Modeling Mixed-Lubrication of a Shoe-Floor Interface Applied to a Pin-on-Disk Apparatus

Abstract

While slip-and-fall accidents are a serious health concern, few attempts have been made to tribologically model the shoe-floor-contaminant interface. To this end, modeling techniques are introduced here for shoe and floor materials operating in mixed lubrication. The proposed analytical model results are compared with experimental data in order to assess the validity of the developed model. Coefficient of friction (COF) values are generated using a pin-on-disk apparatus across a range of sliding speeds with two different shoe materials operating in the mixed-lubrication regime. The model solves for the contact condition using Hertzian contact mechanics theory and the hydrodynamic pressure condition using the Reynolds equation. The amount of contact deformation is adjusted iteratively such that the summed force from the fluid and contacting asperities is equivalent to the total normal force. The model predicts friction values based on the proportion of the load supported by the fluid versus the proportion of the load supported by contacting asperities. The model-generated COF-velocity plots showed close agreement with experimental values for both shoe materials studied. In addition, the model predicts that as the speed between the surfaces increases, the hydrodynamic lift increases. This in turn decreases the contact area and the load borne by the contacting surfaces. Hence, the model presented serves as an initial step towards developing shoe-floor-contaminant friction models.