An analytical method for obtaining cutter workpiece engagement during a semi-finish in five-axis milling

In five-axis milling, determining the continuously changing Cutter Workpiece Engagement (CWE) remains a challenge. Solid models and discrete models are the most common methods used to predict the engagement region. However, both methods suffer from long computation times. This paper presents an analytical method to define the CWE for toroidal and flat-end cutters during semi-finish milling of sculptured parts. The staircase workpiece model that resulted from rough milling was used to verify the method. The length of each cut at every engagement angle can be determined by finding two points: the lower engagement (LE) point and the upper engagement (UE) point. An extension of the method used to calculate the grazing point in swept envelope development was utilized to define the LE-point. The test showed that the existence of an inclination angle significantly affected the location of the LE-point. For the UE-point, it was first assumed that the workpiece surface was flat. A recalculation of the CWE was then performed to obtain a more accurate engagement profile with the actual surface. A technique called the Toroidal-boundary method was employed to obtain the UE-point when it was located on the toroidal side of the cutting tool. Alternatively, a method called the Cylindrical-boundary method was used to calculate the UE-point for a flat-end cutter on the cylindrical side of the toroidal cutter. The proposed model was successfully used to generate CWE data for two model parts with different surface profiles. The accuracy was verified twice: first, by comparing the coordinates of the UE-points with respect to the workpiece surface and second, by using Siemens-NX. The results proved that the proposed method was accurate. Moreover, because this method is analytical, it is more efficient in terms of computation time compared with discrete models.