Mixed Lubrication Problems Research Articles

An Assessment of Quantitative Predictions of Deterministic Mixed Lubrication Solvers

Abstract The ability to simulate mixed lubrication problems has greatly improved, especially in concentrated lubricated contacts. A mixed lubrication simulation method was developed by utilizing the semi-system approach which has been proven to be highly useful for improving stability and robustness of mixed lubrication simulations. Then different variants of the model were developed by varying the discretization schemes used to treat the Couette flow terms in the Reynolds equation, varying the evaluation of density derivatives and varying the contribution of terms in the coefficient matrix. The resulting pressure distribution, film thickness distribution, lambda ratio, contact ratio, and the computation time were compared and found to be strongly influenced by the choice of solution scheme. This indicates that the output from mixed lubrication solvers can be readily used for qualitative and parametric studies, but care should be taken when making quantitative predictions.

Research on Mixed Lubrication Problems of the Non-Gaussian Rough Textured Surface With the Influence of Stochastic Roughness in Consideration

Abstract In order to find the effects of surface topography on the tribological properties of the rough textured surfaces, an improved mixed lubrication model allowing specifying the standard deviation, the skewness, and the kurtosis was developed. In this model, by considering the non-Gaussian properties of rough surfaces, an improved average flow model was combined with a modified statistical elastoplastic asperity contact model. The performances of the slider bearings with two arrays of anisotropic textures were studied in terms of Stribeck curves. It appears that the tribological properties of the anisotropic textures are sensitive to the sliding direction. Meanwhile, the surfaces with more negative skewness or the lower kurtosis can obtain better tribological performances related to friction and wear.

Influence of piston ring profiles and oil temperature distribution on cylinder liner lubrication of a marine two-stroke engine

In the paper a comprehensive model of a piston-ring-cylinder (PRC) system has been presented. The local thickness of the oil film can be compared to height of the combined surface roughness of a cylinder liner and piston rings. Equations describing the mixed lubri-cation problem based on the empirical mathematical model formulated in works of Patir, Cheng and Greenwood, Tripp have been ap-plied. The main parts of the model have been experimentally verified abroad by the author at the marine engine designing centre. In contrast to the previous papers of the author concerning the PRC system of combustion engines, new calculation results for a ma-rine two-stroke engine have been presented. Firstly the right selection of barrel-shaped sliding surface of piston rings has been analysed. Secondly the influence of oil temperature distribution along the cylinder liner on the lubrication of the PRC system has been assessed. The developed model and software can be useful for optimization of the PRC system design.

Influence of piston ring pack configuration on blowby and friction losses in a marine two-stroke engine

In the paper a comprehensive model of a piston ring pack motion on an oil film has been presented. The local thickness of the oil film can be compared to height of the combined surface roughness of a cylinder liner and piston rings. Equations describing the mixed lubrication problem based on the empirical mathematical model formulated in works of Patir, Cheng and Greenwood, Tripp have been combined and used in this paper. In addition a model of gas flow through the labyrinth seal of piston rings has been developed. The main parts of the model and software have been experimentally verified abroad by the author at the marine engine designing centre. For the selected two-stroke marine engine, the influence of the number of piston rings used and the type of the top ring lock (straight or overlapped) on blowby to piston underside and on friction losses of the piston-ring-cylinder (PRC) system have been investigated. The developed model and software can be useful for optimization of the PRC system design

Influence of sliding surface roughness and oil temperature on piston ring pack operation of an automotive IC engine

In the paper a comprehensive model of a piston ring pack motion on an oil film has been presented. The local oil film thickness can be compared to height of the combined roughness of sliding surfaces of piston rings and cylinder liner. Equations describing the mixed lubrication problem based on the empirical mathematical model formulated in works of Patir, Cheng and Greenwood, Tripp have been combined and used in this paper. The developed model takes the following phenomena into account: hydrodynamic and contact forces, spring and gas forces acting on piston rings. The rings motion concerning low and high temperature of cylinder surface has been compared. These results concern cases of hydrodynamic and mixed lubrication. Changes of oil wetted area and contact zone of piston rings have been shown. In addition the oil film thickness distribution along cylinder liner and all the forces acting on piston rings have been analysed and discussed. The results have been presented in form of relevant diagrams. The developed model and software can be utilized for optimization of piston rings design.

