Models Of Suspension Forces Research Articles

Coupling Suspension Force Regulator Considering Time-Varying Characteristic for a Bearingless Switched Reluctance Motor

The 12/14 bearingless switched reluctance motor (BSRM) was designed to restrain the coupling of torque current to suspension system. However, the robustness of the suspension system is reduced due to the time-varying current and displacement stiffness coefficients, thereby hindering its high reliable application in the on-board flywheel battery for vehicle. A coupling suspension force regulator (CSFR) that consists of a position decoupling suspension force model (PDSFM) and a dynamic coupling observer (DCO) is designed to solve the above-mentioned problem. The time-varying model of the suspension force is established based on the Maxwell stress method and finite element analysis, which is further decomposed into PDSFM and time-varying coupling suspension force component. The PDSFM is used for the feedback model of suspension system to construct a steady suspension system. The DCO is designed based on the PDSFM to capture the time-varying coupling suspension force component as an external disturbance and feed forward compensation to the suspension control system. The time-varying suspension system is effectively transformed into a time-invariant steady suspension system through the effective cooperation of the PDSFM and DCO. The validity of the CSFR is verified through simulations and experiments.

Mechanism model of suspension force for spherical bearingless flywheel machine

The flywheel energy storage system (FESS) has drawn more and more attentions in the past decades, and its operation performance is greatly dependent on the suspension characteristics of the flywheel machines. This paper proposed a new mechanism model of the suspension force for the spherical bearingless flywheel machine (S-BFM), which may be applied for the machine optimal design, performance analysis or efficiency evaluation. In the proposed model. the magnetic field partition method was used to solve the permeability of the machine in different diffused flux regions. The inherent characteristics of the rotor eccentricity and magnetic circuit saturation are considered by combining maxwell tensor method and equivalent magnetic circuit method. By considering the rotor eccentricity, magnetic circuit saturation and diffusion flux, the proposed model processes higher precision over the traditional model, and its outputs are quite close to that of the finite element analysis (FEA).

Design and Multi-Objective Optimization of a Composite Cage Rotor Bearingless Induction Motor

To improve the quality of starting torque and suspension force, a composite cage rotor bearingless induction motor (CCR-BIM) is designed, which adopts a composite cage rotor structure that combines an inner rotor and an outer rotor. First, the overall structure of the CCR-BIM is designed, the composite cage rotor of the CCR-BIM is specially designed and analyzed for the induction principle, and the mathematical model of suspension force and torque is deduced. Second, the initial structural parameters are determined, and motor qualities, such as starting torque quality and suspension force quality, are compared and analyzed between the proposed motor and BIM using a finite element model (FEM). Third, based on the response surface model (RSM), a multi-objective improved NSGA-II is constructed, and the three optimization objectives of starting torque, suspension force, and suspension force pulsation are optimized. Finally, the results of the experimental setup prove that the starting torque increases by 6.98%, the suspension force increases by 5.45%, and the suspension force pulsation decreases by 18.54%. The effectiveness of the proposed motor and the correctness of the multi-objective optimization strategy are verified.

Mechanism Model of Suspension Force for Spherical Bearingless Flywheel Machine

Mechanism Model of Suspension Force for Spherical Bearingless Flywheel Machine

Robust Controller Design for Maglev Suspension Systems Based on Improved Suspension Force Model

The electromagnetic suspension-type maglev train can reach ultrahigh-speed using long stator linear synchronous motors; however, slot effect makes the motors suffer from suspension force ripple, since it causes the nonsinusoidal airgap magnetic field distribution. It has been expounded that the suspension electromagnet system is highly nonlinear and unstable in open loops. Additionally, maglev trains experience disturbances and uncertainties in service. Therefore, the robust disturbance-rejection control for electromagnet suspension system is highly necessary to maintain a constant airgap position. In this article, it is intended to propose a novel robust controller for suspension systems which ensures superior system performances despite suspension force ripple, disturbances, and uncertainties while sustaining stable suspension despite system nonlinearity. First, field harmonics are investigated along with slot effects, and an improved nonlinear mathematical model of electromagnetic force is derived. Second, the controller based on the improved force model is formulated. Then, the performance of the designed controller is evaluated on a maglev suspension system with disturbances and uncertainties. Simulation and hardware-in-the-loop experimental results demonstrate that the improved suspension force model is more accurate than the conventional models, and the corresponding controller excels in attenuating larger disturbance without sacrificing tracking performances at different speeds.

