Fast and Robust Approach to Find the Gouge-free Tool Position of the Toroidal Cutter for the Bézier Surface in Five Axis Machining - Singh, Mukhmeet (University of Waterloo, 2020)
One of the approach used for tool path generation for Bézier surfaces is the Multipoint machining (MPM) approach, in which the toroidal cutter touches the machined surface at two points of contact. Multipoint machining helps in reducing the machining time by providing the tool path data that machines the surface in wider strips positioning the tool in the close proximity to the surface. The tool path generation using MPM is computationally expensive and time consuming, as it involves the solving of non-linear transcendental equations that require numerical methods. Numerical method such as Newton’s method are a time consuming and iterative process, and are not always able to give a solution. In this work, two methods, the ‘Drop, Rotate and Drop (DRD) method’ and the ‘Vertical and Circular Ray Firing (VCRF) method’, are developed, implemented and tested on bi-cubic Bézier surfaces using a Hi-Dyn tilt-rotary simultaneous five axis machining center. These methods follow the Multipoint machining approach. The DRD method limits the use of Newton’s method for convergence to the solution of two unknowns or variables. Whereas, the VCRF eliminates the use of Newton’s method for obtaining the solution and instead uses the implicit equations for firing the rays vertical or circular from the surface towards the toroidal cutter surface. Hence, the methods developed in this work give a fast and robust approach for generating tool path data for the Bézier surfaces.
Keywords: Five-axis machining; CNC machining; Multipoint machining; Tool path planning; Tool path generation; Machining; Machine-tools