Mixed lubrication problems in the presence of textures: An efficient solution to the cavitation problem with consideration of roughness effects

In order to consider the effect of the local surface properties, such as textures and roughness, a mass-conserving model is specifically developed based on the Elrod–Adams model. The classic flow factor methodology is incorporated in this model to deal with the roughness scale. Meanwhile, by reformulating the cavitation conditions according the Fischer–Burmeisster equations, the system of discretized equations for this model is changed to be unconstrained. The computational efficiency of the developed model is similar to that when cavitation is not considered. Finally, this model is evaluated in the predicting the performance of the textured ring/liner system under the start-up process.

A Mathematical Model for the Mixed Lubrication of Non-Conformable Contacts With Asperity Friction, Plastic Deformation, Flash Temperature, and Tribo-Chemistry

A mathematical model is presented in this paper for rolling-sliding contacts operating in a mixed regime of elastohydrodynamic lubrication and boundary lubrication. The model is based on the framework of Johnson et al. (1972, “A Simple Theory of Asperity Contacts in Elastohydrodynamic Lubrication,” Wear, 19, pp. 91–108). It incorporates into this framework a number of important asperity-level variables including asperity friction, friction-induced plastic flow, flash temperature, and boundary-film tribo-chemistry. The model yields a number of variables useful for the assessment of the state of the mixed lubrication. They include the load sharing between fluid and asperities, area of asperity contacts, and fraction area of asperity contacts undergoing plastic flow along with experimentally measurable variables such as the traction coefficient, friction power intensity, and temperature of the overall contact. The model is limited to mixed-lubrication problems in which the load is mainly carried by the fluid pressure and the total area of asperity contacts is a small percentage of the Hertz area. Further development is possible to formulate a model into a wider mixed-lubrication regime using some modeling concepts developed in this paper in conjunction with other modeling techniques.

On the λ ratio range of mixed lubrication

Mixed lubrication is a mode of fluid lubrication in which both hydrodynamic lubricant film and rough surface asperity contact coexist. Mixed lubrication problems are usually associated with significant surface roughness effect. A common belief is that full-film lubrication occurs when the λ ratio, defined as average film thickness divided by composite root mean square roughness, is greater than 3.0, while boundary lubrication corresponds to λ < 0.5–1.0. Mixed lubrication, therefore, is roughly in the range 0.5–1.0 < λ < 3.0. However, these considerations were established long ago based on early stochastic analyses, which did not adequately consider rough surface asperity interaction and correlation, as well as reduction of asperity heights caused by surface deformation. Recent experimental studies and deterministic numerical simulations suggested that the λ ratio range of mixed lubrication needs to be re-visited. Actually, when the λ ratio is greater than 0.6–1.2, little or no asperity contact is found in either experimental results or numerical solutions. If λ is around 0.05–0.1, there may still be a considerable portion of load, e.g. greater than 10–15%, being supported by lubricant films. It appears that mixed lubrication spans a λ ratio range roughly from 0.01–0.05 up to 0.6–1.2, according to the numerical simulation results presented in this article. This estimated range is in a reasonably good agreement with experimental observations found in the literature.

Development of algorithm for 3D mixed Elasto-Hydrodynamic lubrication analysis

In this study, new 3-dimensional mixed lubrication algorithm is developed. For a converged solution of the mixed lubrication problem, the asperity contact pressure is calculated for the amount of asperity contact occurred due to insufficient lubricant pressure, then the procedure adding the asperity contact pressure to the hydrodynamic pressure is continually iterated until the further asperity contact amount does not occur. This algorithm has advantage that the pressure and the film shape can be calculated from Reynolds equation for all mixed lubrication region without any specific boundary condition for edge of asperity contact region. In order to investigate usefulness of this algorithm, we conducted the mixed lubrication analysis for the spherical contact with a single asperity and a rough surface and showed that the developed algorithm gives a stable convergent solution even in which severe contact takes place due to asperity height being considerably large.

