具有微织构形貌的结合面法向接触刚度分形模型的研究

研究微织构结合面上的表面形貌参数对结合面法向接触刚度的影响。根据微织构表面的形貌特征,将微织构表面分为织构前表面和织构区域两部分,由分形接触理论计算出织构前表面上微凸体的基本参数,忽略织构区域底部未接触部分,将微凸体在接触载荷作用下的变形分为三个阶段:弹性阶段、弹塑性阶段、塑性阶段。由接触力学理论,首先建立织构前表面上单个微凸体的法向接触刚度模型。然后由微观到宏观,结合微织构表面的织构形貌特征,构造整个宏观微织构结合面的法向接触刚度计算模型,研究不同的表面形貌参数对于微织构界面上法向接触载荷、微凸体因载荷产生的变形以及法向接触刚度的影响。经过仿真分析之后,结果表明,当微织构结合面的法向接触载荷不断增大时,结合面的法向接触刚度总体呈单调上升趋势;并且随着织构密度的增加,结合面上由于织构形貌的存在,使得一部分微凸体未产生变形,从而减小结合面的法向接触刚度,并且当法向载荷增加时,这种效果会更加明显;在相同的接触载荷下,塑性指数越高,处于塑性变形状态的微凸体就越多,从而使具有微织构形貌的结合面的法向接触刚度变大。     

结合面法向接触刚度分形预估模型及其仿真研究

从微观角度出发,基于结合面的"固-隙-固"接触模型、摩擦学理论和分形接触理论建立了考虑域扩展因子影响的结合面法向接触刚度的分形预估模型,在一定程度上完善了结合面动力学参数的分型模型.通过仿真分析揭示了法向载荷、分形维数、尺度参数以及单个微凸体接触刚度和材料参数对结合面法向接触刚度的影响。仿真分析表明:结合面法向刚度系数随着法向载荷的增大而增大,增大结合面法向载荷有利于提高结合面的法向接触刚度;在不同分形维数的范围内,法向接触刚度均随着结合面分形维数不同而不同.此外,法向接触刚度随着分形特征长度尺度参数的增大而减小,随着单个微凸体接触刚度的增大而增大;而材料参数的增大,使得法向接触刚度也增大.     

尺度相关的分形结合面法向接触刚度模型

基于分形理论,利用双变量Weierstrass-Mandelbrot函数模拟三维分形结合面,建立尺度相关的三维分形结合面法向接触刚度模型。推导出各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件。确定结合面上各等级微凸体的面积分布密度函数,推导出法向接触刚度和法向接触载荷的解析表达式。计算结果表明：当结合面上的微凸体只能发生弹性变形,即自身等级小于弹性临界等级的微凸体,该部分微凸体引起的法向接触刚度和对应法向载荷关系呈非线性。当微凸体的等级大于弹性临界等级,在结合面接触过程中,微凸体弹性变形引起的法向接触刚度与对应的法向载荷关系为线性,非弹性变形引起的法向接触刚度与法向载荷关系为非线性。微凸体的等级范围对结合面的刚度影响较大,在相同的法向载荷作用下,高等级微凸体的结合面产生较高的法向接触刚度,即结合面越平整,结合面的法向刚度越高。     

弹塑形变的结合面法向刚度分形模型及仿真

为了探索微凸体的更真实的变形状态,同时进一步完善结合面的接触刚度分形模型,对M-B分形模型进行了修正,分析了微凸体在弹性、弹塑性以及塑性各阶段的变形状态.从宏观和微观相结合的角度,建立了基于分形理论和赫兹接触理论的结合面法向刚度分形预估模型,该模型具有几何特性和尺度独立性.通过仿真分析揭示了相关参数对结合面法向接触刚度的影响.仿真结果表明:结合面法向接触刚度随着法向载荷、分形维数以及材料特性参数的增大而增大,分形维数对法向接触刚度的影响尤为明显;而结合面的法向接触刚度随着分形尺度参数的增大而减小.     

考虑微凸体水平距离分布及相互作用的结合面法向接触刚度建模

在涉及微凸体侧接触的粗糙表面接触建模过程中,通常需要假定微凸体之间侧接触的角度分布规律。提出一种考虑微凸体水平距离分布及相互作用的结合面法向接触刚度建模方法,该方法不再需要假定角度分布规律,而是基于首次发现的单个粗糙表面微凸体水平距离正态分布规律,根据统计学理论进行考虑微凸体相互作用的结合面法向接触刚度建模。对模型进行数字仿真发现：结合面法向接触刚度与接触载荷均随着微凸体水平距离标准差的减小而增大,并且考虑微凸体相互作用会使得结合面的法向接触刚度减小。结合面法向接触刚度随弹性模量的增大而减小,随材料硬度的增大而增大。通过有限元仿真结果与模态试验结果对比可知,基于模型的有限元仿真前三阶固有频率与试验所得结果基本吻合,并且误差相对GZQ模型更小。旨在通过研究单个粗糙表面微凸体水平距离分布,突破侧接触建模时接触角度分布函数仍需假设的理论瓶颈,为更加准确地预测结合面接触特性奠定基础。     

