Construction of a non-linear analytical model for the rotation parts building up process using regression analysis

Abstract

We show how with the help of nonlinear paired regression, namely cubic regression, having experimental data, it is possible to investigate the relationship of tangential stresses between different layers of a cylindrical part during build-up. Six pairs of dependencies (models) between tangential stresses are considered. For each pair of dependencies, the accuracy of the built model was assessed using the average error of approximation and Fisher's F-criterion, and a comparative analysis was conducted. Despite some contradictions that arose during the evaluation of the models according to various regression parameters it was established that at least four of the six models are optimal and allow to adequately model the process of the formation of the stress-strain state in the details and elements of structures with significantly lower costs even before the stage of manufacturing finished products.

Keywords

• nonlinear paired regression
• stress-strain state
• mathematical modeling
• cubic regression
• coefficient of determination
• average error of approximation