A stochastic grinding force model considering random grit distribution

Incorporating the random nature of grit distribution, this paper presents a closed form expression for the stochastic grinding force as a function of the grinding conditions and grit distribution. The stochastic grit density function is introduced to describe the random grit distribution of the rotating wheel. The dynamic grinding force is formulated as the convolution of a single-grit force and the grit density function. The single-grit force is obtained from analysis of the grinding geometry and treated as a deterministic impulse response of the grinding process. The spectrum characteristics of the grinding force are investigated in the frequency domain, where the power spectrum density (PSD) of the total grinding force can be expressed as a product of the energy spectrum density of the single-grit force and the PSD of the grit density function. The analytical nature of the PSD expression of the grinding force allows the identification of the PSD of the grit density function and the mechanistic grinding coefficients, and facilitates the analysis of the effects of the grit distribution and grinding conditions upon the grinding force. A series of grinding experiments were performed and their results discussed to validate this model. The results show that predictions drawn from the theoretical model are substantiated by the PSD, variance, and time domain signal of the experimentally measured grinding forces under various grinding conditions.