具有连续光滑特性的结合面接触刚度模型

结合面接触刚度直接影响着机械系统的静、动态力学性能和精度保持性水平.基于微凸体在弹性、弹塑性以及完全塑性接触变形过程中,接触刚度具有连续、光滑特性的思想,首先提出利用Hermite多项式插值函数,来弥补单一微凸体接触刚度建模时存在的不连续等缺陷,建立了具有连续光滑特性的单一微凸体接触刚度新模型;然后基于统计学方法,建立了结合面的法向接触刚度模型;最后将所建模型与GW、ZMC、KE和BRAKE模型进行对比分析.结果表明:本文模型实现了单一微凸体接触刚度在不同接触状态之间连续且光滑地转变;对于光滑表面形貌,基于GW、ZMC、KE以及BRAKE模型预测的接触刚度与本文模型结果的差异较小,其中本文模型最接近于纯弹性的GW模型;当表面粗糙度增大时,GW模型与其他几种模型的差异逐渐增大,此时本文模型与考虑微凸体多种变形阶段的ZMC模型吻合较好;再次表明载荷与表面粗糙度是影响刚度的两个主要因素,即随着载荷的增大或表面粗糙度的减小,接触刚度递增.     

机械结合面法向接触刚度和阻尼的理论模型

基于统计接触理论和等效粗糙接触表面假设,考虑微凸体在加卸载及动态载荷下的变形特征,建立了结合面法向静、动态接触模型,获得了单位面积法向静、动态接触刚度与接触阻尼(基础特性参数)。基于Kadin和Etsion的粗糙表面弹塑性卸载接触模型,通过引入微凸体卸载过程中残余变形与最大变形量及最大接触载荷之间的函数关系,建立静态加卸载接触模型。针对结合面间简谐动态相对位移,利用泰勒公式对静态接触载荷和接触刚度进行展开,得出了动态接触载荷、接触刚度的增量以及动态接触载荷下的能量损耗,建立了法向动态接触刚度和接触阻尼的计算模型。分析了结合面面压、动态位移幅值及振动频率对动态接触刚度和接触阻尼的影响规律,研究表明:法向动态接触刚度相对静态接触刚度有微小偏移增量,动态接触刚度增量和接触阻尼随法向面压及动态位移幅值的增大而非线性增大,动态接触刚度增量随振动频率增加呈非线性增大,而接触阻尼则随振动频率增加呈非线性减小。通过理论计算与试验结果的对比分析,证明了本文建立的结合面法向静、动态接触刚度及接触阻尼理论模型的正确性。     

机械结合面法向接触刚度分形理论模型

基于分形理论同时考虑微凸体的弹性、第一弹塑性、第二弹塑性、完全塑性四个阶段的变形状态,得出单个微凸体在各变形阶段的接触刚度模型,从而得出影响单个微凸体法向接触刚度的相关参数。引入频率指数并得出各变形阶段频率指数的临界值,推导出频率指数值处于不同区间时结合面的接触刚度模型。模型仿真结果表明,分形维数D取1. 1～1. 9时,随着D值的增大,无量纲法向接触刚度的值单调增大;微凸体频率指数处于各个区间时无量纲法向接触刚度的值随法向实际接触面积的增大均增大。     

基于分形几何与接触力学理论的结合面法向接触刚度计算模型

基于分形几何理论和接触力学理论,用分形理论表征粗糙表面微凸体参数,考虑微凸体由弹性变形向弹塑性变形以至最终向完全塑性变形转化的过程,建立各变形阶段微凸体的接触刚度模型。在此基础上,提出机械结合面法向接触刚度计算模型,该模型揭示了在不同的塑性指数下,结合面法向接触载荷与法向接触刚度之间的关系。结果表明,在塑性指数较小时,微凸体的变形以弹性为主,法向接触载荷与接触刚度之间表现为近似线性关系;随着塑性指数的增加,微凸体变形主要以塑性为主,法向接触载荷与接触刚度之间表现为较强非线性关系。对已有的铣削加工和磨削加工情况下的结合面法向接触刚度试验结果,利用该模型进行数值计算、仿真和分析。结果表明:提出的模型更与试验曲线吻合。     

