Effects of non-Newtonian couple stresses on the squeeze film characteristics between two different spheres

Abstract

Based upon the Stokes micro-continuum theory, a study of the effects of non-Newtonian couple stresses upon the squeeze film characteristics considering different sphere-to-sphere geometries has been presented. The non-Newtonian squeeze-film Reynolds-type equation between two spheres with different ratios is derived to take account of the non-Newtonian effects of couple stresses arising from the lubricant blended with various additives. A closed-form solution for the film pressure, the load-carrying capacity, and the response time is then obtained. Compared with the corresponding Newtonian-lubricant case, the influence of non-Newtonian couple stresses provides an increase in the load capacity, and therefore lengthens the response time to prevent sphere-to-sphere contact. In all, the effects of non-Newtonian couple stresses on the squeeze film characteristics are more emphasized under lower squeeze-film heights with larger couple-stress parameters and radius ratios. When the value of the radius ratio approaches infinity, the present results provide a close agreement with the sphere—plane systems of Conway and Lee (Conway, D. and Lee, H. C. Impact of a lubricated surface by a sphere. ASME J. Lubr. Technol., 1975, vol. 97, pp. 613–615) and of Lin (Lin, J. R. Squeeze film characteristics between a sphere and a flat plate: couple stress fluid model. Comput. Struct., 2000, vol. 75, pp. 73–80), respectively.