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.     

核电循环泵行星齿轮热弹流润滑研究

核电齿轮箱的良好润滑性能是核电循环泵可靠运行的重要保障,充分考虑齿面形貌和齿廓修形等因素对内/外啮合齿轮副的影响是准确评估其润滑特性的前提。建立典型工况下核电循环泵行星传动系统斜齿轮热弹流润滑模型,首先将斜齿轮副的啮合状态几何等效为圆锥滚子的接触问题,然后考虑斜齿轮接触变形和齿廓偏差,计算得到内/外啮合齿轮副接触区域不同位置的油膜厚度、承载压力、摩擦应力和闪温等参数。考虑齿面磨合作用,采用移动平均滤波方法对未经磨合的初始形貌进行光滑处理,分析了齿面形貌对润滑行为的影响,最后采取齿廓修形改善润滑特性。结果表明：粗糙度和齿廓修形均会对润滑特性产生明显的影响,齿面粗糙形貌会造成油膜厚度减小,进而影响其润滑特性,弱化润滑油膜的承载能力;通过齿廓修形可以改善齿轮啮合边界处的几何过渡,降低该区域的应力集中和表面温度,从而明显改善啮合线终端的润滑状态。     

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.     

Thermal and non-Newtonian analysis on mixed liquid–solid lubrication

A mixed liquid–solid lubrication theory is proposed which concerns the effect of solid particle, liquid lubricant and rubbing surface topography. Especially, it focuses on the circumstances when particle diameter, surface composite roughness and oil film thickness are in the same order of magnitude. A mathematical model containing Reynolds equation, particle load carrying equation, asperity contact equation and heat balance equation is constructed to simulate the mixed liquid–solid lubrication. Moreover, the introduction of non-Newtonian constitutive equation and the rheological parameters related to heat and pressure makes the model closer to practical application. Some typical examples have been analyzed to explore the characteristics of mixed liquid–solid lubrication. In these examples, the effects of the mixed liquid–solid lubricant, the particle diameter and mass concentration, the surface composite roughness, and the material properties are discussed. The simulating results are accordant with early experimental researches, which indicated that the mathematical model is in agreement with the practical mixed liquid–solid lubrication. The input parameters in the examples can be adjusted to adapt to versatile applications.     

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.     

点接触混合润滑中两种求解模型的比较

混合润滑是典型零部件主要的润滑状态,根据表面形貌表征方式的不同,混合润滑模型一般分为统计学模型和确定性模型两类.为研究2种模型求解粗糙表面点接触混合润滑性能的差异,通过基于平均流量模型和GW模型的统计模型、基于统一Reynolds方程的确定性模型,分析并比较不同表面粗糙度、卷吸速度、载荷以及润滑油环境黏度时2种模型预测...     

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.     

Integrated wear prediction model for cylindrical gear with variable hyperbolic circular arc tooth trace under mixed elastohydrodynamic lubrication

Cylindrical gear with variable hyperbolic circular arc tooth trace (VH-CATT) is a new type of gear. Sliding wear is the main mode of the surface failure of multiple mechanical parts. Both the lubrication state and contact temperature considerably influence wear characteristics, which may aggravate the transmission performance of gear pairs. Wear, contact temperature, as well as lubrication states are jointly explored. Therefore, an integrated wear prediction model was proposed through taking into account flash contact temperature and surface roughness of VH-CATT cylindrical gears in mixed elastohydrodynamic lubrication. According to the equivalent ellipse contact model of VH-CATT cylindrical gears and tooth surface equation, normal curvature and velocity relations for VH-CATT cylindrical gears were observed, and the normal meshing force was obtained through the consideration of load sharing coefficients and quality grades. Flash contact temperature was estimated by using the literature. This study proposes analytical solutions for investigating how various surface roughness, operation, and geometric parameters affect asperity contact ratio (ACR), asperity contact pressure (ACP), flash contact temperature (FCT), as well as wear depth (WD) related to driving gears. ACR, ACP, FCT, as well as WD initially decrease and then increase from engaging-in to engaging-out processes. The minimum occurs at the pitch point. The WD declines as module, cutter radius, and rotational velocity increase while augmenting when surface roughness and torques increase. The maximum and minimum wear depths in driving gears occur at the dedendum and pitch point, respectively. Its overall wear is reduced by 23.16 % compared to the wear of spur gears. The results are valuable for the studies of tooth pitting, wear resistance, and fatigue life improvement for VH-CATT cylindrical gear. These studies can provide verification data and references required for engineering designs and VH-CATT cylindrical gear operations.

