Real-time Variable Feedrate Parametric Interpolator for Cnc Machining

In modern commercial CAD and systems, a wide variety of part shapes for dies and molds are usually represented in parametric curves (or surfaces) like the Bezier curve, B-spline, and NURBS. However, conventional CNC machines only provide line or circular interpolators. In order to perform the machining of molds, the shapes and desired tool paths designed using CAD/CAM systems are typically approximated with very small line or circular segments. Such approximation approaches inherit several disadvantages: (1) for accurate machining the data file size is usually quite large so that the data transmission load is substantially increased; (2) will lead to velocity and acceleration discontinuity at the junction of line segments and may cause a shock or variation in mechanical system. These drawbacks suggest that the conventional interpolators fail to meet the requirements of high-speed machining in modern industry. Therefore the need to develop new parametric interpolators for CNC machines cannot be overlooked. The machining method used for parametric curves (or surfaces) is illustrated in Fig. 1 (Koren et al., 1993) where parametric interpolator converts the parametric curve (or surface) segments designed in CAD systems to each axis’s servo command of CNC machines. Based on firstand secondorder Taylor’s expansion or Runge-Kutta method, several investigators have proposed different kinds of parametric interpolators to generate servo commands for applications in constant feedrate control problems (Koren et al., 1993; Shpitalni et al., 1994; Wang et al., 1998; Kuo et al., 2000). Nevertheless, the capability of performing variable feedrate control is invaluable in high-speed machining applications and deserves more study. Huang and Yang (1992) developed a cubic spline interpolator by using the first-order Euler approximation method to study the variable federate control problem. Their method yielded satisfactory performances as long as the curvature of the curve for machining was small. Yang and Kong (1994) proposed a parametric interpolator for variable feedrate based on the firstand secondorder Taylor’s expansion. This is a comparative study REAL-TIME VARIABLE FEEDRATE PARAMETRIC INTERPOLATOR FOR CNC MACHINING