Analytical calculation of the envelope surface for generic milling tools directly from CL-data based on the moving frame method

Two closed-form solutions for calculating tool envelope surfaces are proposed based on the moving frame method. They have several advantages: (a) Given a sequence of cutter location (CL) data before post-processing into NC code, although we do not know the special configuration of machine tool, the tool envelope surface can be calculated accurately; (b) The two methods fit for a generic milling tool with a surface of revolution, such as a cylindrical cutter, conical cutter, drum cutter, and so on; (c) Since the calculation is developed based on the representation of the parametric form of the generating curve, it is convenient to use Bézier method, B-Spline or NURBS to unify the representation of the cutters and calculation of tool envelope surfaces. Several examples are presented to prove their effectiveness and good adaptability. The two methods can be used for NC machining simulation, evaluation and correction of the tool path.