Computerized generation of surfaces with optimal approximation to ideal surfaces

The authors propose a new method for generation (by grinding or cutting) of a surface (∑ g) with the optimal approximation to the theoretical (ideal) surface (∑ p). The method is based on the following ideas: (1) A region of space is swept out by the tool surface ∑ t performing certain motions with respect to ∑ p. The surface of the tool (as grinding wheel or cutter) is a surface of revolution with a circular arc in axial section, and a circular cone in particular cases. (2) The space swept out by ∑ t is considered as a family of surfaces ∑ t, and the envelope to this family is surface ∑ g (generated surface) that must be in optimal approximation to the theoretical surface ∑ p. (3) The continuous varied setting and orientation of ∑ t with respect to ∑ p are executed by a multi-degree-of-freedom machine, that is a computer numerical controlled (CNC) machine. The approach developed can be applied for grinding of face-gears, helical involute gears with modified topology, ruled undeveloped surfaces and others. An example of application is considered.