Multi-Objective Optimization Design of Nonlinear Magnetic Bearing Rotordynamic System

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Wan Zhong ◽  
Alan Palazzolo ◽  
Xiao Kang
Keyword(s):  
Power Loss ◽  
Optimization Design ◽  
Hot Spot ◽  
Load Capacity ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Control Law ◽  
Steady State Operation ◽  
Mass Minimization ◽  
Compact Design

Nonlinear vibrations and their control are critical in improving the magnetic bearings system performance and in the more widely spread use of magnetic bearings system. Multiple objective genetic algorithms (MOGAs) simultaneously optimize a vibration control law and geometrical features of a set of nonlinear magnetic bearings supporting a generic flexible, spinning shaft. The objectives include minimization of the actuator mass, minimization of the power loss, and maximization of the external static load capacity of the rotor. Levitation of the spinning rotor and the nonlinear vibration amplitude by rotor unbalance are constraint conditions according to International Organization for Standardization (ISO) specified standards for the control law search. The finite element method (FEM) was applied to determine the temperature distribution and identify the hot spot of the actuator during steady-state operation. Nonlinearities include magnetic flux saturation, and current and voltage limits of power amplifiers. Pareto frontiers were applied to identify and visualize the best-compromised solutions, which give a most compact design with minimum power loss whose vibration amplitudes satisfy ISO standards.

Single Plane Radial, Magnetic Bearings Biased With Poles Containing Permanent Magnets

2003 ◽  
Vol 125 (1) ◽  
pp. 178-185 ◽  
Author(s):  
Andrew Kenny ◽  
Alan B. Palazzolo
Keyword(s):  
Power Loss ◽  
Permanent Magnets ◽  
Load Capacity ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Single Plane ◽  
Side Load ◽  
Coil Inductance ◽  
Coil Resistance ◽  
Radial Magnetic Bearing

Magnetic bearings biased with permanent magnets have lower coil resistance power losses, and the magnets can also be used to help support a constant side load. In this paper, the performance of a single plane radial magnetic bearing biased with permanent magnets in several poles is presented. Although it has less load capacity and stiffness than a similarly sized electrically biased single plane heteropolar bearing, it does not require bias current, and its ratio of load capacity to coil resistance power loss is significantly better. This type of permanent magnet bearing has only a single plane of poles. It can be distinguished from the homopolar bearing type which has two planes and which can also be biased with permanent magnets. Magnetic circuit models for the novel single plane bearing are presented along with verification by finite element models. Equations for the key performance parameters of load capacity, stiffness, coil inductance and resistive power loss are also presented.

scholarly journals Development and Experimental Validation of Auxiliary Rolling Bearing Models for Active Magnetic Bearings (AMBs) Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Anna Tangredi ◽  
Enrico Meli ◽  
Andrea Rindi ◽  
Alessandro Ridolfi ◽  
Pierluca D’Adamio ◽  
...  
Keyword(s):  
Load Capacity ◽  
Critical Phenomenon ◽  
Magnetic Bearing ◽  
Design Tool ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Active Magnetic Bearings ◽  
Short Period ◽  
Auxiliary Bearing ◽  
Bearing System

Nowadays, the search for increasing performances in turbomachinery applications has led to a growing utilization of active magnetic bearings (AMBs), which can bring a series of advantages thanks to their features: AMBs allow the machine components to reach higher peripheral speeds; in fact there are no wear and lubrication problems as the contact between bearing surfaces is absent. Furthermore, AMBs characteristic parameters can be controlled via software, optimizing machine dynamics performances. However, active magnetic bearings present some peculiarities, as they have lower load capacity than the most commonly used rolling and hydrodynamic bearings, and they need an energy source; for these reasons, in case of AMBs overload or breakdown, an auxiliary bearing system is required to support the rotor during such landing events. During the turbomachine design process, it is fundamental to appropriately choose the auxiliary bearing type and characteristics, because such components have to resist to the rotor impact; so, a supporting design tool based on accurate and efficient models of auxiliary bearings is very useful for the design integration of the Active Magnetic Bearing System into the machine. This paper presents an innovative model to accurately describe the mechanical behavior of a complete rotor-dynamic system composed of a rotor equipped with two auxiliary rolling bearings. The model, developed and experimentally validated in collaboration with Baker Hughes a GE company (providing the test case and the experimental data), is able to reproduce the key physical phenomena experimentally observed; in particular, the most critical phenomenon noted during repeated experimental combined landing tests is the rotor forward whirl, which occurs in case of high friction conditions and greatly influences the whole system behavior. In order to carefully study some special phenomena like rotor coast down on landing bearings (which requires long period of time to evolve and involves many bodies and degrees of freedom) or other particular events like impacts (which occur in a short period of time), a compromise between accuracy of the results and numerical efficiency has been pursued. Some of the elements of the proposed model have been previously introduced in literature; however the present work proposes some new features of interest. For example, the lateral and the axial models have been properly coupled in order to correctly reproduce the effects observed during the experimental tests and a very important system element, the landing bearing compliant suspension, has been properly modelled to more accurately describe its elastic and damping effects on the system. Furthermore, the model is also useful to characterize the frequencies related to the rotor forward whirl motion.

