A stochastic model of plane grinding dynamic for the texture formation analysis

A mathematical model of plane grinding by the tool which is modeled as a disc with distributed on its surface abrasive grains, owning random geometric characteristics in the paper is analyzed. Cutting is modeled separately by each grain under kinematically given tool motion. The system of equations, describing the relations between the surface coordinate cut by permanent grain and the surface coordinate machined by previous grain, is obtained. The solution for a single track is analyzed, determining the configuration of workpiece surface under multiple grains’ passages. An array of varying dimension is used, in order to store the change of all grains’ cutting thickness in grinding process. The interaction forces at each grain being in contact with the machined surface are summarized at each time step. The dynamic model is based on the consideration of insufficient rigidity of the technological system characteristics, which is inherent while grinding of complex parts in aircraft and space industry. The arising vibrations can significantly affect on precision and surface quality. The problem is especially important in processing complex parts, such as turbine blades, where the precision and surface roughness, residual stresses define the process efficiency. The estimation of system parameters and cutting conditions influence on the machined surface errors generated while processing simulation is analyzed. It was shown that system vibration is excited with the frequencies of grain pass (rotation frequency) and with the eigenfrequencies of the elastic dynamical system also, which are typical for the regenerative mechanism of excitation.