Asperity Contact Model Research Articles

A numerical procedure for calculating roughness parameters for the Greenwood-Tripp model of asperity contact based on 3D measurements

This study introduces the proposed deterministic methodology for calculating the roughness parameters involved in the Greenwood-Tripp equation for asperity contact pressure. A robust methodology that takes into consideration the maximum possible peak morphology and establishes more stringent calculation conditions is proposed. The stability of the proposed method is examined on various samples taken from different engine components using an optical interferometer. The roughness parameters obtained from different methodologies and using different optical interferometer resolutions are compared, and then, these parameters are introduced into simulation model that employs the Greenwood-Tripp equation. The results demonstrate the sensitivity of the simulation model to the roughness parameters used.

Effects of surface morphology on the performance of water-lubricated thrust bearings

Purpose As the crucial support component of the propeller power system, the reliability of the operation of submersible pumps is influenced by the lubrication performance of water-lubricated thrust bearings. When the water-lubricated thrust bearings are under start-stop or heavy load conditions, the effect of surface morphology is crucial as the mixed lubrication regime is encountered. This paper aims to develop one mixed lubrication model for the water-lubricated thrust bearings to predict the effects of surface skewness, kurtosis and roughness orientation on the loading carrying capacity and tribological behavior. Design/methodology/approach This paper developed one improved mixed lubrication model specifically for the water-lubricated thrust bearing system. In this model, the hydrodynamic model was improved by using the height of the rough surface and its probability density function, combined with the average flow model. The asperity contact model was improved by using the equation for the Pearson system of frequency curves to characterize the non-Gaussian aspect of surface roughness distribution. Findings According to the results, negative skewness, large kurtosis and lateral surface pattern can improve the tribological performance of water-lubricated thrust bearings. Optimizing the surface morphology is a reasonable design method that can improve the performance of water-lubricated thrust bearings. Originality/value In this paper, one mixed lubrication model specifically for the water-lubricated thrust bearing with the effect of surface roughness into consideration was developed. Based on the developed model, the effect of surface morphology on tribological behavior can be evaluated. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-08-2023-0247/

Research on the Secondary Motion of Engine Piston Considering the Transport of Lubricating Oil

<div>At present, it is generally considered in the analysis of the secondary motion of engine piston that the piston skirt–cylinder liner friction pair is fully lubricated in an engine operating cycle. However, in practice, when the piston moves upward, the amount of lubricating oil at the inlet may not ensure that the friction pair is fully lubricated. In this article, the secondary motion of piston is studied when the transport of lubricating oil is considered to determine the lubrication condition of piston skirt–cylinder liner friction pair. The secondary motion of piston is solved based on the combined piston motion model, hydrodynamic lubrication model, asperity contact model, and lubricating oil flow model. The secondary motion equation of piston is solved by the Broyden method. The hydrodynamic lubrication equation is solved by the finite difference method. The asperity contact between piston skirt and cylinder liner is calculated by the Greenwood model. The flow of lubricating oil is analyzed based on the theory of fluid mechanics. The results indicate that, when the actual transport of lubricating oil is considered to determine the lubrication condition of piston skirt–cylinder liner friction pair, the secondary motion of piston is remarkably different from that in which the flooded lubrication is assumed in an engine operating cycle. Therefore, it is helpful to improve the accuracy and make the analysis closer to the actual engine operating situation that the transport of lubricating oil is considered in the analysis of the secondary motion of engine piston.</div>

A mixed-lubricated friction model of water lubricated bearing based on fractal theory

To the water lubricated bearing, its mixed-lubricated friction model is generally established based on the traditional statistical model, whose accuracy is not high due to the inaccurate characterization of surface topography. Therefore, this paper employs the fractal theory that has scale-independent characteristics and high precision to characterize the surface topography of the bearing and journal, and then establishes the fractal contact model of asperity, combining the average Reynolds equation of the film, proposes a mixed-lubricated friction model based on fractal theory. The scanning experiments of surface topography are carried out to obtain the fractal parameters and measurements of the friction coefficient are performed to verify the effectiveness of the proposed mixed-lubricated model. Subsequently, the proposed mixed-lubricated friction model is employed to analyze the effects of the number of groove, the position of groove and the fractal parameters on the lubrication and friction characteristics of the water lubricated bearing. Results indicate when the grooves are in the non-main load-carrying regions, the friction characteristics of the bearing slightly changes, and the lower surface roughness is beneficial to improve the lubrication and friction properties of the bearing.

