Investigation of the strain distribution with lubrication during the deep drawing process

A lubrication/friction model can be implemented in FEM codes to predict the contact area ratio, friction coefficient and strain distribution in lubricated deep drawing process. In the lubrication analysis, the surface roughness effect on lubrication flow is included by using Wilson and Marsault's average Reynolds equation that is appropriated for mixed lubrication with severe asperity contact. With regard to the asperity contact theory, the well-known flattening effect is considered. Friction is expressed in terms of variables such as lubricant film thickness, sheet roughness, lubricant viscosity, interface pressure, sliding speed, and strain rate. The proposed lubrication/friction model combined with a finite element code of deep drawing process to predict the contact area ratio, friction coefficient and strain distribution. Numerical results showed that the present analysis provides a good agreement with the measured strain distributions.     

Die-Workpiece Interfacial Behaviors in Axisymmetric Forging Processes with Flat Dies

A new piezo-viscous, average flow model combined with an advanced slab method is used to investigate the lubrication in axisymmetric forging processes with flat dies. Interactions between lubricant transport and surface roughness are studied. Influence of friction on the outward motion of the workpiece is also considered. It is shown that the lubricant is transported outward in a speed slower than half the surface speed, and the film thickness is smaller than the case of the smooth surface if asperity contact is not severe. However, when asperity contact is pronounced, the lubricant pressure distribution is quite different from the prior research. Mixed lubrication is observed in most of the region where asperity contact occurs. Boundary lubrication can only be found in a narrow area near the workpiece edge.     

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.     

A multi-scale model for friction in cold rolling of aluminium alloy

A simple and robust friction model is proposed for cold metal rolling in the mixed lubrication regime, based on physical phenomena across two length scales. At the primary roughness scale, the evolution of asperity contact area is associated with the asperity flattening process and hydrodynamic entrainment between the roll and strip surfaces. The friction coefficient on the asperity contacts is related to a theoretical oil film thickness and secondary-scale roll surface roughness. The boundary friction coefficient at the “true” asperity contacts is associated with tribo-chemical reactions between fresh metal, metal oxide, boundary additives, the tool and any transfer layer on the tool. The asperity friction model is verified by strip drawing simulations under thin film lubrication conditions with a polished tool, taking the fitting parameter of the boundary lubrication friction factor on the true contact areas equal to 0.1. Predicted values of average friction coefficient, using a boundary friction factor in the range 0.07–0.1, are in good agreement with measurements from laboratory and industrial rolling mill trials.     

A Model for Wear and Friction in Cylinder Liners and Piston Rings

Abstract

A one-dimensional elstohydrodynamic mixed lubrication wear and friction model is developed. The model can predict the effects of surface roughness, asperity contact, temperature-pressure-viscosity on wear, lubrication, and friction of the piston rings and cylinder liner. Wear is predicted based on the surface asperity contact pressure. The cylinder bore wear and the ring pack friction during an engine break-in are simulated and compared with the experimental results. The influence of cylinder wall temperature and surface roughness on friction and wear is investigated. The ring pack friction due to oil viscous shearing and asperity contact is found to reach its minimum at a certain oil temperature.     

Calculation of mixed lubrication at piston ring and cylinder liner interface

This paper reports on the theoretical analysis of mixed lubrication for the piston ring. The analytical model is presented by using the average flow and asperity contact model. The cyclic variations of the nominal minimum oil film thickness are obtained by numerical iterative method. The total friction is calculated by using the hydrodynamic and asperity contact theory. The effects of the roughness height, pattern, and engine speed on the nominal minimum film thickness, friction force, and frictional power losses are investigated. As the roughness height increases, the nominal oil film thickness and total friction force increase. Also, the effect of the surface roughness on the boundary friction is dominant at low engine speed and high asperity height. The longitudinal roughness pattern shows lower mean oil film pressure and thinner oil film thickness compared to the case of the isotropic and transverse roughness patterns.     

冷轧铝工作区的混合润滑特性研究

为研究冷轧铝工作区的混合润滑特性,基于平均流量理论建立考虑表面粗糙度的冷轧铝工作区混合润滑模型,并通过相关文献的数据验证模型的正确性.在不同轧制速度、润滑油黏度以及前后张应力条件下对整个工作区内的润滑特性进行分析,研究轧制工艺参数对油膜厚度、接触面积比以及应力分布的影响.仿真结果表明:随着轧制速度的提高,轧制压力有一定...     

混合润滑条件下的斯特封高速摩擦与密封特性

为准确研究斯特封高速摩擦与密封特性,基于混合润滑理论,综合流体空化效应、密封接触变形和微观粗糙峰接触等因素影响,建立了斯特封摩擦与密封的数值计算模型.研究了往复运动速度和密封压力对油膜厚度、摩擦力和泄漏量的影响,搭建了往复密封试验台来验证模型的准确性.结果表明:计算摩擦力与实验摩擦力相近.混合润滑模型能更好地模拟高速柱...     

