ARX modelling and compensation of roundness errors in taper turning

The forecasting compensatory control (FCC) strategy is successfully applied to the taper turning process to improve the roundness accuracy of the workpiece during cutting. This strategy: which is based on active error sensing, stochastic modelling and forecasting control, is capable of compensating both repeatable and non-repeatable errors. In the stochastic modelling, the effect of cutting force is considered, thus yielding an autoregressive model with exogeneous input (ARX). The resultant force is obtained from the outputs of the piezoelectric force sensor while the relative motion error between the tool and the workpiece is determined by means of a master taper and a capacitive sensor. The forecast error is sent to a piezoelectric actuator that moves the cutter to compensate for the error motion. Practical rests were performed on an experimental lathe with the FCC system rising models with different orders and forgetting factors. A maximum improvement of 33% can be achieved by this FCC strategy rising ARX (3,3) and forgetting factor of 0.997.