Abstract
This paper presents a new procedure to numerically compute multi-point tool positions for five-axis machining for tensor product Bezier surfaces. The developed method first drops the toroidal tool along the vertical axis and then iteratively rotates the surface to determine the second point of contact between the tool and the surface. The surface tilt gives the rotation of the tool axis that positions the tool to have multiple points of contact with the unrotated surface. The mathematical model involves higher order rational equations and Newton’s method is used to numerically determine the solution. The developed algorithm is implemented in C++ and is tested for several bi-order Bezier patches from bi-cubic up to bi-order eight with uniformly and non-uniformly distributed control points. A comparative study with the earlier developed multi-point tool positioning methods (Duvedi et al. Int J Adv Manuf Technol 95:219–232, 2018, 97: pp. 279–295, 2018) is presented. The study shows that the developed method is computationally more efficient and reliable than previous methods. The accuracy of developed method is verified using the 3D graphical simulations in Maple and by actual five-axis machining.
Published Version
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