Abstract
The number of knee replacement surgeries have increased rapidly over the past few years. However, these implants can have limited life due to the issue of wear. An accurate lubrication model is an important component in understanding and designing joints to deliver lower joint wear and the risks associated with such wear.
One of the main challenges in tribological modelling of the knee implant is capturing the effects of the complex geometry on the joint performance. Most current models assume a single point of contact, with zero pressure and deformation assumed elsewhere. Unlike the hip implant, which can be described as a circular or elliptical contact, the knee implant involves a geometry that cannot be easily approximated into a regular shape. For this reason, the elastohydrodynamic lubrication equations become computationally expensive and challenging to solve. Finite element methods are required to capture the complex geometry and calculate deformations and how they vary spatially over the joint surface. Furthermore, the irregularity and asymmetry of the geometry provides no guarantee that well-defined contact points exist.
A mixed lubrication model for a human knee implant is presented, incorporating the irregularity of the knee geometry. Tribological conditions in the mixed lubrication regime are calculated using a statistically representative description of surface roughness. This approach involves using the flow factors approach of Patir and Cheng (1978), and the Greenwood and Tripp (1970) approach for asperity contact. From this, the evolution of both the gross geometry and the change in surface roughness due to wear is determined.
