Recursive estimation of the parts production process quality indicator

Abstract

Consideration is given to a mathematical representation for manufacturing of batch parts on a metal-cutting machine tool. Linear dimensions of machined parts are assumed to be the major quality indicator, deviation from these dimensions is determined by size setting of machine tool and ensemble of random factors. It is allowed to have absolutely precise pre-setting of machine tool, effects from setup level offsetting due to deformation in process equipment on the specified indicator are disregarded. Consideration is given to factors which affect the tool wear, with two definitions of tool wear being provided. Reasons for development of random error in processing, dependence of measurement results on error as well as distribution laws and some parameters of random values are provided. To evaluate deviation of size setting value in each cycle, it is proposed to apply a recursive algorithm in description of investigated dynamic discrete process in the space state. Kalman filter equations are used in description of process model by means of first-order difference equations. The algorithm of recursive estimation is implemented in the mathematical software Maple. Simulation results which prove effectiveness of algorithm application to investigate the given dynamic system are provided. Variants of algorithm application and opportunities of further research are proposed.