An Engineering Model for Three-Dimensional Elastic-Plastic Rolling Contact Analyses

Fatigue life of heavily loaded rolling bearings is strongly dependent on elastic-plastic material properties. For bearing steels these elastic-plastic properties can be accurately obtained by performing monotonic or half-compressive tests. A three-dimensional strain deformation analysis based on the incremental theory of plasticity and the use of Prandtl-Reuss relations in conjunction with the von Mises yield criterion was developed in order to evaluate the permanent deformation in dry contacts loaded above the elastic limit in case of normal loading. The Ramberg-Osgood stress-strain relation for two martensitically hardened variants of SAE 52100 bearing steel considered the nonlinear kinematic and/or isotropic material behavior. Parameters describing the influence of retained austenite are modeled by using a nonlinear isotropic law. Pressure distribution and contact surface displacements during incremental loading are evaluated by using a conjugate gradient method and the internal stress field is derived by using the superposition principle. Further, a fast analysis of smooth surfaces in elastic-plastic static and rolling contact is developed based on analytical relations for the internal stress field. Cyclic evaluation of plastic strains and residual stresses is carried out until shakedown. In order to verify the theoretical model, rolling contact tests under high normal load were performed. Residual stresses and residual profiles measurements show excellent agreement between numerical and measured cyclic values.     

Analyzing Elastic-Plastic Real Rough Surface Contact in Running-in

A numerical method is presented for evaluating the elastic-elastic contact of real rough surface contacts during running-in. For the surface contact, an elastic-plastic model based on the variational method is applied to analyze the pressure distribution and contact area of worn surfaces during running-in. In conjunction with the classical statistic model of Greenwood and Williamson, the numerical result showed that the plasticity index Ψ was decreased to one in the elastic range as running-in proceeded. In comparison with the Hertzian solution, the influence of the asperities is very significant on the pressure distribution, thereafter causing a higher peak value of contact pressure. For the subsurface, the interior stress from the von Mises criterion was calculated to evaluate the subsurface stress field subject to both normal and tangential forces. In the calculated of the interior stress, the total stress is decomposed into a fluctuating component and a smooth component. The fluctuating part is solved by using FFT from the concept of the convolution theorem while the smooth part is obtained directly by analytical solution. Calculations of contact area and subsurface stress on experimentally produced surfaces whose topography has been determined using an atomic force microscope and friction coefficient front sliding have been carried out. The results showed that asperities and friction coefficient gave rise to stress increase in the near-surface stress field and produced a high stress zone towards the surface. As a result, transverse asperity cracking was produced. The calculations and supporting experimental evidence clearly confirmed that the reduction of peak pressure during running-in decreased the plastic deformation of contact.     

真实粗糙表面接触模型的研究

真实工程表面并不是完全光滑的。当两物体相互接触时 ,真实表面实际上是微凸体间的接触。分析真实粗糙表面间的接触对研究摩擦、磨损和润滑起着非常关键的作用。合理地描述润滑状态和摩擦热边界条件也取决于对真实接触状态的求解。本文从 3个方面研究了粗糙表面接触计算模型的主要构成 :粗糙表面轮廓的描述、确定接触压力和表面位移之间关系的计算公式以及求解几何非线性接触问题的方法。最后给出了算例     

利用FFT和共轭梯度法求解偏载滚子副的接触应力

根据弹性接触理论,引入弹性趋近量变化函数,将偏载工况下的接触问题转化为一个线性补余问题,同时建立力和力矩平衡方程,利用共轭梯度法求解了接触应力,其中,弹性变形计算部分利用FFT求解。通过分析不同工况参数对接触应力分布的影响:发现随着偏载角或滚子载荷的增大,最大接触应力、偏载效应以及力矩均增大;偏载角增大,偏距呈线性关系增大,滚子载荷增加,偏距呈双曲线分布减小;比较偏载工况下相交圆弧修形滚子、相切圆弧修形滚子以及对数母线滚子的接触应力分布,可知对数母线滚子的抗偏载能力最强。计算结果显示目前该方法具有高效的计算速度和收敛性。     

基于啮合角函数的非圆齿轮重合度求解

从几何学角度,以啮合角函数计算的非圆齿轮齿廓曲线方程与齿顶曲线方程为基础,建立了非圆齿轮重合度与极角的关系,分析了影响重合度的因素.通过研究齿廓曲线的极限啮合位置、根切界限点、齿顶变尖点等问题,引入了极限重合度概念,并提出了一种新的精确控制非圆齿轮重合度的方案.     

Analytical evaluation of stresses and displacements of stuffing-box packing based on a flexibility analysis

Although stuffing boxes are old systems used to ensure stem valve sealing, the analytical developments of the stresses and the displacements generated during assembly and operation are very limited and seldom verified and the studies carried out on these devices are either restricted or not accessible. Moreover, even with the evolution of calculation and simulation means, studies based on numerical models are rare.This work proposes a simplified analytical approach, using the theory of thick-walled cylinders to analyse the stresses and displacements in stuffing box systems. The magnitude and distribution of the lateral contact pressures generated at the housing-packing-stem interfaces as a result of the application of the gland axial stress are determined as a function of the radial flexibility of the different components involved. The results of the developed approach are compared and validated against the more accurate finite elements axisymmetric models.     

