Mathematical Modelling and Computer Simulation of Rotors Dynamics in Active Magnetic Bearings on the Example of the Power Gas Turbine Unit

Abstract

The paper considers the use of mathematical and computer modelling methods for the analysis of the technical state of complex rotary machines with controlled electronic components. These are active magnetic bearings (AMBs) with control systems. Assessment of the vibrational state of any rotor system is one of the most important tasks in their design and synthesis. Stationary and non-stationary processes take place in such systems. The main focus of the research is the use of a specially designed mathematical apparatus and software for implementation of proposed techniques for assessing the dynamic behaviour of rotors of power engineering turbomachines with active magnetic bearings in the entire range of excitation frequencies. Mathematical modeling is based on analytical representation using Lagrange-Maxwell magnetomechanical equations. The Runge-Kutta procedure is applied for numerical simulation. These methods and computer tools have several advantages over existing ones since they take into account completeness of a nonlinear relationship between mechanical, magnetic, and electrical processes occurring in the system, including continuous or discrete control actions. Created analytical and numerical approaches allowed to perform the modelling of rotor dynamics occurring in an energy gas turbine installation taking into account AMBs. Design calculation studies and analysis of the rotor dynamics of turbocompressor and turbogenerator of this installation show advantages of the proposed method for systems including AMBs. All the results of numerical studies are verified by comparison with numerical and experimental data known from open sources of information.