Principle and Performance Analysis for Heterpolar Permanent Magnet Biased Radial Hybrid Magnetic Bearing

In order to solve the nonlinear problem and strong coupling of three-pole magnetic bearings, a heterpolar permanent magnet biased radial structure is proposed. Firstly, the structure and working principle of the heterpolar permanent magnet biased radial hybrid magnetic bearing are introduced, and the mathematical models of suspension forces are established by the equivalent magnetic circuit method. Secondly, in the case of the same volume and the same ampere-turn, the force-current characteristics and maximum carrying capacity of the couple-piece type three-pole structure and the heterpolar permanent magnet biased radial structure are obtained through theoretical analysis and 3D finite element method (FEM) analysis, respectively, and the data obtained are analyzed and compared. Finally, the theory analysis and experiment results show that compared with the couple-piece type three-pole structure, the nonlinearity among the suspension forces and the control currents of the heterpolar permanent magnet biased radial structure is obviously reduced, and the maximum bearing capacity of the heterpolar permanent magnet biased radial structure is increased by 29.4%, which proves the rationality of the radial heterpolar permanent magnet biased radial structure and parameters.

A novel five-degree-of-freedom AC-DC hybrid magnetic bearing

To reduce the volume, axial length and cost, a radial three-pole five-degree-of-freedom (5-DOF) integrated hybrid magnetic bearing (HMB) is studied, which the rotor can be levitated stably in one unit. Firstly, the configuration and suspension principle are introduced. The mathematical models of suspension forces are deduced by the magnetic circuit analysis. Then, according to radial and axial bearing capacity, the design method of main parameters is given. Finally, the magnetic circuit, suspension mechanism, air gap flux density, force-current relationships are calculated and analyzed by three-dimensional finite element method. The research results have shown that the structure of the 5-DOF integrated HMB is reasonable, and the suspension mechanism, mathematical model and design method are correct.

Numerical Modeling of Suspension Force for Bearingless Flywheel Machine Based on Differential Evolution Extreme Learning Machine

The analytical model (AM) of suspension force in a bearingless flywheel machine has model mismatch problems due to magnetic saturation and rotor eccentricity. A numerical modeling method based on the differential evolution (DE) extreme learning machine (ELM) is proposed in this paper. The representative input and output sample set are obtained by finite-element analysis (FEA) and principal component analysis (PCA), and the numerical model of suspension force is obtained by training ELM. Additionally, the DE algorithm is employed to optimize the ELM parameters to improve the model accuracy. Finally, absolute error (AE) and root mean squared error (RMSE) are introduced as evaluation indexes to conduct comparative analyses with other commonly-used machine learning algorithms, such as k-Nearest Neighbor (KNN), the back propagation (BP) algorithm, and support vector machines (SVMs). The results show that, compared with the above algorithm, the proposed method has smaller fitting and prediction errors; the RMSE value is just 22.88% of KNN, 39.90% of BP, and 58.37% of SVM, which verifies the effectiveness and validity of the proposed numerical modeling method.

Full‐period suspension force accurate modelling for a novel bearingless switched reluctance motor

In the traditional bearingless switched reluctance motor (BSRM) system, the electromagnetic coupling between the torque system and suspension system is unavoidable. In this Letter, the present BSRM has the advantages of electromagnetic decouple with independent torque-suspension magnetic circuit design. However, the further in-depth study shows that the BSRM has an obvious suspension force fluctuation according to its asymmetry structure. Thus, it is necessary to build an accurate suspension force mathematical model considering commutation ripple. In this frame, a magnetic field segmentation method is proposed and the accurate suspension force model is built with Maxwell stress method and its reliability and precision are verified, modified based on finite element analysis.

