反之则方柱形保持架更稳定;球形兜孔保持架的运动由球引导,方柱形和圆柱形兜孔保持架则由套圈引导;随着间隙比的增大,保持架的轴向摆动范围逐渐增大,且方柱形、圆柱形和球形兜孔保持架的轴向摆动范围依次减小;保持架的磨损率与其运动稳定性呈负相关,且球形兜孔保持架的磨损率高于其他两种保持架。

滑动效应对球轴承滚动体缺陷频率影响的研究

在弹流润滑作用下,球轴承滑动效应引起的滚动体缺陷频率低于理论值,不利于对球轴承进行故障诊断,为此,建立了一种考虑弹流润滑作用下球轴承滑动效应的轴承动力学模型,研究了球轴承滑动效应对滚动体缺陷频率的影响。首先,基于轴承动力学理论和弹流润滑理论,分析了球轴承内各部件间的等效刚度与等效阻尼;然后,根据部件间受力关系,建立了考虑滑动效应的含滚动缺陷故障轴承动力学模型;最后,分析了弹流润滑作用下轴承滚动体与轴承内外圈间的滑动效应,获取了滑动效应对滚动体缺陷频率的影响,并通过试验对模型的正确性进行了验证。研究结果表明:由于球轴承滑动效应的存在,滚动体缺陷频率约为理论值的93.6%;通过增大载荷可抑制滑动效应对滚动体缺陷频率的影响,滚动体缺陷频率约为理论值的96.3%,但由于滑动效应始终存在,滚动体缺陷频率始终低于理论值。该研究结果为弹流润滑作用下球轴承的打滑抑制与故障诊断提供了参考依据,丰富了轴承故障动力学建模理论。

考虑内圈中心偏移和钢球均匀磨损的深沟球轴承振动特性分析

为研究轴承内圈中心偏移和钢球磨损对滚动轴承振动特性的影响,以深沟球轴承为例提出一种计算钢球接触变形的方法,建立了考虑钢球均匀磨损的滚动轴承动力学模型,分析钢球不同磨损程度对轴承系统振动特性的影响。结果表明:与传统模型相比,考虑轴承内圈中心偏移影响模型的振动位移偏大,结果更接近实际情况;钢球磨损后内圈振动位移的幅值变大,同时会导致保持架转动频率及其倍频的出现,并在钢球通过频率两侧出现明显的边频带;随着钢球磨损程度增大,内圈振动位移的幅值也随之增大,当钢球磨损量达到一定程度时钢球将不与内圈接触并承载。

基于非线性接触特征的角接触球轴承动态响应分析

针对角接触球轴承几何结构特征,建立一种基于复杂工况下角接触球轴承动态响应分析模型,并考虑角接触球轴承非线性接触特征的影响。将考虑能量损耗的耗散接触力模型和Coulomb摩擦力修正模型引入到角接触球轴承动力学方程中,采用Newton-Rapson法获得含间隙的角接触球轴承动力学特性,并在滚动轴承实验台上进行动态响应特征实验,分析不同工况下间隙对角接触球轴承动力学特性的影响规律。计算结果表明:间隙的引入增加了角接触球轴承元素之间的非线性接触特征,并会引起高频冲击,而工况条件的变化会引发角接触球轴承动态响应的变化。

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.

Vibration analysis of a single row angular contact ball bearing with the coupling errors including the surface roundness and waviness

Roundness and surface waviness are main manufacturing errors on the components of single row angular contact ball bearings(ACBBs).An analytical study for vibrations of the ACBBs with coupling errors including the roundness and waviness can be useful for the vibration control of the rotating machinery.However,most previous works only focused on the single error modelling method.In this paper,an improved time dependent displacement excitation(TDDE)model is proposed to consider the coupling errors including the roundness and waviness on the inner and outer races of an ACBB.The TDDE model for the roundness and waviness is established by using a combination of several sinusoidal functions.A dynamic model in the previous study is improved to consider the influences of coupling errors including the roundness and waviness.The Hertzian contact theory and Dowson’s method are adopted to calculate the bearing contact stiffness.The time-and frequency-domain vibrations for the experimental and simulation results are compared to show some model validation.The influences of roundness orders and waviness amplitudes on the vibrations of the ACBB are analysed.The obtained results show that the coupling errors including the roundness and waviness have some influence on the time-domain impulse waveform and frequency-domain spectrum characteristics of the bearing accelerations.The differences of the vibrations between the coupling errors and sing error are from 4%to 42%.This paper can provide a useful guidance for the accurate diagnosis of surface imperfections in the ACBBs.

表面织构对角接触球轴承润滑性能的影响

为研究油气润滑状态下表面织构对角接触球轴承润滑性能的影响,在角接触球轴承的内圈滚道上设计表面织构,基于气液两相流理论,采用多重参考坐标系(MRF)模型和流体体积(VOF)法,对高速角接触球轴承腔内润滑油流动特性进行数值分析,对比分析长沟槽、短沟槽、矩形、圆柱形4种表面织构对角接触球轴承润滑性能的影响,发现长沟槽形的表面织构对改善角接触球轴承的润滑性能效果最为显著,并进一步分析长沟槽形表面织构结构参数对轴承润滑性能的影响。结果表明:轴承腔内油相体积分数随着沟槽深度和面积率的增大先增大后减小,随着沟槽宽度的增加逐渐增大,存在最佳织构参数使得轴承腔内油相体积分数最大。因此,合理地设计织构参数能有效提高角接触球轴承润滑性能,该研究结果对角接触球轴承表面织构设计具有一定的参考价值。