W. E. ten Napel

Surface Roughness Effects in an EHL Line Contact

In this paper the influence of surface roughness on the pressure profile and film thickness in a steady state EHL line contact is investigated using input from an actually measured roughness profile in the calculations. Pressure profiles and film shapes for different load conditions are shown. The presented results strongly indicate that in the steady state situation considered here a significant deformation of the roughness profile occurs. As a result the often used λ parameter being the ratio of film thickness and standard deviation of the roughness (h/σ) with σ based on the undeformed roughness profile may give misleading information as far as the effect of the roughness on pressure and film shape is concerned.

Numerical Simulation of the Overrolling of a Surface Feature in an EHL Line Contact

In this paper a Multigrid extension of a stationary solver is outlined for the EHL solution of a line contact under transient conditions. The solver is applied to calculate pressure and film thickness profiles at each time step when an indentation is moving through the contact, which results in an asymmetric pressure profile. The time-dependent results are compared with the stationary solutions. The pressure as a function of time is presented as well as the integrated pressure (over time) as a function of the spatial coordinate. These time-dependent pressures are used to compute the sub-surface stress field, which shows higher stresses below the trailing edge of the indentation. Therefore the risk of fatigue is higher below the trailing edge of the indentation, as is experimentally observed. The transient pressures can be used for a fundamental study of the emitted frequency spectrum of rolling bearings, as used in condition monitoring.

Advanced Multilevel Solution of the EHL Line Contact Problem

The application of multilevel multi-integration to the calculation of the elastic deformation integrals and the use of an alternative relaxation process in the multilevel solution of the governing equations have resulted in an algorithm solving the EHL line contact problem in 0(n In n) operations, also for highly loaded situations. The reduction in computing time thus obtained was used to solve the problem using large numbers of nodal points and to study the pressure spike. The presented algorithm will enable fast and accurate solution of surface roughness and transient problems.

Multilevel solution of the elastohydrodynamically lubricated circular contact problem part 2: Smooth surface results

A fast multilevel solver for the solution of the elastohydrodynamically lubricated circular contact problem has been applied to the standard situation assuming the running surfaces to be perfectly smooth. Pressure profiles and film shapes for various operating conditions, are shown and overview graphs of the minimum, central and average film thickness as a function of the governing parameters covering a wide range of operating conditions are presented.

Lubrication in cold rolling: Elasto-plasto-hydrodynamic lubrication

A model has been developed with respect to hydrodynamic lubrication in cold rolling. The basic model describes the configuration of a rigid, perfectly plastic sheet rolled by a rigid work roll. The governing equations have been solved throughout the complete contact area, i.e. the inlet, the work zone and the outlet zone. Multi-level techniques have been applied to solve these equations together with boundary conditions, resulting in an algorithm solving the problem in O(n) operations. This means that the distribution of the pressure and the traction force in the lubricant film, and the shape of this film, as well as the plastic deformation of the sheet, can be accurately calculated for a large number of nodal points on a minicomputer. Subsequently elastic deformation, work hardening and dynamic behaviour of the flow stress have been incorporated in the model. It will be shown that the influence of these effects on the film thickness or the pressure distribution is considerable.

The Influence of Elastic Deformation of the Roll and the Sheet in a Hydrodynamically Lubricated Cold Rolling Process

A model has been developed for simulating hydrodynamic lubrication in cold rolling. Both Roelands’ and Barus’ viscosity-pressure relations have been applied. Thermal effects regarding heat development caused by plastic deformation as well as work hardening have been included. Furthermore, elastic deformation of the surfaces has fully been incorporated in the model, i.e., elastic deformation of both the strip and the rolls. The governing equations have been solved numerically throughout the entire contact i.e. inlet, work and outlet zone using a very dense grid. Multigrid techniques have been used to solve the equations. It will be shown here that roll flattening has a significant effect on film thickness. However, elastic deformation of the strip material in the inlet region even has a more pronounced effect on film thickness and thus on several process conditions. Furthermore, it is shown that the choice of the viscosity-pressure parameter is limited. Higher values of this parameter cause excessive shear stresses on the strip surface.