Deterministic solutions and thermal analysis for mixed lubrication in point contacts

A deterministic numerical model has been developed for simulation of mixed lubrication in point contacts. The nominal contact area between rough surfaces can be divided into two parts: the regions for hydrodynamic lubrication and asperity contacts (boundary lubrication). In the area where the film thickness approaches zero the Reynolds equation can be modified into a reduced form and the normal pressure in the region of asperity contacts can be thus determined. As a result, a deterministic numerical solution for the mixed lubrication can be obtained through a unite system of equations and the same numerical scheme. In thermal analysis, the solution for a moving point heat source has been integrated numerically to get surface temperature, provided that shear stresses in both regions of hydrodynamic lubrication and asperity contacts have been predetermined. A rheology model based on the limit shear stress of lubricant is proposed while calculating the shear stress, which gives a smooth transition of friction forces between the hydrodynamic and contact regions. The computations prove the model to be a powerful tool to provide deterministic solutions for mixed lubrication over a wide range of film thickness, from full-film to the lubrication with very low lambda ratio, even down to the region where the asperity contact dominates.     

Stribeck Curve Under Friction of Copper Samples in the Steady Friction State

The friction and wear of a pure copper block (99.98 wt% Cu) against a hardened steel disc were studied. The effect of sliding velocity and load on the friction coefficient and wear rate of Cu samples during steady tests was studied. Elasto-hydrodynamic (EHL), mixed (ML) and boundary lubrication (BL) regions were analyzed using the Stribeck curve. The lubrication number of Schipper, Z, was used in the analysis of the Stribeck curve. The transitions from one lubrication region to another are discussed. The mixed EHL region is characterized by stable low values of the friction coefficient, wear rate and temperature. Straight asperity contact is the dominant mechanism under friction of Cu–steel pair in the BL region. High-friction coefficients and wear rates, thin lubricant films and large wear grooves indicate straight asperity contact between rubbed surfaces in the BL region. Although the dominant mechanisms in the mixed EHL and BL regions are different in principle, a steady friction state is preserved in both cases. It is expected that the steady friction state in the BL and mixed EHL regions is associated with deformation and fracture of surface layers but these process occur at different scale levels. It was shown that under friction of Cu–steel pair, two types of ML regions are observed. The first is the stable steady friction of mixed EHL with low values of the friction coefficient and wear rate. The second type of the ML region is the region of unstable friction and wear when a decrease of lubricant film leads to a change of external (roughness, temperature, friction and wear) and internal (strain and stress) parameters. It was found out that a transition to the unstable ML region occurs within a narrow range of Z parameter under definite values of the load and sliding velocity.     

Numerical and Experimental Studies on Tribological Behaviors of Cu-Based Friction Pairs from Hydrodynamic to Boundary Lubrication

When studying the tribological behaviors of a Cu-based friction pair in different lubrication regimes, calculation of the real contact area of asperity contacts is crucial but difficult. In this work, a mixed lubrication model in plane contacts is developed, and pin-on-disc tests are carried out. The real contact area ratio, load sharing ratio, and friction coefficient are investigated. Effects of sliding velocity, temperature, and pressure are considered. The results show that when the maximum contact area ratio is about 14.6%, the load sharing ratio of asperity contacts is about 95%. The friction coefficient obviously increases from less than 0.04 to about 0.15 as the regime changes from hydrodynamic to boundary lubrication. Asperities have a significant influence on the local lubrication of a Cu-based friction pair, and the action of hydrodynamic pressure cannot be ignored.     

A numerical method for the calculation of lubricant pressures in bearings with mixed lubrication

A model for mixed lubrication, assuming that the total normal load applied to the plane of the lubricated surfaces is carried partly by the hydrodynamic action of the lubrication film and partly by asperity contacts and that the total friction force between the lubricated surfaces is partly due to viscous friction and partly to asperity contacts, was used to develop a numerical solution for pressure distribution in a bearing experiencing mixed lubrication. The geometry treated and the pressure distribution obtained were for a simple slider bearing, but the method could easily be extended to other shapes. The model is based on measured roughness of a real surface. Real load carrying capacity and drag can therefore be determined since they are related directly to bearing pressure distribution     

