Разработка математических моделей для анализа чувствительности колебаний деталей машин

Abstract

The purpose of the paper is to develop mathematical models and algorithms based on the finite element method to analyze the sensitivity of vibrations of machine parts and structural elements to changes in design parameters. The paper presents an algorithm for sensitivity analysis based on the finite element method, as well as the calculation results of sensitivity of compressor blade free oscillations to the changes in its profile thickness. The finite element method in displacements is used. The classical Gauss method is used to solve the systems of linear algebraic equations. As a result of conducted researches the developed method of frequency sensitivity coefficients is offered for the analysis of oscillations. Based on the developed mathematical models, algorithms and methods the analysis of the rotor blade eigen oscillation sensitivity to the changes in profile thickness is analyzed. The calculation results have shown that the error of the frequency prediction by the sensitivity coefficients is small as compared to the calculation of the modified models. Consequently, the sensitivity coefficients can be used to assess possible designs of the blade. The presented calculation results demonstrate a rather small error, which allows to apply the developed analysis method of eigen frequency oscillation using sensitivity coefficients for the optimal design of the gas turbine rotor blades. The use of sensitivity coefficients provides the possibility to estimate the effect of the change in the local profile thickness on the blade oscillation spectrum. This significantly increases the efficiency of work on structure optimization when designing it.