A DYNAMIC MATHEMATICAL MODEL FOR COMPUTER AIDED GRINDING BY DATA DEPENDENT SYSTEMS

Wavelength decomposition by Data Dependent Systems (DDS) is applied to wheel and workpiece profiles (along transverse and longitudinal directions) and major wavelength components were isolated. The randomness of wheel profile arising from the location and height of grains has been deconvoluted by DDS methodology to provide a "characteristic grain". The "characteristic grain" arises from the superimposition of a large wavelength for the grain and a small wavelength for the cutting edges. Thus the topography of the wheel has been modeled as a combination of these two waveforms. The large wavelength representing the grain has been used in establishing an expression for the elastic deflection of the grain. Due to the elastic deflection, the small wavelength representing the cutting edges cuts a smaller "characteristic groove" on the surface, which provides a prediction of the RMS of the ground surface along the transverse direction. The Spanzipfel effect due to the grains and Kinematic effect due to the cutting edges together play a predominant role in the surface generation along the longitudinal direction, whereas the cutting edges leave their imprints on the surface along the transverse direction. Analytical expressions for predicting the roughness and wavelengths along the transverse and longitudinal directions have been derived including the elastic deflections of the grain and the wheel. The fracture and attritious wear rates have been used in updating these expressions with the progress of cut. Estimates provided by these expressions were verified by experimental results.; The tangential and normal grinding force components have been analyzed by fitting the DDS models. Adequate DDS models obtained for these force signals are decomposed to provide the plowing, cutting and sliding components. The specific energy associated with each of these modes was calculated from the horizontal force components. The component of energy increasing with the progress of cut has been identified to provide the reason for "work-burn". An estimate of the number of dynamic cutting edges from the surface profiles and the number of dynamic active grains from the force signals were obtained. This provides an insight into the surface generation mechanism in grinding and hence a possible strategy for computer control of the grinding process can be obtained.