FEM Comparison of Ball and Roller Bullgears

A structural finite element model has been developed for calculating the forces transmitted through the rolling elements (load distribution) in a bullgear assembly. The elastic structural model consists of 3-D beam elements used to approximate the global race deflection and non-linear springs that approximate the combined rolling element/raceway contact deflections. For rollers, an upperbound on the contact stress (assuming linear variation of force along the length of the roller) is estimated by modeling the rollers as pairs of nonlinear springs. The finite element approach iteratively solves the contact forces at each, rolling element. Contact stresses are then calculated from the contact, forces using Hertz contact theory. This approach is applied to analyze two proposed designs of ball and crossed roller bearing, bullgear assemblies used for rotating the radar antenna on top of a ship's mast. The loads analyzed include those arising from wind loading and from out-of-flatness of the inner race of the bearings due to deflection of the mast. The distribution of the load and the maximum contact stresses for the proposed bullgear assemblies are estimated and compared. It is found that the maximum contact stress in the crossed roller bearing is less than that in the ball bearing for both types of loads. Furthermore, the analysis shows that the out-of-flatness loading produces significantly higher stresses than wind loading.     

考虑滚子位置变化的圆柱滚子轴承非线性刚度特性分析

以圆柱滚子轴承为研究对象,考虑轴承运转过程中滚子周向位置分布的周期性变化,对经典圆柱滚子轴承载荷分布理论进行改进,并对由此引起的轴承刚度时变特性进行分析,同时研究圆柱滚子轴承平均刚度及平均接触滚子数随径向力的非线性变化规律。为了对改进理论算法进行验证,采用有限元接触分析方法对圆柱滚子轴承刚度及滚子接触状态进行分析。研究结果表明,改进理论算法和有限元接触法均能准确预测轴承瞬时刚度的时变特性及平均刚度随径向力的非线性变化特性,同时证明轴承平均接触滚子数的改变是轴承刚度变化的根源。基于改进理论算法进而分析轴承初始径向游隙、径向力、滚子设计数量等关键参数对圆柱滚子轴承性能的定量影响规律。     

基于ANSYS的四列圆柱滚子轴承接触应力和刚度分析

对四列圆柱滚子轴承的接触应力、变形以及径向刚度进行了研究.建立了四列圆柱滚子轴承的有限元三维模型,基于ANSYS和Hertz接触理论,阐述了建模过程中的关键步骤,结合短应力线轧机的应用实例,计算了轴承滚子、内圈的接触应力与变形分布,直观表达了交错排列滚子之间的应力分布情况,计算结果和Hertz理论值相比较,具有较好的一致性.通过计算不同载荷下的轴承变形（轴承内孔轴线的相对位移）,获得了轴承刚度随径向载荷变化的规律.     

The lubrication of roller bearings subjected to couples

Roller bearings are generally designed to carry mainly radial loads with additional bearings employed to carry any axial loads. Occasionally, limited space prevents the use of these additional bearings, so that the roller bearing itself must carry the axial load. This must be taken by flanges on both the inner and outer races. The effect on the rollers themselves is to modify the load distribution on their generator contact surfaces because the rollers are now subjected to a couple in addition to the radial load. A similar effect is produced if two flanged (or unflanged) roller bearings support a loaded shaft. As its ends are nominally direction fixed, the rollers must be subjected to terminal couples, thus causing a modification to the load distribution at the contact surfaces. The effect of such forces on the footprint shape and on the bearing lubrication is investigated.     

On the Dynamics of Lubricated Cylindrical Roller Bearings,Part II: Linear and Nonlinear Vibration Analysis

This article is the second part of two companion papers. In the first article, curve-fitted relations of stiffness and damping coefficients of a single roller-to-race contact of lubricated roller bearings were developed. In the present work, these relations are applied to a rotor–bearing system. Two cases are studied to investigate the influence of lubricated cylindrical roller bearings on the vibration characteristics of the rotor system. In the first case, lubricated contacts are simulated as a linear spring–damper model. The overall stiffness and damping matrices are calculated by using the dynamic coefficients of individual load sharing rollers. These matrices are used in the finite element analysis of flexible rotor. In the second case, the nonlinear structural vibration of a lubricated cylindrical roller bearing is studied. Equations of motion of bearing elements are derived using the Lagrange equation. A nonlinear load–deflection contact model developed through the derived curve-fitted relations of dynamic coefficients is used in the equations of motion. Equations of motion are solved by a fourth-order Runge-Kutta integration method. The response of bearing elements under free vibration and due to rotating unbalance is studied for damped and undamped cases. Furthermore, results obtained using elastohydrodynamic finite and infinite contact theories are compared.     

