Modelling lubricated friction for dynamic contact systems

Multi-valued friction is often observed in lubricated contact systems operating under unsteady sliding conditions. In the past, this behaviour has been modelled using a measured time delay between changes in sliding velocity and resulting changes in friction. More recent work has revealed that fluctuations in normal separation are the principal cause of this deviation from steady friction behaviour. This paper demonstrates that tangential contact dynamics can result in apparent deviations from steady friction that can resemble true deviations found from fluctuations in normal separation. Two different dynamic models are considered. One model accommodates the tangential rider dynamics of a friction test apparatus. The other model considers the possibility of tangential dynamics associated with asperity contacts.     

Static friction coefficient of some plastics against steel and aluminum under different contact conditions

The static friction behavior was investigated in the case of POM-based polymers containing additives, designated DE20076, DE100KM and DE12017 as well as Nylon-66 designated ZY103HSL, when in contact with AISI 1045 steel and 6061 aluminum alloy. A designed apparatus that detects the exact moment corresponding to the transition from rest to slip was used to measure the coefficient of static friction. The impact of normal load, dwell time before slip, apparent area of contact and lubrication by water and paraffin oil on the static friction characteristics was studied. A decrease of the static coefficient of friction with low normal load followed by a levelling off governed by its effect on the real area of contact and stiffness of the counterface was observed. This also yielded a linear decrease of slip acceleration as well as stick time. A polynomial equation, which increases monotonically, was found to express well the effect of stick time on static friction, independently of the materials in contact. Adhesive effects were generated by the presence of both lubricants with the result of increase of the static coefficient of friction.     

Modeling the effect of skewness and kurtosis on the static friction coefficient of rough surfaces

Engineering surfaces possess roughnesses that exhibit asymmetrical height distributions. However, the Gaussian distribution is most often used to characterize the topography of surfaces, and is also used in models to predict contact and friction parameters. In this paper, the effects of kurtosis and skewness on different levels of surface roughness are investigated independently. This is accomplished by adopting the Pearson system of frequency curves and used in conjunction with a static friction model for rough surfaces to calculate the friction force and friction coefficient. This study is the first attempt to independently model the effect of kurtosis and skewness on the static friction and friction coefficient. It is predicted that surfaces with high kurtosis and positive skewness exhibit lower static friction coefficient compared to the Gaussian case. More importantly, it is predicted that, for high kurtosis values, the static friction coefficient decreases with decreasing external force rather than increasing as seen with increasing skewness. This is a very promising result for applications involving smooth lightly loaded contacts such as magnetic storage devices and microelectromechanical systems. The practical significance of the present model is specifically demonstrated on static friction predictions in magnetic storage head–disk interfaces. Such predictions can be used to determine the optimal characteristics of such devices prior to fabrication to achieve lower friction in terms of surface roughness, mechanical properties, apparent contact area, and operational environment.     

Static friction of litchi stalk/clamp head contact: comparing material,clamp texture and stalk diameter

Abstract

The static friction characteristic was investigated in the case of litchi picker’s clamp heads made of PVC plastic, silicone and rubber, carved with textures of circular, sawtooth, plain and grid, when in contact with litchi stalks. An experimental device was developed and used to measure the static coefficient of friction between a flat surface and cylinder. Clamp heads made of rubber were found to have the biggest static coefficient of friction, and clamp heads made of PVC plastic were found to have the smallest static coefficient of friction. Clamp heads carved with circular texture were found to have the biggest static coefficient of friction, and clamp heads carved with grid texture were found to have the smallest static coefficient of friction. And for specimens of different sizes, the bigger the diameter, the bigger the static coefficient of friction. Results suggest that the best clamp heads for a litchi picker are made of rubber, carved with circular texture, and a bigger clamping force is required to pick smaller stalks.     