Comparison of three-pole AMB and HMB for magnetic suspended molecular pump

2018 ◽  
Vol 32 (34n36) ◽  
pp. 1840074
Author(s):  
Jintao Ju ◽  
Xiaobin Liu ◽  
Zegang Xu ◽  
Chao Gu ◽  
Yilin Liu
Keyword(s):  
Power Loss ◽  
High Vacuum ◽  
Three Dimensional ◽  
Radial Force ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Active Magnetic Bearing ◽  
Rotating Speed ◽  
Characteristics Analysis ◽  
Current Characteristics

Molecular pumps have been widely used in the vacuum metallurgy, coating, semiconductor manufacturing and many other fields in which the high vacuum, ultra-clean environment is needed. The application of magnetic bearings can bring many advantages for molecular pump, such as eliminating the friction, decreasing the power loss, lowering the maintenance costs, and increasing the rotating speed and service life. Besides, the magnetic bearings can fundamentally solve the vacuum chamber pollution problem which is caused by the backflow of lubrication oil steam. The three-pole magnetic bearings are the simplest structure of radial magnetic bearings and can be driven by three-phase converter which has the advantages of low costs, small volume and low power loss. In this paper, the performance of the three-pole active magnetic bearing (AMB) and hybrid magnetic bearing (HMB) are compared based on radial force–current characteristics analysis. Firstly, the mathematical model of three-pole AMB and HMB is built by equivalent magnetic circuit model, and the radial force–current characteristics are analyzed. Then, simulation by the three-dimensional (3D) finite element method (FEM) is performed. Finally, the experiment is conducted. The FEM results are consistent with the analytical results, showing that the nonlinearity and coupling of three-pole HMB are lower than three-pole AMB. The reason of causing nonlinearity and coupling is also discussed.

Hybrid (hydrodynamic + permanent magnetic) journal bearings

2007 ◽  
Vol 221 (8) ◽  
pp. 881-891 ◽  
Author(s):  
H Hirani ◽  
P Samanta
Keyword(s):  
Permanent Magnets ◽  
Load Capacity ◽  
Rapid Development ◽  
Experimental Studies ◽  
Radial Force ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Axial Thrust ◽  
Hydrodynamic Bearing ◽  
Load Carrying

Survey of patents on bearings indicates the maturity of hydrodynamic and rapid development of magnetic bearings. Active magnetic bearings are costlier compared with permanent magnetic bearings. To understand the performance characteristics of permanent magnetic bearings, an experimental setup has been developed. Experimental studies on radial permanent magnetic bearings demonstrated the drawbacks, such as high axial thrust and low load capacity. This has led the authors to hybridize the permanent magnet with hydrodynamic technology and to explore the possibility of achieving the low starting torque of a permanent magnetic bearing and the medium to high load carrying capacity of a hydrodynamic bearing in a single bearing arrangement. Simulation is carried out in order to reduce axial force-effect and enhance the radial force supported by the permanent magnetic bearing. Results of simulation on permanent magnetic bearing have been compared with that of published research papers. Finally an algorithm has been developed to investigate the coupling of forces generated by permanent magnets and hydrodynamic actions. Results of load sharing have been reported. The experimentally measured displacements of the shaft running at 500, 2000, and 3000 r/min have been plotted. The effect of hydrodynamics on shaft orbit has been illustrated.

