On the modeling of boundary conditions for determining the critical speeds of rotation of rotors

Abstract

The article is devoted to the definition of boundary conditions that allow achieving adequate results when calculating the critical speeds of rotation of rotors based on finite element models. Experimental determination of the frequencies of free vibrations of a laboratory rotor on ball bearings was carried out using a vibration measuring complex developed by the authors. Numerical studies of the free vibrations of a laboratory rotor and a cylindrical pipe with a wall thickness to length ratio of 1/10 were performed on the basis of a three-dimensional finite element model under various boundary conditions. Movable and fixed cylindrical hinges corresponding to floating bearings are used as supports in the calculation scheme of the laboratory rotor. Due to the fact that the dimensions of the bearings along the length of the shaft are small compared to the total length, it is assumed in the calculation model that the shaft is hinged along the edges at separate points of one circle on each bearing. Shaft mounting options at two, four and eight points are considered. The options for fastening a cylindrical pipe in the extreme sections at two points, a quarter of a circle and a full circle are considered. Comparison of experimental and numerical results, solutions obtained analytically and on the basis of the finite element method is carried out. An analysis of the modes of natural vibrations showed that with various options for fixing a cylindrical pipe, vibration modes arise associated with the deformation of the pipe as a shell. For example, when fixing a pipe along a quarter of a circle, among the forms №1-№10, only the second corresponds to the deformation of the pipe as a beam. The results of the study of free vibrations of a laboratory rotor show that the best option for boundary conditions, which makes it possible to approach the results of the experiment, is fastening on each bearing at two points located on the neutral line of the cross section when the rotor is bent. Numerical studies of the eigen frequencies of a cylindrical pipe show that it is with this type of boundary conditions that one can obtain results that are closest to the analytical solution.