Computerized Generation of Surfaces with Optimal Approximation to Ideal Surfaces

摘要

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