Influence of temperature on the friction performance of gear oils in rolling–sliding and pure sliding contacts

The friction behaviour of five different gear oils in rolling–sliding and pure sliding contacts and how temperature influences their friction properties were investigated. It is found that increasing temperature decreases boundary friction with gear oils that contain friction modifiers while not for other gear oils, at all contact pressures investigated. In mixed lubrication region, temperature decreases friction at low contact pressures while increases friction at high contact pressures. The effect of slide–roll ratio on friction is significant in boundary lubrication region especially at higher temperature while less significant in mixed lubrication region at both low and high temperatures. The ranking of gear oils for friction in boundary and mixed lubrication regimes is similar both in rolling–sliding and pure sliding contacts, regardless of temperature. Copyright © 2013 John Wiley & Sons, Ltd.     

The influence of surface roughness and the contact pressure distribution on friction in rolling/sliding contacts

A numerical contact model is used to study the influence of surface roughness and the pressure distribution on the frictional behaviour in rolling/sliding contacts. Double-crowned roller surfaces are measured and used as input for the contact analysis. The contact pressure distribution is calculated for dry static contacts and the results are compared with friction measurements in a lubricated rolling/sliding contact made with a rough friction test rig. The mean pressure is suggested as a parameter that can be used to predict the influence of surface roughness on the friction coefficient in such contacts. The results show two important properties of the friction coefficient for the friction regime studied in this paper: (1) there is a linear decrease in friction coefficient as a function of the slide-to-roll ratio, and (2) the friction coefficient increases linearly with increasing mean contact pressure up to a maximum limit above which the friction coefficient is constant. The absolute deviation of experimental results from the derived theory is for most cases within 0.005.     

Modelling rolling contact phenomena in a pouch belt conveyor system

This paper presents a simplified approach to modelling the rolling contact phenomena that occur at the surface of a wheel driven rubber belt. The main aim of this approach is to determine the rolling friction due to hysteresis and the relationship between traction and slip in wheel driven belt conveyors. The resulting model is an expansion of an existing linear viscoelastic model consisting of a three parameter Maxwell model combined with a Winkler foundation that is used to determine the rolling friction due to hysteresis in a conventional conveyor with a flat belt. Adaptations are introduced to incorporate a curved belt surface and to analyse the relationship between traction and slip. Attention is also paid to matching the model parameters to the viscoelastic properties of an actual rubber sample and subsequently the usefulness of more complex Maxwell models regarding rolling friction and traction is investigated.     

低速灵敏球轴承摩擦力矩分析

低速灵敏球轴承小而稳定的启动力矩和动态力矩对于导航系统的姿态控制至关重要,其工况通常是低速稀油润滑,黏性摩擦被忽略而重点推导接触区因弹性滞后、自旋及差动滑动引起的摩擦力矩。借助拟静力学分析得到了赫兹接触区纯滚动线的位置,积分求出了自旋及差动滑动引起的摩擦力矩,进而估算出灵敏球轴承的摩擦力矩,为验证所推公式的计算结果将其与相关文献的理论值及试验实测值进行了比较。在数学模型基础上,进一步讨论了轴承内外圈沟曲率因数这一重要结构参数对摩擦力矩的影响。     

On the decrease in contact area for spheres and cylinders rolling on a viscoelastic plane

A theory is presented for predicting the variation with speed of the contact area for spheres and cylinders rolling on a dry, viscoelastic plane. Two distinct effects are shown to occur, due to size and shape variations respectively. The size effect is an overall reduction in contact area because of elastomer stiffening at very high forward speeds, whereas the shape effect produces contact asymmetry at lower speeds. Both effects are a manifestation of the hysteresis properties of the viscoelastic plane. A complex Voigt model with variable parameters is used to simulate the dynamic performance of the plane, and there is close agreement with experimental data. An important application is the rolling behaviour of pneumatic tyres on rough road surfaces.     

Rolling and sliding: Separation of adhesion and deformation friction and their relative contribution to total friction

This study is concerned with determining the relative contribution of adhesion and deformation friction using rolling and sliding method. The challenges associated with in-vivo friction testing were overcome by utilising a novel substrate that mimics the viscoelastic behaviour and surface texture of human skin combined with a repeatable and reproducible test setup. The results show that in the dry state, deformation friction contributes 20% of the total friction while the remaining proportion is due to adhesion. These proportions are affected by probe material where for PTFE, deformation friction contributes 30% of the total friction. For the lubricated state, the contribution of deformation friction to total friction increases approaching 50–50% at the higher sliding speeds and normal loads investigated.     

