Accurate interpolation of machining tool-paths based on FIR filtering

This paper presents a novel real-time (online) interpolation algorithm based on Finite Impulse Response (FIR) filters to generate smooth and accurate reference motion trajectories for machine tools and motion systems. Typically, reference tool-paths are composed of series of linear (G01) or circular (G02) segments. Basic point-to-point (P2P) feed motion can be generated by interpolating each segment with trapezoidal or S-curved velocity profile. However, smooth and accurate transitions between path segments are necessary to realize non-stop contouring motion. In this study, FIR filters are utilized, and the reference tool-path is filtered to interpolate a non-stop rapid feed motion. By using a chain of FIR filters, acceleration and jerk continuous motion profiles are generated from velocity pulse commands. A segment interpolation timing technique is developed to control the contour errors during non-stop real-time interpolation of tool-paths. Furthermore, by utilizing FIR filters for interpolation, frequency spectrum of the interpolated motion profiles is controlled. The time constant (delay) of the filter is tuned to create notches around the lightly damped vibration modes of the motion system, which allows mitigation of unwanted vibrations and thus enables delivering accurate feed motion. Simulation studies and industrial scale experimental validations are provided to illustrate effectiveness of the developed interpolation technique.