Force modeling for 2D freeform grinding with infinitesimal method

Abstract A universal method of grinding force modeling in arbitrary 2D freeform grinding is proposed, which is based on the infinitesimal approach. The main idea of this method is to discretize the freeform surface into a group of surfaces with very small widths along the profile of the surface cross section, which can be considered as flat surfaces inclined at different angles. The form grinding process can be considered as a series of inclined flat surface grinding, where the normal grinding force of each flat inclined surface is divided into portions along specific directions. The process of inclined flat surface grinding at certain angle is equivalently converted to flat surface grinding in terms of the same abrasive wheel peripheral velocity and workpiece velocity but different cutting depth and contacting curvature in inclined view plane. A mathematical model of grinding force in flat surface grinding (FSG) is established, where the sliding stage, plowing stage and chip formation stage are considered respectively with 9 coefficients which are determined with linear regression from the grinding experiments. The forces in form grinding are then obtained by summing the individual inclined surfaces grinding forces, which are verified via rail form grinding (RFG). The algorithm was validated by means of the grinding experiments with average relative percentage errors of 6.08% and 7.01% respectively on tangential grinding force and normal grinding force in FSG and average relative percentage errors of 8.47% and 10.37% respectively on longitudinal grinding force and vertical grinding force in RFG.