Manufacturing error and misalignment effect on the transient lubrication behavior of dynamically loaded journal bearing with micro-groove

The novelty of this paper is to numerically investigate the effect of manufacturing error and misalignment on the transient lubrication behavior of dynamically loaded journal bearings with micro-groove. Based on the average Reynolds equation considering the mass conservation cavitation algorithm, the asperity contact model, and the force balance equation, the mixed lubrication model under time-varying dynamic loads is developed. Meanwhile, mathematical functions are given for the bearings with different surface profiles, including the circumferential and axial manufacturing errors of the bearing, the horizontal and vertical deflection angles of the journal, and the micro-grooves with different distribution forms. According to this model, the lubrication characteristics of the bearing are systematically investigated at different horizontal and vertical deflection angles, amplitudes, spatial numbers, and phase angles of the circumferential waviness, as well as shape profiles of the axial error. In addition, the performance parameters of dynamically loaded journal bearings with ideal and actual surfaces under different micro-groove distributions are comparatively evaluated. Numerical results show that manufacturing errors and misalignment have a remarkable effect on the transient behavior of dynamically loaded journal bearings, and the coupling effect will be more consistent with practical engineering. It can be found that the distribution form of the micro-groove surface directly affects the friction reduction effect of bearing systems. The numerical model can serve as a meaningful guideline for the optimum design of dynamically loaded journal bearing with micro-groove.

A New Contact Model of Sphere Asperity in the Fully Plastic Regime Considering Strain Hardening

Abstract Understanding the contact characteristics of rough surfaces is essential to explain engineering phenomenon in interface. In order to improve accuracy of contact model, a novel simplified fully plastic contact model of sphere asperity was proposed considering material properties based on fractal theory. First, based on Von Mises yield criteria, maximum contact pressure factor was derived. Second, relationships taking into consideration strain hardening effects were proposed to describe contact area based on the fully plastic contact area index and contact pressure. Then, the critical interference at inception of fully plastic deformation was derived. Lastly, validations were conducted for different materials. The results show that the present work is remarkably consistent with experimental results and has higher accuracy than other models.

A Mixed Lubrication Deterministic Model of an Elastic Support Water-Lubricated Tilting Pad Thrust Bearing

In order to study the effect of surface roughness on lubrication performance of an elastic support water-lubricated tilting pad thrust bearing, a mixed lubrication (ML) deterministic model is hereby presented based on a unified Reynolds equation model. This very model incorporates the elastic–plastic deformation of asperities and polymer matrix of the thrust pad, as well as the elastic deformation of the rubber support. The randomly distributed surface roughness of the thrust pad is generated by a mathematical model and shares the same distribution characteristics as the measured surface roughness. The Greenwood and Williamson asperity contact model and thin plate deformation model are combined to solve the asperities contact stress and deformation. Meanwhile, the bearing ML performance is compared with the results calculated by a thermohydrodynamic (THD) lubrication model and a thermo-elasto-hydrodynamic (TEHD) lubrication model, while the film thickness is also compared with measurements. The results show that the water film thickness calculated by the ML model is smaller than that by the THD model and the TEHD model, but the water film temperature is higher. The roughness has a great influence on the contact area ratio and the lubrication state, but little effect on the average film thickness. A higher roughness indicates a higher rotational speed required for the bearing to achieve full hydrodynamic lubrication. The film thickness calculated by the mixed lubrication model is closer to the measured results. Overall, it is proved that the mixed lubrication model can more accurately predict the lubrication performance of bearings. Compared to the thin plate deformation model, the elastic deformation simulation based on the half-infinite space model severely overestimates the elastic deformation of the pad surface, making it unsuitable for calculating the elastic deformation of the polymer matrix of the thrust pad under contact force or water film pressure. This ML deterministic model provides an effective means for high-precision prediction of the lubrication performance of the elastic supported water-lubricated thrust bearings coupled with multi-layer soft materials.

Experimental and Numerical Study of the Mixed Lubrication Considering Boundary Film Strength.

