Elastohydrodynamic Point Contact Research Articles

On the linear finite element analysis of fully coupled point contact elastohydrodynamic lubrication problems

The fully coupled approach for the solution of elastohydrodynamic lubrication point contact problems requires the numerical solution of the elasticity problem on a large 3D domain. A sufficiently fine computational mesh is required to obtain the elastic deformation solution to the necessary accuracy, and hence, a sufficiently accurate elastohydrodynamic lubrication point contact solution. This article discusses the accuracy of an elastohydrodynamic lubrication point contact solution over different finite element meshes. We present a family of efficient 3D meshes which can be used to calculate accurate elastohydrodynamic lubrication point contact solutions at a minimal computational cost. This article also illustrates the fact that the unstructured hierarchical meshes can lead to a poor quality elastohydrodynamic lubrication solution unless an appropriate post-processing, smoothing technique is applied.

An efficient preconditioned iterative solution of fully-coupled elastohydrodynamic lubrication problems

This paper presents the fast preconditioned iterative solution to large sparse linear systems arising from the application of Newton and quasi-Newton methods to fully coupled elastohydrodynamic lubrication line and point contact problems. The new blockwise preconditioner that is presented combines the use of multigrid for the linear elasticity block and a separate approximation to precondition the Reynolds block. Two variants of the solver are considered, based upon the use of algebraic and geometric multigrid respectively. Numerical results are presented in order to validate the discretization and solution method and then to contrast the performance and efficiency of the proposed solution strategies compared to the use of a state-of-the-art sparse direct solver. These results demonstrate that, unlike the sparse direct solver, the preconditioned iterative approach is able to perform at computational and memory costs that both grow linearly with the number of unknowns.

Numerical simulation of an elastohydrodynamic point contact taking into account local irregularities of the moving surface

We formulate and numerically solve the problem of elastohydrodynamic point contact, taking into account that one of the two lubricated contact surfaces has a single irregularity in the form of a hump or hole. Three variants are considered: movement of a surface with an irregularity relative to a fixed smooth surface (slip mode); movement of a surface with an irregularity at a rate equal to the speed of a smooth surface (rolling mode); and movement of a smooth surface relative to a stationary surface with an irregularity (pure slip mode). For the first two modes the problems is solved in a non-stationary statement and for the third it is solved in a stationary statement. The features of influence of the kinematic conditions on distributions of pressure and thickness of the lubricant slick in the contact zone are shown. A numerical algorithm for solving systems of equations and inequalities was based on the Newton method and application of an implicit difference scheme for approximating unsteady equations.

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.

Estimation of Cavity Length in EHL Rolling Point Contact

Reciprocating lubricated contacts sometimes suffer from oil starvation due to cavitation at the reversal of motion. However, the behavior of cavities is not well understood such that starvation can be theoretically predicted. In this study, the length of cavity in a steady state elastohydrodynamic lubricated point contact was calculated. For numerical simulation, a modified Elrod algorithm was used. An equation was obtained for the cavity enclosed in the oil meniscus. The equation was constructed with Moes dimensionless parameters M and L, assumed pressure of cavity, and viscosity pressure index of the lubricant. The dimensionless cavity length (or the ratio of cavity length by Hertzian contact radius) is proportional to the product of M−a and Lb. Careful examination of the equation elucidated that the cavity length is dominated by the viscosity, sum velocity, cavity pressure, and geometry of the contact. Experimental measurements with a ball-on-disk apparatus have shown good agreement. The validity of the equation suggests that the algorithm is applicable for complete transient simulations. In practice, the estimated cavity length can be a parameter for starvation.

Influence of a surface irregularity on the rigidity of a lubricated contact

A technique is presented for numerical solution of the problem of the elastohydrodynamic point contact characteristic of antifriction bearings and tooth gears, taking into account that on the surface in the contact area there is an irregularity in the form of a hill or a dimple. Distributions of pressure and thickness of the lubricant film in the contact area are obtained. The influence of the type of irregularity on the elastic characteristics and rigidity of the elastohydrodynamic point contact is shown. The presented results may be used in calculations of concentrated lubricated contacts. The mathematical model of the elastohydrodynamic contact is described by a system of nonlinear integrodifferential equations with a free boundary (the outflow boundary of the contact area). The computational algorithm is based on the Newton method.

A finite element approach of thin film lubrication in circular EHD contacts

So far, most of the numerical studies concerning elastohydrodynamic point contact lubrication have been realized using finite differences. This paper describes a finite element approach for the modelling of both, thick and thin film lubrication in circular contacts under isothermal elastohydrodynamic regime. Multigrid techniques are used to accelerate the convergence and reduce calculation time. The use of the finite element method (FEM) offers two advantages: first, the existence of high level ready-to-use Finite Element commercial software which reduces the time spent in implementing the method and second, the easier adaptability to different and various physical models such as lubricant rheology, starvation effects, thermal effects, non-Newtonian behaviour, etc. The numerical model is presented in detail and an example of its adaptation taking into account non-Newtonian effects is shown. Finally, a comparison is made between Newtonian and non-Newtonian solutions, exhibiting differences obtained when using both models, especially at high shear rates where the film thickness and the friction coefficients are overestimated by a Newtonian approach.