考虑摩擦和微凸体相互作用的结合面接触刚度和阻尼模型

基于三维分形理论,建立了同时考虑摩擦和微凸体相互作用影响的结合面法向接触刚度和接触阻尼分形模型。通过对所建模型仿真,分析了摩擦因数、分形维数、分形粗糙度参数和接触载荷对接触刚度和接触阻尼的影响。研究结果表明,该模型的接触刚度和接触阻尼随着法向载荷和分形维数的增大而增大,且会随着分形粗糙度参数的增大而变小;接触刚度随着摩擦因数的增大而减小,而接触阻尼则随着摩擦因数的增大而先增大后减小。另外将仅考虑微凸体相互作用和既无摩擦又无微凸体相互作用的情况进行了对比分析,进而得到当分形维数D=2.4时,微凸体相互作用会稍微增大接触刚度;当D≥2.5时,微凸体相互作用会减小接触刚度,且减小的程度越来越大;当2.4≤D≤2.9时,微凸体相互作用会减小接触阻尼。此外,将所建模型的仿真计算结果与实验数据进行对比分析,验证了所建模型的正确性。     

图案化介质磁盘-磁头气体润滑动态特性分析

在小扰动条件下,提出应用偏导数法在复数域内求解可压缩气体润滑的动态Reynolds方程,以计算任意磁盘表面形状的磁盘-磁头气膜润滑的动态刚度和阻尼系数。以圆柱形和立方形比特图案化介质(BPM)磁盘为研究对象,研究了磁单元尺寸参数对气膜动态系数的影响,并比较了两种BPM对应的动态性能。数值结果表明,与光滑磁盘相比,图案化介质磁盘对应的气膜润滑动态刚度系数和阻尼系数大大减小,且随磁单元高度增大,动态系数逐渐减小。相比圆柱形BPM,立方形BPM对应的气膜具有较大动态刚度和阻尼系数,计算结果可为图案化介质磁盘的设计提供重要的理论依据。     

中子应力谱仪样品承重台回转支承载荷分析

针对中子应力谱仪样品承重台(简称“中子谱仪样品台”)旋转运动机构用三排圆柱滚子回转支承的特殊结构和受载情况,基于Hertz理论,实现了力学分析模型的建立和求解,在此基础上通过有限元法分析了中子谱仪样品台极限工况下滚子与滚道之间的接触特性,然后分析了轴向载荷、径向载荷、滚子数量对回转支承刚度的影响。研究结果表明：在中子谱仪样品台极限工况下,上排滚子与滚道的接触区域等效应力最大,为76.98MPa,外圈滚道的最大等效应力为14.82MPa,内圈滚道最大等效应力为11.26MPa;刚度分别随轴向载荷、径向载荷和滚子数目的增大而增大,且均成非线性关系,当轴向载荷增至1200kN、径向载荷增至300kN时,轴向刚度和径向刚度增长趋势明显减慢,当上排与下排滚子数量增至170时,轴向刚度的增大趋势明显加快。研究结果为中子谱仪样品台旋转运动机构的设计提供了参考。     

精密钢球传动减速机构的瞬时接触热特性分析

基于Hertz接触理论,以精密钢球传动减速机构为研究对象,建立了减速机构啮合副齿面接触分析模型。分析了钢球与摆线槽齿面间的瞬时接触域,在此基础之上,分析输入轴转速、负载对减速机构热特性的影响,得到钢球与齿面间接触域的瞬时生热率和瞬时摩擦温升。分析结果表明：钢球与摆线槽齿面的瞬时接触域是时变接触椭圆;输入轴转速和负载对瞬时生热率和瞬时摩擦温升都有明显影响,但转速的影响更大;瞬时摩擦温升在常规转速下随转速单调递增,在超低转速下随转速先递减再递增。研究结果为精密钢球传动的三维热力耦合分析奠定了理论基础。     

Analytical and Numerical Models for Tangential Stiffness of Rough Elastic Contacts

The paper considers elastic contact of rough surfaces and develops a simple analytical expression for the stiffness of the contact under tangential loading, which predicts that the contact stiffness is proportional to normal load and independent of Young??s Modulus. The predictions of this model are compared to a full numerical analysis of a rough elastic contact of finite size. The two approaches are found to be in good agreement at low loads, when the asperity spacing is large, but the numerical approach predicts much lower stiffnesses at medium and high loads. It is shown that the overall stiffness cannot exceed that of the equivalent smooth contact, and a simple means of modifying the analytical approach is proposed and validated.     