Improved Elastic Contact Model Accounting for Asperity and Bulk Substrate Deformation

An improved elastic contact model for a single asperity system is proposed accounting for both the effects of bulk substrate and asperity deformations. The asperity contact stiffness is based on the Hertzian solution for spherical contact, and the bulk substrate stiffness on the solution of Hertzian pressure on a circular region of the elastic half-space. Depending on the magnitude of the applied load, as well as the geometrical and physical properties of the asperity and bulk materials, the bulk substrate could have considerable contribution to the overall contact stiffness. The proposed single asperity model is generalized using two parameters based on physical and geometrical properties, and is also verified using finite element analysis. A parametric study for a practical range of geometric and physical parameters is performed using finite element analysis to determine the range of validity of the proposed model and also to compare it with the Hertz contact model. The single asperity model is extended to rough surfaces in contact and the contact stiffness from the proposed model and the simpler Greenwood–Williamson asperity model are compared to experimental measurements.     

Influence of Mixed-Lubrication and Rough Elastic-Plastic Contact on the Performance of Small Fluid Film Bearings

A previously developed deterministic elastohydrodynamic (EHD) numerical model for small fluid film bearings functioning in the mixed lubrication regime is extended in this work by considering the rough contact. Several simplifying hypotheses are made: the shaft is considered rigid and smooth, turning at low speeds (isothermal regime), and the pad is assumed to have an elastic-perfectly-plastic behavior. The Reynolds equation is solved on a very fine mesh and the elasto-plastic pad deformation caused by the hydrodynamic pressure is taken into account. A deterministic active set-based method is used for determining the contact pressure, the contact extent, and the corresponding deformation. The results are presented for a partial journal bearing configuration, with a linear shaft velocity of 0.47 m/s under specific pressures varying up to 50 MPa. Two pad materials are considered, and the lubricant is either isoviscous or piezoviscous oil. The simulation results, presented as a function of the bearing specific pressure, include eccentricity, the film thickness, the friction torques, the contact extent, etc. Stribeck curves showing the evolution of the friction coefficient in the hydrodynamic and mixed lubrication regimes are also discussed.     

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.     

A Transient Dynamic Analysis of Mechanical Seals Including Asperity Contact and Face Deformation

Face seals are typically designed to be in contact at standstill. However, as speed and pressure build up, the seal faces deform from their factory flat conditions because of viscous and dry friction heating, as well as mechanical and centrifugal effects. It is imperative that such deformations form a converging gap for radial flow to ensure stable operation and to promote favorable dynamic tracking between stator and rotor. A numerical simulation is presented for the transient response of a face seal that is subjected to forcing misalignments while speeds and pressures are ramped up and down. Asperity contact forces and transient face deformation caused by viscous heating are included. A new closed-form solution is obtained for the elastoplastic contact model, which allows seamless transition between contacting and noncontacting modes of operation. The model is then used to calculate face contact forces that occur predominantly during startup and shutdown. The viscous heating model shows that the time-dependent deformation (coning) is hereditary and that it lags behind the instantaneous heat generation. The dynamic analysis provides a numerical solution for the seal motion in axial and angular modes. The eventual build up of hydrostatic pressure and coning during startup generates opening forces and moments that separate the seal faces, resulting in noncontacting operation. The reverse occurs during shutdown; however, because of the thermal time constant a seal may continue to leak even after it returns to standstill. The analysis and simulation results compare very well with a closed-form solution that predicts a critical speed of separation of contacting seals.     

平动齿轮机构连续传动条件的分析方法

平动齿轮机构中,过啮合点的齿廓公法线为动直线,故其啮合点轨迹不再是直线。本文采用求解两齿廓切点的方法探讨了该机构的齿廓啮合过程,在连续求解齿廓方程的基础上,可求出任一时刻同时参加啮合的轮齿对数,从而可判定传动是否连续进行,为平动齿轮机构的设计提供了理论依据。     

一种简化的点接触热弹流模型及其完全数值解

本文提出了一个简化的点接触热弹流计算模型并进行了完全数值求解。与现有的完全数值模型相比，采用本模型进行求解具有计算量小，精度适中的特点，更适合工程计算的要求。文中对多种工况下点接触热弹流的摩擦牵引性能和表面闪温特性进行了数值分析。     

完全接触条件下轴孔过盈配合的解析解

在过盈配合的设计标准中,将空间问题处理成平面应力问题,必然会产生误差.建立弹性力学轴孔过盈配合空间轴对称模型,采用完全接触条件,用级数法推导了满足边界条件和完全接触条件的空间轴对称问题的Papkovich-Neuber解.得到轴孔过盈配合的解析解,所得的解析解可以作为过盈配合设计的标准.所得的解析解中含有贝塞尔函数,可...     

