Thermal effect in hydrodynamic lubrication of line contacts-Piezoviscous effect neglected

Thermal effect in high-speed rolling element bearings has been investigated numerically following a computationally efficient method developed by Elrod and Brewe [11. Viscous shear heating effects on both film thickness and rolling friction are investigated for a line-contact geometry assuming fully flooded lubrication. Thermal load-carrying capacity and rolling friction of the line contact have been numerically calculated for varying rolling speeds from 5 to 40 m/s and dimensionless film thickness between 10⁻⁴ and 10⁻³. Results indicate marked influence of viscous shear heating on the load-carrying capacity, film thickness and rolling traction at high rolling speeds. Neglecting thermal effect at high rolling speeds would lead to gross overestimation of load capacity, film thickness and traction. Results are presented for pressure and temperature distribution within the contact for various rolling speeds and film thicknesses.     

Mixed film lubrication of strip rolling using O/W emulsions

A numerical study on the oil concentration effect of O/W emulsion in cold rolling operating in the mixed film lubrication regime has been carried out. The developed scheme is able to calculate oil concentration at any point within the inlet zone (IZ) and work zone (WZ), rolling pressure, film thickness, and contact ratio for various rolling speeds. Hence the intertwined effects of oil concentration of the supplied emulsion and rolling speed on strip rolling are discussed. The study encompasses mixed film regime with speeds S range from 10⁻⁵ to 10⁻³ and supplied emulsion's oil concentration levels λ_ds range from 5% to 90%. The result shows that a moderate rise in oil concentration occurs in the IZ followed by a rapid one at the beginning of the workzone. In most cases, the oil in the emulsion would have been transformed from disperse phase to continuous phase throughout the WZ. Notwithstanding further concentration, which depends on the oil concentration of the supplied emulsion, could still occur in the WZ. The effect of the concentration process is predominantly seen in the development of the lubricant pressure whilst its effect on the total pressure is less pronounced. The analysis of the results suggests that it is possible to lower the emulsion oil concentration without detrimental effects on the rolling process; and from the analysis of the outlet film thickness, it is shown that the variation of emulsions’ oil concentration could control the exit lubricant film thickness and consequently the strip surface quality.     

Characteristics analysis of aero-engine whole vibration response with rolling bearing radial clearance

For the influence of rolling bearing radial clearance on the whole vibration in the aero-engine whole system, a real engine rotorbearing- casing whole model is established. The rotor and casing systems are modeled by means of FEM; the support systems are modeled by lumped-mass model; rolling bearing radial clearance and strong-nonlinearity of Hertz contact force at four different supports are considered. The coupled system response is obtained by the numerical integral method. The characteristics of the whole vibration response are analyzed. For rolling bearing at a typical support, the rotor, outer ring of rolling bearing and casing response characteristics at different rotating speeds are analyzed. The changing law of contact forces for each ball and the global contact forces at different speeds are analyzed. The influence of the radical clearance on the contact forces on the whole vibration is analyzed. The results show that the contact forces will be larger and the acceleration amplitude jumps obviously when the radial clearance is increased, and due to the variable stiffness of the rolling bearing, the natural frequency will appear when the stiffness changes fiercely, that is frequency-locked phenomenon. When the radical clearance is larger and the rotating speed is between two critical speeds, the rotor squeezes the outer ring now and then. Reducing the radical clearance can reduce the whole vibration and increase the rotor’s stability.     

Numerical simulation of wheel rolling over rail at high-speeds

In the paper, a contact element method was used to analyze a wheel rolling over a rail at high-speeds. The rolling contact of the wheel and rail was considered as a two-dimensional rolling contact in a pure rolling and steady state. The loads applied to the wheel are the different axle-loads of train and the inertia forces caused by accelerations of the wheel in its pure rolling state. The convergence of non-linear numerical analysis on frictional contact was reached through repeated contact calculations. The normal contact pressure and tangential traction on wheel/rail contact surface were obtained for the different axle-loads and the different rolling speeds. The highest rolling speed in the numerical simulation is 400 km/h. Through the detailed numerical simulation and analysis, it was found that there exist some differences between the traditional Hertzian contact pressure and the present normal pressure. With the speed increasing the normal contact pressure becomes larger in the leading area of the contact surface, and becomes smaller in the trailing area of the contact surface. However, in the trailing area the tangential traction become larger, and in the leading area becomes smaller with the speed increasing.     

