A non-uniform friction distribution model for partial slip fretting contact

In partial slip fretting contact, the coefficient of friction (CoF) is often assumed to be constant along the contact surface. The literature shows that the CoF is related to the relative slip, which varies in the slip region of a partial slip contact. This study develops a methodology to consider the effects of non-uniform CoF distribution in the slip region. Two cases were investigated. In the first case, the axial stress on the substrate (specimen) was absent, while the axial stress was present in the second case. In both cases, the CoF was assumed to be static, kept constant in the stick zone, and varied linearly in the slip region. A closed form solution was developed to determine the stick/slip region size and the equivalent constant CoF for the no-axial stress case, and it was supplemented with finite element analysis. In the second case, where an axial stress was applied on the specimen, the stick/slip region size and the equivalent constant CoF were determined by finite element analysis. The equivalent constant CoF with an axial stress was slightly greater than that without the axial stress due to the larger slip zone size. The stress state in the contact region based on the equivalent constant CoF was comparable to its counterpart from the linearly varying CoF case.     

Effect of variable friction coefficient on contact tractions

Friction coefficient plays an important role in determining the contact tractions and consequently the stresses that drive damage mechanisms in components subjected to fretting fatigue. Friction coefficient evolves to different magnitudes at different points in the contact interface. Effect of this spatial variation in friction coefficient on the shear distribution for contacts involving similar isotropic materials has been presented in this paper. Full sliding tests have been conducted to obtain friction coefficient as a function of sliding distance. Well characterized set of experiments to determine the average friction coefficient in fretted specimens is briefly discussed. Existing analysis for obtaining the shear traction for arbitrary smooth profiles has been modified to take the variation of friction coefficient from one point to another into account. Using this analysis, spatial variation of friction coefficient in fretted specimens has been obtained. It has been found that using a constant friction coefficient (equal to the slip zone friction coefficient) throughout the contact zone is a good enough approximation in most of the cases. However, in some cases, when the slip zones extend into regions where the friction coefficient has not reached the asymptotic value, actual distribution of friction coefficient gives a different shear stress distribution as compared to a constant slip zone friction coefficient.     

Finite Element Analysis of Precursors to Macroscopic Stick–Slip Motion in Elastic Materials: Analysis of Friction Test as a Boundary Value Problem

In this study, we apply the finite element method to investigate precursor to frictional sliding phenomena arising immediately prior to macroscopic stick–slip transitions in elastic bodies within the framework of a continuum theory. Using a numerical model that mimics an actual experimental system, we study the behavior of contact surface nodes to assess the influence of stiffness, driving velocity, initial conditions, and discretization conditions on the propagation characteristics of microscopic slips. In particular, we show that the initial distribution of frictional stress arising due to the Poisson effect has a significant effect on the propagation characteristics in slip regions. Next, based on the results of a finite element analysis of precursor phenomena that accounts for the influence of bulk compliance, we consider the determination of parameters in rate-dependent friction models. With regard to the behavior of sliding friction, we show that the relationship between friction tests and friction models is fundamentally different from the relationship between material tests and constitutive models for material deformation. We conclude that a proper understanding and classification of friction tests, friction models, and the relationship between these tests and boundary value problems are crucial ingredients in the application of computer-aided engineering techniques to sliding-friction phenomena; indeed, friction tests must ultimately be treated as boundary value problems.     

On the theory of power transmission by a flat,elastic belt

Frictional power transmission from a pulley to a thin, flat, elastic belt is studied. The derivation of a new formula for the tension ratio $\text{T}{}_1\text{T}{}_2$ in the creep regime stems from the quasi-static equilibrium equations and includes the effects of belt elasticity, flexural rigidity and varying coefficient of friction along the contact arc. The dynamic coefficient of friction at any point on the contact arc is determinable from slip and tension measurements on an operating belt A simplified solution is found by utilization of experimental slip measurements reported by Grimmer and Thormann. A condition of constant tangential shear stress is consistent with these data. Euler's formula proves to be inconsistent with the test data. A solution in the slip regime is proposed that reduces to Eulerian form in the case of slip over the entire contact arc.     

