应用Winkler弹性基础模型的间隙铰接副磨损预测

间隙铰接副磨损与机构动力学之间存在交互耦合作用.通过Winkler弹性基础模型既可表达铰接副共形接触反力用于构建多体力学方程,又可得到界面接触压力分布用于磨损计算,从而可获得较Hertz理论对共形接触问题更好的计算准确度,且避免有限元方法计算接触压力分布导致的计算耗时性.以曲柄滑块机构为例的分析和实验结果表明:虽然有限元方法可得到更高的磨损预测精度,但Winkler模型对微间隙铰接副磨损预测具有可接受的精度和更好的计算效率,从而可为含间隙铰接副机械系统摩擦学设计提供简便的算法.     

几何修形对低速圆柱滚子轴承混合润滑性能的影响研究

针对圆柱滚子轴承直母线滚子在接触出现的边缘应力集中现象，采用对滚子进行几何修形的方法，运用拟动力学分析方法开展轴承滚子受力和相对运动关系分析. 在此基础上，综合考虑轴承接触工况、滚子修形参数和真实表面粗糙度等因素，建立圆柱滚子轴承混合润滑数学模型，分析滚子修形参数和转速对轴承润滑性能的影响. 结果表明:从润滑角度判断，滚子母线凸度量δ和滚子端头圆角半径r均存在一个优化区间，使得最大受载滚子接触表面最大油膜压力和次表层最大von Mises应力σ显著减小，边缘效应弱化；δ和r对中心膜厚h_c和摩擦系数f的影响较小；转速的增大会使h_c变厚，f_c和σ减小，且混合润滑状态下转速对修形滚子的σ变化显著，修形后的滚子较未修形的滚子润滑性能要好.      

齿向修形对滤波减速器润滑性能的影响分析

综合考虑了滤波减速器齿向修形参数、真实齿面粗糙度和瞬态效应等因素,建立了轮齿混合润滑数学模型,数值计算了不同修形参数值对应不同啮合点的最大压力和中心膜厚,分析了齿面粗糙度和转速对润滑性能的影响.结果表明:修形参数r和Ry均存在一个优化范围,使得轮齿表面最大油膜压力显著降低,边缘效应弱化,而中心膜厚则随着r和Ry的增大而逐渐增大;未修形轮齿边缘油膜压力受粗糙度的影响而急剧增大,边缘效应更加显著,修形后轮齿的边缘效应得到了明显改善,因此,轮齿修形也因粗糙表面的存在而显得更加重要;随着转速逐渐降低,轮齿表面的平均油膜厚度逐渐变小,接触比逐渐增大,轮齿表面由弹流润滑逐渐转为混合润滑,最后演变为边界润滑.     

采用二次等参体元时的接触判据

当二次等参体元用于分析接触问题时,接触面上节点集中接触力不同号给建立接触判据造成困难。本文建立了由节点集中接触力计算接触面上分布接触力节点值的方法,从而可顺利建立接触判据。此方法已成功应用于工程中的弹性固体接触问题分析,文末给出了一个计算实例。     

一种求解弹性接触问题的缩减二次规划方法

基于势能原理以节点位移为设计变量、以接触条件为约束方程构建了无摩擦弹性接触问题的二次规划数学模型,在此基础之上利用力平衡线性约束方程的特解和由基础解向量构成的奇异模态矩阵,提出一种新的基于奇异坐标变换的自由度缩减方法,大大降低了二次规划的规模,并使得二次规划模型不再含显性等式约束;根据弹性接触力学体系的特点,通过人为假定接触自由度位移模式,提出了一种简单高效的奇异模态矩阵的计算方法.通过两圆柱接触、轴孔间隙配合接触两个数值算例的对比分析,验证了对于弹性接触问题的求解,缩减二次规划方法有效克服了传统方法计算量大、对求解参数设置敏感、收敛困难的问题.     