Experimentally Determined Rotor Power Losses in Homopolar and Heteropolar Magnetic Bearings

1999 ◽  
Vol 121 (4) ◽  
pp. 697-702 ◽  
Author(s):  
M. E. F. Kasarda ◽  
P. E. Allaire ◽  
P. M. Norris ◽  
C. Mastrangelo ◽  
E. H. Maslen
Keyword(s):  
Power Loss ◽  
Eddy Currents ◽  
Magnetic Bearing ◽  
Tip Clearance ◽  
Magnetic Bearings ◽  
Power Losses ◽  
Clearance Ratio ◽  
Detailed Measurement ◽  
Rotor Losses ◽  
Flux Path

The identification of parameters that dictate the magnitude of rotor power losses in radial magnetic bearings is very important for many applications. Low loss performance of magnetic bearings in aerospace equipment such as jet engines and flywheel energy storage systems is especially critical. Two basic magnetic bearing designs are employed in industrial practice today: the homopolar design, where the flux paths are of a mixed radial/axial orientation, and the heteropolar design, where the flux paths are primarily radial in nature. The stator geometry and flux path of a specific bearing can have a significant effect on the rotor losses. This paper describes the detailed measurement of rotor losses for experimentally comparable homopolar and heteropolar designs. The two test bearing configurations are identical except for geometric features that determine the direction of the flux path. Both test bearing designs have the same air gap length, tip clearance ratio, surface area under the poles, and bias flux levels. An experimental test apparatus was used where run down tests were performed on a test rotor with both bearing designs to measure power losses. Numerous test runs where made for each bearing configuration by running multiple levels of flux density. The components of the overall measured power loss, due to hysteresis, eddy currents, and windage, were determined based on theoretical expressions for power loss. It was found that the homopolar bearing had significantly lower power losses than the heteropolar bearing.

High-Speed Rotor Losses in a Radial Eight-Pole Magnetic Bearing: Part 1—Experimental Measurement

1998 ◽  
Vol 120 (1) ◽  
pp. 105-109 ◽  
Author(s):  
M. E. F. Kasarda ◽  
P. E. Allaire ◽  
E. H. Maslen ◽  
G. R. Brown ◽  
G. T. Gillies
Keyword(s):  
Power Loss ◽  
High Speed ◽  
Large Scale ◽  
Eddy Currents ◽  
Magnetic Bearing ◽  
Rate Of Change ◽  
Magnetic Bearings ◽  
Power Losses ◽  
Loss Mechanism ◽  
Pole Configuration

The continual increase in the use of magnetic bearings in various capacities, including high-speed aerospace applications such as jet engine prototypes, dictates the need to quantify power losses in this type of bearing. The goal of this study is to present experimentally measured power losses during the high-speed operation of a pair of magnetic bearings. A large-scale test rotor has been designed and built to obtain unambiguous power loss measurements while varying a variety of test parameters. The test apparatus consists of a shaft supported in two radial magnetic bearings and driven by two electric motors also mounted on the shaft. The power losses of the spinning rotor are determined from the time rate of change of the kinetic energy of the rotor as its angular speed decays during free rotation. Measured results for the first set of magnetic bearings, a pair of eight-pole planar radial bearings, are presented here. Data from three different parameter studies including the effect of the bias flux density, the effect of the bearing pole configuration, and the effect of the motor stator on the power loss are presented. Rundown plots of the test with the bearings in the paired pole (NNSS) versus the alternating (NSNS) pole configuration show only small differences, with losses only slightly higher when the poles are in the alternating pole (NSNS) configuration. Loss data were also taken with the motor stators axially removed from the motor rotors for comparison with the case where the motor stators are kept in place. No measurable difference was observed between the two cases, indicating negligible windage and residual magnetic effects. Throughout most of the speed range, the dominant loss mechanism appears to be eddy currents.

Rotor Power Losses in Planar Radial Magnetic Bearings — Effects of Number of Stator Poles, Air Gap Thickness, and Magnetic Flux Density

1998 ◽  
Author(s):  
P. E. Allaire ◽  
M. E. F. Kasarda ◽  
L. K. Fujita
Keyword(s):  
Magnetic Flux ◽  
Flux Density ◽  
Eddy Current ◽  
Power Loss ◽  
Magnetic Bearing ◽  
Air Gap ◽  
Magnetic Bearings ◽  
Magnetic Flux Density ◽  
Power Losses ◽  
Loss Mechanism

Rotor power losses in magnetic bearings cannot be accurately calculated at this time because of the complexity of the magnetic field distribution and several other effects. The losses are due to eddy currents, hysteresis, and windage. This paper presents measured results in radial magnetic bearing configurations with 8 pole and 16 pole stators and two laminated rotors. Two different air gaps were tested. The rotor power losses were determined by measuring the rundown speed of the rotor after the rotor was spun up to speeds of approximately 30,000 rpm, DN = 2,670,000 mm-rpm, in atmospheric air. The kinetic energy of the rotor is converted to heat by magnetic and air drag power loss mechanisms during the run down. Given past publications and the opinions of researchers in the field, the results were quite unexpected. The measured power losses were found to be nearly independent of the number of poles in the bearing. Also, the overall measured rotor power loss increased significantly as the magnetic flux density increased and also increased significantly as the air gap thickness decreased. A method of separating the hysteresis, eddy current and windage losses is presented. Eddy current effects were found to be the most important loss mechanism in the data analysis, for large clearance bearings. Hysteresis and windage effects did not change much from one configuration to the other.

