Contact between a sphere and rough plates

The contact between a smooth sphere and a rough plate is theoretically analysed for a mixed asperity contact theory in which asperities with displacements below and above a critical value are deformed elastically and plastically respectively. Contact asperities that are all deformed elastically or plastically independently are also analysed. There are some differences between the analytical results that are obtained for mixed, elastic and plastic contacts. Analytical results were confirmed by experimental investigations in which a smooth steel sphere was pressed against rough steel and copper plates under various loads. To observe indentations a rough plate was coated with a lamp black film after it had been coated with an evaporated carbon film in vacuo. The compliances between a smooth steel sphere and rough steel and copper plates were also measured under various loads with differential transformers. Theoretical and experimental results are in general agreement.