Gorazd Stumberger

Optimization of radial active magnetic bearings using the finite element technique and the differential evolution algorithm

An optimization of radial active magnetic bearings is presented in the paper. The radial bearing is numerically optimized, using differential evolution-a stochastic direct search algorithm. The nonlinear solution of the magnetic vector potential is determined, using the 2D finite element method. The force is calculated by Maxwells stress tensor method. The parameters of the optimized and nonoptimized bearing are compared. The force, the current gain, and the position stiffness are given as functions of the control current and rotor displacement.

Determination of force and flux linkage characteristics of radial active magnetic bearings

The current and position dependence force and flux linkage characteristics of the studied radial active bearings are determined by the finite element computations in the entire operating range. Based on results of the performed computations the considerable impact of magnetic nonlinearities and cross coupling effects on properties of radial active magnetic bearings is established. The obtained characteristics are incorporated into the dynamic mathematical model, which is based on the current and position dependent radial forces and partial derivatives of flux linkages.

Magnetically Nonlinear Dynamic Models of Synchronous Machines: Their Derivation, Parameters and Applications

This chapter deals with the magnetically nonlinear dynamic models of synchronous machines. More precisely, the chapter focuses on the dynamic models of the permanent magnet synchronous machines and reluctance synchronous machines. A general procedure, which can be applied to derive such magnetically nonlinear dynamic models, is presented. The model is of no use until its parameters are determined. Therefore, some available experimental methods, that are appropriate for determining parameters of the discussed models, are presented. The examples given at the end of the chapter show, how the magnetically nonlinear dynamic models of discussed synchronous machines can be applied. Generally, in all synchronous machines the resultant magneto-motive force and the rotor move with the same speed. This condition is fulfilled completely only in the case of steadystate operation. However, during the transient operation, the relative speed between the resultant magneto-motive force and the rotor can change. In the case of permanent magnet synchronous machines, the force or torque that causes motion appears due to the interaction between the magnetic fields caused by the permanent magnets and the magnetic excitation caused by the stator currents. On the contrary, in the reluctance synchronous machines the origin of motion is the force or torque caused by the differences in reluctance. Most of the modern permanent magnet synchronous machines utilize both phenomena for the thrust or torque production. A concise historic overview of the development in the field of synchronous machine modelling, related mostly to the machines used for power generation, is given in (Owen, 1999). When it comes to the modern modelling of electric machines, extremely important, but often neglected, work of Gabriel Kron must be mentioned. In the years from 1935 to 1938, he published in General Electric Review series of papers entitled ``The application of tensors to the analysis of rotating electrical machinery.’’ With these publications as well as with (Kron, 1951, 1959, 1965), Kron joined all, at that time available and up to date knowledge, in the fields of physics, mathematics and electric machinery. In such way, he set a solid theoretical background for modern modelling of electric machines. Unfortunately, the generality of Kron’s approach faded over time. In modern books related to the modelling and control of

Linearization of Radial Force Characteristic of Active Magnetic Bearings Using Finite Element Method and Differential Evolution

Active magnetic bearings (AMBs) are used to provide contact-less suspension of a rotor (Schweitzer et al., 1994). No friction, no lubrication, precise position control, and vibration damping make AMBs appropriate for different applications. In-depth debate about the research and development has been taken place the last two decades throughout the magnetic bearings community (ISMB12, 2010). However, in the future it is likely to be focused towards the superconducting applications of magnetic bearings (Rosner, 2001). Nevertheless, the discussion in this work is restricted to the design and analysis of “classical” AMBs, which are indispensable elements for high-speed, high-precision machine tools (Larsonneur, 1994). Two radial AMBs, which control the vertical and horizontal rotor displacements in four degrees of freedom (DOFs) are placed at the each end of the rotor, whereas an axial AMB is used to control the fifth DOF, as it is shown in Fig. 1. Rotation (the sixth DOF) is controlled by an independent driving motor. Because AMBs constitute an inherently unstable system, a closed-loop control is required to stabilize the rotor position. Different control techniques (Knospe & Collins, 1996) are employed to achieve advanced features of AMB systems, such as higher operating speeds or control of the unbalance response. However, a decentralized PID feedback is, even nowadays, normally used in AMB industrial applications, whereas prior to a decade ago, more than 90% of the AMB systems were based on PID decentralized control (Bleuer et al., 1994).

Optimization of Radial Active Magnetic Bearings by Using Differential Evolution and the Finite Element Method

Magnetic bearings are a system of electromagnets, which makes possible contact-less suspension of a rigid body. The work presented here deals with the optimization of radial active magnetic bearings for a spindle drive. The bearings are optimized by differential evolution. The optimization aim is to achieve a maximum force at a minimum mass of the entire construction. Predefined design parameters are the bearing outer diameter, the shaft diameter, the air gap and the minimal generated force. The dependency of the objective function on the design parameters is not known in analytical form due to the magnetically nonlinear properties of the iron core. Therefore, the objective function of each individual parameter set in the population of the optimization algorithm is evaluated by the finite element method.