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.
Wear is difficult to predict in mixed lubricated articulating surfaces and the time of computation is one of the challenges due to the deterministic definition of roughness on a micro-scale. This research aims to efficiently capture the wear and the evolution of the roughness of mixed lubricated bearing surfaces, employing a statistical description of the roughness. A numerical model was developed which characterizes the wear of a loaded and lubricated pin-on-plate system, assuming a rough non-wearing pin and a rough wearing plate. The part of the load, which is borne by asperities in contact, is derived from the Greenwood-Williamson approach and the rest, which is carried by the fluid film, is based on the Patir-Cheng flow factors lubrication method. Wear is computed in the areas of direct solid contact only. For simplicity, the depth of the pin and plate are assumed infinite in order to reduce the lubrication problem to one-dimension. The roughness and asperities are described by their Cumulative Distribution Functions (CDFs). As the plate runs-in the pin, the roughness of the plate is worn by the roughness of the pin, and the process is continued until steady wear is attained. The local gap-dependent flow factors influence the load carried by the thin film of the lubricant, whereas, the local gap-dependent overlap of asperities of the pin and the plate determines the true contact load. The sum of fluid and solid contact load is balanced with the applied load, adjusting the separation between the plate and the pin. The plate asperity CDFs are updated assuming Archard's wear model for the solid contact only and the asperity wear is extrapolated to update the roughness of the plate.Aims
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