A New Algorithm of Minimum Zone for Rapid Evaluating Straightness with Large Number of Samples

摘要

The number of samples should be large enough and the computing speed should be as fast as possible for exactly evaluating the value of form errors and decreasing the value of their uncertainties. This view has been verified by the research of MZ (minimum zone) evaluation form errors and their uncertainties. A new algorithm of MZ method for evaluating Straightness error of surface line element, which is suitable for large number of samples, is put forward in this paper. It is the valid characteristic point method with the rapidly contracted constraint zone. Its mathematical model is established, its fundamental is illustrated in detail and its basic procedure is described. By applying the judging criteria of alternate and characteristic points to search the gradient of enveloping line, the new algorithm constructs automatically a constraint zone of the gradient of the envelope line of the MZ and contracts it rapidly. It searches and finds quickly the gradient of the enveloping lines of the MZ and gets exactly the minimum value of the Straightness error. Its compute complexity is analyzed. The new algorithm has many advantages such as getting the minimum value of the Straightness error in first iteration, fast calculation speed and the maximum number of iterations only O (2log_2 n) ( n represents the number of samples). The new algorithm can be applied to CMM ( coordinate measuring machine) that can accomplishment MZ evaluating straight-ness and uncertainty of Straightness error with large number samples and high evaluation accuracy.