Roughness,friction and wear: The effect of contact planform

Recent theoretical and experimental findings suggest that the statistical properties which affect friction vary slowly with the dimensions of the nominal area. This variation is due to the existence of random long spatial fluctuations which are outside the bandwidth of features imposed by the surface preparation process and which longer wavelengths completely dominate contact behaviour. This leads to the suspicion that the second of Amontons' laws, i.e. that the limiting static friction is independent of the shape of the nominal area, is not absolutely true. A relation is derived which connects the limiting static friction with the statistical contact properties and with a dimension of the nominal area. In an experiment devised to test this relation, the limiting static friction was measured for three rectangular steel specimens whose nominal area and normal load were kept constant and whose length to breadth ratio varied. The limiting static friction was found to be linearly related to the specimen length in agreement with theoretical predictions. Regression analysis of 36 measurements established that the probability of this result being due to chance was less than 1 in 500. Supporting evidence for this hypothesis has also been found from wear experiments reported in the literature.     

Plastic deformation of surface layer during rigid cylinder rolling and sliding

Steady-state plastic deformation of the surface layer induced by the rolling and sliding of a rigid cylinder is investigated using ideal plastic plane strain theory taking into consideration contact friction. The plastic region and length of the contact arc related to the forces and the moment applied to the cylinder are calculated. Results are studied for rolling friction theory in the case of large contact loads and for surface plastic-layer deformation to increase the wear resistance and fatigue strength of machine parts.     

Dynamics in the Bridged State of a Magnetic Recording Slider

A novel region of tribological interaction is explored by inducing near contact between the magnetic recording slider and disk. In this study, we performed frictional measurements over a wide range of subambient air pressure and disk rotation rate. Since the slider is supported over the disk by an air bearing, it has been found that cycling from ambient to subambient and then back up to ambient pressure over several minutes of time forms a frictional hysteresis loop. The high-friction branch of the loop, referred to as the bridged state, is characterized by an average frictional displacement and resonant vibration of the suspension mount assembly. The bridged state is currently employed for accelerated wear testing of magnetic slider/disk/lubricant systems. Future magnetic recording systems designed to operate at increasingly lower physical spacing will need to take into account these frictional forces which accompany the incipient contact between the lubricated disk and slider with finite surface roughness. A single degree of freedom model is solved to determine the equivalent dynamic friction force on the slider as an impulse series with random impulse frequency and amplitude from the measured frictional displacement in the bridged state. The mean slider-disk spacing in the bridged state is derived from the experimental friction force, the spacing probability density function, and the adhesion stress from the Lifshitz model for dispersion interaction energy.     

An Adhesion-Dominated Rolling Friction Regime Unique to Micro-scale Ball Bearings

We demonstrate that micro-scale rolling bearings exhibit friction and wear properties markedly different from their macro-scale counterparts. A microfabricated testing platform uses variable rolling element diameters or vapor-phase lubricated interfaces to independently test friction force with varying contact area and surface energy. A linear, consistent, relationship between friction force and contact area is observed among different rolling element diameters. When surface free energy is altered through the introduction of vapor-phase lubrication, an 83 % decrease in friction is observed. When coupled with observed ball material adhered to the raceway, there is strong evidence for adhesion-dominated rolling friction regime at the micro-scale.     

A study on the effect of surface topography on rough friction in roller contact

The friction behaviour of gear teeth in the context of tribology can have a strong effect on housing vibration, noise and efficiency. One of the parameters that greatly influences the friction under certain running conditions is surface roughness. In this work, rough friction was studied in lubricated sliding of roller surfaces, which were manufactured to simulate the real gear surfaces. By examining 3D surface topography of two mating bodies, both surface roughness and its effect on friction behaviour can be studied. In a previous study, a rough-friction test rig has been designed, constructed and initially verified. The types of surfaces involved in this study are ground, shot-peened, phosphated and electrochemically deburred. These rollers were subjected to the same friction testing procedures. Roller surfaces were then examined, and correlation between the topography and the frictional behaviour was analysed. Friction behaviour was interpreted in terms of Stribeck curves (friction coefficient as the function of Hersey parameter (ην/p)). The results showed that electrochemically deburred and certain phosphated surfaces provide lower friction coefficient values which are competitive to fine-ground surfaces in lubricated rolling/sliding contact.     

