Contributions of adhesion and hysteresis to coefficient of friction between shoe and floor surfaces: effects of floor roughness and sliding speed

Abstract

Improving shoe–floor friction in order to reduce slip and fall accidents requires thorough understanding of the factors that contribute to friction. The friction between a sliding viscoelastic material (shoe) and a hard surface (floor) has two major components: adhesion and hysteresis. This study aimed to quantify the effects of floor roughness and sliding speed on adhesion and hysteresis to determine how each component contributes to the coefficient of friction. Experiments were conducted on a pin on disc tribometer using ceramic tiles with three levels of roughness, six sliding speeds, two common shoe materials and four liquid lubricants. Hysteresis was measured using a lubricant that minimised adhesion. Dry and lubricated adhesion was measured by subtracting hysteresis from the coefficient of friction. Analysis of variance regression models were used to determine the contributions of hysteresis, dry adhesion, sliding speed and fluid to lubricated coefficient of friction. Increased floor roughness led to increased hysteresis, while increased sliding speed reduced both adhesion and hysteresis. These findings are consistent with theory that states that larger asperities increase hysteretic deformation and that sliding speed affects deformation and real area of contact between a viscoelastic material and a hard surface. The model correctly predicted 83% of variation in coefficient of friction based on dry adhesion, hysteresis and fluid dependent constants. The sensitivity of hysteresis friction to shoe material and floor roughness indicates that optimising these parameters may be effective at reducing slip accidents on oily floor surfaces.     

The effect of surface topography on the wear of steel

The pattern of roughness and wear has been obtained by varying the speed, the number of passes and the pre-roughness of the samples in both dry and lubricated sliding conditions. Three-dimensional graphs of wear versus speed versus sliding time and roughness of the worn surfaces were produced and a linear relation between the variation of the roughness and the amount of wear at a high number of passes has been determined. The initial dry wear rate is influenced by the prior surface roughness. In the case of lubricated conditions the influence of prior roughness is not pronounced. In dry sliding the smooth surfaces in the running-in stage roughen and the rough surfaces become smoother, while in lubricated conditions both surfaces become smoother in the first few passes. Sliding perpendicular to the lay produces rougher surfaces and more wear than is the case in the parallel direction.     

Theory of viscoelastic lubrication

We study the lubricated (wet) contact mechanics of a smooth hard cylinder sliding on a randomly rough nominally flat surface of a linear viscoelastic solid. We calculate the rolling and sliding friction, and study the transition from the boundary lubrication to the elasto-hydrodynamic lubrication regime. For the viscoelastic contact the minimum (average) separation does not monotonically increase with the sliding velocity, and the Stribeck curve exhibits new structures not shown for elastic solids.     

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.     

Contact Mechanics and Friction on Dry and Wet Human Skin

The surface topography of the human wrist skin is studied using an optical method and the surface roughness power spectrum is obtained. The Persson contact mechanics theory is used to calculate the contact area for different magnifications, for both dry and wet condition of the skin. For dry skin, plastic yielding becomes important and will determine the area of contact observed at the highest magnification. The measured friction coefficient [M.J. Adams et al., Tribol Lett 26:239, 2007] on both dry and wet skin can be explained assuming that a frictional shear stress σ_f ≈ 15 MPa acts in the area of real contact during sliding. This frictional shear stress is typical for sliding on polymer surfaces, and for thin (nanometer) confined fluid films. The big increase in the friction, which has been observed for glass sliding on wet skin as the skin dries up, can be explained as resulting from the increase in the contact area arising from the attraction of capillary bridges. This effect is predicted to operate as long as the water layer is thinner than ～14 μm, which is in good agreement with the time period (of order 100 s) over which the enhanced friction is observed (it takes about 100 s for ～14 μm water to evaporate at 50% relative humidity and at room temperature). We calculate the dependency of the sliding friction coefficient on the sliding speed on lubricated surfaces (Stribeck curve). We show that sliding of a sphere and of a cylinder gives very similar results if the radius and load on the sphere and cylinder are appropriately related. When applied to skin the calculated Stribeck curve is in good agreement with experiment, except that the curve is shifted by one velocity-decade to higher velocities than observed experimentally. We explain this by the role of the skin and underlying tissues viscoelasticity on the contact mechanics.     