Experimental and numerical study of O/W emulsion lubricated strip rolling in mixed film regime

An experimental and numerical study of cold rolling lubricated by O/W emulsion has been carried out. The strip rolling experiment was carried out on a Hille experimental rolling mill with a view to study the performance of emulsion lubrication in terms of practical rolling parameters. Accordingly, rolling parameters such as rolling force and torque were measured. The experimental measurements compare favourably with the computed results from a numerical scheme developed by the authors. The scheme, based on a two-phase lubricant model, is capable of calculating the oil concentration at any point within the inlet zone and work zone, rolling pressure, film thickness, and fractional contact area ratio associated with strip rolling under mixed film lubrication at different rolling speeds. Using this scheme, the intertwined effects of an emulsion’s parameters such as: oil concentration, mean oil droplet size, and rolling speed on strip rolling were investigated. The numerical study encompassed the mixed film regime for speed, S ranges from 10⁻⁴ to 10⁻², supply oil concentration level λ_ds from 1 to 10%, and oil droplet size D _S from 5 to 10. Experimentally, the differences between water, oil and emulsion-lubricated rolling are not discernible except for film thickness. At a low speed of 10 RPM, force and torque of water-lubricated rolling are marginally higher than oil- or emulsion-lubricated ones. However, the difference between emulsion and neat oil is not apparent. The numerical results show the occurrence of a moderate oil concentration increase in the inlet zone followed by a sharp one at the beginning of the work zone. The effect of the concentration process is predominantly seen in the film thickness and the lubricant pressure whilst its effect on the total pressure is less pronounced. The analysis of the results suggests that it is possible to lower the emulsion oil concentration without any adverse effect on the rolling process. This principle can be used to control the outlet lubricant film thickness and hence the surface quality of the rolled strip.     

Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium

This work aims at studying the stress relaxation behavior of a nominally flat (rough) surface of a viscoelastic material in contact with a rigid half space. The effect of temperature will be included through the concept of activation energy using Arrhenius's equation. A synthesized Cantor-Borodich (C_B) profile is used to construct the rough surface. C_B profile has two scaling parameters, a and b, and different heights h_i for each generation of asperities. This simple model is applicable for fractal surfaces in which a single exponent (the fractal dimension) is enough to describe their quality.The surfaces in contact are viscoelastic, and they are assumed to behave according to the linear Maxwell model. An asymptotic power law is obtained, which relates the force and the bulk temperature acted on the punch to its approach. This model is valid only when the approach between the punch and the half space is in the range of the roughness size. The proposed model admits an analytical solution for the case when the deformation is linear thermo-viscoelastic. The obtained model shows a good agreement when compared with the experimental results obtained by Handzel-Powierza et al. [Handzel-Powierza Z, Klimczak T, Polijaniuk A. On the experimental verification of the Greenwood-Williamson model for the contact of rough surfaces. Wear 1992;154:115-24].     

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.     

A study of the relationships governing starting rolling friction

In this study the behaviour of the small displacement of starting rolling friction in the rolling contact between a flat surface and rollers is investigated and a rolling friction force-displacement relationship in the region of the starting rolling displacement is proposed by using the fact that the area of the hysteresis loop increases linearly with the nth power of the rolling friction.Furthermore, the behaviour of the hysteresis loop at the rolling contact surface has been investigated experimentally and theoretically. It was found that the area of the hysteresis loop increases linearly with the second power of the rolling distance in the region of a starting rolling displacement.     

