Multiple Objective Optimization Design of the Magnetic Bearing Supported Rotordynamic System

Magnetic bearings have been widely used in turbomachinery field due to their advantages from the non-contact mechanism and the absence of a lubrication requirement. This study focuses on modeling and predicting the rotordynamic and thermal performances of the nonlinear active magnetic bearing supported rotordynamic system with flexible rotor and flexible foundation effects, and then optimizing the design of the magnetic bearing actuator and the control law to achieve the multiple goals simultaneously. Nonlinearities, including the nonlinear magnetic bearing force with respect to the rotor displacement and the control current, the flux saturation, and the power amplifier current and voltage saturation, are analyzed to improve the prediction of the rotordynamic system. Two-dimensional finite element method is used to determine the temperature distribution on the actuator and predict the hot spot temperature during rotor steady state operations. A multiple-input multiple-output (MIMO) flexible support model effects on rotordynamic behavior of the system are addressed. Multiple system properties and performances, like the bearing actuator mass, the maximum vibration amplitude, the power loss, and the external static load, are set as goals to be optimized. Genetic algorithms, including Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Neighborhood Cultivation Genetic Algorithm (NCGA), are selected as the main optimization strategies due to their advantages in solving complicated optimization problems

Design and simulation of magnetic thrust and radial bearing system

Active magnetic bearings (AMBs) are used in many high speed machinery applications because of their advantages of no contact, no wear, no need for lubrications and ability to operate in high rotational speeds. AMBs represent an alternative solution to traditional mechanical bearing due to their contactless working principle. Touchdown bearings are needed in AMBs to prevent system damage under certain conditions such as sudden impact or sudden change of unbalance. In these conditions, rotor may make contact with touchdown bearings. AMBs may have the capability to accommodate sudden impact without contact though this will require novel design of control strategy for thrust and touchdown bearing. The purpose of this work is to provide platform for the robust control design research of flexible rotor-AMB touchdown systems. To this end research work concentrates on the design, construction and simulation of magnetic thrust and touchdown system. The report begins with the identifications of flexible rotor AMB system configuration. In this content accurate rotor system model considering AMB, thrust and touchdown discs was obtained using FEM technique according to Timoshenko beam theory. Design of flexible rotor AMB system requires careful attention towards rotordynamic design aspect such as observability and controllability and it is important that actuator and sensor location are away from the nodal point. Identification of flexible rotor-AMB system model is achieved in a series of steps. Free-free undamped mode shapes were obtained in this work which predicts the dynamic behaviour of the flexible rotor. The plot of the free-free mode shapes and natural frequencies results have shown that the system is controllable and observable. Second, Campbell diagram was generated to see the effect of gyroscopic behaviour on the splitting of natural frequencies into forward and backword modes. Campbell diagram results showed satisfactory behaviour of flexible rotor. The second goal of this work is to acquire technical design, modelling of electromechanical components and control unit. Magnetic actuator design specifications were obtained based on magnetic circuit analysis. Unigraphics software was used to carry out detail design and 3D modeling/assembly of electromechanical components. In this context purchase cost estimation was identified based on quotations. Purchase of rotor model components were made outside. The third goal of a thesis work is to verify the flexible rotor system model using experimental test. Hammer used as a force transducer was used in the test as excitation of the system and accelerometer used to measure response of the system. The experimental result validates the FEM technique because it is in reasonably good agreement with simulation results. The experimental mode shape results showed rotor will perform well within design speed range

Chatter milling modeling of active magnetic bearing spindle in high-speed domain

A new dynamical modeling of Active Magnetic Bearing Spindle (AMBS) to identify machining stability of High Speed Milling (HSM) is presented. This original modeling includes all the minimum required parameters for stability analysis of AMBS machining. The stability diagram generated with this new model is compared to classical stability lobes theory. Thus, behavior’s specificities are highlighted, especially the major importance of forced vibrations for AMBS. Then a sensitivity study shows impacts of several parameters of the controller. For example, gain adjustment shows improvements on stability. Side milling ramp test is used to quickly evaluate the stability. Finally, the simulation results are then validated by HSM cutting tests on a 5 axis machining center with AMBS