Stick–slip friction in dissimilar polymer pairs used in automobile interiors

The static and dynamic friction of dissimilar pairs of plastics used in automotive interiors was measured as a function of normal load, system stiffness, and surface roughness. Glass fiber filled polypropylene (FPP) was slid on polycarbonate (PC) and glass fiber filled styrene–maleic–anhydride copolymer (SMAC) in a single pass, unidirectional sliding test. The friction was characterized by the value of static coefficient of friction (COF) and the number of stick–slip cycles during sliding. It was found that the FPP/PC and FPP/SMAC pairs had fewer instances of stick slip than FPP/FPP, PC/PC, and SMAC/SMAC pairs except for one of the SMAC polymers. The surface texture which had the smallest average radius of peak curvature, had the lowest value of static COF. The decrease in the static COF of polypropylene (PP) caused by the addition of glass fiber was most likely caused by the increase in elastic modulus and hardness.     

Modelling of contact and friction in aluminium extrusion

A physical model capable of predicting the friction and sticking/slipping lengths in the bearing channel during unlubricated aluminium extrusion processes is presented. The model takes into account the pressure build up in the extrusion direction in relation with the bearing–extrudate friction and how it will be influenced by die geometry such as die angle and bearing length. The results show that a high friction coefficient in the bearing will increase the sticking length and shorten the slipping length. The results are in good agreement with experimental findings documented by previous researches.     

Calculation method and control value of static stiffness of tower crane

The static stiffness of tower cranes is studied by using the proposed formulations and finite element method in this paper. A reasonable control value based on theoretical calculation and finite element method is obtained and verified via collected field data. The results by finite element method are compared with the collected field data and that by the proposed formula. Corresponding to theoretical formulations and field data, it is found that the results by finite element method are closer to the real data.     

The significance and use of the friction coefficient

The quantity known as the friction coefficient (or ‘coefficient of friction’) has long been used in science and engineering. It is easy to define, but not easy to understand on a fundamental level. Conceptually defined as the ratio of two forces acting, respectively, perpendicular and parallel to an interface between two bodies under relative motion or impending relative motion, this dimensionless quantity turns out to be convenient for depicting the relative ease with which materials slide over one another under particular circumstances. Despite the fact that both static and kinetic friction coefficients can be measured with little difficulty under laboratory conditions, the time- and condition-dependent characteristics of friction coefficients associated with both clean and lubricated surfaces have proven exceedingly difficult to predict a priori from first principles.The shaky nature of friction's fundamental underpinnings, has not prevented investigators from compiling lists of friction coefficients and publishing them for general use. Problems often arise, however, when engineers attempt to use tabulated friction coefficients to solve specific problems in mechanical design or failure analysis. The systems-dependence of frictional behavior is sometimes ignored, leading to misapplication of published data. This is particularly true for applications in nano-technology and others that differ from typical laboratory size scales. This paper will review the measurement and use of static and kinetic friction coefficients, discuss their usefulness, and describe the sources of frictional resistances in terms of shear localization.     

Determining coefficients of friction in compaction of refractory metal powders

Knowing the coefficients of friction in tool compaction of powders of metals and alloys allows one to rationally design technological equipment for manufacturing powder semifinished products experiencing minimal warping under vacuum or hydrogen sintering. This is of particular significance when consumable electrodes are produced from powders of refractory metals being compacted as rather long fillets that are curved in sintering if any irregularities in the density in the cross section and in the fillet bulk are present. Both well-known and new methods are analyzed for finding the coefficients of friction in powder compaction, in particular in cylindrical containers. Stable and valid measurement results are shown to be unachievable. A new method for experimental determination of the coefficients of friction under powder compaction is described. It consists in comparing the force parameters of one- and two-sided compaction. This method allows finding the coefficient of side pressure and contact friction (on the cylindrical surface of the container) during the formation of briquettes of TsM-2A alloy with different concentrations of plasticizer and solvent. A positive effect of a plasticizer and negative one of a solvent on the coefficient of friction is stated.     

Normal displacement and dynamic friction characteristics in a stick-slip process

The dynamic friction-velocity relationship in the slip stage of stick-slip vibration was investigated with a pin-on-flat apparatus. A reasonable relationship was derived from the measured displacement and acceleration of the sliding element, using a computing technique which provided smooth, reliable curves. It was found, from an examination of the effect of data smoothing on computed friction characteristics, that the moving average method can be recommended. Variation of normal displacement of the sliding body during the slip period was examined together with tangential displacement and electrical contact resistance. The friction-velocity relationship was well explained by an assumption that the instantaneous friction variation results from the change in real area of contact resulting from normal displacement occuring in an elastic contact.     

