Generation of Freeform Surfaces by Diamond Machining

Diamond fly-cutting is a classical method for generating concave toroidal surfaces with radii r1 and r2 in two mutually perpendicular cross-sections, where r1 equals the fly-cut radius rf, and r2 must be larger than the tool nose radius rε (cf. Fig.1). Eventually, if r1=r2, or r2= ∞, spherical or cylindrical surfaces may result. If the midpoint M of the fly-cutter can be moved in all three spacial coordinates x,y,z with respect to the workpiece (the angular orientation of the fly-cut plane being fixed), oneand two-dimensional arrays can be created with the following geometrical options: