Evaluating method for testing of simple geometry and complete gauging of the work pieces with defined tolerance zones

摘要

The presented new method is based on Chebyshev principle, which is stabilized by an arbitrary small weighing factor of least-squares principle in order to permit the reliable and repeatable examination of the best fit geometric elements in a simple or a very complex geometry, by non-precise parts of work pieces or by CNIM measurements of lower accuracy. The examination of the best fit geometric elements in a simple or a very complex geometry according to Chebyshev principle is effected with help of presented method which is used as a preliminary stage of the Chebyshev evaluation, with which the norm-fair Chebyshev evaluation is practically always guaranteed. The convergence of the new evaluation method corresponds to the least square principle, while the Chebyshev precision is reached in the full-minimization of the amount intervals. It is proven, that the direction vector of many standard geometric elements can be inclined by a very small angle and/or slightly shifted without changing the best Chebyshev form, By using all these advantages, the method is successfully implemented by complete gauging of the work-pieces within tolerance zones as defined by ISO 2692. There is an absolute requirement that the Chebyshev method for all different elements must be stable on each improvement step during the iterative process of solving very large non-linear equations, besides all tolerated conditions and different surface's qualities. Using presented method for geometry quality control in automotive and machinery building industry, in plastic forming etc., an evaluation is ensured of the best least fault zone according to Chebyshev principle of a single element as well as the least shape of each element by testing of work pieces under enveloping conditions. The new method characterizes a convergence independent of the measuring points dispersion.