基于BP神经网络和有限元分析的深穴圆柱滚子的优化设计

针对直素线圆柱滚子轴承在工作中滚子端部出现应力集中,降低轴承接触疲劳寿命的问题,采用了深穴圆柱滚子。结构合理的深穴圆柱滚子轴承可以有效改善普通直素线滚子轴承受载后滚子两端的边缘应力集中现象。采用ABAQUS有限元分析软件对深穴圆柱滚子轴承进行了三维接触有限元分析,应用BP神经网络对滚子深穴结构进行了优化,优化后滚子两端部位的边缘应力集中明显减小,轴承的接触疲劳寿命和承载能力得到提高。     

基于修正L-P模型的轮毂轴承载荷分布与弯曲疲劳寿命分析

以第三代轮毂轴承为研究对象,推导了弯矩作用下滚动体与内滚道、外滚道的接触变形与接触载荷,提出了更为准确的接触载荷分布计算模型,分析了不同工况下轮毂轴承内部接触载荷和接触角的周向分布规律。在轮毂轴承内部载荷分布的一次修正基础上,考虑不同位置角的滚道材料和滚动体的接触疲劳,利用乘积定律进行统计处理,得到了第三代轮毂轴承疲劳寿命的修正L-P模型。结合ISO281—2007寿命修正计算方法,针对润滑现象进行二次修正,得到了经过润滑修正的第三代轮毂轴承疲劳寿命模型。利用旋转弯曲疲劳试验机进行了轴承的弯曲疲劳试验,试验结果显示,该疲劳寿命模型计算得到的理论值与试验值的误差在10%以内,验证了模型的正确性。     

Effect of Silicon Nitride Balls and Rollers on Rolling Bearing Life

Three decades have passed since the introduction of silicon nitride rollers and balls into conventional rolling-element bearings. For a given applied load, the contact (Hertz) stress in a hybrid bearing will be higher than that of an all-steel rolling element bearing. The silicon nitride rolling-element life as well as the lives of the steel races were used to determine the resultant bearing life of both hybrid and all-steel bearings. Life factors were determined and reported for hybrid bearings. Under nominal operating speeds, the resultant calculated lives of the deep-groove, angular-contact, and cylindrical roller hybrid bearings with races made of post-1960 bearing steel increased by factors of 3.7, 3.2, and 5.5, respectively, from those calculated using the Lundberg-Palmgren equations. An all-steel bearing under the same load will have a longer life than the equivalent hybrid bearing under the same conditions. Under these conditions, hybrid bearings are predicted to have a lower fatigue life than all-steel bearings by 58% for deep-groove bearings, 41% for angular contact bearings, and 28% for cylindrical roller bearings.     

圆柱滚子轴承的非对称修形

传统的修形理论仅适用于对称修形,而对称修形虽然可以避免直母线浪子引起的滚动体两端的“边缘效应”,但无法克服由偏载产生的“偏载效应”。根据接触力学理论,通过有限元方法对滚动轴承的分析,提出了浪子非对称修形新方法。有限元分析结果表明,提出的非对称修形方法既可以避免“边缘效应”,又可以克服“偏载效应”,从而使非对称修形滚子轴承有更高的承载能力和使用寿命。     

变桨轴承钢球/沟道接触载荷分布规律

工程实践表明,安装基础刚性、螺栓预紧力、安装表面平面度等各种因素对风力发电机变桨轴承的运行性能有显著影响,钢球/沟道接触载荷分布规律是研究转盘轴承运行性能、承载能力及寿命等的基础。讨论了一种用弹簧单元模拟钢球/沟道接触的有限元建模方法,并给出了应用实例,研究了安装基础刚性、螺栓预紧力、安装表面平面度等对变桨轴承钢球/沟道载荷分布规律的影响。     

风电转盘轴承载荷谱的设计应用

建立了偏航、变桨轴承的空间力系及载荷方程,介绍了风电转盘轴承在各种设计要求下的静强度载荷谱和滚动接触疲劳载荷谱,并以此为基础对某型号风电转盘轴承进行了校核。     

Effect of Roller Geometry on Roller Bearing Load–Life Relation

Cylindrical roller bearings typically employ roller profile modification to equalize the load distribution, minimize the stress concentration at roller ends, and allow for a small amount of misalignment. The 1947 Lundberg-Palmgren analysis reported an inverse fourth-power relation between load and life for roller bearings with line contact. In 1952, Lundberg and Palmgren changed their load–life exponent to 10/3 for roller bearings, assuming mixed line and point contacts. The effect of the roller–crown profile was reanalyzed in this article to determine the actual load–life relation for modified roller profiles. For uncrowned rollers (line contact), the load–life exponent is p = 4, in agreement with the 1947 Lundberg-Palmgren value, but crowning reduces the value of the exponent, p. The lives of modern roller bearings made from vacuum-processed steels significantly exceed those predicted by the Lundberg-Palmgren theory. The Zaretsky rolling-element bearing life model of 1996 produces a load–life exponent of p = 5 for flat rollers, which is more consistent with test data. For the Zaretsky model with fully crowned rollers, p = 4.3. For an aerospace profile and chamfered rollers, p = 4.6. Using the 1952 Lundberg-Palmgren value p = 10/3, the value incorporated in ANSI/ABMA and ISO bearing standards, can create significant life calculation errors for roller bearings.     