Lubrication in soft rough contacts: A novel homogenized approach. Part II - Discussion

In M. Scaraggi, G. Carbone, B. N. J. Persson and D. Dini, Soft Matter, 2011, 7, DOI: 10.1039/c1sm05128h (Ref. 1), we have presented a novel mean field theory of mixed lubrication for soft contacts. This theory has been developed within the framework of homogenization techniques. It is based on a perturbation second order accurate expansion; a rigorous averaging process is applied to obtain the average flow equations without the need of any preliminary fully deterministic calculations of the mixed-lubrication problem. The theory allows to calculate the flow factors and the shear stress factors taking into account the coupled effect of asperity–asperity and asperity–fluid interactions occurring at the interface. In this second paper we present the main results of the theory and we discuss the transition from the boundary lubrication regime, where the normal load is supported through asperity–asperity interactions (sometimes mediated by boundary films), to the hydrodynamic regime, where a thin fluid film prevents the surfaces from being in direct contact. We show that fluid-induced asperities flattening, as well as local percolation effects and roughness anisotropic deformation all occur at the contact interface. Finally we describe the origin of the macroscopic friction laws (the so called Stribeck curves) in terms of local average shear stresses.

Numerical analysis of piston ring pack operation

In the paper a model of a piston ring pack motion on an oil film has been analysed. The local oil film thickness can be compared to height of the combined roughness of mating surfaces of piston rings and cylinder liner. Equations describing the mixed lubrication problem based on the empirical mathematical model formulated in works of Patir, Cheng [6, 7] and Greenwood, Tripp [3] have been combined [12] and used in this paper. A model of a gas flow through the labyrinth seal of piston rings has been developed [13, 15]. In addition models of ring twist effects and axial ring motion in piston grooves have been applied [14, 15]. In contrast to the previous papers of the author, an experimental verification of the main parts of developed mathematical model and software has been presented. A relatively good compatibility between the experimental measurements and calculated results has been achieved. In addition this study presents the simulation results for an automobile internal combustion engine

Theoretical studies of elastohydrodynamic lubrication of artificial hip joints

Theoretical studies of fluid-film lubrication in artificial hip joints are reviewed. The importance of developing effective numerical tools to solve realistic and complex lubrication problems in artificial hip joints has been emphasized. The elastic deformation of the bearing surfaces has been shown to play a dominant role in promoting elastohydrodynamic lubrication in various forms of artificial hip joints using different bearing surfaces. Both the bearing geometry and the structural supports can have a significant effect on the predicted lubricant film thickness. The importance of elastic deformation is further enhanced synergistically with the transient variation in load and speed to ensure a maximum effectiveness of the transient elastohydrodynamic lubrication mechanism in artificial hip joints. The recent application of the fast Fourier transform technique, in conjunction with the finite-element method to calculate the elastic deformation, not only enables more complex structural supports to the acetabular cup to be considered, but also offers the potential of analysing both transient and mixed lubrication problems in artificial hip joints.

Mixed Elastohydrodynamic Lubrication in a Partial Journal Bearing—Comparison Between Deterministic and Stochastic Models

The analysis of the mixed lubrication phenomena in journal and axial bearings represents nowadays the next step towards a better understanding of these devices, subjected to more and more severe operating conditions. While the theoretical bases required for an in-depth analysis of the mixed-lubrication regime have long been established, only small-scale numerical modeling was possible due to computing power limitations. This led to the appearance of averaging models, thus making it possible to generalize the trends observed in very small contacts, and to include them in large-scale numerical analyses. Unfortunately, a lack of experimental or numerical validations of these averaging models is observed, so that their reliability remains to be demonstrated. This paper proposes a deterministic numerical solution for the hydrodynamic component of the mixed-lubrication problem. The model is applicable to small partial journal bearings, having a few centimeters in width and diameter. Reynolds’ equation is solved on a very thin mesh, and pad deformation due to hydrodynamic pressure is taken into account. Deformation due to contact pressure is neglected, which limits the applicability of the model in those cases where extended contact is present. The results obtained with this deterministic model are compared to the stochastic solution proposed by Patir and Cheng, in both hydrodynamic and elastohydrodynamic regimes. The rough surfaces used in this study are numerically generated (Gaussian) and are either isotropic or oriented, having different correlation lengths. It is shown that the stochastic model of Patir and Cheng correctly anticipates the influence of roughness over the pressure field, for different types of roughness. However, when compared to the smooth surface solution, the correction introduced by this model only partially compensates for the differences observed with a deterministic analysis.