A class of slipline field solutions for metal machining with slipping and sticking contact at the chip-tool interface

In the present investigation slipline field solutions for orthogonal machining are presented when the plastically stressed region in the chip/tool contact length consists of both slipping (τk) and sticking (τ=k) zones. The interface friction in the slipping region is assumed to obey Coulomb's law and the fields are analysed using the linear approximation to the above non-linear boundary value problem as suggested by Dewhurst. The range of validity of the above slipline fields is examined from the consideration of overstressing of rigid vertices in the assumed rigid regions. Results are presented for variation of cutting forces, cutting ratio, chip curl radius and contact length with variation in rake angle and interface friction coefficient. Solutions incorporating elastic effects are obtained by the method suggested by Childs. Results from the theoretical analysis are compared with experimental values reported in literature.     

Modeling of surface roughness effect on dry contact friction in metal forming

Interfacial conditions such as friction and roughness substantially affect the process characteristics of metal forming. This study developed a dry friction model that accounted for the adhesion and interference effects of surface roughness. A sliding friction coefficient was suggested to provide fundamental information about the interfacial conditions of the contact surface. The proposed model was easily verified by published experiments and predicted values agreed with experimental results. Accordingly, friction coefficient ?? clearly increased as relative roughness R _m (=?roughness of tool $ R_a^T $ /roughness of workpiece $ R_a^M $ , measured as interference effect) increased. Simulations confirmed that the friction coefficient ?? decreased as dimensionless stress S _m (=?contact pressure p _m /tensile strength $ \sigma_u^0 $ ) increased at small strain hardening exponent n-values. Under the conditions of large n and small R _m values, the friction coefficient ?? initially decreased and then increased. It then slightly decreased as dimensionless stress S _m increased. However, this trend became less apparent as relative roughness R _m increased since friction coefficient ?? simply decreased.     

Thermal Behaviour of a Slipping Wet Clutch Contact

Wet clutches are used in automatic transmissions to enable gear changes and also to reduce energy loss in the torque converter. These friction devices are susceptible to stick–slip effects, which result in the vehicle giving an unsteady ride. Stick–slip effects can be avoided by ensuring the wet clutch and lubricant combination produces a friction coefficient that increases with sliding speed. Although wet clutches have been studied throughout the industry for many decades, the mechanism of the generated friction is still not fully understood. It is known that, because of the fibrous nature and thus very large roughness of friction material, the overall contact between clutch plates actually consists of many small, independent, contact units, which are the sites of the generated friction. Some authors have suggested that a temperature rise due to friction either at these contact units or of the overall clutch plate may be important in controlling friction behaviour. In this study, the flash temperatures at the contact units formed in the wet clutch contact have been measured using an infrared camera. Three friction materials have been tested. It was found that measured flash temperature in a pure sliding system similar to that present in a slipping clutch remain well below 5 °C, and are therefore unlikely to play a major role in the observed friction-speed dependency of slipping wet clutches at speeds below 2 m/s.     

Some Observations on Frictional Force During Fretting Fatigue

Frictional force behavior during fretting fatigue and its interdependence on other fretting variables are investigated. Both coefficient of static friction and the normalized frictional force (i.e., the ratio of frictional force and normal contact load) increase during the earlier part of a fretting fatigue test and then both reach to a stabilized value. The variation of temperature in the contact region and normalized frictional force with increasing cycle numbers and bulk stress show similar trend implying that normalized frictional force represents the average friction in the contact region during a fretting fatigue. An increase in bulk stress, relative slip, and hardness of pad material results in an increase of the normalized frictional force, while an increase in contact load, frequency and temperature decreases the normalized frictional force. The normalized frictional force is also affected by the contact geometry. On the other hand, coefficient of static friction increases with an increase in the hardness of mating material, temperature and roughness from shot-peening treatment, but is not affected by contact geometry and displacement rate. Further, the normalized frictional force is not affected by the contact geometry, roughness and applied bulk stress level when fretting fatigue test is conducted under slip controlled mode, however it increases with increasing applied relative slip and decreasing contact load in this case.     

