The Minimax Principle for Estimating the Shape Error in the Measurement of Complex Surfaces

In modern production, Coordinate Measuring Machines are widely used. One of the important tasks in the mathematical processing of measurement results is to compensate for the location of surfaces. Solving this problem allows finding the errors in the form, location of surfaces, and then determine the geometric characteristics of the products. In practice, two methods of compensating for the location of surfaces have been applied: Least Squares Method and Minimum Zone Tolerance. The article suggests a new method – Minimax. The idea is to minimize the maximum deviation of the surface form. Dependencies and examples of calculations for the measurement of elementary surfaces (plane, sphere, and cylinder) and complex surfaces (bodies of rotation and feathers of the turbine blade) are given. Comparative analysis showed that the Minimax Method has an advantage when processing the results of measuring complex surfaces. The resulting calculation error in the form is less by 5-9% than in the Least Squares Method.