Radial Force Model Research Articles

Investigation of design methodology for doubly-fed bearingless flux reversal motor

This article integrates the technology of bearingless motors with the basic theory of magnetic flux reverse motors, proposes a doubly fed bearingless magnetic flux reverse motor, and conducts research on its structural design, operating mechanism, electromagnetic performance analysis, mathematical model, control method, digital control system, and other aspects. The basic structure of a new type of doubly fed bearingless magnetic flux reverse motor is designed, and the principle of radial suspension force generation is studied. The performance related to torque and radial suspension force is analyzed. A mathematical model of torque and radial suspension force is established, including magnetic field distribution, no-load permanent magnet flux, and no-load back electromotive force. A doubly fed bearingless magnetic flux reverse motor system is designed and constructed, and inductance experiments are conducted.

Experiments and modeling of fluctuating frictional force of pipeline inspection gauges

At present, pipeline inspection gauge (PIG) is the main means to ensure the reliability of oil and gas transportation pipelines. Due to the unstable friction between the PIG and the pipeline, the failure and blockage of the PIG often occurs. In this paper, the theoretical modeling and experimental measurement of fluctuating friction on PIG are studied. Firstly, considering the coupling relationship between cylindrical shell and conical shell, the contact radial force model between PIG and pipeline is derived. Based on which, the nonlinear frictional model of PIG is proposed, and the parameters are measured by several experiments. Then an experimental platform is developed to measure the fluctuating friction force of PIG in actual operation, and verify the accuracy of the proposed model. The motion characteristic analysis and dynamics research are carried out, and the PIG creeping phenomenon caused by fluctuating friction is explained. Finally, based on the proposed nonlinear friction model, the influence of parameters is analyzed. The conclusions based on the proposed model and the experiments results can provide technical supports for practical engineering application.

Online Control Strategy for Radial Vibration Suppression of PMSM by Multiharmonic Current Injection Method

In the radial vibration suppression of the motor, the current harmonic injection method is an effective method. The radial force model of surface permanent magnet synchronous machine (SPMSM) is analyzed, and the relationship of the frequency, amplitude and phase between harmonic current and radial vibration harmonic is obtained. A current harmonic injection method is derived by using the current closed-loop transfer function in vector control, which can adjust the frequency, amplitude and phase of current harmonics to realize the change in the amplitude of radial vibration harmonics. one current harmonic is selected to suppress one even-order radial vibration harmonic, and the gradient descent method is adopted to online calculate the frequency amplitude and phase of the current harmonics injected at the minimum amplitude of radial vibration harmonics. In order to avoid the influence of the single current harmonic on the high radial vibration harmonics, a sequential vibration suppression method is proposed to realize the comprehensive suppression of every low-even-order vibration harmonics. Finally, an on-line control system for the radial vibration suppression of SPMSM with multi-current harmonics injection is designed. The prototype is a 750W SPMSM, the amplitude of all low-even radial vibration harmonics are suppressed significantly by this method, which verifies the correctness and effectiveness of this method.

Analysis on accuracy of rotor‐locked transient‐response‐based vibration model for switched reluctance machines

This paper investigates the accuracy of rotor-locked transient-response (RLTR)-based vibration model for switched reluctance machines (SRM). RLTR is stator vibration stimulated by abrupt change of radial force when turning off one phase of SRM with rotor being locked, the total vibration of SRM can be modelled as linear superposition of RLTR series. An electromechanical model is built to clarify the generation of SRM vibration, it is revealed that some velocity-depend terms in electromechanical model would be neglected when rotor is locked, it leads to inevitable difference of RLRT between rotor-locked condition and rotational condition, the difference is illustrated through multi-physics simulation. A harmonic radial force model is proposed to quantitatively evaluate the accuracy of RLTR-based vibration model, radial force spectrums with locked rotor and rotational rotor are compared to predict relative error between RLTR-based vibration and actual vibration. The influence of turn-off angle and velocity on accuracy of RLTR-based vibration model is also analysed. The accuracy of RLTR-based vibration model is evaluated through experiment on 3-phase 12/8 SRM, the results showed that: (1) the accuracy of RLTR-based vibration model is impacted by turn-off angle and velocity; (2) relative error between RLTR-based vibration and actual vibration can be predicted using harmonic radial force model. This paper illustrates the generation mechanism of modelling error for commonly used RLTR-based vibration model of SRM, the proposed error prediction method could lead to improved accuracy on SRM vibration model through error compensation.