Experimental Evidence of Micro-EHL Lubrication in Rough Soft Contacts

An experimental investigation of the lubricated steady-sliding contact for elastically soft solids is reported. We show that the anisotropic character of the surface roughness has a strong influence in determining the transition from boundary lubrication, where the normal load is fully supported by the asperity–asperity interactions, to the hydrodynamic regime, where a thin fluid layer completely separates solid surfaces from direct contact. In particular, tests have been carried out using a ball-on-flat test configuration to measure the friction coefficient at the contact between a smooth steel ball and a rough PDMS as a function of the sliding speed. The most noteworthy result is that the presence of roughness anisotropy strongly modifies the classical shape of the Stribeck curve as a consequence of local micro-EHL conditions which occur at the contact interface.     

Effects of Interfacial Strength and Roughness on the Static Friction Coefficient

A finite element model is used to simulate sliding inception of a rigid flat on a deformable sphere under combined normal and tangential loading. Sliding inception is treated as the loss of tangential contact stiffness under combined effects of plasticity, crack propagation and interfacial slip. Energy dissipation distribution is used to quantify the relative contribution of these mechanisms on the increased compliance during tangential loading. Materials with different strength and toughness properties, and varying local interface conditions ranging from fully adhered to finite friction, are studied to relate variations in plastic deformations, crack and slip to the sliding inception. For fully adhered contact condition, crack and fracture toughness have no effect on sliding inception, with plasticity, the dominant failure mechanism. A measure of recoverable strain (yield strength to Young’s modulus ratio) is found to be the most influential parameter in sliding inception. Interfacial slip is expectedly the dominant mechanism for sliding inception for lower coefficient of friction, modeling lubricated contacts. Interplay of plasticity and interfacial slip is found to govern the onset of sliding for higher local friction coefficients. Furthermore, the single asperity results are incorporated in a statistical model for nominally flat contacting rough surfaces under combined normal and tangential loading to investigate the stochastic effects due to surface roughness and material property uncertainties. The results show that the static coefficient of friction strongly depends on the normal load, material properties, local interfacial strength and roughness parameters.     

Surface lay effect on rough friction in roller contact

Surface lay describes the direction of the predominant surface pattern. A properly designed surface texture configuration has been recognised as a vital issue affecting lubrication and sliding in machinery applications in the literature. Gaining understanding of this tribological phenomenon is no doubt beneficial in facilitating the production of more efficient machine parts and thus reduces production cost. This paper describes an experimental method to investigate the effect of surface lay on lubricated rolling/sliding of ground roller surfaces. By using the rough friction test rig, different surface lay contacts can be simulated and the friction can be measured. Friction behaviour was interpreted in terms of Stribeck curves (friction coefficient as the function of Hersey parameter [ην/p]). Results show that an optimal contact lay angle that provides a minimum friction value is achievable through rig testing. The relative sliding speed direction has a symmetrical effect on friction at the same lay orientation; for sliding speed angles less than about 80°, the larger the angle, the lower the friction, and vice versa.     

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.     

Effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings with couple stress fluids

This paper presents the theoretical study of the effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings. A more general form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The generalized average Reynolds-type equation is derived for the rough porous step-slider bearing lubricated with Stokes couple stress fluid. The closed-form expressions for the mean load carrying capacity, frictional force and the coefficient of friction are obtained. The performance of the rough porous step-slider bearing is compared with a corresponding smooth porous step-slider bearing. The numerical computations of the results show that the negatively skewed surface roughness pattern increases the load carrying capacity and decreases the coefficient of friction whereas the adverse effects were found for the positively skewed surface roughness pattern.     

Numerical analysis of viscous elastohydrodynamic point contact under stationary conditions

A model is proposed for study of the effect of nonelastic qualities of contacting bodies separated by a fine lubricant film on the contact characteristics. The problem is studied of the movement of the fine lubricant film between the rigid spherical surface and the mobile viscoelastic-layer surface rigidly adhering to the base. A unidimensional Kelvin model of the viscoelastic medium serves as the rheological model of the viscoelastic layer. The calculation results show that the pressure is distributed in the viscous elastohydrodynamic point contact film very much differently from the pressure distribution in the UHD contact, particularly at slow sliding velocities. The friction coefficient is a nonmonotonous function of the sliding velocity. The friction coefficient drops at slow velocities to a minimum as the velocity accelerates, and then it grows.     

Thin film lubrication of sliding point contacts of AISI 52100 steel

The mechanism of thin film lubrication of sliding point contacts of AISI 52100 steel has been studied as a function of load, sliding speed, composition and temperature of the lubricant.Below certain critical combinations of Hertzian pressure, speed and temperature the surfaces are kept apart by an elastohydrodynamic lubricant film. The load carrying capacity of this film depends primarily on the effective viscosity of the lubricant in the contact region which decreases with bulk oil temperature and with increasing sliding speed, because of friction induced thermal effects. After breakdown of the EHD film, boundary lubrication may still prevent severe adhesive wear. The transition from the boundary lubricated regime towards the regime of severe adhesive wear is a function of load (normal force), speed and bulk oil temperature and possibly depends on the conjunction temperature. Irrespective of the initial lubrication condition, oxidation of the steel surfaces leads to the (re)establishment of low friction, mild wear conditions.     

