Smoothing the extrapolation of four-axis simultaneous control in ruled surface WEDM

Abstract

Four-axis simultaneous control is indispensable when machining workpieces with tapers or ruled surfaces in wire electrical discharging machining (WEDM). Complex geometries are interpolated by a CNC controller according to the predefined correlated curves located respectively on the top and bottom surfaces of the workpiece. Complex geometries can be interpolated by adopting a sophisticated algorithm namely Unit Generalized Arc Length Increment (UGALI). Normally, the upper and lower wire guides have certain distances to the top and bottom surfaces of the workpiece respectively. Therefore, a post-processing calculation for the corresponding motions of both the upper and lower wire guides is necessary, which is so called extrapolation. However, short line segments generated by the extrapolation are not smooth due to enlarged truncation errors of the interpolation. Truncations errors lead to unsmooth motions of the upper and lower wire guides, which can bring disturbances to the discharge gap control.In this paper, a method of improving the extrapolation for the four-axis simultaneous control is proposed to smoothen the motion and keep the discharge gap state stable. Within the tolerance of geometrical error, unsmooth motions of the upper and lower wire guides calculated by the extrapolation are merged by a look-forward reading and analyzing continuous multi-step extrapolated trajectories. In addition, servo feedrate optimization is also adopted in this study. By combining an appropriate number of extrapolation trajectories, the motion becomes smoother and the servo control of discharge gap becomes more stable. For verification, simulations and a machining test with on-line extrapolation smoothing and the discharge gap servo control optimization are carried out as well. Simulation and experimental results reveal that the proposed algorithm can help to reduce reversals of motor rotations, keep the machining state stable, thereby, resulting in the improvements of the machining efficiency.