Experimentally Determined Rotor Power Losses in Homopolar and Heteropolar Magnetic Bearings

1998 ◽  
Author(s):  
M. E. F. Kasarda ◽  
P. E. Allaire ◽  
P. M. Norris ◽  
C. Mastrangelo ◽  
E. H. Maslen
Keyword(s):  
Power Loss ◽  
Eddy Currents ◽  
Magnetic Bearing ◽  
Tip Clearance ◽  
Magnetic Bearings ◽  
Power Losses ◽  
Clearance Ratio ◽  
Detailed Measurement ◽  
Rotor Losses ◽  
Flux Path

The identification of parameters that dictate the magnitude of rotor power losses in radial magnetic bearings is very important for many applications. Low loss performance of magnetic bearings in aerospace equipment such as jet engines and flywheel energy storage systems is especially critical. Two basic magnetic bearing designs are employed in industrial practice today: the homopolar design, where the flux paths are of a mixed radial/axial orientation, and the heteropolar design, where the flux paths are primarily radial in nature. The stator geometry and flux path of a specific bearing can have a significant effect on the rotor losses. This paper describes the detailed measurement of rotor losses for experimentally comparable homopolar and heteropolar designs. The two test bearing configurations are identical except for geometric features that determine the direction of the flux path. Both test bearing designs have the same air gap length, tip clearance ratio, surface area under the poles, and bias flux levels. An experimental test apparatus was used where run down tests were performed on a test rotor with both bearing designs to measure power losses. Numerous test runs where made for each bearing configuration by running multiple levels of flux density. The components of the overall measured power loss, due to hysteresis, eddy currents, and windage, were determined based on theoretical expressions for power loss. It was found that the homopolar bearing had significantly lower power losses than the heteropolar bearing.

Dynamic Load Capabilities of Active Electromagnetic Bearings

1991 ◽  
Vol 113 (3) ◽  
pp. 598-603 ◽  
Author(s):  
K. R. Bornstein
Keyword(s):  
Dynamic Load ◽  
Load Capacity ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Saturation Point ◽  
Dynamic Capacity ◽  
Static Capacity ◽  
Wide Range ◽  
Selection Of

Magnetic bearings are finding increasing use in a wide range of applications. It is well known that the static capacity of a bearing can be determined by its saturation point. The static capacity has often been the prime criterion for the selection of magnetic bearing size. The dynamic capacity of a bearing is a much more complicated function. This paper will develop equations to express the dynamic load capacity of a magnetic bearing in terms of its amplifier size, the frequency of excitation, the magnetic airgap, the method of force actuation, and certain nondimensional terms.

Optimized Realization of Fault-Tolerant Heteropolar Magnetic Bearings for Active Vibration Control

1999 ◽  
Author(s):  
Uhn Joo Na ◽  
Alan Palazzolo
Keyword(s):  
Lagrange Multiplier ◽  
Global Minimum ◽  
Fault Tolerant ◽  
Load Capacity ◽  
Active Vibration Control ◽  
Fault Tolerant Control ◽  
Optimization Method ◽  
Magnetic Bearing ◽  
Magnetic Bearings ◽  
Control Voltage

Abstract The nature of coupling in the heteropolar magnetic bearings permits other remaining active coils in the stator to assume actions of the failed coils to produce the same force resultants. This fault-tolerant control usually reduces load capacity because the redistribution of the magnetic flux which compensates for the failed coils leads to premature saturation in the stator or journal. Distribution matrix of voltages which consists of redefined biasing voltage vector and two control voltage vectors can be optimized in the manner that peak flux density is minimized. An elegant optimization method using Lagrange Multiplier is presented in this paper. The redistribution matrices calculated with Lagrange Multiplier method were compared with Maslen and Meeker’s solutions, local minima are guaranteed and also the global minimum can be obtained if an effective global minimum searching algorithm is used. The linearized control forces can be realized up to certain combination of 5 poles failed for the 8 pole magnetic bearing. Position stiffness and voltage stiffness are calculated for the fault-tolerant magnetic bearings. Simulations show that fault-tolerant control of the multiple poles failed magnetic bearings with a horizontal flexible rotor can be stabilized with reduced load capacity.

Sign in / Sign up

Export Citation Format

Share Document