FIR filter-based continuous interpolation of G01 commands with bounded axial and tangential kinematics in industrial five-axis machine tools

This article proposes a kinematic method to continuously interpolate G01 commands in industrial five-axis machine tools. Finite impulse response (FIR) filters are adopted to generate the time-optimal and jerk-limited trajectory of linear segments. The translational motion and the rotary motion are filtered in the workpiece coordinate system (WCS) and the machine coordinate system (MCS), respectively. A scaling principle is established to synchronize the translational and rotary motions with respect to the time durations of the FIR filters, and at the same time, to minimize the cycle time. Different from the existing two-step geometrical methods, G01 commands are continuously interpolated by directly overlapping the adjacent kinematic profiles in one step. Based on the proposed concept of admissible area, the induced corner errors are restricted under the given tolerances by modulating the overlapping times. To ensure that both the axial and tangential kinematic constraints are well respected, a new prediction and correction scheme (PCS) is proposed to predict the maximum reachable tangential kinematic constraints of the translational motion, and at the same time, to correct the maximum reachable axial kinematic constraints of the rotary motion. By doing so, both good machining quality and good tracking performances are achieved. Simulations and experimental results verify that the G01 commands can be continuously interpolated and well tracked with bounded axial and tangential kinematics.