A REDUCED QUADRATIC PROGRAMMING METHOD FOR ELASTIC CONTACT PROBLEMS

基于势能原理以节点位移为设计变量、以接触条件为约束方程构建了无摩擦弹性接触问题的二次规划数学模型,在此基础之上利用力平衡线性约束方程的特解和由基础解向量构成的奇异模态矩阵,提出一种新的基于奇异坐标变换的自由度缩减方法,大大降低了二次规划的规模,并使得二次规划模型不再含显性等式约束;根据弹性接触力学体系的特点,通过人为假定接触自由度位移模式,提出了一种简单高效的奇异模态矩阵的计算方法。通过两圆柱接触、轴孔间隙配合接触两个数值算例的对比分析,验证了对于弹性接触问题的求解,缩减二次规划方法有效克服了传统方法计算量大、对求解参数设置敏感、收敛困难的问题。     

三维轮轨法向接触力学行为弹塑性理论分析

基于Hertz接触理论和双线性强化模型,建立了轮轨法向接触弹塑性理论分析模型,分析了轮轨法向接触力学响应特征,讨论了轴重对接触压力和接触变形的影响规律。同时,基于三维轮轨接触有限元模型模拟了轮轨接触力学行为,并引入理论误差系数分析了弹性模型和双线性强化模型对轮轨接触力学响应预测结果的差异性。结果表明,轮轨最大接触压力和接触变形量均随轴重的增大而增大;双线性强化模型的理论误差系数较小,采用双线性强化分析模型能较准确地预测轮轨接触弹塑性力学行为。研究结果可为轮轨系统安全服役和损伤评估提供理论和技术支持。     

多体无摩擦弹性接触问题的罚有限元法

一、引言弹性接触问题属于局部非线性问题,这是由于系统的接触状态不能事先确定而引起的。一般用有限元法进行求解时,首先要假定接触区域,然后根据接触定解条件来建立系统的刚度方程,由此可解出各节点的位移分量并计算出各接触节点的法向力     

跨声速和低超声速翼身组合体翼根修形的原理与方法

本文在前文[5]的基础上,论述了翼身组合体考虑到面积律要求和压力场要求时翼根区综合修形的原理与方法.特别指出,合理的下单翼安排将会相应地减少降低组合体零升波阻所需的机身修形量,从而在结构布局上更易于实现机身修形.     

高速列车车轮踏面磨耗预测方法的研究

高速铁路的发展满足日益增长的运输需求,同时带来了轮轨型面磨损问题.通过磨耗预测模型对车轮踏面磨耗量进行预测,及时对磨损的车轮踏面进行镟修,对于列车安全运行具有重要意义.通过建立轮对-钢轨三维有限元模型进行接触计算,提出一种基于有限元算法的摩擦功计算方法,即接触节点的摩擦功等于接触摩擦力与节点相对位移的乘积,实现车轮踏面磨耗预测.通过接触计算,发现接触斑中心处的接触摩擦力较大,相对位移量较小,摩擦功较小;将接触斑摩擦功叠加得到车轮踏面摩擦功,数值曲线呈中部大边缘小,且随牵引力的增大而增大;通过动力学计算,发现列车在直线钢轨运行初期的车轮横移量近似呈正态分布;对列车在直线钢轨上运行不同里程的车轮踏面进行磨耗预测,发现预测型面与实测型面具有相同的磨耗趋势,即车轮名义滚动圆处磨耗最严重,且磨耗宽度随列车运行里程增加而逐渐增大;应用有限元法计算磨耗功并预测车轮踏面磨耗,具有一定的研究意义和实用价值.     

Study on teeth profile modification of cycloid reducer based on non-Hertz elastic contact analysis

To solve the problem of contact failure for heavy-duty cycloid reducers, the teeth mesh was originally studied as a Non-Hertz elastic contact problem. An analysis method called non-Hertz flexibility matrix method (NHFMM) for the teeth contact was developed for the teeth profile modification of pin gear. The NHFMM analysis shows that the edge concentrated pressure calculated by non-Hertz method is 2.11 times of that by Hertz method on the pin teeth without profile modification. In the end, the analysis results of NHFMM were verified by a specially designed photo-elastic experiment.     

