Computational fluid dynamics in theoretical simulations of elastohydrodynamic lubrication

The work presented in this thesis concerns computer simulations of lubrication processes, and the main part deals with simulations in the elastohydrodynamic lubrication (EHL) regime. The thesis summarises the work performed in the five papers referred to as Paper A, B, C, D and E. The aim is to give the reader a more explanatory description of the investigations performed in the papers and of the physical processes present in EHL. Lubrication is a sub-area of tribology, which is the science of interacting bodies in relative motion, two other sub-areas being wear and friction. Lubrication is commonly referred to as a way of reducing friction and protecting the surfaces from wear. Typical devices where EHL is present are machine components. Examples of these are bearings, cams and gears. The lubricant can in such an application have many different tasks. The ultimate goal is that the surfaces in motion should be separated by a fluid film, thus reducing the friction and wear. That leads to low frictional losses and long operating life for the machine components. This goal is, however, not always fulfilled, and to protect the surfaces from wear when the lubricating film collapses, there are additives added to the lubricant. Commonly, lubricants contain of a number of additives, but these are not in focus in this thesis. Common to many EHL-applications, especially machine components, are thin lubricating films and high fluid pressures. The high pressures result in elastic deformation of the contacting bodies. The lubricating films in such applications are very thin, often in the range 0.1-1 10^-6m with pressures ranging from 0.5-3 GPa. The contact diameter is approximately 1 mm and the time a fluid element needs to pass through the contact is approximately 0.1 ms. The altering geometrical scales and rapid changes in the physical variables, such as pressure, viscosity and temperature etc., make numerical simulations to a challenging task. The variables of primary interest in the numerical simulations are: film thickness, pressure, temperature and friction. The film thickness is an important variable that gives information as to whether the surfaces are separated by the lubricating film. It is the lifting force generated by the hydrodynamic pressure that governs the separation of the surfaces in motion. However, even if a lubricating film is present, EHL machine components deteriorate when they have been in service for a long time. It is then that the cycling in pressure and temperature leads to fatigue of the surfaces, so that the level of these variables is also of importance. The friction that has developed in the EHL-contacts leads to a loss of energy, which increases the temperature in the conjunctions. Friction is therefore important not only for the efficiency, but also when thermal aspects have to be considered. The physical processes present in EHL are inter-disciplinary, closely related to other fields of science such as fluid mechanics, solid mechanics, and rheology. In almost all numerical simulations of lubrication performed today, the hydrodynamics are modelled by an equation referred to as the Reynolds equation. This equation is derived from a simplified form of the momentum equations, which are combined with the continuity equation; and the result is a Poisson equation for the fluid pressure. The assumptions made when deriving this equation limit the size of the computational or spatial domain, and the equation cannot predict pressure variations across the lubricating fluid film. In the work presented in this thesis, an extended approach, where the technique is based on CFD (computational fluid dynamics), is used to simulate the lubricant flow. The extended approach is here based on more complete forms of the equations of momentum, continuity and energy and the above degeneracy will be removed. That implies, if such an approach works, that it should now be possible to simulate the lubricant flow under conditions where the Reynolds equation is not valid. So far, only few attempts have been made to use the CFD-technique. From the preceding discussion of rapid changes in accordance with elastic deformation of the contacting surfaces, a great deal of work has been carried out to modify the numerical algorithm in the CFD-software to fit EHL-problems. The CFD- software used throughout the work in this thesis is CFX4 (2003).Godkänd; 2004; 20061030 (haneit