Pivoting and Slip in an Angular Contact Bearing

Pivoting slips are calculated for the ball-race and ball-ball contacts in a retainerless bearing. The calculation is kinematic, ignoring all inertial loadings. Pure spin and uniform precession of the balls are considered. Pivoting slip magnitudes are compared with several other kinds of slip which have previously been reported in an R4 size bearing.     

Dynamic and coupling influences on basic speed ratio of an angular contact bearing

A general expression for basic speed ratio, a fundamental characteristic number for an angular contact ball bearing, is used to explain some previously reported data. Estimates of ball-race slip induced by ball orbit drag and separately by ball spin drag are given. Some dynamic effects are also discussed.     

考虑接触特性的滚动轴承系统建模与仿真分析

根据Hertz接触理论和滚动轴承功能原理,以SKF6208深沟球轴承为参考,在ADAMS/View软件环境下设计建立了基于Impact函数的滚动轴承多体动力学仿真模型。通过实体接触条件下的轴承运转过程动态仿真分析,计算获得了滚珠与内圈、外圈及保持架之间的接触力动态分布规律。指出:轴承系统在启动瞬间(0~0.22 s)存在一定滑动,且接触力变化频率较大;进入滚动阶段(0.22~0.4 s)后,接触力变化频率减小,且呈周期性分布。仿真结果验证了滚动轴承的启动打滑现象,符合实际运行工况。为深入研究滚动轴承系统的接触机理及动态载荷提供了技术参考。     

A Method for Measuring the Intensity of a Line Load Around a Shaft or Tube

The slip flow effect is considered to estimate the load capacity and the dynamic coefficients of an elastically-supported gas foil hearing when the local Knudsen number for the minimum film thickness is greater than 0.01. The compressible Reynolds equation with slip flow conditions is used to evaluate the load capacity. The linearized dynamic coefficient equations are obtained by the perturbation method. Numerical predictions compare the static and dynamic force performances considering slip flow at room-to-high temperate with the performance of elastically-supported foil bearing without slip flow for a range of bearing compliances and bearing numbers. It has been shown that the slip flow effect on the load capacity and the dynamic coefficients at high temperature is significant in the region of low bearing numbers.     

考虑疲劳故障的圆柱滚子轴承打滑失效分析

考虑滚道疲劳剥落故障、滚动体与保持架之间的非连续接触等因素,建立圆柱滚子轴承的非线性弹性接触显式动力学模型,研究不同剥落故障位置、径向载荷、内圈转速对滚动体和保持架打滑特性的影响规律;将仿真结果与理论解进行对比,验证有限元模型的有效性。研究结果表明:滚动体在非承载区更容易出现打滑;相同工况下剥落故障会使得滚动体和保持架的打滑率大幅增加,其中复合故障下的打滑率增加最多,内圈故障和外圈故障下的打滑率增幅基本相同;增大径向载荷能有效减轻轴承的打滑现象,但载荷增加到一定程度后对打滑的抑制效果不明显;低转速工况下内圈和外圈疲劳故障对轴承打滑率的影响不大,随着转速的提高疲劳故障对打滑率的影响愈加明显。     

Rolling-Sliding Analysis in Ball Bearing Considering Thermal Effect

An analytical method is applied in the calculations of ball contact angles varying with the position angle of a ball bearing with a centrifugal force. This is further extended to investigate the thermal slipping behavior occurring at the contact surface of the inner raceway. The sliding velocities at the contact area are analyzed in the present study by the ball bearing contact mechanisms. The shear stress created at this contact surface is evaluated by considering the temperature-pressure dependence of the lubricant viscosity. The contact temperature of a ball and the inner raceway is obtained if the frictional heat created by the shear stress is available. Under the condition of controlling the outer raceway temperature, the thermal deformations of all components of a ball bearing are taken into account in the evaluation of bearing performance. Comparisons are made for several parameters, including the normal load, linear slip velocity, and linear traction force, between the results of considering the thermal effect or ignoring it. The friction torque evaluated by taking the thermal effect into account is higher than the torque evaluated when ignoring the thermal effect.     

Numerical investigation of the combined effects of slip and texture on tribological performance of bearing

Slider bearings are used in many applications. An increase in the load support may allow for saving of energy. In this work, in order to enhance the load support and decrease the friction force, a combined textured surface bearing using boundary slip is discussed. A modified Reynolds equation with slip is adopted. With the main goal of evaluating the effects of slip and texture, a parametric analysis is performed. For the given operating conditions, texturing features as well as slip pattern are analysed in detail. The numerical analysis is undertaken under the condition of different gap ratio values and the slip-textured area. The results show that combined techniques of slip and texture have a significant effect on the improvement of the tribological performance of bearing, that is, a high load support but low friction force. The gap ratio of the bearing is shown to have a significant effect on the lubrication behaviour. It is found that even with a smallest gap ratio (parallel gap), a high load support can be produced. However, it is also shown that the gap ratio appears to contribute to the generated friction force and the volume flow rate more than the boundary slip. Further analysis indicates that the optimum slip-text zones for certain gap ratio are highlighted. These findings may provide references for designing hydrodynamic-textured slider bearing considering boundary slip.     