Temperature rise due to sliding in rolling/sliding elastohydrodynamic lubrication line contacts: an efficient numerical analysis for contact zone temperatures

An efficient numerical method based on Lobatto quadrature analysis is adopted for a rigorous analysis of temperature in elastohydrodynamic lubrication (EHL) line contacts. Temperature distributions are calculated for maximum Hertzian pressures and rolling speeds varying between 0.5 to 2.0 GPa and 1 to 30 m/s, respectively. Significant mid-film temperature and surface temperature increases have been observed at higher rolling speeds with an increase in loads and slip ratios. Results have been compared with the results of Manton, S. M., O'Donoghue, J. P. and Cameron, A., Temperatures at lubricated rolling/sliding contacts. Proceedings of the Institution of Mechanical Engineers, 1967–68, 182(417), 813–824. An empirical equation is presented for the prediction of non-dimensional maximum mid-film temperature in the contact zone in terms of the dimensionless thermal loading parameter Q, dimensionless load W and slip S, as:

     

Dynamic analysis of indentation rolling resistance of steel cord rubber conveyor belt

To study the variation trend of the indentation rolling resistance of a rubber conveyor belt under different environmental temperatures, the sinusoidal compression displacement test was first carried out on the rubber matrix at six temperatures between -20 °C and 40 °C by a high and low temperature universal testing machine. Elastic modulus E₁, E₂ and loss factor tan θ of the rubber matrix were identified using the Fourier series. Then, the dynamic contact characteristics between the idling roller and conveyor belt were analyzed by the viscoelastic mechanics theory. Hence, the calculation equation of the indentation rolling resistance in the full thickness direction of the conveyor belt was deduced. Finally, a practical calculation and experimental verification of the indentation rolling resistance of the steel cord rubber conveyor belt at different temperatures were conducted. The results showed that the drop of the indentation rolling resistance of the conveyor belt was significant when the temperature was increased in the range of -20–10 °C. In the range of 10–40 °C, the influence of the increase of the ambient temperature on the indentation rolling resistance was relatively weak. Additionally, it is found that the contact force in the vertical direction and the idling roller diameter are important factors that affect the indentation rolling resistance of the conveyor belt. The influence of belt speed on the indentation rolling resistance is weak.     

The elastohydrodynamic transition speed for spheres sliding on lubricated rubber

An elastohydrodynamic number derived elsewhere in the literature [1] characterizes the onset of hydrodynamic support for a rigid sphere sliding on a lubricated viscoelastic base. This number includes elastic properties of the base track, in contrast with previous studies where such have been neglected. A generalized coefficient of sliding friction has been defined as the actual coefficient of friction divided by the tangent modulus of the viscoelastic material. Experimental plots of the coefficient of friction versus sliding speed for spheres sliding on lubricated rubber are shown to produce a relatively sudden decay in coefficient at the transition speed from “dry” to elastohydrodynamic contact. These plots in turn fit closely on a master curve of generalized coefficient of friction versus the elastohydrodynamic number.The inclusion of surface roughness on the sphere produces both a higher value of the generalized coefficient prior to the transition speed and a higher sliding velocity at which the transition itself occurs. Furthermore, the rate of decay for the generalized coefficient of friction appears distinctly greater for rough spheres. The overall effect of roughness is to reduce the difference between the dry and wet coefficients of sliding friction. Random abrasion of the spheres with emery paper of known grit size appears to be an effective method of inducing surface roughness on the spheres. The nature of all the experimental curves may be satisfactorily explained by squeeze-film theory.An important application of the sliding of smooth and rough spheres on a lubricated flexible base is the sliding/slipping behaviour of automobile tyres on a wet road surface during normal rolling.     

Multilevel solution for thermal elastohydrodynamic lubrication of rolling/sliding circular contacts

A fast multigrid approach is presented for the analysis of thermal elastohydrodynamic lubrication (EHL) under rolling/sliding circular contacts at high loads and high slip ratios with low computing time on a personal computer. This fast solver combines directiteration, multigrid, Newton-Raphson, Gauss-Seidel iteration, and multilevel multi-integration methods into one working environment that can reduce the computational complexity from O(n³ to O(nlnn) for the thermal EHL problem under rolling/sliding circular contacts. Since the couped Reynolds and energy equations are simultaneously solved by the Newton-Raphson scheme, the iteration for the convergence solution is less than those of the classical approach. Results show that thermal effects on the pressure profile and film thickness are significant for a wide range of loads, speeds and slip ratios. The maximum midfilm and surface temperature rise in the Hertzian contact region increases with increasing slip ratio, dimensionless speed, and load. The minimum film thickness decreases with increasing load and slip ratio, and decreasing dimensionless speed.     