Rotors on Active Magnetic Bearings: Modeling and Control Techniques

In the last decades the deeper and more detailed understanding of rotating machinery dynamic behavior facilitated the study and the design of several devices aiming at friction reduction, vibration damping and control, rotational speed increase and mechanical design optimization. Among these devices a promising technology is represented by active magnetic actuators which found a great spread in rotordynamics and in high precision applications due to (a) the absence of all fatigue and tribology issues motivated by the absence of contact, (b) the small sensitivity to the operating conditions, (c) the wide possibility of tuning even during operation, (d) the predictability of the behavior. This technology can be classified as a typical mechatronic product due to its nature which involves mechanical, electrical and control aspects, merging them in a single system. The attractive potential of active magnetic suspensions motivated a considerable research effort for the past decade focused mostly on electrical actuation subsystem and control strategies. Examples of application areas are: (a) Turbomachinery, (b) Vibration isolation, (c) Machine tools and electric drives, (d) Energy storing flywheels, (e) Instruments in space and physics, (f) Non-contacting suspensions for micro-techniques, (g) Identification and test equipment in rotordynamics. This chapter illustrates the design, the modeling, the experimental tests and validation of all the subsystems of a rotors on a five-axes active magnetic suspension. The mechanical, electrical, electronic and control strategies aspects are explained with a mechatronic approach evaluating all the interactions between them. The main goals of the manuscript are: • Illustrate the design and the modeling phases of a five-axes active magnetic suspension; • Discuss the design steps and the practical implementation of a standard suspension control strategy; • Introduce an off-line technique of electrical centering of the actuators; • Illustrate the design steps and the practical implementation of an online rotor selfcentering control technique. The experimental test rig is a shaft (Weight: 5.3 kg. Length: 0.5 m) supported by two radial and one axial cylindrical active magnetic bearings and powered by an asynchronous high frequency electric motor. The chapter starts on an overview of the most common technologies used to support rotors with a deep analysis of their advantages and drawbacks with respect to active magnetic bearings. Furthermore a discussion on magnetic suspensions state of the art is carried out highlighting the research efforts directions and the goals reached in the last years. In the central sections, a detailed description of each subsystem is performed along with the modeling steps. In particular the rotor is modeled with a FE code while the actuators are considered in a linearized model. The last sections of the chapter are focused on the control strategies design and the experimental tests. An off-line technique of actuators electrical centering is explained and its advantages are described in the control design context. This strategy can be summarized as follows. Knowing that: a) each actuation axis is composed by two electromagnets; b) each electromagnet needs a current closed-loop control; c) the bandwidth of this control is depending on the mechanical airgap, then the technique allows to obtain the same value of the closed-loop bandwidth of the current control of both the electromagnets of the same actuation axis. This approach improves performance and gives more steadiness to the control behavior. The decentralized approach of the control strategy allowing the full suspensions on five axes is illustrated from the design steps to the practical implementation on the control unit. Furthermore a selfcentering technique is described and implemented on the experimental test rig: this technique uses a mobile notch filter synchronous with the rotational speed and allows the rotor to spin around its mass center. The actuators are not forced to counteract the unbalance excitation avoiding saturations. Finally, the experimental tests are carried out on the rotor to validate the suspension control, the off-line electrical centering and the selfcentering technique. The numerical and experimental results are superimposed and compared to prove the effectiveness of the modeling approach

Nonlinear Control of a Flexible Rotor Magnetic Bearing System: Robustness and the Indefinate Model

Previously published control strategies for magnetic bearings primarily focus on linear optimal control techniques. While these methods afford many advantages, conspicuously absent from the literature are detailed attempts at nonlinear control. Here, we obtain the equations of motion of an overhung flexible rotor supported in magnetic bearings with two different levels of model sophistication. We derive a generic nonlinear controller in the manner of feedback linearization, and compare the eigenanalysis and transient response of the two rotor models under the action of this >perfect model> controller. We then proceed to obtain a robust nonlinear controller through the sliding mode technique and demonstrate that robustness by implementing it on an uncertain model.Center for Electromechanic

Multi - objective sliding mode control of active magnetic bearing system

Active Magnetic Bearing (AMB) system is known to inherit many nonlinearity effects due to its rotor dynamic motion and the electromagnetic actuators which make the system highly nonlinear, coupled and open-loop unstable. The major nonlinearities that are associated with AMB system are gyroscopic effect, rotor mass imbalance and nonlinear electromagnetics in which the gyroscopics and imbalance are dependent to the rotational speed of the rotor. In order to provide satisfactory system performance for a wide range of system condition, active control is thus essential. The main concern of the thesis is the modeling of the nonlinear AMB system and synthesizing a robust control method based on Sliding Mode Control (SMC) technique such that the system can achieve robust performance under various system nonlinearities. The model of the AMB system is developed based on the integration of the rotor and electromagnetic dynamics which forms nonlinear time varying state equations that represent a reasonably close description of the actual system. Based on the known bound of the system parameters and state variables, the model is restructured to become a class of uncertain system by using a deterministic approach. In formulating the control algorithm to control the system, SMC theory is adapted which involves the formulation of the sliding surface and the control law such that the state trajectories are driven to the stable sliding manifold. The surface design involves the transformation of the system into a special canonical representation such that the sliding motion can be characterized by a convex representation of the desired system performances. Optimal Linear Quadratic (LQ) characteristics and regional pole-clustering of the closed-loop poles are designed to be the objectives to be fulfilled in the surface design where the formulation is represented as a set of Linear Matrix Inequality optimization problem. For the control law design, a new continuous SMC controller is proposed in which asymptotic convergence of the system’s state trajectories in finite time is guaranteed. This is achieved by adapting the equivalent control approach with the exponential decaying boundary layer technique. The newly designed sliding surface and control law form the complete Multi-objective SMC (MO-SMC) and the proposed algorithm is applied into the nonlinear AMB in which the results show that robust system performance is achieved for various system conditions. The findings also demonstrate that the MO-SMC gives better system response than the reported ideal SMC (I-SMC) and continuous SMC (C-SMC)