Axisymmetric smooth contact for an elastic isotropic infinite hollow cylinder compressed by an outer rigid ring with circular profile

A contact problem for an infinitely long hollow cylinder is considered. The cylinder is compressed by an outer rigid ring with a circular profile. The material of the cylinder is linearly elastic and isotropic. The extent of the contact region and the pressure distribution are sought. Governing equations of the elasticity theory for the axisymmetric problem in cylindrical coordinates are solved by Fourier transforms and general expressions for the displacements are obtained. Using the boundary conditions, the formulation is reduced to a singular integral equation. This equation is solved by using the Gaussian quadrature. Then the pressure distribution on the contact region is determined. Numerical results for the contact pressure and the distance characterizing the contact area are given in graphical form. The English text was polished by Yunming Chen     

Two-dimensional Hertzian contact problem with surface tension

In the present paper, we consider a two-dimensional contact problem of a rigid cylinder indenting on an elastic half space with surface tension. Based on the solution of a point force acting on a substrate with surface tension, we derive the singular integral equation of this problem. By using the Guass–Chebyshev quadrature formula, the integral equation is solved numerically to illuminate the influence of surface tension on the contact response. It is found that when the contact width is comparable with the ratio of surface tension to elastic modulus, surface tension significantly alters the pressure distribution in the contact region and the contact width. Compared to that of the classical Hertzian contact, the existence of surface tension decreases the displacements on the half plane and yields a continuous slope of normal stress and displacements across the contact fringe. In addition, it predicts the increase of hardness as the radius of indent cylinder decreasing. The obtained results are useful for the measurement of mechanical properties of materials based on the indentation technique.     

Contact stress analysis of an elastic half-plane containing multiple inclusions

This paper presents a two-dimensional contact stress analysis to investigate the effects of multiple inclusions on the contact pressure and subsurface stresses in an elastic half-plane. The boundary element method is used to analyze the contact problem where a set of integral equations is derived on the contact region and the matrix–inclusion interfaces. As the contact region is unknown a priori, an iterative procedure is implemented to determine the actual contact region and the contact pressure, and the tractions and displacements on the matrix–inclusion interfaces are obtained by solving the integral equations numerically. Numerical results show that the inclusions near contact surface could cause significant alterations in the contact pressure distribution. The stiff inclusions could toughen the surrounding material and reduce the internal stresses while the soft inclusions could increase the subsurface stresses.     

New analytical and numerical results for two-dimensional contact profiles

Recently, a generalized Coulomb law for elastic bodies in contact has been developed by the author, which assumes that the tangential traction is the difference of the slip stress of the contact and the stick area, whereby each stick area corresponds to a smaller contact area. It holds for multiple contact regions also. Several applications for elastic half planes, half spaces, thin and thick layers and impact problems have been published. For plane contact of equal bodies with friction, it provides exact solutions, and the interior stress field can be expressed with analytical results in closed form. In this article, a singular superposition of flat punch solutions is outlined, in which the punches are aligned with an edge of the contact area. It is shown that this superposition satisfies Coulomb's inequalities directly, and new results for the Muskhelishvili potentials of several profiles are presented. It is illustrated how problems of singularity and multi-valuedness of complex functions can be solved in closed form, and the Chebyshev approximation used by earlier authors can be avoided. For comparison, some previous solutions for symmetric profiles are appended. Some results for the interior stress field, the pressure, the frictional traction and the surface displacements are compared with FEM solutions of an equivalent problem. The small differences between both methods show characteristic features of the FEM model and the theoretical assumptions, and are shortly explained. Further, this example can be used as benchmark test for FEM and BEM programs.     