For the influence of boundary film on the lubrication state of sliding friction pairs, a boundary film strength model was proposed that can comprehensively reflect the influences of film thickness, pressure, shear stress and temperature. The model parameters were obtained through fitting the test results. Then, a mixed lubrication model considering boundary film strength was established by coupling the boundary film strength model with the hydrodynamic lubrication model and the asperity contact model. The calculation program was developed using the Fortran language, which can effectively capture the tribological characteristics and action ratios of the fluid, boundary film and dry friction components. Simultaneously, the mixed lubrication model was applied to the journal bearing. A parametric analysis was performed to investigate the influences of different working conditions on lubrication performance. Under current operating conditions, the results show that: when the speed is above 200 r/min or the viscosity is higher than 0.09 Pa·s, the boundary film breakdown rate is almost 0 and the friction coefficient is lower than 0.02; when the roughness is reduced from 1.8 μm to 0.8 μm, the ultimate load of the journal bearing rises from 27 MPa to 36 MPa, an increase of about 33%; when the load exceeds 36 MPa or the temperature is higher than 100 °C, more than 25% of the boundary film breaks and the dry friction component accounts for more than 60% of the total friction, which leads to a sudden increase in the friction coefficient. Hence, the study of mixed lubrication considering boundary film strength provides theoretical guidance for accurately reflecting the actual lubrication state and improving the mechanical energy efficiency of friction pairs.

Surface topography effect on tribological performance of water-lubricated journal bearing under mixed-EHL regime

Water-lubricated journal bearings (WLJB) are one of the important components of the stern tube shaft. Surface topography of WLJB is an important aspect in the design of stern tube shaft, and significantly affects the lubrication characteristics of WLJB. This work aims to investigate the effect of non-Gaussian surface topography on tribological performance of water-lubricated journal bearing (WLJB) under mixed-elastohydrodynamic lubrication (mixed-EHL) regime. The non-Gaussian flow factors, and a normalized Weibull probability density function is used to tackle the non-Gaussian roughness in hydrodynamic and asperity contact models respectively. From results, it is observed that skewness (S sk ) significantly affects both asperity contact pressure and hydrodynamic pressure along circumferential direction of bearing. It is concluded that for skewness, S sk = −1 to 1, lambda ratio falls between 1 to 3. The relation between altitude angle and skewness is established. The effect of bearing length to diameter (L/D) ratio on lubrication performance of WLJB is also discussed in detail.

Weight analysis of the factors affecting friction performance of textured surface in rotary vane actuator end seal

A contact model of asperities between polyurethane and metal was developed. The friction coefficient of the textured surface was solved by combining the virtual rough surface, the average Reynolds equation, and the point contact elastic deformation equation. An orthogonal test simulation was conducted to analyze the correlation between parameters and friction performance. The results show that the order of the influencing factors is: root mean square roughness > texture shape > area ratio > texture depth, of which root mean square roughness is a highly significant factor, and texture shape and area ratio are generally significant factors, and texture depth is an insignificant factor. This provides a reference for further optimizing the friction performance of the end seal.

Modeling and experimental investigation of wear and roughness for honed cylinder liner during running-in process

The tribological property of piston ring and cylinder liner has a great influence on exhaust emissions and service performance of internal combustion engines. To explore the effects of surface topography on tribological property of coated piston ring and honed cylinder liner, the hydrodynamic contact model, asperity contact model and wear model during running-in process are established. Considering the non-Gaussian property of rough surfaces into the contact models, the influences of surface parameters on contact pressure are investigated. Due to the influence of operational condition on lubrication performance, the degradation rate of oil is taken into the wear model. Based on this, the change characteristics of the wear process, coefficient of friction and roughness are investigated. To verify the validity of the proposed models, the tribological test is conducted. The results show that the numerical results are in good agreement with the experimental results, and reasonable surface parameters can improve the anti-wear performance of the system during running-in process.

Numerical and experimental study on the effect of surface texture with roughness orientation considered under a mixed lubrication state

Purpose The purpose of this paper is to investigate the effects of surface texture with roughness orientation considered on tribological properties under a mixed lubrication state numerically and experimentally. Design/methodology/approach Based on the average Reynolds equation and asperity contact model, the impacts of surface texture parameters and roughness orientation on lubrication properties have been calculated using finite difference method. Tin–bronze samples with various prescribed surface texture geometric parameters and roughness orientation were fabricated by laser surface texturing technique, and the tribology performance of the textured surface was studied experimentally. Findings The effects of surface geometric parameters and roughness orientation parameters have been discerned. The experimental observations are in good agreement with the numerical prediction, which suggests that the numerical scheme adopted in this work is suitable in capturing the surface texture and roughness effect under mixed lubrication state. Originality/value By meticulously controlling the surface roughness and surface texture geometric characteristics based on the laser surface texturing process, samples with prescribed surface texture parameters and roughness orientation consistent with that in theoretical studies were fabricated and the theoretical model and results were verified experimentally.