Static coefficient of rolling friction under heating

The effect of heating, the normal load, and the radii of the members in contact on the static coefficient of rolling friction is considered. The design of a new apparatus for measuring the parameters of rolling friction over an inclined plane at elevated temperatures is presented. A need to specify the effect of the type of the materials in contact, as well as the roughness and contact geometry, on the static coefficient of rolling friction is emphasized.     

Lubrication of Strip Rolling in the Low-Speed Mixed Regime

An analytical model for strip rolling in the low-speed mixed lubrication regime is developed. An average Reynolds equation for longitudinal saw-tooth surfaces under conditions of high fractional contact area, is combined with an analysis for asperity flattening under conditions of bulk plastic flow, to treat lubrication in the mixed regime. Analyses for the inlet zone and work zone and the influence of pressure on viscosity are included in the model. The model indicates that hydrodynamic lubrication effects are important at much lower speeds than previously considered possible. The film thickness predicted by the model is somewhat smaller than that measured using the oil drop method in rolling aluminum alloy with a mineral oil.     

Stress-In-Motion (SIM) system for capturing tri-axial tyre–road interaction in the contact patch

A unique measuring system for the quantification of tri-axial (3-D) tyre contact force (or stress) distributions was designed, developed and used in several studies since 1994. The uniqueness of the system is defined by a textured measuring surface in order to represent a typical “textured” road surface. The system is referred to as the Stress-In-Motion (SIM) system. A single SIM measuring pad testing area comprises a total of 1020 supporting pins and a transverse array of 21 sensing elements, covering the entire tyre contact patch with in a single run. The SIM pad measuring system is modular in concept, allowing multiple SIM measuring pads to be used for e.g. wide base truck tyres, or a dual tyre configuration, or full axle measurements – using a quad SIM pad measuring system configuration. Tyre contact force (or stress) distributions are simultaneously captured in the three orthogonal directions X, Y and Z for a single, dual or full axle truck tyre configuration. Each of the sensing elements has a 9.7 mm diameter circular contact surface area (∼73.9 mm²) and is dimensionally optimised, allowing measurements in various tyre rolling conditions on a textured measuring surface. The textured surface induces some pre-conditioning of tyre–road contact properties, as it has small gaps around all supporting and measuring pins. The system is installed flush with the road surface, preferably on a rigid support base, and can be used for real tyre (or truck) rolling conditions. A single SIM measuring pad contains 63 strain measuring channels (3 × 21) for the sensing elements. Aspects such as SIM system design, sensing element calibration, system usage and outputs of specially developed software are illustrated. Several results of tri-axial road contact stress distributions are also presented.     

Investigation of the temperature distribution in the elastohydrodynamic oil film

Results of investigations of the temperature distribution in elastohydrodynamic (EHD) contacts carried out on a two-disc machine for various contact parameters (rolling and sliding speeds and maximum Hertz pressures) are reported in this paper.The experiments were carried out with the aid of thin layer temperature transducers made of titanium that were evaporated onto the disc's surface in vacuum.Analysis of the errors affecting the temperature measurements in EHD contact was also carried out. It was shown that contact pressure and transducer insulation had a substantial influence on the precision of the temperature measurements made by the thin layer transducer. Error analysis has permitted the determination of the real value of the temperature rise in the contact zone by the application of suitable corrections.It was found that the relative sliding velocity and the contact loading force have substantial and similar influences on the maximum temperature rise in the EHD contact; however, the influence of the rolling velocity is relatively small.A simple empirical formula which permits the calculation of the maximum temperature rise in the contact zone as a function of load and velocity for the investigated oil is presented in this paper. The general formula as a function of non-dimensional parameters is also given. It was found that theoretical formulae which include the exact dependences of the viscosity variation on pressure and temperature (e.g. the Kannel equation) provide the best fit to the experimental results.Good agreement of the results obtained with other researchers' experimental results was also found.     

