The high-precision machining is restricted by truncation error and computational burden of second-order derivative in the second-order Taylor expansion (STE) interpolator which is usually used by scholars due to its advantages of high-precision and G3 continuity or higher. In conventional methods, the improved accuracy of interpolation parameter in the Taylor expansion interpolator will lead to a great increase in the computational burden of higher-order derivatives or compensation methods, resulting in degraded real-time performance. To tackle the bottlenecks, Non-uniform rational B-Splines (NURBS) feedrate direct interpolator (FDI) is proposed in the paper. The FDI for NURBS is divided into three parts, S-shaped acceleration/deceleration algorithm, feedrate scheduling, and the proposed FDI. In feedrate scheduling, four typical scheduling patterns are established to reduce the complexity of feedrate scheduling based on S-shaped flexible acceleration/deceleration and are used to obtained the maximum starting feedrate with feedrate constraint. The round method of feedrate duration must be adopted due to the non-integer multiple between interpolation period Ts and the generated duration time based on S-shaped acceleration/deceleration in conventional methods, while the proposed FDI completely follows the original feedrate produced by the feedrate scheduling. FDI is an equation in the continuous time domain rather than an inequality like STE, which can ensure the accuracy of interpolation parameter in theory. Furthermore, Computerized Numerical Control (CNC) system are inherently discrete-time systems, not continuous-time systems. Based on discrete features, the FDI equation is discretized to follow the precision of original feedrate duration which is the exact mapping of NURBS curve. The consistent precision greatly ensures the accuracy of the interpolation parameter in theory. Only with the original feedrate, can FDI directly obtain theoretically accurate interpolation parameter without any round and compensation method. With the proposed FDI, feedrate synchronous interpolator (FSI) method is proposed for dual-NURBS in five-axis machining. Only the tool tip interpolation parameter needs to be calculated by FDI and the interpolation parameter of tool orientation can be obtained by FSI directly with optimal tool attitude and high real-time performance. The FSI can make the tool orientation vector closer to the surface normal direction, which is more conducive to improving the cutting quality. Experiments were carried out on the machine tool to demonstrate the advantage of the proposed method in improving machining efficiency and the accuracy of interpolation parameter, simultaneously.
EtherCAT is a real-time Ethernet protocol and has been widely used in the field of motion control owing to its high speed (100 or 1000 Mbps), low processor occupancy, and good synchronization performance in slaves. However, the master-slave synchronization method is blank in the EtherCAT protocol. The study proposes a novel master-slave synchronization method that relies on the stable sync0 of reference slave by adjusting the trigger moment of master interpolation period to settle packet loss caused by EtherCAT master-slave un-synchronization, adaptively and dynamically. Furthermore, the proposed method improved EtherCAT to a whole new level, indicating that the EtherCAT master no longer depended on the real-time operating system (RTOS). In addition, a synchronization predictive compensation mechanism was adopted to eliminate the compensation lag defect of existing synchronization methods. Compared with conventional studies, the synchronization method improved compensation efficiency, settled inaccurate compensation with evaluation derived from different working frequencies, and eliminated accumulative error in clock. Finally, the proposed method added almost no computation and communication load and only required eight or 16 bytes to modify the EtherCAT frame coding in the interpolation period. Experiments were carried out on machine tools to demonstrate the advantage of the proposed method in improving the synchronization performance, with an average communication jitter of only 32-71 ns.
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