Modelling interfacial tribochemistry in the mixed lubrication regime

The need to reduce the cost of components is driving more and more machine elements to operate under mixed lubrication conditions. With higher operating pressures, the lubricant film is becoming thinner and eventually reaches nanometre scales, comparable to the surface roughness. Thus, understanding the mixed lubrication phenomenon is becoming increasingly important. However, the mixed lubrication phenomenon is difficult to capture experimentally and the lubricant additive ZDDP (Zinc Dialkyl Dithio Phosphate) shows its full antiwear character in the mixed lubrication conditions. This research stems from the need for models that can simulate contact mechanics, lubrication and tribochemistry in a single framework. This is the key to understanding and optimizing the lubrication systems to meet future needs. To this end, a numerically efficient procedure based upon the tridiagonal solution of the Reynolds equation is developed and is implemented, in Fortran to solve the equations line by line to incorporate more information from the current iteration step. The asperity contacts are handled by the unified solution algorithm. A new strategy to simulate plastic deformation in a lubricated contact is developed. Under practical loading conditions, the pressures inside the contact can reach values far above the material yielding limit. Thus, an efficient numerical scheme is devised to include the elastic perfectly plastic behaviour in the EHL solution procedure to simulate realistic contact conditions with minimal increase in computational cost. The Boussinesq deformation integrals result in a convolution of pressure and the deformation which is solved using Fast Fourier Transforms (FFTs) by modifying the solution domain to create a cyclic convolution. Code is developed to allow exploration of the highly optimized C-based library (www.fftw.org). The use of FFTs speeds up the solution process many times and makes the use of denser grids and larger time scales accessible. A mesh size of 129 x 129 is found to give reasonable results. The simulation results from the current study agree very well with the previously published results. The evolution of contact area ratio and the central film thickness exhibit a Stribeck type behaviour and the transition speeds at which the contact transits from EHL to mixed and from mixed to complete boundary lubrication can be precisely identified. Existing tribofilm growth models developed for boundary lubrication are reviewed and a model based on the interface thermodynamics is adapted and integrated with the mixed lubrication model to simulate tribochemistry. The problems with existing EHL concepts such as lambda ratio and central film thickness are identified and new definitions are proposed to allow understanding of the mixed lubrication mechanics. The mutual interaction between the tribofilm growth and lubricant film formation is studied. Finally the wear of the tribological system is studied and the wear track profiles are predicted. The new model is then applied to study a ball-on-disc system to explore wear, tribochemistry and roughness evolution. The ZDDP tribofilm growth is studied and the it is found that the final ZDDP tribofilm thickness is very weakly affected by increasing SRR but the rate of formation and removal are strongly affected by the SRR value. The tribofilm growth results are validated against published numerical and experimental results. It is found that the antiwear action of the ZDDP tribofilm is not only due to its chemical action but the ZDDP tribofilm helps to entrain more lubricant and improves contact performance. The presence of tribofilm roughens the contact and the contact area and load ratio both increase due to tribofilm growth. It was also found that the use of conventional EHL parameters to analyse the behaviour of tribosystem is misleading. The flattening of the roughness inside the contact and the proper identification of the central film thickness are crucial to the interpretation of the mixed lubrication results. The roughness of the ball generally decreases due to wear but the presence of tribofilm limits this reduction. Contrary to this, the surface roughness of the ball generally increases due to wear but the presence of tribofilm results in increased roughness of the ball.