Vibration and Control of Flexible Rotor Supported by Magnetic Bearings

Active vibration control of flexible rotors supported by magnetic bearings is discussed. Using a finite-element method for a mathematical model of the flexible rotor, the eigenvalue problem is formulated taking into account the interaction between a mechanical system of the flexible rotor and an electrical system of the magnetic bearings and the controller. However, for the sake of simplicity, gyroscopic effects are disregarded. It is possible to adapt this formulation to a general flexible rotor-magnetic bearing system. Controllability with and without collocation sensors and actuators located at the same distance along the rotor axis is discussed for the higher order flexible modes of the test rig. In conclusion, it is proposed that it is necessary to add new active control loops for the higher flexible modes even in the case of collocation. Then it is possible to stabilize for the case of uncollocation by means of this method

Design and Development of a Next Generation Energy Storage Flywheel

Energy storage is crucial for both smart grids and renewable energy sources such as wind or solar, which are intermittent in nature. Compared to electrochemical batteries, flywheel energy storage systems (FESSs) offer many unique benefits such as low environmental impact, high power quality, and larger life cycles. This dissertation presents the design and development of a novel utility-scale FESS that features a shaftless, hubless rotor. The unique shaftless design gives it the potential of a doubled energy density and a compact form factor. Its energy and power capacities are 100 kWh and 100 kW, respectively. The flywheel is made of high-strength steel, which makes it much easier to manufacture, assemble, and recycle. Steels also cost much less than composite materials. In addition, the system incorporates a new combination active magnetic bearing. Its working principle and the levitation control for the flywheel are presented. The development of an integrated, coreless, permanent-magnet (PM) motor/generator for the flywheel is briefly discussed as well. Initial test results show that the magnetic bearing provides stable levitation for the 5443-kg flywheel with small current consumptions. Furthermore, this dissertation formulates and synthesizes a detailed model for designing and simulating a closed-loop control system for the proposed flywheel system at high speed. To this end, the magnetic bearing supporting structure is considered flexible and modeled by finite element modeling. The magnetic bearing is characterized experimentally by static and frequency-dependent coefficients, the latter of which are caused by eddy current effects and presents challenges to the levitation control. Sensor- runout disturbances are measured and included in the model. System nonlinearities in power amplifiers and the controller are considered as well. Even though the flywheel has a large ratio of the primary-to-transversal moment of inertias, Multi-Input-Multi-Output (MIMO) feedback control demonstrates its effectiveness in canceling gyroscopic torques and stabilize the system. Various stages of PD controllers, lead/lag compensators, and notch filters are also implemented to suppress the high-frequency sensor disturbances and structural vibrations

Electromechanical Simulation of Actively Controlled Rotordynamic Systems with Piezoelectric Actuators

Theories and tests for incorporating piezoelectric pushers as actuator devices for active vibration control are discussed. It started from a simple model with the assumption of ideal pusher characteristics and progressed to electromechanical models with nonideal pushers. Effects on system stability due to the nonideal characteristics of piezoelectric pushers and other elements in the control loop were investigated

Magnetic bearings-state of the art

Magnetic bearings have existed for many years, at least in theory. Earnshaw's theorem, formulated in 1842, concerns stability of magnetic suspensions, and states that not all axes of a bearing can be stable without some means of active control. In Beam's widely referenced experiments, a tiny (1/64 in diameter) rotor was rotated to the astonishing speed of 800,000 rps while it was suspended in a magnetic field. Despite a long history, magnetic bearings have only begun to see practical application since about 1980. The development that finally made magnetic bearings practical was solid state electronics, enabling power supplies and controls to be reduced in size to where they are now comparable in volume to the bearings themselves. An attempt is made to document the current (1991) state of the art of magnetic bearings. The referenced papers are large drawn from two conferences publications published in 1988 and 1990 respectively