角接触球轴承保持架柔性多体动力学分析

考虑套圈、钢球和保持架的结构弹性变形与动态接触关系,建立了角接触球轴承柔性多体接触动力学有限元仿真模型。在不同引导游隙、转速和径向力下,运用ANSYS/LS-DYNA仿真分析了角接触球轴承的动力学性能,以及保持架的动态冲击应力和稳定性。计算讨论了角接触球轴承的动态接触应力,获得了保持架的角速度、动态冲击应力、质心运动轨迹等仿真结果,它们与理论计算结果具有较好的一致性。结果表明,球轴承运动速度的变化对保持架的动态冲击应力和稳定性的影响较大。     

Dynamic analysis and grinding tracks in the magnetic fluid grinding system: Part II. The imperfection and ball interaction effects

To model the effects of the geometrical imperfections on the ball motion and its grinding track, it is therefore necessary to combine a dynamic model of the support system of balls with the previous model. For the geometrical imperfections on the ball, because of the interaction between the contact loads and the ball-spin speed, it causes the friction contact condition to remain at the interfaces with lower contact loads and lower ball-spin speeds in the separation case at the initial stage. Consequently, the variation in the ball-spin angle and the area covered by the grinding tracks is small. However, when the intermittent separation occurs at the geometrical imperfections on the ball orbit, it causes a large oscillation in the ball-spin angle and the ball-spin speed. Consequently, the effect of the imperfections in the ball orbit on the area covered by the grinding tracks is larger than that of the ball geometry. Ball–ball contacts cause a large oscillation in the ball-spin angle resulting in a uniform distribution of the grinding tracks. Hence, the effect of ball–ball contacts is one of the most important mechanisms in achieving a uniform distribution of the grinding tracks.     

Study on dynamic friction characteristics in reciprocating friction drive system

The dynamic friction characteristics of a reciprocating friction drive system are investigated under conditions of dry contact using 0·45% carbon steel pair. Three friction modes are found during the operation, i.e. stick-slip, sticking and a transition region. The critical operating conditions in classifying these three modes are examined under various driver speeds, normal loads and spring constants. The critical values of driver speed and normal load increase with increasing spring constant. Generally, in the friction drive system the disappearance of the stick-slip results in smooth rolling. It is also found that the slope at the first period of slip on the traction force–relative slip velocity curve would have a transition from negative to positive value when the friction mode of stick-slip changes into sticking. Moreover, results show that the sticking mode gives the best positioning accuracy with the least wear on the contact surfaces. In addition, a transition from severe wear to mild wear is found when the friction mode is transferred from stick-slip to sticking only.     

Numerical simulation of wheel rolling over rail at high-speeds

In the paper, a contact element method was used to analyze a wheel rolling over a rail at high-speeds. The rolling contact of the wheel and rail was considered as a two-dimensional rolling contact in a pure rolling and steady state. The loads applied to the wheel are the different axle-loads of train and the inertia forces caused by accelerations of the wheel in its pure rolling state. The convergence of non-linear numerical analysis on frictional contact was reached through repeated contact calculations. The normal contact pressure and tangential traction on wheel/rail contact surface were obtained for the different axle-loads and the different rolling speeds. The highest rolling speed in the numerical simulation is 400 km/h. Through the detailed numerical simulation and analysis, it was found that there exist some differences between the traditional Hertzian contact pressure and the present normal pressure. With the speed increasing the normal contact pressure becomes larger in the leading area of the contact surface, and becomes smaller in the trailing area of the contact surface. However, in the trailing area the tangential traction become larger, and in the leading area becomes smaller with the speed increasing.     

The determination of coefficient of friction between a cylindrical indenter and a plastically deformed body by caustics

The contact between an elastic cylindrical indenter and a plastically deformed bar is examined. For this study it is assumed that the normal and tangential loads in the contact zone are related by a Coulomb-type relation. In order to determine the coefficient, which relates the normal and tangential loads, the method of reflected caustics was used. For the evaluation of this coefficient a single measurement of an appropriate length has to be made on the caustic, which was formed at the contact area of the two materials. This measurement allows the determination of the coefficient and in the case when the normal distribution of the contact load is known, the tangential load distribution can be readily obtained. The method was applied to the case of an uniformly distributed load, applied to an elastically deformed cylindrical indenter, which deforms the indented bar plastically.     

Friction and wear of blended polyoxymethylene sliding against coated steel plates

Measurements were made of the dynamic friction coefficients and specific wear rates of several thermoplastics rubbing against relatively soft coatings on steel plates. Polyoxymethylene (POM)-based composites were investigated using reciprocating, line contact tests against two types of corrosion-protected steel plates (electro-deposited cathodic epoxy layers, called “E-coatings”, and galvanised plates). In addition to virgin POM, composites containing glass fibres, polytetrafluoroethylene (PTFE) fibres, PTFE micro-powder, and high-viscosity silicon oil were investigated. Sliding speeds ranged from 0.05 to 0.3 m/s, and normal loads ranged from 5 to 30 N. The E-coating failed at high loads and velocities. The beneficial effects of lubricating additives in tests with uncoated steel counterfaces were also observed with the coated steel surfaces. POM with glass fibre additives was found to be more abrasive than the base material. The considered non-conformal contact produced similar friction and wear trends than those obtained for the conformal contact.