Precise Bi-arc Curve Fitting Algorithm by Fixing Error at Optimal Point

摘要

The manufacturing error must be minimized in order to obtain precision products. The control modules of numerically controlled manufacturing systems usually have a linear and circular interpolation processor, such that the path for aspheric surface, expressed by complicated equation, has to be interpolated. The interpolation of aspherical surface path must precisely meet the allowable tolerance. Linear interpolation of the aspheric surface path for CNC machining generates an enormous amount of NC code to satisfy the extremely small tolerance, and produces scallops on the machined surface due to the acceleration and deceleration of the tool during every linear motion. Alternatively, interpolations with bi-arcs are used. In this paper, in order to minimize the error induced by the path of cutting tool and to shorten the calculating time of interpolation, a precise biarc interpolation method is proposed. The developed algorithm of biarc interpolation meets the given tolerance precisely. This is guaranteed by an analytical proof and error maps. Another advantage is its ability to calculate about five times faster than the existing arc interpolation, since iterative calculations for the maximum error can be omitted. The developed algorithm has been used for the precise aspheric machining.