Study On The Free Form Surface Modeling And Five-axis NC Machining Of Sculptured Surface

With the development of the science and technology, more and more products with complex curved surfaces appear, In order to achieve higher efficiency and better quality, the level of designing and machining complex surfaces must be improved. Free form curves and surfaces modeling and free surface NC machining of technology become an important research interest in CAD/CAM technology.Based on NURBS (Non-Uniform Rational B-Spline) theory, the modeling methods of NURBS curve and surface are researched in this paper. The matrix forms of cubic NURBS curve and bi-cubic NURBS surface are derived, which are used to inverse the control points by the known data points of curve and surface. According to the different boundary conditions, additional equations are calculated; besides, the boundary tangent vector is given by the three-point circle method. The bi-cubic NURBS surface inversion boundary condition is derived when intermediate control points are used for data points.Focusing on five-axis NC machining of sculptured surface with the flat-end cutter, its paths are generated based on the constant scallop height principle. Based on space alternate coordinate, the mathematical model of the effective cutting shape is established and the effective curvature radius is calculated on the cutting contact point. The tool step is established by using chord-line method established, and the machining strip width is taken the place of by effective processing bandwidth, which depends on the intersection points between the scallop heights offset curve of normal section along the path interval direction on the machined surface. Avoiding to the tail interference at the bottom of tool and curvature interference, a beneficial tool posture angles must be determined, and the expression of tool inclination angle of is given.Finally, when the simulation of surface machining is used the MATLAB software, tool path is planned based on the different initial path. The method that the tool runs along the direction of maximum surface curvature radius is reasonably practicable, and effectively improves the machining efficiency and accuracy.