Actual contact area growth caused by interaction of junctions in dry friction

Experimental data characterizing dry friction processes between strain-hardenable metallic bodies under various normal loads are presented. It is shown that changes both in tangential force and friction coefficient observed in experiments are accompanied by a corresponding growth in the actual contact area (i.e. total area of metallic junctions) between contacting surfaces. Variations of actual contact area are explained as a result of interaction of metallic junctions, caused by their coalescence, which depends on the distances between actual contact area spots. The results obtained reveal some peculiarities of the process seizure.     

An upper-bound analysis of friction in metal forming

In the analysis of metal forming processes, a knowledge of friction is important, especially when the microstructure evolution and criteria for limiting phenomena are predicted by numerical simulation. The friction wave model has been studied by several researchers. Their analyses are mainly based on the assumption that there is no plastic deformation of the bulk material. However, it is necessary to clarify the influence of bulk material deformation on the surface asperity deformation. This paper deals with the development of a friction wave model by considering the influence of bulk material on the surface asperity deformation. The situation of rough tool—smooth workpiece (RT—SW) contact during forming process has been investigated. Based on this condition, an admissible velocity field is constructed for the upper bound analysis. The relationship between the normal pressure and the sliding resistance is established over a large range of pressure. The role of surface roughness, bulk displacement and bulk strain on metal forming friction is analysed.     

Modelling of plowing and shear friction coefficients during high-temperature ball-on-disc tests

During high-temperature ball-on-disc tests of aluminium against steel, hot aluminium deforms and wear track evolves. The individual contributions of plowing and shearing to the apparent friction and the contact pressure are unknown. The aim of the research was to develop a model capable of determining these parameters. It was found that during high-temperature ball-on-disc tests, the plowing friction accounted for only about 1% of the apparent friction, although the plowing friction coefficient increased with increasing wear lap, while the shear friction played a dominant role in determining the apparent friction measured. The mean contact pressure decreased significantly as the test proceeded.     

The influence of contact geometry on friction and wear characteristics

This paper describes some results of evaluating the influence of contact geometry on tribological characteristics. Friction characteristics obtained for a distributed contact (pin‐on‐disc and block‐on‐ring), a linear concentrated contact (pin and vee‐block and block‐on‐ring) and a point concentrated contact (ball‐on‐disc and three cylinder‐cone) are presented. The wear scars were analysed using scanning electron microscopy (SEM) and energy dispersive spectrometry (EDS). The results show different values of friction and wear coefficients for the different types of contact geometry. The paper also assesses the effect of non‐test characteristics, e. g., vibration.     

Atomistic study of lateral contact stiffness in friction force microscopy

The effective stiffness of a friction force microscope tip–substrate system is an important parameter that describes the relationship between lateral force and elastic deformation. In this study, we use a multi-spring model to simplify the system, where two contributions, the tip apex stiffness and the lateral contact stiffness, are discussed in detail. Molecular dynamics simulations are used to characterize stiffness by simulating a tip apex subject to shear or sliding over a substrate surface. The results show that, although the height of the tip apex and tip–substrate orientation affect the various stiffness contributions, the contact itself dominates the overall compliance.     

Residual stress in some elasto-plastic problems of rolling contact with friction

The problem or rolling contact is of a great interest from the practical and cognitive points of view. It concerns for example a wheel passage on a rail, as well as many other processes where rolling or rolling with sliding is involved. Particularly, residual stresses distributions in the subsurface area due to plastic deformations are of significant importance: these stresses strongly influence fatigue limit and cracking tendencies of the material. A motion of the wheel on the rail (or of a roller on a strip) often has a very complex character: it consists of rolling, sliding in the longitudinal direction due to brakings and accelerations, sliding in the transversal direction, etc. Investigations conducted on this field by many authors have not yet delivered a unique solution. The aim of this paper is to determine the influence of some of these components of the wheel motion (separately and in common action) on residual stresses distributions. The problem has been investigated numerically by the FEM method, using the program SEGLA developed by the authors. The program can be applied to solving linear and nonlinear 2D, axisymmetric and 3D problems with elasto-plastic effects in the nonlinear contact and fracture mechanics. It uses three, four, six, eight and nine-node elements and also the special “spring” elements to model contact. The applied algorithm allows automatic analysis of these fragments of boundary, which enter and leave the contact; in the area where the “new” contact is created the program introduces additional elements.     