Validation of statistic and deterministic asperity contact models using experimental Stribeck data

Contact models are used, among others, to describe the asperity contact in lubricated contacts. In recent decades, a large number of contact models have been developed based on different approaches. In this article a selection of classical statistical contact models are compared with a deterministic FE model. The validation of the different approaches was carried out applying an indirect methodology. By comparing a numerically determined Stribeck curve, on which the characteristics of the contact model has a significant influence, and experimentally determined Stribeck curves, the applicability of the different contact models can be evaluated. The influence of elastic and elastoplastic material behaviour in the deterministic contact model on the asperity contact pressure curves and Stribeck curves, respectively, was examined during the investigations. The results show, that the elastic FEM contact model and the statistical model according to Greenwood and Tripp provide the best agreement with the experimental Stribeck data. This can be attributed to the fact that the roughness peaks are smoothed immediately in the early contact stage and the smoothed surface behaves almost elastically.

A mixed lubrication model for inter-ply friction behaviour of uncured fabric prepregs

Inter-ply friction plays a dominant role in the generation of fiber-path defects (e.g. wrinkling) in the consolidation stage of composites manufacturing. In particular, for most thermoset prepregs, the mixed lubrication regime can be a dominating factor controlling the frictional response over the range of the processing window. This article presents a generic computational modelling approach to describe the mixed lubrication regime by combining an inverse hydrodynamic‐lubrication (IHL) theory and an asperity contact model. A homogenized resin film thickness can be derived from this analysis, rather than postulating it as in earlier conventional models. Thermal effects and fiber bed compliance in the inter-layer contact area as well as the influence of the resin rheology are assessed, finally enabling the model to be verified against inter-ply friction experiments under a wide range of processing conditions. The model has been exemplified on a fabric carbon/epoxy prepreg.

Hydrodynamic Performance of Positive Surface Textured Patterns under Mixed Lubrication

It is proved that the optimal design of surface textures (positive or negative) improve the lubrication performance by generating extra hydrodynamic pressure at the interface of the sliding pairs. In the present work, the effect of various positive surface textures on hydrodynamic performance of parallel sliding contact under mixed lubrication is researched. The modified Reynolds equation and asperity contact model are solved simultaneously to assess the hydrodynamic pressure and minimum film thickness for different shape of textures. The results depict that elliptical shaped texture generate high hydrodynamic pressure as well as minimum film thickness at the conjunction than the other texture shapes.

A Fluid–Solid–Heat Coupling Analysis for Water-Lubricated Rubber Stern Bearing Considering the Deflection of Propeller Shaft

The novelty of the present study is that it investigates the effect of propeller shaft deflection, caused by the propeller self-weight and interfacial mixed forces, on the fluid–solid–heat (FSH) coupling performance of water lubricated rubber stern bearing (WLRSB). In the FSH coupling model, the generalized average Reynolds equation and the Kogut–Etsion asperity contact model are used to determine the hydrodynamic and the elastic–plastic contact behaviors of WLRSB. In the thermal analysis, the journal, water film, and rubber bushing are considered as an integrated system (JWR system) using the Euler method. To prove the correctness of the developed model, the predicted results are verified by comparisons with the experimental results given in the literature. In addition, to assess the effect of the force-driven deflection during FSH simulation, comparisons of the FSH predictions between the aligned journal case and the deflected journal case are carried out. The results indicate that, especially under a heavy load condition, the deflection of the stern shaft should be incorporated into the lubrication gap between the journal–rubber interface during the analysis of FSH performance of the JWR system.

Numerical prediction of the frictional losses in sliding bearings during start-stop operation

With the increased use of automotive engine start-stop systems, the numerical prediction and reduction of frictional losses in sliding bearings during starting and stopping procedures has become an important issue. In engineering practice, numerical simulations of sliding bearings in automotive engines are performed with statistical asperity contact models with empirical values for the necessary surface parameters. The aim of this study is to elucidate the applicability of these approaches for the prediction of friction in sliding bearings subjected to start-stop operation. For this purpose, the friction performance of sliding bearings was investigated in experiments on a test rig and in transient mixed elasto-hydrodynamic simulations in a multi-body simulation environment (mixed-EHL/MBS). In mixed-EHL/MBS, the extended Reynold’s equation with flow factors according to Patir and Cheng has been combined on the one hand with the statistical asperity contact model according to Greenwood and Tripp and on the other hand with the deterministic asperity contact model according to Herbst. The detailed comparison of simulation and experimental results clarifies that the application of statistical asperity contact models with empirical values of the necessary inputs leads to large deviations between experiment and simulation. The actual distribution and position of surface roughness, as used in deterministic contact modelling, is necessary for a reliable prediction of the frictional losses in sliding bearings during start-stop operation.

