Lubrication flow in grinding

In the machining process known as grinding, fluid is applied to regulate the temperature of the workpiece and reduce the risk of expensive thermal damage. The factors that influence the transport of this grinding fluid are not well understood; however, it is important to gain understanding in order to try to avoid the unnecessary cost incurred from its inefficient application. In this work, we use the method of matched asymptotic expansions to derive the multiscale system of equations that governs the flow. Under the lubrication approximation, we show that it is possible to calculate the flow rate through the grinding zone without having to solve for the flow far from the grinding zone. Additional empirically determined boundary conditions do not need to be imposed. With this lubrication model, we quantify the effect of experimental parameters on the flow field in the grinding zone and study how the flow regime responds to changes in these parameters.