含扩展裂纹板计及厚度效应的载荷—位移曲线解析闭合解

准确预测长寿命结构在其服役期内的剩余强度,是当前结构设计工程师面临的一个重大课题。而裂纹扩展过程中,精确的载荷—位移曲线将为这一问题的突破提供一种非常高效的方法。为此,在考虑厚度效应的断裂韧度与阻力曲线理论基础上,对含穿透裂纹板在裂纹扩展过程中的载—荷位移曲线进行理论与试验研究。用卡氏定理导出含驻止裂纹试件承受载荷作用时,外部载荷与试件中点挠度的关系表达式。引入计及厚度效应的断裂韧度与阻力曲线理论,导出裂纹扩展时试件中点处载—荷位移曲线的解析闭合解。进行准静载单调加载下的裂纹扩展试验。所得数据与由载荷—位移曲线解析闭合解得到的计算结果基本吻合,充分验证该解析闭合解的有效性。     

An Improved Approach for 3D Rolling Contact Fatigue Simulations with Microstructure Topology

Several 2D and 3D numerical models have been developed to investigate rolling contact fatigue (RCF) by employing a continuum damage mechanics approach coupled with an explicit representation of microstructure topology. However, the previous 3D models require significant computational effort compared to 2D models. This work presents a new approach wherein efficient computational strategies are implemented to accelerate the 3D RCF simulation. In order to reduce computational time, only the volume that is critically stressed during a rolling pass is modeled with an explicit representation of microstructure topology. Furthermore, discontinuities in the subsurface stress calculation in the previously developed models for line and circular contact loading are removed. Additionally, by incorporating a new integration algorithm for damage growth, the fatigue damage simulations under line contact are accelerated by a factor of nearly 13. The variation in fatigue lives and progression of simulated fatigue spalling under line contact obtained using the new model were similar to the previous model predictions and consistent with empirical observations. The model was then extended to incorporate elastic–plastic material behavior and used to investigate the effect of material plasticity on subsurface stress distribution and shear stress–strain behavior during repeated rolling Hertzian line contact. It is demonstrated that the computational improvements for reduced solution time and enhanced accuracy are indispensable in order to conduct investigations on the effects of advanced material behavior on RCF, such as plasticity.     

车用尿素溶液一体化气动供给系统设计

针对柴油机Urea-SCR系统需求,设计开发了一种车用尿素溶液一体化气动供给系统,该系统集成了尿素溶液的存储、计量喷射、雾化等功能。利用汽车压缩空气作为尿素溶液的驱动力及辅助雾化的动力来源,该供给装置具有结构简单紧凑、工作可靠、计量精确等优点。详细分析了系统的组成、工作原理、设计要求等内容,阐述了气动式SCR系统的结构,制作了供给系统的样机,并与重型柴油机进行了ESC和ETC联合试验。试验结果表明,该供给系统能根据柴油机的运转工况,喷入雾化良好、计量精确的尿素溶液,显著降低排气中的NOx浓度,使柴油机排放水平达到国IV法规要求,对实现SCR系统国产化具有重要意义。     

An Investigation of the Process Parameters for Calibre Rolling Using a Complex Analytical Model

Calibre rolling is a complex 3D boundary problem. Several analytical methods were applied to analyse this topic and some progress was achieved. However, it was difficult to include both analytical precision and CPU time saving in the calibre rolling analysis. In this paper, the simplicity of the 3D slab method and the precision of 3D rigid-plastic finite element method were combined to develop a complex analytical model. This model can rapidly simulate calibre rolling and the results obtained match well with the experimental ones. A complex analytical model can be used for discussing the influence of each process parameter on calibre rolling, which can assist the efficient process design of calibre rolling and find the optimal combination of each process parameter.     

弹流润滑点接触问题数值解研究

采用微机对弹性流体动力润滑点接触问题的数值解进行了研究，得出了不同工况下该问题的数值解。经比较所得数值解与公开发表的研究结果一致，且所用方法简明、直观，结果可靠。     

Contact and wear of paper-based friction materials for oil-immersed clutches—wear model for composite materials

Paper-based friction materials are widely used for oil-immersed clutches in automatic transmissions for passenger cars. It is known that repetition of engagements of the clutches causes wear of the friction materials leading to running-in with an increase in contact area. Observation of the contact of a typical paper-based friction material has been made by contact microscopy using the reflection of polarized light. The results have shown that contact is made at the top of its particulate and fibrous constituents, and comparison with the results of laser microscopy has revealed that the contact area observed by the contact microscopy is the contour contact area. An analysis has been made to describe this behavior by employing a mechanical model in which spherical and columnar asperities are supported by an elastic halfspace and wear under the loads they support. Analytical results describe the observed change in the contour contact area and demonstrate applicability of the model to wear of composite materials.