柔性间隙影响下涡旋压缩机主轴系统动力学特性研究

考虑到涡旋压缩机主轴系统的高速回转特性,将自由运动和接触变形两状态非连续接触模型应用于间隙运动副动力学建模。以某卧式涡旋压缩机为依据,在不同运动副间隙下构建基于ADAMS/View的主轴系统刚柔耦合模型。通过柔性接触条件下的动力学仿真计算,深入分析了主轴系统核心部件(如动涡盘、曲轴、十字滑环及轴承)的运行状态及承载情况。结果显示：在理想间隙(间隙为0)下,柔性曲轴质心轨迹为一带有波动的非标准圆,而在非理想状态下,曲柄销与滚针轴承存在多处接触碰撞;当轴承内部存在间隙时,Z方向上的支反力更为连续和集中,且其波动幅度随着间隙增大而减小;间隙为0.01 mm时对于动涡盘加速度影响较大,不利于容积腔形成和气体压缩,而选择0.03 mm或0.05 mm间隙值时,可避免轴承系统发生应力集中和疲劳破坏,同时有助于轴承系统维护和十字滑环防自转。     

Experimental determination of the equivalent stress at the frictional surfaces of a slip bearing in a heavily loaded contact

The significant influence of the frictional forces on the bush deformation in a heavily loaded contact is shown. The results of comparative tests are presented. The coefficients for calculating the equivalent stress at the frictional surfaces of a slip bearing are determined.     

An analytical approach on the tribological behaviour of pocketed slider bearings with boundary slip including cavitation

Slider bearing performance depends on the boundary conditions at the interface between the solid surfaces and the fluid. This paper presents the combined effect of pockets and boundary slip on the load support and friction of parallel sliding systems using analytical solutions for a simple pocketed bearing. The effect of cavitation was of particular interest with respect to the inlet suction mechanism. It was demonstrated that applying boundary slip in a pocketed slider bearing gives a reduction in load support compared with the textured bearing without wall slip. Adding slip over the whole surface could retard the presence of cavitation. The influence of boundary slip is explored, and was found to significantly affect the frictional behaviour. Copyright © 2016 John Wiley & Sons, Ltd.     

A flat punch pressed against an elastic interlayer under conditions of slip and separation

The problem of a square-ended rigid punch bearing on an elastic half-plane through the medium of an elastically dissimilar interlayer is considered, under plane deformation. The interlayer is in frictional contact with both the punch and half-plane. Regions of slip and separation along the interface are found, and it is shown how these phenomena affect the stress state in the immediate neighbourhood of the contact. This problem is of direct, practical interest to the design of interfacial bearing pads employed in supporting glass plates in structural applications.     

Rotor System Oscillations under the Rotor Rotation Inside Floating Elements

Rotor system oscillations are considered for the rotation of the rotor inside lightweight moving elements (for example, inside floating seal rings, and hydrostatic bearings). In this case, the ring runs around the rotor in a direct precession mode (hula-hoop type of oscillations). The oscillations of the rotor-floating ring system are studied taking into account hydrodynamic forces in the gap and contact forces of dry friction. A solution is obtained in analytical form. It is shown that the ring precession speed under the running-around is close to its own frequency at a given rotation speed. Trajectories are plotted for the motion of the ring.     

基于打滑条件下的履带车辆转向分析

研究履带车辆转向性能时传统履带车辆转向理论不考虑履带接地段的滑转与滑移,计算结果与实际存在一定差别。在分析履带与地面相互作用的基础上,基于滑转滑移条件讨论履带车辆平稳转向的实际过程,导出了履带牵引力、制动力、转向阻力矩、转向半径和转向角速度的表达式,采用迭代法求其数值解,和传统转向理论的相关结果作了定量比较,并进行了实车试验。结果表明,考虑履带接地段打滑后相对转向半径约为不考虑打滑时的转向半径的1．5倍,即约为履带车辆接地长L与履带中心距B之比,转向角速度约为不考虑打滑时的2／3,考虑履带接地段打滑时转向半径与转向角速度同实车试验测定的数据相比误差在3％左右。表明建立的考虑履带打滑时的转向模型更符合履带车辆转向实际。     

