Regularization of ill-conditioned problems in geometrical measurements

Abstract

In measurements of small segments of geometrical objects such as circles, spheres, cylinders etc., object parameters are defined with large errors, that can essentially exceed both errors in the part manufacturing and errors in measurements. That's why such measurements could not be performed on coordinate measurement machines (CMM), but in the same time there is a great requirement in them in industry. Large errors are caused by ill-conditioned problem of small segments measurements. The method allowing to improve conditionality of considered problems by their mathematical regularization and to raise decision accuracy is described in this article. Offered method expands CMM possibilities, allowing to perform measurements that were not performed on them earlier.

Keywords

geometrical measurements / small segments / ill-conditioned problems / coordinate measuring machines

References

[1] Тихонов А.Н. О решении некорректно поставленных задач и методе регуляризации //ДАН СССР. 1963. Т. 151, № 3. с. 501-504.

[2] Тихонов А.Н. О регуляризации некорректно поставленных задач//ДАН СССР. 1963. Т. 153, № 1. с. 49-52.

[3] Тихонов А.Н., Арсенин В.Я. Методы решения некорректных задач. М.: Наука, 1979. 288 с.

[4] Суслин В.П., Джунковский А.В., Шутер М.Г. Новый метод определения геометрических параметров объектов при измерениях на малых областях // Законодательная и прикладная метрология. 2008. № 6. с. 39-42.

[5] МИ 2569-99. Машины координатно-измерительные портального типа. Методика поверки. М.: ВНИИМС, 1999. - 10 с.

RIGHTS & PERMISSIONS

Souslin V.P., Dzhunkovskiy A.V.