Friction and wear of highly-elastic solids

It is shown that the normal forces set up by large shear deformations make sliding impossible when a critical compressive deformation, of the order of 10%, is imposed on a sliding block of highly-elastic material. When the compressive load is maintained constant, rather than the deformation, the way in which the compressive stress is distributed leads to sliding only by means of slip bands which originate at the leading edge of the block and then pass through the contact zone from front to back, as found by Schallamach¹. Thus, a discontinuity is predicted in frictional sliding as the compressive stress is increased from zero, and this occurs at a critical value which depends upon the coefficient of friction, the shear modulus of the material, and the detailed shape of the contact zone. Corresponding changes in wear behavior are inferred.     

Investigation of the overall friction coefficient in single-pass scratch test

Single-pass scratch test on bilinear elastic–plastic materials with a conical indenter was simulated using a three-dimensional finite element model. The influence of the interfacial friction coefficient μ_s and the apical angle α of the indenter on the induced maximum tangential force F_T, normal force F_N, and the overall friction coefficient μ=F_T/F_N, were systematically studied. It was found that the induced tangential force is greater than the normal force when the apex is small and vice versa when the apex is large. The tangential force increases with μ_s, but the normal force decreases with μ_s. The overall friction coefficient μ was found to increase linearly with μ_s and tangent of the attack angle of the indenter. The relationship between the adhesion frictional component (μ_a), the plowing frictional component (μ_p), and the interfacial friction coefficient μ_s was analyzed. An analytical model for the overall friction coefficient μ was also developed based on the interaction between the indenter and the specimen and compared to the numerical results. The model was found to yield a good agreement with the finite element simulation results.     

Temperature at discrete contacts in slipping friction with lubricant

The temperature at individual contacts of rough surfaces, i.e., the flash point T _fl in slipping friction with lubricant, is determined numerically. It is shown that the appearance of T _fl during thermocycling is a high-frequency wave process. The temperature over the depth of the contacting surfaces is determined, in the form of damping temperature waves. The surface temperature in friction with lubricant may be determined using two parameters: the conventional heating thickness of a uniform body; and the heat-assimilation coefficient.     

Flaring and nosing process for composite annoy tube in circular cone tool application

An elasto-plastic incremental finite element computer code based on an updated Lagrangian formulation was developed to simulate the flaring and nosing processes of a metal tube in the asisymmetric condition. The extended r _min technique was used to treat the elastic–plastic stress state and to solve contact problems at the tool–metal interface. A modified Coulomb’s friction law was introduced to treat the alternation of the sliding–sticking state of friction at the contact interface. The forming performed analysis using the finite element method and experiment. To examine the influence of the thickness ratio and the optimum punch semi-angle and friction on the forming load of the two-ply metal tubes consisting of soft aluminum, hard aluminum, and copper. The calculated tube geometries and the relationship between punch load and stroke are in good agreement with the experimental data.     

基于弹流润滑的无级变速器滑移控制安全区域分析

针对无级变速器滑移模式下传动失效概率增大的问题，基于弹流润滑理论分析了不同传递转矩和相对滑动速度情况下，从动轮摩擦副油膜压力、厚度及其剪切应力变化情况，建立了安全裕度模型，基于油膜极限剪切应力与最大剪切应力计算了摩擦副的安全裕度，并确定了滑移控制的安全工作区域，为滑移控制策略的制定与优化提供了依据。研究结果表明：随着从动带轮传递转矩、相对滑动速度的增大，摩擦副的安全裕度逐渐减小；当传递转矩小于130 N·m时，在所有相对滑移速度范围内均可保证摩擦副油膜处于安全状态;当传递转矩大于130 N·m时，随着相对速度的增大，摩擦副油膜失效概率增大。     

A contribution to the theory of friction

The nature of the interaction between a rigid spherical asperity and an asperity governed by the stress/strain law $\text{}\text{?}\text{gs = B}\text{}\text{?}\text{ge}{}^{\mathrm{n}}$ is studied. The interfacial shear stress is defined by fτ_max where $\text{0 </ ? </ 1}$, τ_max being the maximum allowable shear stress at the contact. By integrating the total effect of a population of such surface asperities expressions for the total frictional forces and the total load are derived. The value of the coefficient of friction is thus obtained and the special conditions for perfectly plastic and elastic behaviour are considered. In both cases the friction coefficient is seen to contain a term defined by the deformation and dependent on surface roughness and a term totally defined by ?.     