Enhanced friction model for high-speed right-angle gear dynamics

The modeling of elastohydrodynamic lubrication friction and the analysis of its dynamic effect on right-angle gears, such as hypoid and spiral bevel types are performed in the present study. Unlike the classically applied empirical constant coefficient of friction at the contacting tooth surfaces, the enhanced physics-based gear mesh friction model is both spatial and time-varying. The underlying formulation assumes mixed elastohydrodynamic lubrication (EHL) condition in which the division and load distribution between the full film and asperity contact zones are determined by the film thickness ratio and load sharing coefficient. In the proposed time-varying friction model, the calculation of friction coefficient is performed at each contact grid inside the instantaneous contact area that is being subjected to mineral oil lubrication. The effective friction coefficient and directional parameters synthesized from the net frictional and normal contact forces are then incorporated into a nonlinear time-varying right-angle gear dynamic model. Using this model, the effect of friction on the gear dynamic response due to the transmission error and mesh excitations is analyzed. Also, parametric studies are performed by varying torque, surface roughness and lubrication properties to understand the salient role of tooth sliding friction in gear dynamics. The simulation results are included. But experimental verification is needed.     

Thermoelastohydrodynamic Analysis of Spur Gears with Consideration of Surface Roughness

Thermoelastohydrodynamic lubrication (TEHL) analysis for spur gears with consideration of surface roughness is presented. The model is based on Johnson’s load sharing concept where a portion of load is carried by fluid film and the rest by asperities. The solution algorithm consists of two parts. In the first part, the scaling factors and film thickness with consideration of thermal effect are determined. Then, simplified energy equation is solved to predict the surfaces and film temperature. Once the film temperature is known, the viscosity of the lubricant and therefore friction coefficient are calculated. The predicted results for the friction coefficient based on this algorithm are in agreement with published experimental data as well as those of EHL simulations for rough line contact. First point of contact is the point where the asperities carry a large portion of load and the lubricant has the highest temperature and the lowest thickness. Also, according to experimental investigations, the largest amount of wear in spur gears happens in the first point of contact. Effect of speed on film temperature and friction coefficient has been studied. As speed increases, more heat is generated and therefore film temperature will rise. Film temperature rise will result in reduction of lubricant viscosity and consequently decrease in friction coefficient. Surface roughness effect on friction coefficient is also studied. An increase in surface roughness will increase the asperities interaction and therefore friction coefficient will rise.     

粗糙度各向异性对润滑接触面摩擦的影响

齿轮、轴承、凸轮等重载接触副的性能受表面粗糙度的显著影响。高负载情况下的摩擦因数与润滑接触面粗糙度的各向异性相关。测量的表面粗糙度可以分解为一系列具有不同波长、幅值的正弦表面粗糙度,因此,考虑各向异性正弦表面粗糙度,构建粗糙表面点接触瞬态弹性流体动力润滑(TEHL)模型,提出基于多重网格算法的粗网格构造新方法,提高粗糙表面润滑问题求解的稳健性。研究表面粗糙度各向异性对高负载情况下摩擦因数的影响规律。结果表明,粗糙度的各向异性影响接触面压力、油膜厚度分布、粗糙度形变量,从而影响摩擦因数。提出一个组合函数来量化粗糙度各向异性对摩擦因数的影响,表明全膜润滑到混合润滑的过渡不仅与载荷、速度等工况参数相关,还与粗糙度各向异性相关。     

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.     

Friction Reduction in Mixed Lubrication

Minimization of frictional losses in the drivetrain of heavy-duty vehicles is important from both consumer satisfaction and environmental perspectives. Approaches to friction reduction in these components can be evaluated using simulation-based investigations. However, nearly all drivetrain components operate in the mixed lubrication regime which is difficult to model because both hydrodynamic lubrication and surface contact are significant and therefore, the total friction consists of hydrodynamic friction due to lubricant shearing and boundary film friction at asperity contact locations. Recent advances in simulation methods for mixed elastohydrodynamic lubrication (EHL) have enabled improved virtual design tools, such as those developed by Zhu and Hu and further improved by Liu et al. Here, these simulation tools are used to evaluate friction reduction and predict the effects on a mixed EHL interface under severe operating conditions. Three practical means of friction reduction are discussed based on the experimentally validated mixed lubrication friction model and its predictions made for representative, sample cases.     

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。     

The Subsurface Stress Field Created by Three-Dimensionally Rough Bodies in Contact with Traction

A numerical simulation technique for calculating the complete subsurface stress field for three-dimensionally rough bodies in sliding contact is described. The stresses are calculated using real digitized three-dimensional surface profiles. The effects of the surface roughness and the sliding friction are presented. Using an existing contact simulation code, the digitized surfaces are mathematically pressed together and the real areas of contact and the asperity pressures are calculated. The surfaces are assumed to remain elastic throughout the contact simulation process. The shear forces at the asperity contact interfaces are assumed to be proportional to their calculated normal pressures. The subsurface stresses are then determined with these known normal and tangential forces at the surface.