Pre-sliding Behaviour of Single Asperity Contact

The pre-sliding and static friction force behaviour at asperity level between a smooth ball and a smooth flat surface at different normal loads, as well as friction behaviour during full slip has been studied. The normal load dependence of the friction force and the preliminary displacement is discussed when the mean contact pressure is kept under 100 MPa. The theoretical model to calculate the shear stress and the preliminary displacement in the contact is discussed and the experimental data were used to verify the model. The results show that for low applied normal loads the adhesion force has an influence on the friction force measurements. Furthermore, the results for the friction force and preliminary displacement show good agreement with the theoretical trends. The experiments along with the model can be used to analyse the tangential traction in the contact and the behaviour of the stick–slip area. The measurement results along with the model were used to calculate the maximum shear stress at the point of sliding for different applied normal loads. It is also shown that at low applied normal loads the shear stress is not constant as compared to relatively high applied normal loads due to the presence of adhesion force.     

A theory of viscous hydroplaning

The traction developed in the contact area of a pneumatic tyre rolling and accelerating on a wet road surface is simulated by a block of rubber slipping on a two-dimensional sinusoidal surface covered with a thin water film. The resulting pressure-wedge formation on individual asperities of the surface provides a net uplift which tends to force tyre-tread and surface apart, thus promoting the onset of skidding or viscous hydroplaning. The important factor in minimizing skidding hazards is the provision of an adequate micro-roughness at asperity tips which contributes an adhesional mechanism to the overall friction coefficient. It is shown that in comparison with the adhesional contribution to friction, the contribution of hysteresis and viscous shear of the film are insignificant at low slip speeds.     

An investigation of contact problem between strip and work roll with a smooth straight surface during cold rolling

Under the assumption of elastic roller, and the neglect of heat transfer problem, this paper explores the distribution of elastic deformation of the work roll with initially smooth straight surface in the rolling area during the rolling process, and analyzes the effect of this deformation distribution on the strip shape after rolling.

Based on the large deformation—large strain theory, the update Lagrangian formulation (ULF) and the incremental principle were used to develop 3D elastic-plastic analytical model of aluminum strip rolling. The flow stress was considered the function of strain and strain rate to infer the governing equation containing the effect of strain rate.

Besides, in this article, we propose an iteration procedure to calculate the contact force between strip and work roll, and the contact deformation of the work roll. In the treatment of the contact problem, the work roll was regarded as a rigid body at the beginning of each step. The incremental displacement and contact force of strip nodes were first calculated, and then entered into the first iteration loop. The contact forces of strip nodes were allocated to the work roll to calculate work-roll elastic deformation. The elastic deformation of work-roll nodes would be compensated to the incremental displacement of the strip nodes (the work-roll deformation increment was added on the incremental displacement of strip node). Then the new contact nodal forces were derived from the finite element program of strip. The above procedures were repeated to incorporate the new contact nodal forces into the first iteration loop to obtain the new strip node incremental displacement. An error range was also designated as the comparison standard to compare the displacement increments of the strip from two iterations to determine whether the iteration was completed.

This paper considers the initial shape of work roll is straight and smooth. The elastic deformation distribution on the work roll surface in the rolling area is analyzed to serve as the basis for work-roll radius compensation. Finally, deformation of strip shape is also discussed.     

Experimental evaluation of friction between contacting discs for the simulation of gear contact

Instant gear contact can be simulated with contacting discs, which provides steady operating conditions and eliminates most of the dynamics and manufacturing tolerances involved in real gears, resulting in an accurately controlled contact condition. A high-pressure twin-disc test device was developed, where loading and rolling velocity can be varied continuously. It is equipped with disc bulk temperature, mean contact resistance and friction moment measurements. The test discs were grinded transversal to the disc rolling direction with proper crowning corresponding to the real gear flank properties. The test device was applied by studying the friction behaviour against the slide-to-roll ratio at different contact pressures, rolling velocities and surface roughness. The measurements were performed using mineral base oil in the range of operation conditions often used in industrial gears. In general, the measured friction coefficient behaviour correlates with earlier published results and is logical with measured bulk temperature and mean contact resistance. The limiting shear stress of the lubricant has an essential role in friction behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of Surface Topography on the Tribological Behaviour of Aluminium Alloy 5182 with EDT Surface

Friction is one of the most important parameters in sheet metal forming. Friction conditions are influenced by the texture of the sheet surface, by the surface or coating of the tools and by the lubrication. The aluminium alloy AA 5182 with EDT surface has been studied and tested at various angles between rolling and sliding direction. The friction behaviour observed in experiments at different normal pressures based on Coulomb’s friction law are shown and discussed in this article. Moreover, local surface topography and lubricant distribution in the contact area are described.     

