Evaluation method of sphericity error based on error sphere

Abstract

The invention discloses a sphericity error evaluation method based on error balls. The sphericity error evaluation method comprises the following steps: I, obtaining coordinates and initial data of a measuring point; II, determining an optimization region; III, setting evaluation precision epsilon; IV, calculating coordinates of datum points; V, calculating the sphericity error corresponding to each datum point, and calculating the smallest sphericity error Emin of this iteration and coordinates Omin of the datum point on which the smallest sphericity error Emin is located; VI, ending judgment and outputting results. According to the sphericity error evaluation method based on error balls disclosed by the invention, the dividing process is simplified, the calculation of redundant points is reduced, the efficiency is improved, and the sphericity errors and parameters of the smallest region condition under the set evaluation precision can be obtained.

Description

technical field [0001] The invention relates to a precision spherical surface detection technology, in particular to a spherical error evaluation method based on an error sphere. Background technique [0002] With the development of modern technology, the spherical precision of spherical parts is increasingly required in the fields of aerospace, precision instruments and medical machinery. This puts forward higher requirements for the scientific evaluation of sphericity error. However, there is no clear standard for the evaluation of sphericity error at home and abroad. Therefore, it is of great significance to carry out research on related theories and methods. [0003] At present, the general evaluation methods for sphericity error evaluation are: least square method, minimum area method, minimum circumscribed sphere method and maximum inscribed sphere method. Among them, the evaluation accuracy of the minimum circumscribed sphere method and the maximum inscribed sphere ...

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Problems solved by technology

Among them, the evaluation accuracy of the minimum circumscribed sphere method and the maximum inscribed sphere method is poor. Although the least square method is simple and reliable in calculation, it does not satisfy the minimum area condition as an approximate calculation method.

The minimum area method has the highest evaluation accuracy and is also an arbitration criterion stipulated by the state, but it is a non-differentiable complex optimization problem when it is directly used for the evaluation of sphericity error

At present, relevant scholars often introduce computational geometry, number theory programming theory, etc. to approach the minimum area condition, but the disadvantage is that the principle is relatively complicated, which is not conducive to popularization and use.

However, the theoretical and mathematical foundations of these algorithms are not perfect. For example, the genetic algorithm has problems such as slow convergence speed and "premature", so it is not suitable for popularization.

[0005] Chinese invention patent CN101957191A proposes a roundness and sphericity error evaluation method based on adaptive iterative domain search. This method is simple in principle and can meet the minimum area condition. The calculation problem of redundant orientation points; there are many parameters and the area division parameters and iteration parameters are selected as statistical data, which is not ideal; the termination judgment is based on the preset iteration parameters, which is not accurate enough

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