Abstract. This research paper is aimed to investigating rotor dynamics of multistage centrifugal machines with ball bearings by using the computer programs "Critical frequencies of the rotor" and "Forced oscillations of the rotor," which are implemented the mathematical model based on the use of beam finite elements. Free and forces oscillations of the rotor for the multistage centrifugal oil pump NPS 200-700 are observed by taking into account the analytical dependence of bearing stiffness on rotor speed, which is previously defined on the basis of results' approximation for the numerical simulation in ANSYS by applying 3D finite elements. The calculations found that characteristic and constrained oscillations of rotor and corresponded to them forms of vibrations, as well as the form of constrained oscillation on the actual frequency for acceptable residual unbalance are determined.
IntroductionThe existing numerical methods for calculation of rotor dynamics, which are based on the use of modern programs on the basis of finite element method, use beam elements with taking into account the Bernoulli's Hypothesis or 3D finite elements [1]. In this connection, appliance of 3D models, for example in ANSYS, needs carrying out relatively long operations and computational time [2]. The appliance of beam models [3] is not a long-time process for the initial data preparation, as well as it makes the computational process faster. However, the problem of determination of critical frequencies of rotor systems by using existing programs for the advanced determined dependence of the bearing stiffness and gap seals on rotor speed leads to drawing the Campbell diagram [4] that complicates the computational process with additional graphic constructions. Besides, the determination of rotor oscillations by taking into account the system of imbalances and nonlinear bearing stiffness is the high-complicated scientific problem [5].In accordance with the abovementioned, the aim of this research is a development of methods for determining eigenfrequencies and critical frequencies, as well as characteristics of rotor oscillations by applying a combined using 3D and beam finite elements on the example multistage centrifugal machines. To achieve this aim the following problems are set: 1) determination of the bearing stiffness with taking into account rotor speed by using ANSYS; 2) development of the mathematical model of rotor dynamics with the predetermined dependence of the bearing stiffness on rotor speed;
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