Bivariate Time Series Analysis of the Effective Force Variation and Friction Coefficient Distribution in Wood Grinding

Abstract

A new technique for analyzing the normal and tangential grinding force is presented, which can be used to extract the dynamic characteristics of the grinder structure, the work material, and measurement transducers from experimentally measured forces. The technique involves developing bivariate time series models from the data which represent the dynamics imparted to the random force variation at the wood-stone interface. Removing the dynamics allows a simple model for the grinding force to be postulated, from which the statistical distribution of the resultant force and friction coefficient can be determined. Two sets of data from an experimental wood grinder are analyzed. Based on independent experiments, the frequencies in the measured normal and tangential forces can be related to factors other than the true grinding forces. The methodology developed is used to remove these dynamic effects and find the force and friction coefficient distributions. The mean value of the friction coefficient determined with this method appears to be more sensitive in detecting changes in friction for different grinding conditions.