Experimental Analysis and Full Prediction Model of a 5-DOF Motorized Spindle

The cost and power consumption of DC power amplifiers are much greater than that of AC power converters. Compared to a motorized spindle supported with DC magnetic bearings, a motorized spindle supported with AC magnetic bearings is inexpensive and more efficient. This paper studies a five-degrees-of-freedom (5-DOF) motorized spindle supported with AC hybrid magnetic bearings (HMBs). Most models of suspension forces, except a “switching model”, are quite accurate, but only in a particular operating area and not in regional coverage. If a “switching model” is applied to a 5-DOF motorized spindle, the real-time performance of the control system can be significantly decreased due to the large amount of data processing for both displacement and current. In order to solve this defect, experiments based on the “switching model” are performed, and the resulting data are analyzed. Using the data analysis results, a “full prediction model” based on the operating state is proposed to improve real-time performance and precision. Finally, comparative, verification and stiffness tests are conducted to verify the improvement of the proposed model. Results of the tests indicate that the rotor has excellent characteristics, such as good real-time performance, superior anti-interference performance with load and the accuracy of the model in full zone. The satisfactory experimental results demonstrate the effectiveness of the “full prediction model” applied to the control system under different operating stages. Therefore, the results of the experimental analysis and the proposed full prediction model can provide a control system of a 5-DOF motorized spindle with the most suitable mathematical models of the suspension force.

Modeling and control of a bearingless permanent magnet synchronous motor

This paper presents a suspension force modeling method of BPMSMs based on Maxwell stress tensor method. By deducing the magnetic flux density of the airgap in BPMSMs using magnetic circuit analytic approach, the suspension force model with rotor eccentricity is established. And then the suspension force of a surface-mounted BPMSM is computed by the finite element method. Furthermore, in order to confirm the performance of the BPMSM and the magnetic suspension in real time, a prototype machine and its control scheme is set up and then corresponding experimental study is carried on. Rotor stabilization with magnetic levitation by using Maxwell tensor modeling method is verified by the simulation and experimental results.

Suspension Force Modeling for a Bearingless Permanent Magnet Synchronous Motor Using Maxwell Stress Tensor Method

Bearingless permanent magnet synchronous motors (BPMSMs) have been received more and more attention during the past few decades. To realize the high-performance control for rotation and levitation, we will first need to obtain the accurate suspension force model of a BPMSM. In this work, different from conventional suspension force models, a modeling scheme for the suspension force of a BPMSM is presented by taking into account rotor eccentricity with the Maxwell stress tensor modeling scheme. The theoretical value of a suspension force model is compared by the two-dimensional finite element (FE) analysis, and calculation results reveal that the theoretical value closely agree with the FE computed one. Furthermore, the digital control system is devised by taking advantage of TMS320F2812, and a test platform for experiments is then set up. In accordance with the corresponding findings of the experiments, the rotor stabilization with magnetic levitation can be achieved. The results lay a theoretical and experimental foundation for further study of the BPMSM.

SUSPENSION FORCE MODELING AND ELECTROMAGNETIC CHARACTERISTICS ANALYSIS OF AN INTERIOR BEARINGLESS PERMANENT MAGNET SYNCHRONOUS MOTOR

Interior bearingless permanent magnet synchronous motors (IBPMSMs) are a new type of machines having two sets of windings in the stator, offering no lubrication and no mechanical friction, high efficiency, robust rotor construction, hybrid torque production nature and flux-weakening capability. In this paper, the suspension force modeling and the static electromagnetic characteristics of an IBPMSM are studied. The suspension force model of the IBPMSM is established and investigated based on the Maxwell tensor method. And then the static electromagnetic characteristics, including permanent magnet (PM) flux linkage, EMF, inductances, electromagnetic torque and suspension force, are discussed with the finite element analysis (FEA) method. The electromagnetic characteristics of the IBPMSM are very helpful for the design and optimization of the motor. The effectiveness of the proposed suspension force mathematical model is verified by comparing the theoretical results with FEA-based predictions. The work in this paper lays an important foundation for the optimization design and control strategies of the IBPMSM.

Bearingless Permanent Magnet Synchronous Motor using Independent Control

Bearingless permanent magnet synchronous motor (BPMSM) combines the characteristic of the conventional permanent magent synchronous motor and magnetic bearing in one electric motor. BPMSM is a kind of high performance motor due to having both advantages of PMSM and magnetic bearing with simple structure, high efficiency, and reasonable cost. The research on BPMSM is to design and analyse BPMSM by using Maxwell 2-Dimensional of ANSYS Finite Element Method (FEM). Independent suspension force model and bearingless PMSM model are developed by using the method of suspension force. Then, the mathematical model of electromagnetic torque and radial suspension force has been developed by using Matlab/Simulink. The relation between force, current, distance and other parameter are determined. This research covered the principle of suspension force, the mathematical model, FEM analysis and digital control system of bearingless PMSM. This kind of motor is widely used in high speed application such as compressors, pumps and turbines.

