Swept volumes of toroidal cutters using generating curves based on the polar coordinates

Modelling the volume swept by a tool as it moves from one programmed position to another in the polar coordinates machining is a challenging task. In this paper, a technique for generating the volume swept by a toroidal cutter in its motion along a given tool path, is presented. This technique is based on identifying “generating curves” along the path and connecting them into a solid model of the swept volume. The swept volume simulations are verified experimentally for a test piece. These are also compared with the simulation results from the Z-map technique. The results of the experimental verification show the method to be accurate to within 1 mm for the three test pieces. It is concluded that the proposed method has the potential of allowing fast simulation and verification of tool path on a polar coordinates.