Analysis of Fluid Flow Under a Grinding Wheel

Fluid flow under a grinding wheel is modeled using a perturbation scheme. In this initial effort to understand the flow characteristics, we concentrate on the case of a smooth wheel with slight clearance between the wheel and workpiece. The solution at lowest order is that given by standard lubrication theory. Higher-order terms correct for inertial and two-dimensional effects. Experimental and analytical pressure profiles are compared to test the validity of the model. Lubrication theory provides good agreement with low Reynolds number flows; the perturbation scheme provides reasonable agreement with moderate Reynolds number flows but fails at high Reynolds numbers. Results from experiments demonstrate that the ignored upstream and downstream conditions significantly affect the flow characteristics, implying that only a model based on the fully two- (or three-) dimensional Navier-Stokes equations will accurately predict the flow. We make one comparison between an experiment with a grinding wheel and the model incorporating a one-dimensional sinusoidal roughness term. For this case, lubrication theory surprisingly provides good agreement with experiment.