Measurements of Temperature Distributions around Longitudinally Grooved Rough Surfaces in Sliding Elastohydrodynamic Point Contacts

This paper describes the temperature measurements in the EHL conjunction area comprising a longitudinally grooved steel ball and a sapphire disk under high slip conditions. The authors measured the temperatures of the oil film as well as both the disk and ball surfaces; furthermore, they estimated the temperature profile across the oil film by means of experimental values. The experimental results show that the temperature of the grooved ball surface increased considerably compared with that of a non-grooved ball. The temperatures of the faster surface for the grooved ball became sensitive to the slip ratio, whereas that for the non-grooved surface was almost constant. The temperature distribution had a higher value at the land zones and a lower one at the grooved zones. The temperature rise in the grooved zones varied qualitatively depending on the thermal conditions of both the sliding surfaces.

Discussion: Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method

Discussion: Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method

Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method Part 2: Results

The paper presents results obtained using a transient analysis technique for point contact elastohydrodynamic lubrication (EHL) problems based on a formulation that effectively couples the elastic and hydrodynamic equations. Results are presented for transverse ground surfaces in an elliptical contact that show severe film thinning at the transverse limits of the contact area. This thinning is caused by transverse (side) leakage of the lubricant from the contact in the remaining deep valley features. Comparison is made between the elliptical contact results on the entrainment centreline and the equivalent line contact analysis. This confirms the importance of edge effects as a likely cause of film collapse and scuffing failure. The surface profiles used in the analysis are taken from test discs used in scuffing experiments and from gears used in micropitting tests. Side leakage is found to be sufficiently severe to cause microasperity contact in the numerical examples presented. This contact mainly occurs close to the edges of the corresponding Hertzian area and correlates in position with the location at which scuffing is found to first occur in the earlier experiments. Comparisons are made with other numerical results for point contact configurations with sinusoidally varying surface features obtained by Zhu (2000) and considerable differences are seen in the calculated extent of asperity contact. The differences are thought to be due to the simplified treatment of the lubrication equation adopted by Zhu.

Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method Part 1: Theory and validation

The paper presents a transient analysis technique for point contact elastohydrodynamic (EHL) lubrication problems using coupled elastic and hydrodynamic equations. Full coupling is made possible by use of a novel differential deflection formulation. The way in which the differential deflection is incorporated into the overall solution method for a point contact is discussed. A range of spatial and temporal discretization methods are incorporated and compared. The method is validated under transient conditions by a detailed comparison with published work produced using a different, independent method incorporating a moving roughness feature. A comparison of the results with different discretization methods leads to the conclusion that spatial central differencing with a Crank-Nicolson temporal discretization is the most effective finite difference scheme, and this is generally equivalent to the finite element discretization given in detail in the paper. A comparison of the results produced for moving rough surfaces suggests that the finite element formulation is preferred.

Particle Entrainment in Elastohydrodynamic Point Contacts and Related Risks of Oil Starvation and Surface Indentation

This theoretical study concentrates on the mathematical analysis of the motion of small (5–50 μm) spherical solid particles in the inlet zone of elastohydrodynamic point contacts, found in various machine elements as, for example, in ball bearings, in order to compute the particle trajectories in the fluid flow. Particles may collide on a moving element of the contact (e.g., a ball in a bearing) or bypass it. For those particles that collide on another element, a fluid and mechanical force analysis reveals if they will be entrapped and, possibly, cause surface damage, or temporarily or finally expelled. Particle rejection is associated with the risk of inlet blockage and fluid starvation, which may further cause film collapse and scuffing. The study gives useful evidence of the probabilities of particle entrapment or rejection, extending the concept to evaluate the probabilities of oil starvation, surface indentation, or both, under various operating conditions.

Studies on the Effect of Spin Motion on Oil Film Thickness in Elastohydrodynamic Point Contacts.

Spin on the contact surfaces between two elements occurs in such diverse machine elements as angular contact ball bearings or continuously variable transmissions adapting traction drives. We experimentally and analytically studied the effect of spin on lubricating oil film thickness on angular contact ball and disk. Oil film thickness was measured under different spin angular velocities for constant rolling velocity and different contact loads using optical interference method. We clarified the effect of spin on minimum and central thickness of oil film and film shape and analyzed thermo-elastohydrodynamic lubrication (TEHL) considering spin under experimental conditions. Analytical and experimental results agreed well.

In-situ Pressure Measurements Using Raman Microspectroscopy in a Rolling Elastohydrodynamic Contact

The physical conditions (pressure, shear stress, temperature) generated in an elastohydrodynamic (EHD) contact are the main parameters governing the evolution of the physico-chemical properties of the lubricant within the contact. This paper presents in-situ measurements of pressure in an EHD point contact using Raman microspectroscopy. Two model lubricants are studied: a pure polyphenyl ether (5P4E) oil and a mixture of this oil with a liquid crystal. The influence of load and speed on the pressure distributions is investigated. The Petrusevich pressure spike is measured and its evolution with the operating parameters is in good agreement with the theoretical predictions. The addition of the liquid crystal to the base oil leads to an important diminution of the mixture viscosity, and consequently of the film thickness in the contact. The different rheological properties of the lubricants induce significant variations of the pressure profiles.