Analysis and Control of Multiphase Permanent-Magnet Bearingless Motor With a Single Set of Half-Coiled Winding

In this paper, a multiphase bearingless motor (MBLM) with a single set of half-coiled winding is proposed, with advantages such as simpler construction and capability of fault-tolerant operation, comparing with the traditional BLM with dual groups of three-phase windings. The magnetomotive force distribution of the half-coiled winding is analyzed. Then, the winding configuration of a five-phase permanent-magnet bearingless motor is introduced, and the inductance of the MBLM is deduced by the modified winding function approach and verified by finite-element analysis. Furthermore, the control system is proposed based on the derived voltage model, torque model, and suspension force model, considering rotor eccentricity. Finally, static and dynamic experiments are provided on a prototype motor to verify the validity of the analysis.

Improved Model and Experiment for AC-DC Three-Degree-of-Freedom Hybrid Magnetic Bearing

Compared with the most popular DC and other emerging AC magnetic bearings, the AC-DC three-degree-of-freedom hybrid magnetic bearing (AC-DC 3-DOF HMB) invented in our research has a lot of advantages in cost savings and consumption reducing. In this paper, to overcome the insufficiency and shortcomings of the previously established classic model, a new mathematical model for suspension force of AC-DC 3-DOF HMB is deduced again to get more accurate results. To illustrate the improvement in the new model, some validation experiments and contrast experiments are designed and implemented to prove their correctness and accuracy. In the validation experiments, the nonlinearity, linearity, electromagnetic cross-coupling and kinematic cross-coupling of suspension force model are validated, which prove the correctness of the improved mathematical model. In the contrast experiments, the encouraging results between the experimentally measured result and two calculated results (classic and improved model results) show that the improved model is closer to the test results. Moreover, system performance comparison results show the control system based on the new model has stronger anti-disturbance characteristics than that based on the classic model. Thus, the improved modeling results on suspension force of AC-DC 3-DOF HMB is more accurate than the traditional results, even if they share the same modeling method (equivalent magnetic circuit method). So only a change of coefficient could help to significantly improve the accuracy of the mathematical model, and also the improved model instance has important reference value for solving other kinds of hybrid magnetic bearings.

Control System Design for AC-DC Three-Degree-of-Freedom Hybrid Magnetic Bearing

To fulfil the objective of high speed, high precision and intelligence in the modern equipment and advanced manufacturing industry, the magnetic bearing is requested to have small volume, low cost and low consumption. In this paper, an AC-DC three-degree-of-freedom hybrid magnetic bearing (AC-DC-3DOF-HMB) is studied, which integrates radial bearing and axial bearing in one of the magnetic bearing. The configuration and principle of AC-DC-3DOF-HMB are expounded, and the mathematical models of suspension forces are given. Then based on the function block diagram of AC-DC-3DOF-HMB control system, its hardware and software configuration are designed. The experiment results show that the rotor can be suspended stably with three degrees of freedom and has a good performance in anti- interference, and the feasibility of the control system design can be verified.

Magnetic suspension force in an induction bearingless motor with a squirrel cage rotor

AbstractTheoretical equations of magnetic force in an induction bearingless motor have been reported. In the bearing‐less motor, both 4‐pole and 2‐pole windings are stored in stator slots for torque and suspension force generation. In the analysis, squirrel cage rotor currents are considered. These currents are induced by both torque and suspension winding currents. Inductance matrix is represented by four sets of three‐phase windings, thus a 12×12 matrix is constructed. A simplification and reasonable assumptions are introduced to obtain understandable expressions for suspension force and torque representation. The rotor flux linkages in an induction bearingless motor are derived, and a simulation model of suspension force is then constructed. It is shown that the response and the phase of suspension force are delayed in the case of cage rotors. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(3): 77–87, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20340

Magnetic Suspension Force in an Induction Bearingless Motor with a Squirrel Cage Rotor

Theoretical equations of magnetic force in an induction bearingless motor have been reported. In the bearingless motor, both 4-pole and 2-pole windings are stored in stator slots for torque and suspension force generation. In the analysis, squirrel cage rotor currents are considered. These currents are induced by both torque and suspension winding currents. Inductance matrix is represented by four sets of three-phase windings, thus 12×12 matrix is constructed. A simplification and reasonable assumptions are introduced to obtain understandable expressions for suspension force and torque representation. The rotor flux linkages in an induction bearingless motor are derived, and then, simulation model of suspension force is constructed. It is shown that the response and the phase of suspension force are delayed in a case of cage rotors.