Friction-Induced Vibration by Stribeck’s Law: Application to Wiper Blade Squeal Noise

This paper is concerned with the squeal noise of a wiper/windscreen contact. It is shown that squeal noise stems from friction-induced self-excited vibrations in the context of Stribeck’s law for friction coefficient. The study is specifically focussed on the instability range of velocities and not on the amplitude of limit cycles. The studied dynamic system consists of a single degree-of-freedom mass-spring-damper oscillator submitted to a velocity-dependent frictional force which follows the Stribeck law. The local stability is analyzed by the first Lyapunov method and results in a stability criterion. Experiments have been performed on a glass/elastomer contact lubricated with water. The tribometer ‘LUG’ provides measurements of the vibrational velocity and friction force versus sliding speed. It is found that the instability appears during the transition between boundary and elastohydrodynamic regimes where the negative gradient of the friction versus velocity curve is steep. The apparition and vanishing of instability are correctly predicted by the steady-state stability criterion.     

Chain length effects in boundary lubrication

The effect of additive chain length on friction coefficient and transition temperature is investigated under different test conditions. Carboxylic acids and normal alcohols with 12 – 18 carbon atoms in the chain were used as additives in n-hexadecane base lubricant. It was found that the magnitude of the friction coefficient decreases as the additive chain length is increased. Matching of the additive chain length with the base lubricant had no effect on the friction coefficient. Similarly, the transition temperature at low sliding speeds increased with increasing chain length and was not affected by chain matching. At higher speeds, the acids containing 16 and 18 carbon atoms did not exhibit a transitional behavior within the studied temperature range. These results are discussed in terms of the separation distance between the contacting surfaces, the intermolecular dispersion forces and the structure of adsorbed layers. It is concluded that, at very low speeds, boundary lubrication is controlled by adsorbed monolayers, whereas at higher speeds, where partial elastohydrodynamic conditions prevail, ordered multimolecular layers may influence lubrication.     

Roughness and Lubricant Effect on 3D Atomic Asperity Contact

Large-scale molecular dynamics simulations were performed to study the sliding process of rough surfaces with and without lubricant. In the dry contact, a linear relationship has been observed between the load and the contact area for surfaces with large root mean square (RMS) roughness. However, it becomes nonlinear when the RMS is small. In the presence of adhesion, small roughness results in a large friction force when the surfaces are flattened and the contact area reaches 60 %. In order to confirm this observation, nonadhesive models have been established with an observation that under the combined influence from roughness and adhesion, the contact area plays a crucial role to determine whether the dry sliding is under the domination of roughness or adhesion. In the lubricated sliding, an increase in friction force has been found for the partially lubricated condition because the asperity contact still accounts for a great deal of resisting force. Besides, the lubricant exerts a comparable resisting force to the sliding.     

Super low friction of DLC applied to engine cam follower lubricated with ester-containing oil

This paper presents a material combination that reduces the friction coefficient markedly to a superlow friction regime (below 0.01) under boundary lubrication. A state approaching superlubricity was obtained by sliding hardened steel pins on a hydrogen-free diamond-like carbon (DLC) film (ta-C) lubricated with a poly-alpha-olefin (PAO) oil containing 1 mass% of an ester additive. This ta-C/steel material combination showed a superlow friction coefficient of 0.006 at a sliding speed of 0.1 m/s. A hydrogencontaining DLC coating/steel combination also showed a lower friction coefficient in air than a steel/steel combination, 0.1 vs. 0.8, but no large reduction was observed when the sliding surfaces were lubricated with ordinary 5W-30 engine oil and the PAO oil containing an ester additive. The friction coefficient of the hydrogen containing DLC/steel combination lubricated with the PAO containing an ester additive was above 0.05. On the other hand, the superlow friction performance demonstrates that the rolling contact friction level of needle roller bearings can be obtained in sliding contact under a boundary lubrication condition. It is planned to apply this advanced DLC coating technology to valve lifters lubricated with a newly formulated engine oil in actual mass-produced gasoline engines. A larger friction reduction of more than 45% is expected to be obtained at an engine speed of 2000 rpm.     

