重载工况下齿面粗糙纹理对弹流润滑影响的分析

通过测量获得了不同纹理方向的齿面粗糙度数值,利用傅里叶非线性变换原理,回归出近似真实分布的齿面粗糙度曲线方程。基于此模型,改变润滑油黏度,进行了57组数值计算,得出平均油膜厚度以及轮齿接触区次表面主剪应力的数值解。结果表明:随着粘度的变化,纵向粗糙纹理的平均膜厚小于光滑接触时的平均膜厚;横向粗糙纹理的平均膜厚大于光滑接触时的膜厚值。此外,次表面主剪应力最大值都大于光滑接触时的相应数值。所以横向纹理的润滑效果比纵向纹理的更佳。     

基于真实粗糙齿面的齿轮传动接触应力分析

现行齿轮传动接触疲劳强度的设计基础是仅适用于一对光滑表面之间干接触的赫兹理论,这显然与齿轮传动实际状况有一定差异。为获得齿轮传动实际状况的齿面压力分布、油膜厚度及轮齿接触区次表面的应力分布,基于实测所得的表面粗糙度数据,采用有限元法对重载齿轮传动进行混合弹流润滑数值分析。结果表明:粗糙齿面接触时的齿面压力分布及轮齿接触区次表面应力分布均明显相异于赫兹分布或基于光滑齿面全膜弹流润滑计算所得的相应分布;齿面粗糙峰谷的存在会使齿面接触应力比赫兹接触应力增大25%左右,且齿面平均油膜厚度的最小值及接触应力的最大值均发生在啮入点而非节点。因此,现行的以赫兹应力为基础、以节点参数为依据进行齿轮传动接触强度设计的做法有失科学性和安全性。     

横向纹理粗糙度对滚动轴承润滑特性的影响

首先通过实测获得了一系列具有横向纹理的表面粗糙度数据;其次,借助傅里叶非线性变换拟合出粗糙度函数,并将其叠加到油膜厚度方程中形成了滚动轴承混合热弹流润滑模型;基于此模型,在固定滚动轴承参数不变的前提下,通过改变接触表面粗糙度之值共进行了45组数值计算;然后,通过对计算结果的回归分析,分别建立了内圈与滚动体接触点处的平均油膜厚度及次表面主剪应力最大值与粗糙度之间的定量关系。     

谐波齿轮传动考虑表面粗糙度效应时的润滑计算

在计及了表面粗糙度影响后,用基于平均流动模型的平均雷诺方程进一步研究谐波齿轮传动齿面的润滑状态,计算剪切膜和挤压膜的教值解,给出齿面最小油膜厚度曲线。结果表明,齿面表面粗糙度增大,由它所引起的动压效应增强,齿面上的润滑油易存留,能够建立起足够的油膜厚度。     

粗糙齿面的弹流润滑数值分析

建立了渐开线直齿圆柱齿轮传动的混合润滑模型,利用傅立叶逼非线性近方法,基于实测出的粗糙齿面数值回归出齿面粗糙度方程。通过实测得不同的粗糙度值,采用多重网格法、多重网格积分法及逐列扫描法进行齿面压力、膜厚及温度的数值计算,从而得到相应的数值解。结果表明:与全膜润滑相比,混合润合状态下的齿面压力和油膜厚度分布呈现剧烈波动;随着齿面粗糙度增大,应力集中越明显;平均油膜厚度同时减小;混合润滑状态下的平均油膜厚度与全膜润滑下的平均油膜厚度之比随着膜厚比的增大,逐渐趋近1。     

