Mathematical modeling is a key tool in engineering as it enables the analysis and prediction of material behavior under specific conditions. This study focuses on material strength, which is one of the most critical aspects of engineering design and manufacturing. Understanding material strength is essential for ensuring the reliability and safety of structures and products. The structure of the paper includes a theoretical overview of the fundamentals of mathematical modeling and regression analysis, a detailed description of the experimental research, the development of a model based on collected data, and the evaluation of the obtained mathematical model. Testing was conducted using a tensile testing machine, with samples of standard dimensions in accordance with EN 10002.

In this paper, we will process the results of experimental and numerical analysis on the example of the boom of a machine tool - a rotary excavator. Rotary excavator SRs 1200/630 KW - 22/2, engine no. 1, field “D”, produced by “LAUHAMER” - German Democratic Republic, is intended for mining coal and tailings at the surface mine of the JP RB “KOLUBARA” Lazarevac mine. During the regular overhaul and after 35 years of operation of the rotary excavator, it was concluded that it would be necessary to assess the stress and deformation state of both the rotary excavator as a whole and its vital parts individually (primarily the excavator booms) through adequate tests. The goal is to determine the critical points on the arrow structure after the tests have been carried out and act preventively to avoid accidents and additional unnecessary costs. By comparing the experimental and numerical results, we obtained a representation of the stresses and strains on the shaft construction and defined the critical stresses and strains.

It is known from theory and practice that the workability of wood depends on structural parameters that are closely related to the physical, mechanical and chemical properties of the type of wood itself, and disturbance parameters that refer to the technological and geometric parameters determined by the specific processing regime. That machinability, in addition to the mechanical output sizes, is often expressed by the quality, that is, the roughness of the processed surface. By defining a mathematical model in the process of planing solid wood in which the input sizes are processing parameters: wood density (ρ), feed rate (m/min) and number of cutting spirals (z), and the spilled sizes are praamters of roughness of the treated surface (Ra and Rz), and by applying optimization methods, optimal solutions for the process of planing solid wood on planer machines will be determined, so that the obtained Yoptim model will aim to improve the workability of solid wood, specifically its roughness of the processed surface.