SMA压电复合减震装置电力学性能及其本构模型

针对形状记忆合金(shape memory alloy,简称SMA)阻尼器控制力不可调和压电摩擦阻尼器启动难的问题,提出了一种SMA单元和压电摩擦单元依次工作的复合减震装置,进行了相应的电力学性能试验,分析了位移幅值、激励频率和输入电压对复合减震装置力学性能的影响。在试验结果的基础上,建立了以速率符号、电压和位移为神经元输入的优化反向传播(back propagation,简称BP)神经网络预测模型。结果表明,该复合减震装置的滞回曲线饱满且基本对称,工作性能稳定,随着电压的增大,滞回环的面积逐渐增大,耗能能力不断增强。在位移幅值为12mm、电压为120V下,单圈耗能量提高了138.23%,等效阻尼比提高了94.23%。两种智能材料经过合理组合而成的SMA压电复合减震装置耗能好、适应性强,可以更好地用于工程结构的减震控制。BP网络预测模型能够较好地跟踪SMA类复合减震装置的输出,而优化后的BP网络更加稳定,能够快速得到误差更小的网络模型,该神经网络算法为SMA类复合减震装置本构模型的建立和应用提供了新途径。     

Features of small oscillations of pendulum on elastic surface with hysteresis friction

Small free oscillations of the physical pendulum supported by two balls lying on an elastically deformable surface have been studied theoretically for the case when the ball displacements are considerably smaller than the contact spot radius. The differential equation of oscillations is derived with account for the surface deformation and the deformation component of the friction force. The deformation component of rolling friction is shown to be a particular case of internal hysteresis friction. The coefficient of elastic rigidity of the support surface and the hysteresis constant are introduced. Formulas for calculating the oscillation amplitude as a function of the time and the oscillation period as a function of the amplitude are derived.     

Reduced dependence on loading parameters in almost conforming contacts

In cases of completely conforming frictionless contact, the contact area generally either decreases or stays the same under load, in which case the extent of the contact area is subsequently independent of load and the stress and displacement fields vary linearly with the loading parameter. Dundurs and Stippes describe such cases as receding contact problems. Here, we demonstrate that similar results apply in the presence of Coulomb friction, in which case the extent of the stick and slip zones and the local direction of sliding are independent of load. We also show that if there is a small initial gap or interference throughout the potential contact area, the extent of the contact area and the stress and displacement fields will approach those of the corresponding receding contact problem as the applied load is increased. If the interface conditions permit adhesion between the contacting surfaces, the extent of the adhesion zone shrinks to zero as the load increases without limit. Progress of the contact configuration towards the limit is governed solely by a dimensionless load factor involving the ratio between the applied load and the initial clearance or interference. This permits results for a variety of initial geometries (due to tolerance variations) to be obtained from a set of finite element results for a single case. Some of these characteristics are demonstrated using a finite element solution of a connecting rod/bushing/gudgeon pin contact. Other interesting applications are those with complex geometries, ranging from biomechanics, as in prostheses, to the design of multiple fasteners.     

基于分形理论的滑动摩擦表面接触力学模型

依据分形理论,考虑微凸体变形特征及摩擦作用的影响建立滑动摩擦表面接触力学模型。采用一个三次多项式来表达弹塑性变形微凸体的接触压力与接触面积的关系,从而满足在变形状态转变临界点处的微凸体接触面积与接触压力转化皆是连续和光滑的条件。推导出滑动摩擦表面临界弹性变形微接触面积、临界塑性变形微接触面积、量纲一真实接触面积的数学表达式。理论计算结果表明,表面形貌一定时,真实接触面积随着载荷的增大而增大;载荷一定时,真实接触面积随着特征尺度系数的增大而减小,随着分形维数的增大先增大后减小;当表面较粗糙时,摩擦因数对真实接触面积的影响很小;随着表面光滑程度的增大,摩擦因数对真实接触面积的影响增大,真实接触面积随着摩擦因数的增大而增大,特别是当摩擦因数较大时,真实接触面积增大的幅度也较大。接触力学模型的建立,为研究滑动摩擦表面间的摩擦磨损性能提供了依据。