Modeling Solid Contact between Rough Surfaces with Various Roughness Parameters

A solid contact model with high accuracy is required for mixed lubrication calculation to predict friction loss and wear in sliding parts by computer-aided engineering; however, existing models have numerous limitations. A new asperity contact model was constructed to determine contact states using the roughness parameters of pairs of surfaces. Although the contact states differed greatly depending on differences in skewness and kurtosis, the calculated results of the proposed model agreed well with the results of direct calculation between various pairs of surfaces. Furthermore, even when the pairs of rough surfaces had the same composite roughness, skewness, and kurtosis, the trend of the increase in the contact force was different when the individual skewness and kurtosis of the surfaces were different. Therefore, we determined that it is necessary to carry out detailed asperity contact calculations when the two rough surfaces differ greatly. We plan to further investigate the influence of skewness and kurtosis on the contact tendency for the elastoplastic deformation by the extended model considering the contact stress distribution of asperities.

High Temperature Sealing of Silicon Oxide/Oxide Bonding Interfaces

High temperature (>1000°C) annealing is necessary to completely close a bonding interface. Using interface synchrotron high energy X-ray reflectivity, we have investigated the sealing behavior of silicon thermal oxide/ silicon thermal oxide interfaces, with different surface roughnesses. Interface X-ray reflection is able to measure accurately the width and the depth of the electron density gap across a bonding interface with a sub-nanometer accuracy, whose product is a good marker of the interface closure.The uncomplete closure of the interface is the result of a balance between attractive and repulsive force between the two bonded solids. These two forces depend on the statistics of asperity and on the mechanical behavior of individual asperity [1]. For attraction, at high temperatures, a key factor is the gain of contact surface area which reduces the surface energy due to uncontacted zones. Repulsion is due to compression of contacting asperities. At high temperature, both elastic and plastic behavior can be expected, with some yield of the asperities compressed above the elastic limit.In the elastic solid regime, we have shown that equilibrium distance of rough silicon oxide to rough siliconoxide bonding can be predicted using standard adhesive contact models such as Johnson-Kendall Roberts (JKR) or Deryagin-Müller-Toporov (DMT) with Gaussian roughness statistics[2]. The equilibrium distance is dependent and sensitive to the Fuller Tabor adhesion parameter, θ=E σ3/2 R1/2 / 2γR where E is the Young modulus, σ the mean roughness, R the radius of the asperity, while 2γ is the adhesion energy at contact points. When θ>>1 , the equilibrium distance is large and the contact area is small (unclosed interface) . When θ<<1 the adhesion energy is strong and the system will have a strong tendency to seal.In the plastic regime, both repulsive and attractive curves share the same dependence with distance so that the system is expected to be unstable, between a weakly evolving unsealed interface and a fully sealed interface when the asperity pressure stress is above the elastic limit.The kinetics of the sealing can also be modeled in this case, monitoring the interfacial gap as a function of time (Figure). It is found that the sealing characteristic time scales directly with the silicon oxide viscosity (Figure insert). This dependence can be understood using the plastic asperity contact model, assuming the fluid part flows according to the Stokes equation around asperities.

A Complete Single Asperity-Based Statistical Gaussian Rough Surface Contact Model

Understanding the corrosion behavior of rough surface contacts needs the contact interaction of rough surfaces at asperity level. Generally, single asperity-based statistical rough surface contact model is predominating one in exploring contact behavior of rough surfaces. The FEM-based single asperity contact model is being used extensively to explain the elastic, elastic–plastic, and fully plastic behavior of the rough surface contacts. The empirical expressions to calculate the exact transitions (elastic to elastic–plastic and elastic–plastic to fully plastic states) are still incomplete. The earlier FEM-based single asperity contact models didn’t give mathematical expressions to exactly calculate the elastic, elastic–plastic, and fully plastic transition states by accounting the combined effect of material properties. In this way, in the present work, empirical expressions are developed to calculate the exact transitions of elastic, elastic–plastic and fully plastic states by accounting the combined effect of Young’s modulus, material yield strength, and Poisson’s ratio. The empirical expressions to calculate the dimensionless contact load and contact area are developed for elastic, elastic–plastic, and fully plastic states in terms of dimensionless interference, E/Y ratio, and Poisson’s ratio. Further, it is observed that the plasticity index is not a complete parameter to explore the contact behavior of rough surface contacts. In high surface plasticity index case, the material properties influence significantly compared to the low surface plasticity index case. The Poisson’s ratio significantly influences in low E/Y ratio materials in all the surface plasticity index cases.