     

Experimental and Numerical Study of Micropitting Initiation in Real Rough Surfaces in a Micro-elastohydrodynamic Lubrication Regime

Micropitting is a form of surface fatigue damage that happens at the surface roughness scale in lubricated contacts in commonly used machine elements, such as gears and bearings. It occurs where the specific film thickness (ratio of smooth surface film thickness to composite surface roughness) is sufficiently low for the contacts to operate in the mixed lubrication regime, where the load is in part carried by direct asperity contacts. Micropitting is currently seen as a greater issue for gear designers than is regular pitting fatigue failure as the latter can be avoided by control of steel cleanliness. This paper describes the results of both theoretical and experimental studies of the onset of micropitting in test disks operated in the mixed lubrication regime. A series of twin disk mixed-lubrication experiments were performed in order to examine the evolution of micropitting damage during repeated cyclic loading of surface roughness asperities as they pass through the contact. Representative measurements of the surfaces used in the experimental work were then evaluated using a numerical model which combines a transient line contact micro-elastohydrodynamic lubrication (micro-EHL) simulation with a calculation of elastic sub-surface stresses. This model generated time-history of stresses within a block of material as it passes through the contact, based on the instantaneous surface contact pressure and traction at each point in the computing mesh at each timestep. This stress time-history was then used within a shear-strain-based fatigue model to calculate the cumulative damage experienced by the surface due to the loading sequence experienced during the experiments. The proposed micro-EHL model results and the experimental study were shown to agree well in terms of predicting the number of loading cycles that are required for the initial micropitting to occur.     

直齿圆柱齿轮表面微凸起磨损的时变热效应弹流润滑分析

以渐开线直齿圆柱齿轮为研究对象,建立考虑表面微凸起的润滑模型,给出相应的膜厚方程.在以往表面粗糙度的研究基础上,对两齿面的表面微凸起在不同磨损程度下的热解进行数值分析.结果表明:齿面上的微凸起会明显影响齿轮间的润滑效果,会对齿轮齿面造成比微点蚀更大的损伤;对于两个表面均存在微凸起的齿面,齿面的磨合磨损主要发生于主动轮上时,相比发生在从动轮上,会减缓对齿轮啮合过程中压力冲击的影响,会使油膜的中心压力、膜厚等变化趋于平缓.     

行星齿轮变速传动的弹流润滑研究

基于弹性流体动力润滑理论,针对行星齿轮变速器内齿轮主动和太阳轮主动的2种工况,分别求出行星齿轮与太阳轮啮合以及与内齿轮啮合时,沿啮合线在啮合点的最小油膜厚度。结果表明:齿轮在节点啮合的润滑情况可以体现齿轮的润滑状况;太阳轮主动的工况,行星轮与内齿轮啮合的润滑条件最差;提高润滑油的黏度可以增加齿轮润滑油膜厚度;增加齿轮压力角的方法提高齿轮油膜厚度的效果明显;提高齿轮啮合的油膜厚度对改善齿轮的润滑状态,降低齿轮的生产成本,具有实际使用价值。     

Temperature Analysis in Lubricated Simple Sliding Rough Contacts

A temperature analysis of dry sliding fully plastic contact is extended to calculate the asperity temperatures between a sliding lubricated rigid smooth plane and a stationary elastic rough surface. First, surface roughness is generated numerically to have a Gaussian height distribution and a bilinear autocorrelation function. Lai and Cheng's elastic rough contact computer program is then used to determine the asperity contact loads and geometries of real contact areas. Assuming different frictional coefficients for shearing the lubricant film at the noncontact areas, shearing the surface film at the asperity contacts and shearing the oxide film as the asperity temperature exceeds a critical temperature, asperity temperature distributions can be calculated. Eight cases in Durkee and Cheng's scuffing tests of lubricated simple sliding rough contacts are simulated by using 20 computer-generated rough surfaces. The results show that scuffing is correlated to high-temperature asperities which are above the material-softening temperature.     

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.     

摆线液压马达啮合副修型优化

摆线转子啮合副是摆线液压马达的核心部分,为了补偿润滑油膜和减小接触应力,需要对啮合副修型优化。以某型号参数的摆线转子啮合副为例,建立了评估摆线液压马达工作时啮合副各接触点接触应力的力学模型和油膜厚度的润滑模型,分析摆线轮修型方法对各点接触应力和油膜厚度的影响。结果表明:采用“正移距+负等距”的修型组合可以有效补偿油膜厚度并且减小接触应力,可为摆线液压马达的设计优化提供理论指导。     

Influence of surface roughness on friction and scuffing behaviour of cast iron under sparse lubrication

Friction and scuffing behaviour of grey cast iron as influenced by the surface roughness under sparse lubrication conditions is studied. The studies are carried out on a three-shoe-on-disc machine under the conditions of parallel sliding. The experiments were conducted at three oil supply rates of 0.10, 0.22 and 0.36 μg/cm² per contact obtained through a mist oiling system and with specimens of cast iron shoes of different roughness values, Ra, between 0.04 and 2.0 μm against a 0.55% C steel disc. In a step load procedure, the friction torque at the end of each load step and the scuffing load are the major parameters measured. Results of friction and scuffing behaviour as a function of roughness and oil supply rates have been discussed.     

