A stochastic explanation of some structural properties of a ground surface

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Abstract
A stochastic theory of grinding is advanced from which some important statistical properties of the resulting ground surface are derived in terms of the basic parameters and dimensions of the grinding wheel used. If a Gaussian abrasive height distribution is assumed it is shown that the workplace height distribution will be negatively skewed. Use of a more rigorous height distribution based on the physical structure of the abrasive predicts that the workpiece height distribution will initially be skewed but will tend to Gaussian with further grinding. The model explains the reduction in roughness of the ground surface when the wheel is sparked out and permits its numerical prediction. Good agreement is found between theory and experiment.