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The paper presents a numerical solution for elliptical point contact conjunctions under combined rolling and sliding motion. This condition is prevalent in many practical applications, such as rolling element bearings and conformal gears. An effective influence Newton-Raphson method is employed in local point distributed or global line distributed low-relaxation iterations. This method enables determination of the pressure distribution and film shape at high loads such as are encountered in many practical applications. Some of the numerical predictions have been validated against experimental results.

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Elastohydrodynamic lubrication was analysed under squeeze-film or normal approach motion for artificial hip joint replacements consisting of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup and a metallic or ceramic femoral head. A simple ball-in-socket configuration was adopted to represent the hip prosthesis for the lubrication analysis. Both the Reynolds equation and the elasticity equations were solved simultaneously for the lubricant film thickness and hydrodynamic pressure distribution as a function of the squeeze-film time was solved using the Newton-Raphson method. The elastic deformation of the UHMWPE cup was calculated by both the finite element method and a simple equation based upon the constrained column model. Good agreement of the predicted film thickness and pressure distribution was found between these two methods. A simple analytical method based upon the Grubin-Ertel-type approximation developed by Higginson in 1978 [1] was also applied to the present squeeze-film lubrication problem. The predicted squeeze-film thickness from this simple method was found to be remarkably close to that from the full numerical solution. The main design parameters were the femoral head radius, the radial clearance between the femoral head and the acetabular cup, and the thickness and elastic modulus for the UHMWPE cup; the effects of these parameters on the squeeze-film thickness generated in current hip prostheses were investigated.

• Abstract: This paper presents numerical solution of isothermal elastohydrodynamic conjunction for concentrated contact of elastic bodies under the elliptical point contact condition. The solution includes the effect of squeeze-film motion that occurs under transient conditions due to the application of cyclic loads and/or oscillating motions in machine elements. It is shown that this time-dependent behaviour increases the load-carrying capacity of the contact which is largely responsible as a mechanism of lubricant film formation when the low speeds of entraining motion yield a low film thickness. An extrapolated oil-film thickness formula is also presented that can be employed under dynamic conditions.

This paper presents predictive analysis of load carrying capacity, tractive efficiency and response time of parallel annular discs intervened with a film of lubricant under combined shear and squeeze film motions. This configuration represents operational characteristics of viscous coupling systems. In particular, the case of viscous dampers for tractive torque generation and distribution in all-wheel-drive off-road vehicles is studied. Various forms of lubricant behaviour, from idealised Newtonian to that of non-Newtonian silicone-based fluids and incompressible isothermal electrically conducting couple stress fluids, subjected to a magnetic field are studied (MHD). The solution for the MHD includes combined solution of modified Reynolds equation and Stoke's micro-continuum for couple stress fluids in squeeze and shear with rotational fluid inertia, an approach not hitherto reported in literature.It is shown that in general MHD couple stress fluids enhance the load carrying capacity of the contact and inhibit the incidence of thin films which can result in direct contact of surfaces. Rotational inertia decreases the load carrying capacity, although in general the MHD fluids show better load carrying capacity and tractive efficiency than the other alternatives. However, they exhibit a lower response time under the assumed isothermal condition. Nevertheless, the MHD fluids are best suited to applications in viscous coupling systems because of their controllability.

Lubrication plays an important role in the wear and friction of metal-on-metal bearings for artificial hip joints. It is generally known that both load and speed can influence the lubrication mechanism. This is particularly important in hip implants, which experience many intermittent start-ups and stops, which may adversely affect the lubrication and increase wear in metal-on-metal hip implants. The effect of start-up and gait initiation upon elastohydrodynamic lubrication (EHL) in a typical metal-on-metal hip implant has been investigated in the present study. A simple ball-on-plane model was used for a full transient EHL analysis under assumed start-up conditions represented by linear variations in both load and speed, but with different development time periods. It was shown that the duration of the start-up period had little effect on the predicted lubrication film thickness during either the start-up or the steady cyclic conditions. It was found that only two to three steps were required to establish a continuous steady cyclic variation of the predicted lubricant film thickness. This suggests that intermittent motions associated with start-up and stop may have only a small effect on the wear of metal-on-metal hip implants.