A discrete system model for form error control in surface grinding

Abstract

Precision and quality have been the critical issues for many industries. For better machining quality, effective models will be needed in order to realize precision control. Surface form error is a difficult issue among the three main geometric features, which are size, form error, and roughness. There are little studies on modeling for form error control. In this study, a discrete system model for form error control in surface grinding is proposed based on three key relationships. Mathematical models describing the workpiece size reduction profile together with workpiece form error profile in relation to grinding pass number are presented. The grinding force constant k w and the unit force deflection y pg( x, z)/ P g can be estimated through experimental testing. Many operational process parameters are actually reflected in the proposed model and further separate studies are necessary for specific and accurate relationship between the operational process parameters and the model parameters. The results of the experimental testing are in good agreement with the theoretical results. For the average size reduction c n , the average relative error is as low as 1.34%. This shows that the proposed model is quite accurate. The proposed model is seen effective in obtaining the theoretical tangential force F t ntheo . The stringent point to point spatial comparison shows that the error between theoretical and experimental results is less than 2.3 μm and the average relative error is less than 6.93%. The proposed model is seen effective in size reduction prediction, which can be used to determine surface form profile y n ( x, z). The average relative error in the temporal comparison is 5.31%. It shows that the proposed model can be used to predict size reduction along the time axis, which is represented by the grinding pass. The results give confidence for use of the proposed control system model for form error control. To avoid the assumption of zero error in the initial workpiece surface, in-process form profile sensor is necessary. Further studies are needed for more accurate verification of the proposed model.