Roundness error compensation in lathe turning through 2-D ARMAX model based FCC

This paper describes the design, simulation, and implementation of a two-dimensional (2-D) exogenous autoregressive moving average (ARMAX) model-based forecasting compensatory control (FCC) system for a lathe turning machine. The 2-D ARMAX model is used to represent the relative motion errors between the workpiece and the cutting tool in the longitudinal and radial directions. Here, the formulation of recursive ARMAX models is necessary to account for the variation of the cutting force, which is the exogenous input to this process. The parameters are estimated online by means of the recursive extended least square (RELS) method. The predicted motion errors, which will adversely affect the workpiece roundness, are compensated by means of a two-axis piezoactuator. An offline simulation model has been developed to find the most suitable model order and parameters. The application of the proposed system to both simulated and actual cutting data has confirmed the effectiveness of the proposed strategy. Experiments revealed that the maximum roundness improvement achieved could be as high as 66% while the average roundness improvement is found to be 52%, which proved the effectiveness of the proposed FCC system.