粗糙表面形貌对滚动轴承油膜刚度的影响

针对滚动轴承表面为粗糙平面且影响轴承油膜刚度的问题,基于弹流润滑理论,引入表征粗糙表面形貌特性的表面粗糙度理论,建立了滚动轴承粗糙表面弹流润滑油膜刚度模型,并进行数值模拟,分析了滚动轴承的表面粗糙形貌对油膜刚度的影响,得到其变化规律。结果表明:随着粗糙度的幅值、波长的改变,油膜膜厚变化不大,但是压力变化十分明显;油膜刚度随粗糙度幅值和波长的变化呈非线性变化,油膜刚度的最大值出现在接触区中心附近,随着粗糙度幅值的增大主峰与第二峰逐渐融合;油膜刚度的变化频率和变化幅度随波长的增大而减小。     

乏油工况下斜齿轮热弹流润滑特性研究*

建立斜齿轮的乏油热弹流润滑模型,并讨论供油量、转速和齿面粗糙度对润滑性能的影响。结果表明:乏油工况下增大入口区供油量,润滑区的膜厚增大而摩擦因数、温升和次表面应力幅值降低;随着供油量增大,乏油润滑特性逐步趋于全膜润滑状态下特性;随着转速升高,润滑膜厚增大但幅度有限,相应温度场增大和次表面应力场增大;齿面粗糙度会使油膜压力出现剧烈的波动,在油膜压力峰位置的次表面会出现应力集中。     

三叉杆滑移式万向联轴器油膜刚度的分析

基于等温线接触弹流润滑理论,在考虑表面粗糙度的同时,建立三叉杆滑移式万向联轴器的油膜刚度计算模型,分析载荷、润滑油卷吸速度及黏度、表面粗糙度波长及幅值对润滑油膜刚度的影响。结果表明：润滑油膜刚度随着载荷及黏度的增大而增大,随着卷吸速度的增大而减小;相比较于载荷和卷吸速度,黏度对油膜刚度的影响相对较小。在远离接触区中心位置,油膜刚度变换幅度较小,在中心位置附近变换幅度最大。随着表面粗糙度波长与幅值的增大,油膜刚度呈非线性变化,且油膜刚度的振荡频率及幅度变小,油膜刚度的最大峰值靠近接触区中心。     

谐波齿轮传动考虑表面粗糙度效应时的润滑计算

在计及了表面粗糙度影响后,用基于平均流动模型的平均雷诺方程进一步研究谐波齿轮传动齿面的润滑状态,计算剪切膜和挤压膜的数值解,给出齿面最小油膜厚度曲线.结果表明,齿面表面粗糙度增大,由它所引起的动压效应增强,齿面上的润滑油易存留,能够建立起足够的油膜厚度.     

修形对直齿锥齿轮弹性流体动力润滑的影响

为解决直齿圆锥齿轮的端啮问题,通过对直齿圆锥齿轮进行齿廓修形,提高小端的油膜承载能力,使得载荷沿齿宽方向分布均匀。齿廓修形先采用二次抛物曲线,再改变主动轮和从动轮的齿顶修缘高度,确定修形参数后,建立直齿圆锥齿轮无限长线接触弹性流体动力润滑模型,压力和膜厚采用多重网格法求解,弹性变形采用多重网格积分法求解。齿顶修缘后啮入点的油膜压力比原来小,油膜厚度变大;二次抛物曲线修形后,啮入瞬时点和啮出瞬时点的油膜压力在赫兹接触区明显降低,赫兹接触区的油膜厚度明显增大,沿啮合线分布的最大油膜压力降低,最小油膜厚度增大,中心油膜压力降低,中心油膜厚度增大;修形参数的变化影响修形后的油膜压力和油膜厚度;修形改变了齿宽方向的载荷分布,直齿圆锥齿轮的小端和大端的载荷差距减少,齿面载荷由端部向齿宽中部转移。研究结果说明,齿廓修形可以改善齿轮的润滑状况,提高啮合过程的油膜压力,减少齿面的摩擦和磨损,同时也可以避免齿面胶合的产生。     