子单元和微单元在轧机轴承载荷边界元法中的应用

针对轧机轴承接触单元中面力不连续问题，提出子单元和微单元新概念，更新已有轧机轴承载荷边界元法面力影响系数，较精确地计算出轧机轴承载荷的三维分布。计算实例表明：计算值与实测值的误差为5％以下。     

SELF-ALIGNING EVEN LOAD MECHANISM OF MULTI-ROW BEARINGS OF LARGE STRIP ROLLING MILL

The load distribution of multi-row bearings of large strip rolling mill is fully analyzed by 3D contact boundary element method (BEM). It is found out that bearings are frequently worn out due to serious uneven load on the multi-row rollers. The constraint mechanism of the previous rolling system is found to be unreasonable by theoretical analysis on heavy machinery structure. A mechanism of self-aligning even load for workroll bearing of 2 050 mm hot rolling mill of Baoshan I&S Co. is developed. This device is manufactured with particular regard to the structure of 2 050 mm hot rolling mill mentioned above. Hence, uneven load on multi-row bearings is greatly relieved and their lives are remarkably prolonged. Meanwhile, theoretical analysis and on-spot tests prove the rationality and validity of the device.     

支承电压与电压变化速率对静电轴承性能影响的研究

从机电耦合的角度研究了静电轴承中高压放大器的输出电压和电压变化速率对系统性能的影响。分析表明,支承电压的选择应结合承载能力、转子不平衡力抑制和对输出电压惰性失真的要求确定,支承电压变化速率与高压放大器的动态功耗相互制约。导出了确定支承电压及其变化速率的关系式,为系统设计提供了理论依据。理论分析结果与实例的试验结果取得了较好的一致性。     

双列调心凹面滚子轴承接触载荷分析

在考虑滚子与套圈、滚子与保持架以及保持架与引导套圈作用力的条件下,建立双列调心凹面滚子轴承动力学模型.以某双列调心凹面滚子轴承为研究对象,与静力学分析模型滚子最大接触载荷计算结果对比,验证了模型的正确性.并分析了工况条件(轴向载荷、径向载荷、倾覆力矩、转速)和结构参数(滚子数量、滚子长度、径向游隙)对滚子最大接触载荷的...     

三排滚子转盘轴承的校核计算方法

针对现有转盘轴承在工程应用中所出现的滚道塑性变形、滚道疲劳剥落和套圈结构断裂这三种失效形式,利用转盘轴承的数值分析模型和有限元分析模型建立了联合载荷作用下三排滚子转盘轴承的校核计算方法。数值分析模型借助于变形协调条件和受力平衡条件解决了滚动体负荷分布的静不定求解问题;有限元分析模型将滚子简化为弹簧单元,而套圈仍然采用实体单元,避免了实体滚子与滚道接触的大量非线性数值求解计算。利用所建立的校核方法计算得出了滚道的抗塑性变形安全系数、滚道的疲劳寿命和套圈的结构强度安全系数,为判定该轴承满足给定应用工况要求的程度提供了依据。     

Stability analysis of a rotor bearing system due to surface waviness and number of balls

In the paper, the stability analysis of a rigid rotor supported by ball bearings has been studied. In the analytical formulation, the contacts between balls and races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark-β with Newton–Raphson method is used to solve the nonlinear differential equations iteratively. The effects of surface waviness and the varying number of balls on stability of rotor bearing system are observed. All results presented in form of fast fourier transformations show that the vibration characteristics of the rotor and its bearings change, when the bearings operate in different regions of their nonlinear load deflection characteristics. From the analysis, it is implied that the number of balls and number of waves in the ball bearing are two important governing parameters affecting its dynamic behavior.     

配对角接触球轴承静态力学特性

根据角接触球轴承实际的工作状态,建立背靠背配对安装形式的角接触球轴承接触模型,计算配对轴承在径向、轴向和力矩载荷联合作用下的载荷分布以及接触应力,并将理论值与Ansys有限元法得出的结果进行对比,验证计算结果的准确性。详细研究了在联合载荷的作用下,配对轴承静态载荷分布以及接触特性的变化规律。研究结果表明:配对角接触球轴承的内圈在联合载荷作用下发生位移,使载荷分布不均匀,接触应力主要集中在载荷对称线附近的部分钢球上,改变联合载荷会使两列轴承载荷分布规律以及接触特性发生变化。     

风力发电机滚动轴承多体接触有限元分析

以风力发电机圆柱滚子轴承为对象,利用有限元法对其静力学和动态特性进行分析研究,建立了滚动轴承多体接触几何及有限元力学模型,分析了不同载荷、不同滚子数目及空心度的变化对应力和变形的影响规律,最后,进行了滚动轴承的有限元模态分析。相关方法和结论为风力发电机滚动轴承的设计制造及相关接触问题的进一步研究提供了科学依据和基础数据。