A Computer Thermal Model of Mixed Lubrication in Point Contacts

This paper presents a transient thermal model for mixed lubrication problems in point contacts. The model deterministically calculates pressure and surface temperature by simultaneously solving a system of equations that govern the lubrication, contact and thermal behaviors of a point contact interface. The pressure distribution on the entire computation domain is obtained through solving a unified Reynolds equation system without identifying hydrodynamic or asperity contact regions. The point heat source integration method is applied to determine the temperature distributions on contact surfaces. The interactions between pressure and temperature are considered through incorporating viscosity-temperature and density-temperature relations in the Reynolds equation, then solving the equation system iteratively. With the successful implementation of an FFT-based algorithm (DC-FFT) for calculation of surface deformation and temperature rise, the numerical analysis of lubricated contact problems, which used to involve a great deal of computation, can be performed in acceptable time. The model enables us to simulate various lubrication conditions, from full film elastohydrodynamic lubrication (EHL) to boundary lubrication, for a better understanding of the effect of surface roughness. Numerical examples are analyzed and the results show that the present model can be used to predict pressure and surface temperature over a wide range of lubrication conditions, and that the solution methods are computationally efficient and robust.

Some insights into asperity temperatures in mixed-film lubrication

This paper investigates some fundamental thermal behavior of asperity contacts in mixed-film lubrication. First, the thermal interaction between the contacting asperity and the lubricant is studied. The analysis is based on transient simulations of a mixed-film contact problem under various contact conditions. The results suggest that the solid/fluid thermal interaction can be strong. The lubricant is shown to play an important role in asperity temperature. It not only generates heat through viscous shearing but also plays a role of cooling by transporting heat out of the thermally intensive asperity contacts. The interaction can significantly reduce asperity temperatures especially under high-speed conditions. The interaction also increases the lubricant temperature away from the asperity contact, thus facilitating thermal coupling among contacting asperities. Another thermal behavior of mixed-film contact studied is the effect of heat flow in the asperity contact in the direction perpendicular to the lubricant entrainment. Results suggest that the effect of this thermal side-flow is significant in low-speed contacts and diminishes when the entraining velocity becomes high. Further, the side-flow effect is much weaker in the mixed-film contact than in the dry contact and may be neglected in the modeling of complex mixed lubrication problems.

The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem

The mixed-lubrication problem is formulated as a nonlinear generalized complementarity problem in which the pressure acting on the load-bearing surface is taken as the unknown, and the lubricant flow and the gap between the surfaces are taken as its complements. An iterative method was developed to find the solution, which satisfies the complementarity condition that at each point on the load-bearing surface, the pressure or at least one of its complements, is zero at all times. Moreover, the pressure and its complements satisfy non-negativity constraints. The solution intrinsically decomposes the load-bearing surface into three distinct subregions: solid-to-solid contact, hydrodynamically lubricated contact, and no contact (or cavitation). It is shown that the mixed-lubrication formulation degenerates into the special cases of hydrodynamic or solid-to-solid contacts under appropriate load and speed conditions. A journal bearing with elastic support is analyzed to illustrate the method of solution. The transition of the lubrication mode from pure hydrodynamic contact to mixed contact is demonstrated.

Discussion: “The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem” (Oh, Kong Ping, 1986, ASME J. Tribol., 108, pp. 598–603)

Discussion: “The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem” (Oh, Kong Ping, 1986, ASME J. Tribol., 108, pp. 598–603)

Closure to “Discussion of ‘The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem’” (1986, ASME J. Tribol., 108, p. 604)

Closure to “Discussion of ‘The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem’” (1986, ASME J. Tribol., 108, p. 604)