考虑表面粗糙度的面齿轮齿面接触应力分析

根据齿轮啮合原理,得出了面齿轮的齿面方程,求得面齿轮齿面曲率。结合赫兹接触理论,推导了点接触面齿轮传动接触点的接触应力及应力沿齿面的分布规律,从齿根到齿顶,齿面接触应力先增大后减小,在靠近齿面中点处达到最大值。由粗糙表面接触理论,分析了面齿轮齿面微观弹塑性变形时的接触面积,并得到粗糙齿面接触时面齿轮齿面接触应力及其分布。对比分析了几种不同粗糙度条件下面齿轮齿面接触应力的变化规律,结果表明:齿面接触应力随表面粗糙度的增大而增大,与齿根处相比,齿顶接触应力受表面粗糙度影响更大。文中的分析可为面齿轮磨损及润滑机理的研究提供依据。     

Deterministic mixed lubrication modelling using roughness measurements in gear applications

The presence of surface roughness on the teeth of hardened and ground power transmission gears is an unavoidable consequence of their manufacture. The paper discusses the effect of surface roughness when the elastohydrodynamic lubricant film thickness developed between the gear tooth surfaces is small compared to the heights of the roughness features. The ratio of these quantities, called the Λ value, may be well below unity in typical applications. For such thin film conditions the moving roughness features cause the elastohydrodynamic contact between the gears to be highly transient in nature. Surface roughness features on the working surfaces of the gears move past each other during meshing and these asperity encounters are associated with extreme pressure perturbations, or with film breakdown and isolated asperity boundary lubrication events. The paper reviews approaches used to study this problem and describes a coupled approach to solving the elastic and hydrodynamic equations. This allows numerical solutions to be obtained for these extreme conditions so that transient contact events associated with mixed lubrication can be predicted in a unified numerical solution scheme. Typical results obtained from such an analysis are presented including surface fatigue modelling and contact strain energy calculations.     

基于差齿面拓扑的轮齿承载拟赫兹接触分析

基于齿条曲面多项式与齿轮公切共轭产形原理,建立了数值齿面、差齿面ease-off模型;通过ease-off曲面映射,解析了齿面接触路径、传动误差、接触线等轮齿啮合特性信息。利用势能法、变形协调方程与拟赫兹接触分析解决了齿面载荷计算、边缘接触应力求解问题,获得了轮齿啮合刚度、传动误差、齿间载荷分担、载荷分布、接触应力等齿面啮合的时变历程特性。计算结果与第三方软件的计算结果具有较好的一致性。     

Enhancement of a simplified model for maximum stress prediction

A simplified model for rapid estimation of maximum subsurface stress was previously reported by the authors. That model was found to predict the upper bound of the maximum von Mises stress in each layer below any surface with good accuracy. In this work, the model is enhanced by quantifying the difference between the predicted upper bound and the maximum stress for a specific rough surface. This is done by evaluating stress predictions for real rough surfaces, sinusoidal surfaces, ideal textured surfaces, and real rough surfaces with imposed computer generated texture. The difference between the predicted upper bound and the surface-specific maximum stress is found to be related to that surface’s roughness. The origin of this relationship is investigated in terms of apparent contact area. The enhanced simplified model provides an efficient means of estimating maximum stress in rough surface contact.     

Implementation of Hertz theory and validation of a finite element model for stress analysis of gear drives with localized bearing contact

An analytical approach for stress analysis of gear drives with localized bearing contact based on the Hertz theory is proposed. The proposed approach provides a complete and effective solution of the contact problem but satisfaction of the hypotheses for application of the Hertz theory is its main drawback. On the other hand, a finite element model has been developed and validated in terms of the contact area, maximum contact pressure, pressure distribution, maximum Tresca stress, and Tresca stress distribution underneath the contacting surfaces. Validation of the finite element model is provided for those cases wherein the Hertz theory can be applied. The obtained results confirm the applicability of the proposed approach for gear drives with localized bearing contact wherein edge contact is avoided by surface modifications and whole crowning of tooth surfaces is provided.     