Thermoelastic Contact of a Shroud Ring and a Cylinder under Unsteady Friction-Induced Heat Release

Mathematical formulation is performed and a solution is found for a quasi-static thermoelastic problem of contact interaction of an elastic shroud ring and a hollow circular cylinder inserted into this ring, which are compressed by a load varied along the axis of the system, under the condition of an unloaded contact over the ring surface or over the circumference contour. The radial displacements of the contact surface of the shroud ring are approximated by displacements of the surface of a long circular hollow cylinder. Unsteady friction-induced heat release caused by the action of friction forces owing to shroud ring rotation over the cylinder with a time-dependent low angular velocity is taken into account. The problem is reduced to a system of integral equations whose structure is determined by the form of thermophysical contact conditions. A numerical algorithm of the solution is proposed, and the influence of the problem parameters on the contact pressure and temperature distributions is considered. Based on an analysis of results, a conclusion is made that the character of axial variation of the compressing load has a significant effect on the distribution of contact pressure in describing the kinematic condition of interaction of bodies in accordance with Hertz’s theory.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 161–178, July– August, 2005.     

对数凸型滚针凸度量设计的新方法

本文利用三维有限长弹性接触问题的数值解法分析了实体套圈滚针轴承中的越程槽结构因素对对数凸型滚针接触压力分布的影响。结果表明,套圈上的越程槽宽度是确定滚针最佳凸度量时应考虑的一个重要因素。据此给出了对数凸型滚针凸度量设计的新方法。该方法可用于各种结构形式滚针轴承的滚针凸度量设计。     

Agricultural tire deformation in the 2D case by finite element methods

The mechanical characteristics of the rubber tire and the interaction between a tire and a rigid surface were investigated by a two-dimensional (2D) finite element (FE) model. The FE model consists of a rigid rim and a rigid contact surface which interact with the elastic tire. Four distinct sets of elastic parameters are used to represent beads, sidewall, tread and lugs. Several sets of tire loads and inflation pressures were applied to the FE model as boundary conditions, together with various displacements and friction conditions. The deformation of the tire profile, the tire displacements in the vertical and lateral directions, the normal contact pressures, the frictional forces and the stress distribution of the tire components were investigated by the 2D FE model under the above boundary conditions. The calculated tire deflections were compared with the measured data. The results show a good fit between calculated and measured data, especially at high load and inflation pressure. The comparison shows that the FE analysis is suitable to predict aspects of the tire performance like its deflection and interactions with the contact surface. Compared with the experimental methods, the FE methods show many advantages in the prediction of tire deformation, contact pressure and stress distribution.     

任意轴对称弹性体吸附接触的广义Maugis模型

通过线性叠加Sneddon方法和Lowengrub-Sneddon方法分别给出的解, 得到了一个弹性半空间 轴对称混合边值问题的一般解，进而研究了两个一般轴对称弹性体的正向无摩擦吸附接触问 题. 考虑任意有效的表面形状(要求中心部分首先进入接触)和任意的表面吸附作用，推广 得到了广义Maugis模型. 该模型是一个半解析的模型，它可以分解成表面形状和表面吸附 作用的分别独立影响的两部分，以及一个关联变形和吸附作用的式子. 利用Dugdale模型近 似表面吸附作用，得到了具有任意有效的表面形状的广义M-D模型. 它在强吸附或软材料条 件下的极限形式是广义JKR模型，而在弱吸附或硬材料下的另一个极限形式是广义DMT模型.     

Computing bounds to mixed-mode stress intensity factors in elasticity

A bounding procedure combined with an effective error bound method for linear functionals of the displacements and a simple two points displacement extrapolation method is presented to compute the lower and upper bounds to the stress intensity factors in elastic fracture problems. First, the displacements of two nodes (or node pairs) on the crack edges are used to construct the linear extrapolation to obtain the stress intensity factors at the crack tip, so that stress intensity factors are explicitly expressed as linear functionals of the displacements. Then, a posteriori bounding method is utilized to compute the bounds to the stress intensity factors. Finally, the bounding procedure is verified by a mixed-mode homogenous elastic fracture problem and a bimaterial interface crack problem.