A thermal analysis of strip-rolling in mixed-film lubrication with O/W emulsions

Increase of both roll and strip surface temperatures can significantly affect a rolling process, roll conditions and strip mechanical properties. A comprehensive thermal analysis in cold rolling, especially in a mixed film regime, is needed to understand how thermal fields develop in roll and strip during rolling. It requires a simultaneous solution of the mixed film model for friction in the roll bite and the thermal model for roll and strip thermal fields. This paper presents a numerical procedure to analyse strip rolling process using lubrication with oil-in-water (O/W) emulsions. The thermal model includes the effect of heat generation due to the strip deformation and frictional shear stress at the asperity contacts. The numerical analysis employs a coupled thermal model and a mixed film lubrication model for calculating the friction and the asperity deformation in the bite. The thermal model considers the initial temperatures of the roll and strip, temperature rise due to the strip plastic deformation and friction. While the O/W mixed-film lubrication model takes into account the effect of surface roughness and oil concentration (%vol) of the emulsion. The thermal effect is analysed in terms of strip surface temperature and roll temperature, which are influenced by rolling parameters such as reduction, rolling speed, oil concentration in the emulsion. The results of the parametric study indicate that the effect of oil concentration on the thermal field is relatively small compared to that of reduction ratio and rolling speed. The reduction ratio increases the maximum interface temperature in the roll bite. In the mixed film regime, rolling speed also increases the maximum interface temperature and alters the temperature field of the strip. The numerical procedure was validated against known experimental data and can readily be extended to hot rolling or used to analyse roll strip temperature subjected to different cooling system.     

供油条件对渐开线直齿圆柱齿轮弹流润滑的影响

以渐开线直齿圆柱齿轮为研究对象,建立齿轮啮合过程中的弹流润滑模型,分析供油条件对齿轮弹流润滑的影响.利用多重网格法,得到在不同供油条件下齿轮啮合过程中的弹流数值解.结果表明:随着供油量的增加,齿轮油膜厚度也随之增加,但当供油量超过一临界值时,油膜膜厚不再增加;乏油对齿轮润滑是不利的,但供油量不是越大越好,存在一临界供油点.     

微观形貌表征对直齿轮跑合弹流润滑的影响

高斯分布粗糙度函数相比余弦粗糙度函数,能更贴近地描述跑合前齿面粗糙轮廓曲线幅度分布。研究高斯分布的齿面粗糙度对齿轮跑合过程中轮齿间油膜压力和膜厚的影响,探讨瞬态效应对轮齿润滑的影响,利用多重网格技术求得齿轮瞬态微弹流润滑的完全数值解。结果表明：采用高斯分布粗糙度时油膜压力变化明显,更符合啮合点出现粗糙峰而形成的轻微冲击对轮齿间油膜的影响,而采用余弦粗糙度时油膜压力则变化相对比较缓和;采用高斯分布粗糙度的最大油膜压力明显大于采用余弦粗糙度的最大油膜压力,故按照余弦粗糙度计算的最大油膜压力与实际最大油膜压力可能有较大偏差。     

汽车差速器锥齿轮差速工况下的润滑特性研究

为了研究差速器锥齿轮摩擦和磨损机制,基于弹性流体动力润滑理论,建立直齿锥齿轮无限长时变弹性流体动力润滑模型,研究行星齿轮分别与左右半轴齿轮啮合时的润滑状况,计算差速工况行星齿轮时变效应下的油膜压力和油膜厚度;研究差速工况下左右半轴齿轮的润滑状况,分别比较左右半轴齿轮同行星齿轮啮合时的润滑特性;研究曲线行驶路段复杂变工况下行星齿轮的润滑状况。结果表明:差速工况下行星齿轮啮合周期内的膜厚变小,且行星齿轮与半轴齿轮的相对滑动加剧;行星齿轮同左右半轴齿轮啮合时的润滑特性不同,左转弯工况时,左半轴齿轮同行星齿轮啮合时的最大压力较大,右半轴齿轮同行星齿轮啮合时的最小油膜厚度较大;曲线行驶变工况下行星齿轮润滑特性也不同,左转弯工况向右转弯工况过渡时的压力减小,膜厚增大。     

计算啮合齿轮轮齿间油膜挤压的齿轮敲击振动模型

本文一个非线性单自由度模型用来分析在汽车手动变速箱中出现的齿轮敲击振动.为了考虑由于啮合齿轮的两轮齿间间隙充的油的阻尼的影响,推荐了一个简单的计及油膜挤压影响的一维模型.该挤压模型假定阻尼力与油粘度和轮齿曲面油膜的延展有关,而这种延展又取决于润滑条件(干聚油坑,飞溅,浸浴).由某些数字仿真提供的结果,进行对一对斜齿渐开线齿轮轮齿碰撞后检定油降低高频振动的能力.特别通过用对传动齿轮谐和运动的影响分析从动齿轮的瞬态响应来研究油粘度和间隙延展对敲击特性施加的影响.