A Mixed-Lubrication Model for Shoe-Floor Friction Applied to Pin-on-Disk Apparatus

Despite the serious health concern associated with slip and fall accidents and the numerous slip testing devices that have been developed, few studies have attempted to tribologically model the shoe-floor interface. To this end, a mixed-lubrication model for shoe-floor interfaces is proposed. The model is applied to a pin-on-disk apparatus and uses contact mechanics and hydrodynamic lubrication modeling with iterative methods to solve the mixed lubrication problem. Outputs of the model are load supported by the fluid and load supported by the contacting asperities. Measurable parameters input to the model are: curvature of the shoe material (pin), material properties of the shoe material, roughness of the shoe and floor material, viscosity of the fluid, sliding speed and normal force. COF estimates are generated as a function of the proportional load borne by the fluid and the contacting asperities. The model COF values replicate the experimental data for the two different shoe materials tested. The peak hydrodynamic pressure was found just outside the contact region and peak contact pressure was at the center of the pin. The model represents a first step towards developing a mixed-lubrication model for an entire shoe-floor surface.