Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Weights for computing vertex normals from facet normals
Journal of Graphics Tools
Optimal tool orientation control for 5-axis CNC milling with ball-end cutters
Computer Aided Geometric Design
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This paper presents a three-dimensional configuration-space (3D C-space) machining method for 5-axis finish machining of tessellated surfaces. To maximize the step-over distance, the curvature matched method (CM2) is used to approximate the cusp height and the step-over distance. A 3D C-space is then built for each cutter contact point (CC point). Every configuration set in this 3D C-space guarantees that the cutter is gouge-free and that the cusp height is less than the machining tolerance. The inclination angle λ by which the cutter is rotated about LY, the yaw angle ω by which the cutter is rotated about LZ and the height δ by which the cutter is lifted along the normal of the surface are three variables used to build the 3D C-space. Next, the optimal cutter orientation is obtained in this corresponding 3D C-space via a special optimization process. The ideal 3D C-space set, the initial 3D C-space set and the objective function of the optimization process are based on machine tool kinematics. Boundary functions are determined by the geometry feature of the 3D C-space. The penalty function method is employed as the optimization method. In this paper, the cutting accuracy is self-guaranteed to be less than the machining tolerance. The cutting speed is set to be as high as possible based on optimal cutter orientation and maximized step-over distance.