A simple theory of asperity contact in elastohydro-dynamic lubrication

The Greenwood and Williamson theory of random rough surfaces in contact has been combined with established elastohydrodynamic theory to provide a theoretical approach to highly loaded lubricated contacts in which the load is shared between hydrodynamic pressure and asperity contact. It is shown that, provided a major part of the load is carried by elastohydrodynamic action, the separation between the two rough surfaces is given (to a first approximation) by the film thickness which would exist between two smooth surfaces under the same conditions of load, speed and lubricant. It then follows that the asperity pressure, both real and apparent, is determined primarily by the ratio of theoretical film thickness to the combined roughness of the two surfaces (h_o/σ). A corollary of this result is that an increase in total load, which has only a small influence on the film thickness, is carried by an increase in fluid pressure and only gives rise to a small increase in asperity contact pressure.     

On the Friction of Carbon Black- and Silica-Reinforced BR and S-SBR Elastomers

Friction of carbon black- and silica-reinforced elastomers is studied experimentally and theoretically, using Persson’s model. The effect of reinforcement fillers on elasticity was determined by dynamical mechanical analysis. Carbon black-filled samples have a higher Young’s modulus than the silica-filled compounds. Silica-filled rubbers have a higher tan (δ) at lower temperatures and a lower loss tangent at higher temperatures, which is a rough indication for higher wet grip and lower rolling resistance, respectively. Friction tests on a ball-on-disk test rig were performed to study the effect of the reinforcement fillers and their amount on the friction between rubber samples (disks) and relatively smooth or rough granite surfaces (balls). The results were discussed and compared with the friction model presented by Persson. It was shown theoretically and experimentally that hysteresis does not play a significant role in the friction of rubber samples in contact with smooth granite and that it plays a minor role in contact with a rough granite sphere. Therefore, the hysteresis contribution of friction can be neglected in the contact of rubbers with just smooth spheres. Moreover, a higher friction coefficient is seen in samples with a higher content of fillers. Silica-filled compounds show a slightly higher coefficient of friction compared with the carbon black-filled compounds. The effect of attached wear debris to the granite surfaces on the friction level has been studied. The results are supported by SEM and confocal microscopic images of the wear debris itself and wear debris attached to the granite spheres, respectively.     

Influence of Polymer Filler on Tribological Properties of Thermoplastic Polyurethane Under Oscillating Sliding Conditions Against Cast Iron

The tribological behaviour of unfilled thermoplastic polyurethane (TPU) and a polymer sphere filled (TPUG) thermoplastic polyurethane have been studied under oscillating sliding condition against cast iron as a counterpart. In the case of unfilled TPU, the wear mechanisms are dominated by particle detachment and roll formation. In principle, TPUG also showed a similar wear mechanism as that of unfilled TPU; in addition, particle pull-out and delamination are also observed. Wear volume of TPUG was significantly higher than that for the unfilled TPU and this is attributed to the different material removal processes taking place in the material during sliding. The polymer spheres as a filler material deteriorated the wear resistance of TPU because of improper adhesion and bonding of filler in the TPU matrix and therefore it contributed to more wear. In case of TPU the friction behaviour was strongly dependant on the temperature and surface roughness of the counter body. The results showed that below the glass transition temperature higher friction values are observed with higher counter body surface roughness. However, above the glass transition temperature, higher friction values are observed with a smoother surface roughness of the counter body. In case of TPUG, the friction behaviour was not significantly dependent on surface roughness of the counter body.     

Influence of Lubricant Additive and Surface Texture on the Sliding Friction Characteristics of Steel under Varying Speeds Ranging from Ultralow to Moderate

A newly developed tribometer that undergoes significant changes in sliding speed, ranging from ultralow (5 μm/s) to moderate (17 cm/s), was used to study the lubricated friction characteristic of steel. In this study, the friction characteristics of stearic acid-formulated oil were studied to clarify the effects of surface roughness or surface roughness texture on friction. Several kinds of specimens having isotropic and anisotropic surface roughness with different textures were used. For an isotropic surface, a rougher surface resulted in low friction under low-speed conditions. The same surface produced high friction under high-speed conditions, where macroscopic hydrodynamic action was predominant. Remarkably less friction was observed in the transverse than in the longitudinal direction when the specimen had anisotropic roughness. This difference was particularly notable under ultra-low-speed conditions. Two other parameters of skewness and kurtosis of roughness distributions show that low friction was obtained when surface roughness distribution approached normal. It appears that the low friction observed with a rough surface or a transverse roughness direction could be explained by the microscopic hydrodynamic action of fluid together with the lubricity of the adsorbed molecular layer.