Simplified Analysis of Non-Newtonian Effects in a Circular Elastohydrodynamic Contact and Comparison with Experiment©

The paper describes a simplified non-Newtonian numerical model of an elastohydrodynamic point contact. It is based on the control volume flow continuity technique described by Holt et al. (9). Observation of the shear stress values produced in the solutions to the problem obtained by Holt has led to the consideration of a simplifying approximation in the non-Newtonian formulation for calculation of flow rates in which the resultant shear stress is approximated by the shear stress in the predominant direction of sliding. This assumption gives easily calculated expressions for the flow rates. The simplification leads to direct evaluations of the surface shear stress components without recourse to an iterative solution of simultaneous transcendental equations. Results of the simplified model are found to agree with the more exact treatment of Holt et al, under realistic operating conditions. A thermal treatment of the oil film for sliding contacts is also included. Experimental measurements of film thickness in contacts with varying degrees of sliding have been carried out which show good agreement with the simplified theory. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Toronto, Ontario, Canada, October 26–28, 1998

Comparison between experiments and numerical solutions for isothermal elastohydrodynamic point contacts

This paper presents multi-level, multi-grid solutions for isothermal elastohydrodynamic circular contacts under pure entraining motion. The solutions are valid for quasi-static conditions and Newtonian lubricants. Multi-grid solutions allow rapid evaluation of contact pressure distributions and corresponding elastic film shapes. This allows the deployment of a large number of elements, thus improving the accuracy of the numerical solution compared with that of conventional finite difference schemes. The numerical results are compared with experimental measurements and reasonable agreement has been obtained under a wide range of operating conditions.

Analysis of isothermal elastohydrodynamic point contacts lubricated by Newtonian fluids using multigrid methods

A multigrid multi-integration method has been used to solve the elastohydrodynamic lubrication (EHL) point contact problem over a large range of loads. Solutions obtained with the multigrid method are compared with those computed with an effective influence Newton method. Good agreement has been obtained, which validates the results obtained by both of these independent methods. Smooth surface problems have been used to test the multigrid method, but an example that takes into account a wavy surface has demonstrated the robustness and the large potential of the multigrid method to analyse EHL problems with three-dimensional surface roughness.

Determination of Viscosity and Pressure in an Elastohydrodynamic Rolling Contact by using Optical Interferometry: A Theoretical Study

Optical interferometry has been used during the last 30 years for film thickness measurements in elastohydrodynamic (EHD) contacts. In the work presented in this paper the possibility of using optical interferometry for determining pressure and apparent viscosity in a fully flooded EHD point contact has been theoretically investigated. The pressure in the contact is computed from elastic deformation theory and force balance. The apparent viscosity can be obtained from the Reynolds equation when the film thickness and the pressure are known. To theoretically examine the sensitivity to measurement errors, different errors have been implemented in a set of ‘exact’ numerical data. From the theoretical study it can be seen that a film thickness map obtained from optical interferometry can be used for determination of both pressure and apparent viscosity measurement in an EHD point contact. The simulated errors that have been used do not influence the pressure within the Herzian region by more than a few per cent. However, to obtain reliable results from the apparent viscosity calculations, the measurements of film thickness, load and elastic modulus must be very accurate. It is seen, for example, that the resolution of the film thickness measurement has to be less than 1 nm to achieve high accuracy.

Measurement and Modelling of Boundary Film Properties of Polymeric Lubricant Additives

Experimental work using ultrathin film interferometry has shown that some polymer solutions in oil form much thicker films at slow speeds in rolling, concentrated contacts than predicted from elastohydrodynamic (EHD) theory. This behaviour can be interpreted as resulting from the polymers forming adsorbed, surface layers of enhanced concentration on the two solid surfaces. Such layers, which are typically 20 nm thick, would be significantly more viscous that the bulk solution and thus produce thicker EHD films. This concept has been supported by modelling the elastohydrodynamic point contact using control volume analysis with a layered surface viscosity. The film thickness behaviour predicted computationally using this technique is quite similar to that found experimentally using polymer solutions.

Prediction of Film Thickness in an Elastohydrodynamic Point Contact Lubricated with a Viscosity Index Improved Base Oil

A simple iterative method is used for the computation of the central film thickness in a fully flooded elastohydrodynamic (EHD) point contact lubricated with a polymeric viscosity index (V1)-improved base oil. The shear stress dependence of the Vl-improved base oil is included in the iterative method. Experimental data are presented on temporary viscosity loss and central film thickness at different temperatures from —8 to 40° C. A good approximation of the central film thickness in an EHD point contact lubricated with V1-improved oil is given by using an iterative method involving the temporary viscosity loss of the Vl-improved base oil. The central film thickness depends on the mean shear stress at the inlet of the contact, and this shear-thinning effect has been accounted for in the calculations.