Analysis of standard uncertainty using the Monte Carlo method for arc measurement on a coordinate measuring machine

In mechanical engineering, products with discontinuous surfaces are used. The peculiarity of their measurement is the high discreteness and non-uniformity of the obtained coordinates. In this paper, we analyzed the influence of arc angle and non-uniformity of coordinates on the standard measuring uncertainty of roundness and arc radius. We used four reference circles: least squares, minimum zone, maximum inscribed, and minimum circumscribed. New computational algorithms using nonlinear optimization have been proposed for maximum inscribed and minimum circumscribed circles. A nonlinear measurement model based on Monte Carlo method was developed for simulation. Measurements of the bearing ring were performed and numerical simulations were carried out. For practical application, MZC is recommended, which guarantees the minimum measurement uncertainty of roundness in the range of 45 to 180 degrees. To estimate the radius, it is advisable to use the mean radius of the minimum zone circles.