Dependence of polymer sliding friction on normal load and contact pressure

The sliding friction of bulk polymers was studied varying the normal load, contact pressure and sliding velocity. The variation of the area of apparent contact A with normal load W was also measured both under the sliding and unloaded conditions. For the sliding condition A ∝ W, while for the unloaded condition A ∝ Wⁿ where n is less than unity. The friction measurements were performed on a tribometer in the low load range and on a lathe using a strain gage dynamometer in the high load range. It was found that the coefficient of friction depends upon the velocity and pressure and the variation can be explained by the adhesion theory of friction in the light of the conditions at the interface. The measurement of sliding friction in an extrusion process shows that the coefficient of friction decreases with contact pressure and the interface friction shear stress is almost equal to the bulk shear strength of the material. All of these findings support the adhesion theory of friction for polymeric materials.     

Rolling-Sliding Analysis in Ball Bearing Considering Thermal Effect

An analytical method is applied in the calculations of ball contact angles varying with the position angle of a ball bearing with a centrifugal force. This is further extended to investigate the thermal slipping behavior occurring at the contact surface of the inner raceway. The sliding velocities at the contact area are analyzed in the present study by the ball bearing contact mechanisms. The shear stress created at this contact surface is evaluated by considering the temperature-pressure dependence of the lubricant viscosity. The contact temperature of a ball and the inner raceway is obtained if the frictional heat created by the shear stress is available. Under the condition of controlling the outer raceway temperature, the thermal deformations of all components of a ball bearing are taken into account in the evaluation of bearing performance. Comparisons are made for several parameters, including the normal load, linear slip velocity, and linear traction force, between the results of considering the thermal effect or ignoring it. The friction torque evaluated by taking the thermal effect into account is higher than the torque evaluated when ignoring the thermal effect.     

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.     

Sliding wear behavior of Fe-Al and Fe-Al/WC coatings prepared by high velocity arc spraying

A comparative study was carried out to investigate the microstructure and tribological behavior of Fe-Al and Fe-Al/WC iron aluminide based coatings against Si₃N₄ under dry sliding at room temperature using a pin-on-disc tribotester. The coatings were prepared by high velocity arc spraying (HVAS) and cored wires. The effect of normal load on friction coefficient and wear rate of the coatings was studied. The microstructure and the worn surfaces of the coatings were analysed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersion spectroscope (EDS). The results showed that, the main phases in both coatings were iron aluminide (Fe₃Al and FeAl) and α. WC/W₂C particles were embedded in the matrix of the composite coating. With adding WC hard particles, the Fe-Al/WC composite coating exhibited higher wear-resistance than Fe-Al coating. But the friction coefficient of both coatings showed little difference. As the load increased, the friction coefficient decreases slightly due to a rise of friction contact temperature and larger areas of oxide film formation on the worn surface, which act as a solid lubricant. Increasing load causes the maximum shear stress occurring at the deeper position below the surface, thereby aggravating the wear. The coating surface is subjected to alternately tensile stress and compression stress during sliding, and the predominant wear mechanism of the coatings appears to be delamination.     

A Load-Dependent Model to Investigate the Velocity Dependence of Friction Coefficient: ZrO2/Polymer Nanocomposite

Using dynamic finite simulations, we investigate how the friction coefficient of ZrO₂/polymer nanocomposite depends on the sliding speed. The load-dependent model we developed corresponds to common friction systems, where the friction couples are sliding under fixed load for various speeds. Here, we study the effect of the sliding speed on the contact distance between two contacting bodies. In accordance with experimental observations and theoretical arguments, we find the contact distance increased with the sliding speed. We show that the dependence of the reaction force on sliding speed can be rationalized by assuming that the frequency dependence of the polymer chains relaxation times is affected by the damping effects of contact stress. By investigating the energy dissipation, we show how the friction coefficient is affected by the sliding speed. The deformation volume and relaxation times decreased with the increasing sliding speed, which result in the decreasing of energy dissipation. Then, the work in pushing the top cylinder across the bottom plateau decreases, results in a reduction of the mean horizontal reaction force and friction coefficient.