A theoretical study of combined effects of non-Newtonian rheology and viscosity-pressure dependence in the sphere-plate squeeze-film system

A theoretical study of the combined effects of non-Newtonian couple-stress lubricants and variation of viscosity with pressure in the squeeze-film motion between a sphere and a flat plate is presented. To account for the couple stress effect arising from a lubricant blended with various additives and to consider the viscosity-pressure dependence, the nonlinear non-Newtonian Reynolds-type equation is derived in accordance with the Stokes microcontinuum constitutive equations cooperated with the Barus formula. Through a small perturbation technique, the analytical approximate solution for the film pressure is obtained. According to the results, the combined effects of couple stresses produced by the spin of microelements and viscosity-pressure dependence provide an enhancement in the load-carrying capacity and lengthen the response time as compared to the classical iso-viscous Newtonian-lubricant case. On the whole, the sphere-plate squeeze-film characteristics are improved, especially for higher values of couple stress parameter and viscosity parameter. An application to a lubrication problem is also illustrated for to assess the extent to design the sphere-plate squeeze-film system considering the combined effects of non-Newtonian couple stresses and viscosity-pressure dependence.