Stress history in rolling–sliding contact of rough surfaces

An investigation into the non-Hertzian, elastic stress history, due to the contact of two rough surfaces is presented. A complex evolution of stress is produced whose magnitude and rate depend strongly upon the roughnesses and speeds of the contacting bodies. The key features of the stress fields are illustrated by plots of stress versus time and horizontal distance, for a range of depths and for various contact conditions. The stresses near the surface are many times higher than in an equivalent smooth contact and the roughness on thecounterface generates a moving stress field which, when sliding is present, greatly increases the number of cycles of stress during each passage of the contact. This may account, in part, for the observation that the rolling fatigue life of hard steels declines more rapidly with sliding speed for rough, than for smooth surfaces and suggests that counterface roughness is especially important in determining the fatigue life.     

Stress drop and contact stiffness measured from stick-slip experiments on PMMA-PMMA friction

We present results from an extensive stick-slip study on PMMA-PMMA dry friction, where we studied the influence of a wide range of normal stresses, loading velocities and roughnesses of the sliding surfaces. In this paper we focus (a) on the analysis of a residual coefficient of friction, i.e., shear stress measured at the end of the slip phase divided by the corresponding normal stress, and (b) on the contact stiffness measured by plotting the relative displacement between sample against the shear stress during the stick phase. It is shown that the residual coefficient of friction (i) decreases as normal stress increases, (ii) shows a slight increase when the roughness of the sliding surfaces increases and (iii) does not vary according to the loading velocity. The contact stiffness proved independent of loading conditions and of the roughness of the sliding surfaces. These results are interpreted in terms of asperity interlocking. This revised version was published online in July 2006 with corrections to the Cover Date.     

关于面齿轮接触和弯曲应力有限元计算方法的研究

根据面齿轮加工基本坐标系和齿轮啮合原理,由刀具齿面方程和坐标转换矩阵建立了面齿轮齿面方程,通过编程计算出面齿轮齿面点,实现了面齿轮三维可视化建模。采用三维有限元分析方法,研究了5种不同载荷条件下面齿轮传动的接触应力、弯曲应力和重合度的变化规律。计算结果表明,随着载荷的增大,面齿轮齿面接触区和重合度增大;在单齿啮合时,面齿轮接触和弯曲应力最大,弯曲应力最大值出现在沿齿高方向靠近中间的位置。本文对面齿轮传动的强度设计具有一定的指导意义。     

Prediction of subsurface stress in elastic perfectly plastic rough components

Understanding and anticipating the effects of surface roughness on subsurface stress in the design phase can help ensure that performance and life requirements are satisfied. One approach used to address this problem is to simulate contact between digitized real, machined surfaces, and then analyze the predicted subsurface stress field. Often, elastic-perfectly plastic contact models are used in these simulations because of their relative computational efficiency. Reported here is an analysis of the magnitude and location of maximum stress predicted using an elastic-perfectly plastic model. Trends are identified which then enable estimation of the upper bound of the simulation results based on surface discretization, operating conditions, and material properties. These estimations can be used as an effective and efficient tool for rapid prediction of maximum subsurface stress in real surface contact.     

含安装误差的鼓形齿轮承载接触分析

基于齿轮范成原理，建立修形后直齿的鼓形面数学模型，并根据齿轮接触分析（Tooth contact analysis，TCA）结果进行齿面接触线上接触点的离散。基于Weber能量法，求解齿间载荷分布，并利用线性规划法，求解齿向载荷分布。在得出齿面的实际载荷分布后，建立鼓形齿面的圆柱体模型。利用赫兹原理，对含安装误差的鼓形齿面进行齿面接触应力分布求解。分析结果发现垂直平面误差较轴平面误差对接触应力分布影响更大，起鼓修形后齿面载荷分布虽然得到明显改善，但接触应力值会有所增大。接触应力分布结果与有限元方法结果规律相一致，证明了该方法的合理性，为齿轮承载接触分析（Loaded tooth contact analysis，LTCA）提供了新的简便方法。