Innovation of NURBS feedrate direct interpolator in five-axis for CNC high-precision and high-efficiency machining

Abstract

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.

NURBS Interpolator with Minimum Feedrate Fluctuation Based on Two-Level Parameter Compensation

“…Wang et al [3] introduced the pre-compensation-based theory to increase machining precision by lowering contour errors while maintaining federate. Cao et al [4] suggested a feedrate direct interpolator (FDI), which can effectively acquire potentially precise interpolation parameters without using rounding or compensation techniques. Li et al [5] employed the Sigmoid function for feedrate planning, considering both geometric and kinematic errors.…”