Classification of lubricants according to cavitation criteria

Cavitation in lubrication liquids has long been known to be detrimental to components in hydraulic systems. Damage has been detected in journal bearings, especially under severe dynamic loading, gears, squeeze film dampers and valves. These findings have led to intensive studies of metal resistance to cavitation erosion, in order to minimize the damage. Results of these studies have been: 1. (a) classification of known materials according to their resistance to cavitation erosion; 2. (b) development of new materials and processes to increase their durability. One of the main achievements in this respect was the establishment of the ASTM G32-92 Standard Method of Vibratory Cavitation Erosion Test. However, very little was done with respect to the liquid phase, e.g. the lubricants. As a consequence there is no standard procedure for testing of lubricants for their cavitation properties and no relevant specifications in national and international standards. This study includes theoretical and experimental investigations. The theoretical approach examines the lubricant in elastohydrodynamically lubricated (EHL) contacts. Using numerical simulations, based on Reynolds equation and elastic deformation theory, the pressure profile and film shape have been computed. It is further investigated how the operating conditions affect the properties, e.g. ?cavitation energy? of zones of sub-ambient pressure values and if a correlation between these results and cavitation erosion criteria can be found. The experimental approach includes testing of 20 liquid lubricants, belonging to the following four groups: mineral oils, mineral-based oils, bio degradable oils and synthetic oils. Testing was performed by vibrating a standard aluminium tip in each oil and periodically recording the gravimetric results. These results enabled the classification of the lubricants according to their cavitance, which is inversely proportional to the mass of solid material eroded by a cavitating liquid under controlled conditions. The results of both approaches can be combined into an engineering tool in the future. This tool may serve the designer to improve the use of existing lubricants and the lubrication industry as an aid for the development of new lubricants with increased cavitance in hydraulic systems.

Paper VI(i) Solving Reynolds' equation for E.H.L. line contacts by application of a multigrid method

Film thickness and pressure profiles have been calculated for E.H.L. line contacts, for a variety of load and rolling speed conditions. Compressibility of the lubricant is taken into account, and the pressure-viscosity relations according to Barus as well as Roelands have been applied. Results of these numerical calculations are compared with well-established asymptotic solutions (Martin-Gumbel, Moes, Grubin). A formula is presented, which incorporates these asymptotic solutions and which accurately predicts the minimum film thickness throughout the entire film thickness plot. A description is given of the difficulties encountered in numerical calculations, in the neighbourhood of these asymptotes.

The effect of the viscosity-pressure behaviour of lubricants on the film thickness in elastohydrodynamically lubricated line contacts

In this paper the influence of the viscosity-pressure relationship on the film thickness for the line contact situation is presented. The viscosity-pressure behaviour of many lubricants differs significantly from the behaviour according to Barus which is commonly used in EHL. This topic is of interest due to the fact that, for instance, water based lubricants, like emulsions, or biodegradable lubricants are frequently used. Also the “liquid to solid” behaviour of lubricants results in viscosity-pressure relations differing from the Barus relation. It will be shown that, if the viscosity-pressure behaviour differs significant from the Barus relation, the presented film thickness formulas in literature are not accurate. The effect on the minimum film thickness of the viscosity-pressure relations according to Roelands and to Bair & Winer, in the different EHL-regimes, will be shown in this paper. On the bases of this investigation a modified film thickness formula will be proposed.

Elastohydrodynamics in counterformal and conformal contacts

Since Peppler [1] in 1936 showed that elastic deformation of the mating surfaces in lubricated concentrated contacts plays a dominant role in the pressure built up and film formation, elastohydrodynamic lubrication (E.H.L.) has become a major field of interest in Tribology (Lubrication, Friction and Wear), all over the world. This, of course, is no surprise, since many contacts in machine elements are counterformal and the life of the machine concerned is mainly determined by the life of its most critical parts i.e. the mating surfaces. Examples are rolling element bearings, gears, seals, cam and tappets, etc. The most widely known example of a conformal contact is a journal bearing. In this paper a review will be given with regard to models and calculational methods concerning film thickness, pressure distribution and traction in E.H.L. and research results, recently obtained at the University of Twente, will be presented. Advantages of application of multilevel techniques will be demonstrated. Additionally some experimental results will be shown and some applications will be discussed.