Preliminary investigation of the effect of dimple size on friction in line contacts

The scale of surface texture is becoming an important issue of surface texture design, particularly for the condition of low speed and high load. Experiments were carried out to investigate the effect of dimple size on friction under line contact condition. The patterns of dimples distributed as square array were fabricated on the surface of brass disks. Each pattern has the same area density of 7%, the same depth over diameter ratio h/d of 0.03, and dimple diameter d varying from 20 to 60 μm. The frictional tests of the brass disk sliding against a stationary cylindrical surface of bearing roller were conducted. It was found that the pattern with dimple diameter of 20 μm presented the effect of friction reduction. For the further understanding of the effect of dimple size under line contact condition, numerical simulations were also carried out to evaluate the hydrodynamic pressure within the contact of cylindrical and plane surfaces. The effects of dimple size and radius of the cylinder on the load carrying capacity were evaluated and discussed.     

The Prediction of Contact Pressure–Induced Film Thickness Decay in Starved Lubricated Rolling Bearings

Under starved conditions the thickness and distribution of the lubricant film in an elastohydrodynamically lubricated (EHL) contact is directly related to the distribution of lubricant on the track in the inlet to the contact. In starved lubricated rolling bearings this lubricant distribution is determined by many effects. The authors have developed a model to predict the oil lost from the track induced by EHL pressure with no replenishment. A complete bearing is modeled with multiple rolling element EHL contacts and with the applied load to the rolling elements varying along the circumference of the bearing. Results of the oil layer thickness on the track are presented for a ball bearing and a spherical roller bearing for different bearing loads and rotational speeds. The predicted layer thickness decay rate for a ball bearing is significantly larger than for a spherical roller bearing and the predicted effect of the bearing load on the decay rate is small compared to the effect of the rotational speed. The predicted decay periods due to the contact pressure effect are small compared to the observed (grease) life of bearings. The results show that a bearing cannot sustain an adequate layer of oil on the running track unless significant replenishment takes place.     

Rolling cylinder on an elastic half-plane with harmonic oscillations in normal force and rotational speed. Part I: Solution of the partial slip contact problem

We study the effect of harmonic oscillations during the steady rolling of a cylinder on a plane in partial slip contact conditions in the limit of small oscillations. The solution is an extension of that given in Barber et al. [1] for infinitely large coefficient of friction. Here, the effect of varying normal load and hence contact area is investigated in detail by analyzing the first order variation of the tangential force and the corresponding relative displacements.In particular, the solution is given in terms of an explicit length scale d in the Flamant solution used as a Green function. Appropriate choice of values of d allows to treat both two-dimensional problems and three-dimensional ones having elliptical contact area sufficiently elongated in the direction of the rotation axis.Also, this analysis can be used as starting point for corrugation calculations in railway tracks, where oscillations in time of the normal forces can result in non-uniform wear and hence in amplification of the corrugation.     

A Novel Surface Texture Shape for Directional Friction Control

An experimental study is presented to evaluate the influence of anisotropically shaped textures on the behaviour of sliding friction and sensitivity to sliding direction. The plate samples were textured with triangular sloped dimples using an ultrafast laser surface texturing technique. Reciprocating cylinder-on-plate tests were conducted with steel sliding pairs using mineral base oil as a lubricant to compare the tribological performance of reference non-textured specimen and dimpled samples. The dimples were designed with varying converging angles in the transverse y–z plane and top-view x–y plane. In this study, no dimple was fully covered in the contact area since the dimples size is much larger than the Hertzian line contact width. Stribeck style dynamic friction curves across boundary, mixed and hydrodynamic lubrication regimes were used to determine the benefit or antagonism of texturing. Observation of the directional friction effect of the anisotropic textures indicated that the converging shapes are beneficial for friction reduction, and the dimpled specimens have a lower friction coefficient particular under prevailing boundary lubrication conditions. It was also found that the real contact length variation rate is a major factor controlling the local friction response. The sloped bottoms of the textures produce effective converging wedge action to generate hydrodynamic pressure and contribute to the overall directional friction effects.