Force characteristics of dry friction when contact oscillates

A comparative evaluation of the applicability of elastoplastic and rigid-plastic force characteristics of dry friction to calculating contact-oscillating systems is discussed. It is shown that elastoplastic characteristics of the hysteretic type are applicable at amplitudes of oscillations less than or comparable with the ultimate predisplacement. The features are considered of the dynamic links in the sliding friction contact that may lead to the known least dependence of the force of friction. It is noted that application of rigid-plastic friction characteristics to calculation of low-amplitude quasi-elastic contact oscillations leads to contradiction with the experimental data.     

Effects of friction laws on metal forming processes

In this paper, the Coulomb friction law and the constant shear friction law were compared and investigated in detail using a rigid-plastic finite element method with emphasis on their application in bulk metal forming. The ring compression test for two different materials was used to evaluate the two friction laws, and then their effects on metal flow lines and forming loads for various friction-sensitive metal forming processes including strip rolling, ring gear forging, multistep extrusion, and pipe shrinkage and expansion were investigated. It was shown that considerable differences exist between the two friction laws, especially in friction-sensitive metal forming processes.     

Modelling the effect of lubrication on friction behaviour

Models of typical characteristics of the surfaces of two solids interfacing one another under pressure and sliding with respect to each other are described in Models 1 (Figure 1) and 2 (Figure 2). In Model 1 (Figure 1) the asperities, wedges of the harder surface indent into the softer surface due to the applied pressure, thus producing opposing ridges on the surface of the softer component. The gap between the opposing asperities is filled with liquid, establishing boundary lubrication. As sliding is maintained, the ridges are mobilized and an eddy flow is established in the trapped lubricant. The power required to mobilize the ridges and to establish eddy flow in the lubricant is calculated and thus the friction resistance to sliding is determined. Simultaneously, the pressure generated in the liquid due to shear is also evaluated. It becomes clear that the height of the ridge due to indentation is inversely proportional to the speed of sliding. The higher the sliding speed, the higher is the liquid pressure that is countering the loading pressure and the smaller is the indentation. At a high enough speed (to be replaced in due course by the Sommerfeld Number) the entire load is supported by the pressure generated in the liquid, indentation is eliminated and hydrodynamic lubrication commences. The classic model for hydrodynamic lubrication where two inclined surfaces glide atop each other is described in figure 2. Here the gap between the two surfaces (q.J a t their closest point is a monotonically increasing function of Sommerfeld Number (S). The resistance to sliding as established through the shear in the liquid determines thefriction value. This model leads directly to the characteristic of Coulomb or Emontons where for diminishing values of Sommerfeld Number the resistance to sliding is proportional to the pressure (τ = μp) and the proportionality factor is equal to the tangent of the angle of inclination (μ = tana). In the present work, the increase infnction with increasing values of the Sommerfeld Number is also determined. Combining the two models one notices that, a t low speed and Somrfeld Number values, the liquid pressure is not sufftcient tofloat the two surfaces and indentation prevails together with boundary lubrication. With increasing speed (Sommerfeld Number) the height of the ridge (by Model 1) decreases, and when it diminishes to values lower than those predicted for the gap between the surfaces in the second model for the same speed, the boundary lubrication ceases and hydrodynamic lubrication commences.     

Finite element methods for contact problems with friction

The numerical treatment of contact problems involves the formulation of the geometry, the statement of interface laws, the variational formulation and the development of algorithms. In this paper an overview with regard to the numerical simulation of frictional problems is presented when general constitutive equations are formulated in the contact interface. To be most general we will apply a geometrical model and its discretization for contact which is valid for large deformations. Furthermore the algorithms to integrate the interface laws will be discussed for the tangential stress components. Special emphasis is laid on the development of algorithms which allow an efficient treatment of frictional contact problems.