In this dissertation, a numerical method to design a curved surface for accurately flank milling with a general tool of revolution is presented. Instead of using the ruled surface as the design surface, the flank millable surface can better match the machined surface generated by flank milling techniques, and provide an effective tool to the designer to control the properties and the specifications of the design surface. A method using the least squares surface fitting to design the flank millable surface is first discussed. Grazing points on the envelope of the moving tool modeled by the grazing surface are used as the sample points and a NURBS surface is used to approximate the given grazing surface. The deviation between the grazing surface and the NURBS surface can be controlled by increasing the number of the control points. The computation process for this method is costly in time and effort. In engineering design, there is a need for fast and effortless methods to simplify the flank millable surface design procedure. A technique to approximate the grazing curve with NURBS at each tool position is developed. Based on the characteristics of the grazing surface and the geometries of the cutting tool, these NURBS representations at a few different tool positions, namely at the start, interior and end, are lofted to generate a NURBS surface. This NURBS surface represents the grazing surface and is treated as the design surface. Simulation results show that this design surface can accurately match the machined surface. The accuracy of the surface can be controlled by adding control points to the control net of the NURBS surface. A machining test on a 5-axis machine was done to verify the proposed flank millable surface design method. The machined surface was checked on a CMM and the obtained results were compared with the designed flank millable surface. The comparison results show that the machined surface closely matches the design surface. The proposed flank millable surface design method can be accurately used in the surface design.

In this dissertation, a numerical method to design a curved surface for accurately flank milling with a general tool of revolution is presented. Instead of using the ruled surface as the design surface, the flank millable surface can better match the machined surface generated by flank milling techniques, and provide an effective tool to the designer to control the properties and the specifications of the design surface. A method using the least squares surface fitting to design the flank millable surface is first discussed. Grazing points on the envelope of the moving tool modeled by the grazing surface are used as the sample points and a NURBS surface is used to approximate the given grazing surface. The deviation between the grazing surface and the NURBS surface can be controlled by increasing the number of the control points. The computation process for this method is costly in time and effort. In engineering design, there is a need for fast and effortless methods to simplify the flank millable surface design procedure. A technique to approximate the grazing curve with NURBS at each tool position is developed. Based on the characteristics of the grazing surface and the geometries of the cutting tool, these NURBS representations at a few different tool positions, namely at the start, interior and end, are lofted to generate a NURBS surface. This NURBS surface represents the grazing surface and is treated as the design surface. Simulation results show that this design surface can accurately match the machined surface. The accuracy of the surface can be controlled by adding control points to the control net of the NURBS surface. A machining test on a 5-axis machine was done to verify the proposed flank millable surface design method. The machined surface was checked on a CMM and the obtained results were compared with the designed flank millable surface. The comparison results show that the machined surface closely matches the design surface. The proposed flank millable surface design method can be accurately used in the surface design.