稀薄效应对动压气体轴承静动特性的影响

为研究稀薄效应对微小间隙下动压气体轴承静动态特性的影响,分别采用连续模型、一阶滑移模型以及在任意克努森数下都与线性玻尔兹曼方程解有较高吻合的WU新滑移模型,基于有限体积法建立考虑稀薄效应的静动态Reynolds方程,给出3种模型下轴承静态承载力与偏心率、轴颈扰动频率与轴承动特性系数的变化关系。数值分析结果表明:随偏心率的变化,连续模型预测的静态承载力最大,一阶滑移次之,WU新滑移模型预测的值最小;随着扰动频率的增加,考虑滑移模型计算的主刚度系数和主阻尼系数均有减小的趋势,且WU新滑移模型计算的主刚度系数和主阻尼系数明显低于连续模型和传统的一阶滑移模型。传统连续模型和一阶滑移模型过高地估计了轴承的静动特性系数,WU新滑移模型计算的结果更为准确。     

Modeling Bearing and Shear Forces in Molecularly Thin Lubricants

Under the effects of high shear rate and confinement between solid surfaces, the behavior of a thin lubricant film deviates from that of the bulk, resulting in significant increases of lubricant viscosity and interfacial slip. A semi-empirical model accounting for the breakdown of continuum theory at the nanoscale is proposed—based on film morphology and chemistry from available experimental and molecular dynamics simulation data—to describe lubricant behavior under shear. Viscosity stiffening and interfacial slip models are introduced into the formulations of the normal (bearing) and shear forces acting on a sphere that moves within a thin lubricant film parallel to a rigid plane. The experimentally measured ‘apparent’ viscosity confounding the effects of both stiffening and slip is used to predict the hydrodynamic forces acting on a fully or partially submerged sphere for the purposes of describing lubricant contact in magnetic storage. The proposed sphere-on-flat model forms the basis of a future, dynamic contact with friction model that will account for lubricant contact in the context of molecularly thin lubricated rough surface contact.     

Experimental analysis of factors influencing the cage slip in cylindrical roller bearing

This paper deals with the effect of operating parameters on cage slip in cylindrical roller bearing. A cylindrical roller bearing test rig is developed to measure the running speed of bearing elements at various operating conditions. The effect of operating parameters namely shaft speed, radial load, viscosity of lubricating oil, number of rollers, and bearing temperature on cage slip are experimentally obtained. The critical load and magnitude of cage slip for various operating conditions are obtained. The non-dimensional number is derived based on the operating parameters. The region where cage slip occurs is developed from the derived non-dimensional number and the experimental data. The temperature raise is experimentally obtained during slip condition and its effect on viscosity is included for calculations. The frictional forces are experimentally obtained and are compared with the theoretical findings. The significant effect of operating parameters on cage slip of cylindrical roller bearing is discussed based on the experimental findings.     

Influence of adsorbed fluids on the rolling contact deformation of MgO single crystals

Basic phenomena associated with rolling contact deformation were studied using MgO as a model bearing material. A hardened steel ball was rolled on MgO single crystals in slow speed reciprocating motion and in high speed circular motion. The resulting deformation was studied by dislocation etch pit techniques. The presence of adsorbed fluids, such as silicone oil, white mineral oil and toluene, with slow speed sliding caused a dramatic change in slip mode and premature surface spalling compared with similar experiments in air or under water. In contrast dimethyl formamide inhibited these slip processes. The results are consistent with the dependence of dislocation mobility on adsorbed species. High speed hydrodynamic rolling with mineral oil lubrication produced a different slip phenomenon entirely than that produced by slow speed rolling. The slip bands resembled those produced in tensile tests and all slip apparently initiated at subsurface sites.     

Theoretical Prediction of Journal Bearing Stability Characteristics Based on the Extent of the Slip Region on the Bearing Surface

Journal bearing performance depends on the boundary conditions at the interfaces between the fluid and the solid surfaces. In the derivation of the Reynolds equation used to predict the bearing performance, the no-slip boundary conditions of the fluid and the solid interfaces are used. Recent research has shown that a slip can occur on specially made surfaces, the conventional no-slip boundary conditions are not valid, and the Reynolds equation is no longer applicable. If the slip is allowed to occur in certain regions, the fluid flow in the bearing can be altered, and the bearing stability characteristics can be improved. In this article, the numerical stability analysis of a journal bearing based on the extent of the slip region on the bearing surface is analyzed. An extended Reynolds equation is derived based on the slip length model, using a no-slip boundary condition against the journal surface and the slip against the bearing surface. A linearized perturbation method is used to determine the stability limit of a rigid rotor supported on two symmetrical journal bearings. Using the linear stability analysis, the linearized stiffness and damping coefficients, the threshold speed, and the critical whirl ratio are evaluated. The effects of the slip parameter on the bearing stability performance are discussed. The results show that with a critical shear stress of zero, an increase in the stability threshold can be achieved with a higher value of the nondimensional slip length and a smaller extent of the slip region on the bearing surface.