Levitation Performances Analysis of a Novel Bearingless Switched Reluctance Motor

To deal with the coupling between the levitation force and torque, a new bearingless switched reluctance motor (BSRM) is presented in the paper, in which the torque flux is separated with the levitation flux. In addition, due to the low cost and power of the three-phase power converter, the radial levitation of the proposed BSRM is driven by a three-phase power converter. The structure of the proposed BSRM is first introduced. The mathematical models of radial levitation force are second established by employing equivalent magnetic circuit approach. Finally, the electromagnetic characteristics of the BSRM, such as flux field distribution, transient levitation force and force-current relationship are investigated through the MagNet 3D. The research results indicate that the novel structure has good performances.

Dynamics Modeling and Experimental Investigation of Gear Mechanism with Coupled Small Clearances.

Internal gear mechanism is widely used in micro-nano satellites due to its compact structure and high precision transmission. However, the vibration coupling caused by the small clearance coupling is more obvious and cannot be ignored under low speed, light load and zero gravity conditions. Based on the geometric relationship between radial clearance and backlash, a coupled model between dynamic backlash and radial clearance of internal meshing gear is established. Based on the conformal contact theory, the radial collision force model of the gear shaft and shaft sleeve considering the small clearances is established. Additionally, a multi-clearance gear rotor system test device is built to measure the vibration acceleration of the internal gear rotor system by an acceleration sensor and transmitted to the industrial computer through a signal collector for data processing. Through the comparison of simulation and experiment, the accuracy of the gear dynamics model is verified. The analysis results show that, compared with the traditional model, the calculation results of the gear mechanism model considering the small clearance coupling is closer to the experimental data.

A Novel Homopolar Four Degrees of Freedom Hybrid Magnetic Bearing

In this article, a novel four degrees of freedom (4-DOF) homopolar hybrid magnetic bearing (HMB) is put forward to reduce the magnetic field coupling of radial 4-DOF. It consists of two pairs of symmetrical radial stators and one rotor, and the radial stators on each side have two pieces, namely, X and Y stator core. Due to the special design of X and Y magnetic poles in the different radial stator cores, the magnetic circuits of X and Y channels are independent of each other. The configuration and operating principle of the homopolar HMB are first discussed, and then, the mathematical model of radial suspension force is deduced by the equivalent magnetic circuit method (EMCM). Besides, some main parameters are given in accordance with the given maximum radial suspension force. Finally, 3-D finite-element (FE) model of the homopolar 4-DOF HMB is established with MagNet software. Meanwhile, the magnetic flux distributions, the magnetic flux density, the force-current relationship of X channel with displacement and current of Y channel are simulated and analyzed. The simulation results indicate that the presented 4-DOF HMB has good performance, and the magnetic fields of X and Y channels decouple well from each other.

Electromagnetic Vibration Analysis of High-Speed Permanent Magnet Synchronous Machines With Amorphous Metal Stator Cores Considering Current Harmonics

This article investigates the electromagnetic vibration characteristics of high-speed (HS) permanent magnet synchronous machines (PMSMs) with amorphous metal stator cores (AMSCs) considering current harmonics. First, an analytical model of radial forces in PMSMs considering current harmonics due to both nonsinusoidal back electromotive force and pulsewidth modulation effects is developed. The cross influences of the two types of current harmonics on vibrations of HS PMSMs in different frequency bands are discussed. Second, the equivalent elasticity modulus parameters of laminated AMSCs are identified by utilizing modal experiment. Third, the influences of slot and pole number combinations on magnetic field harmonic contents and radial force orders for HS PMSMs are investigated by the analytical model. Then, the radial forces of a 15-kW HS PMSM fed by ideal sinusoidal current and experimental current are calculated under different rotational speeds by finite-element method. Finally, the vibrations of the prototype under rated torque and different rotational speeds are tested to verify the theoretical analysis.

Optimal Winding Configuration of Bearingless Flux-Switching Permanent Magnet Motor With Stacked Structure

Winding configurations that are applicable to a novel bearingless flux-switching permanent magnet motor with stacked structure are investigated, and one method to evaluate these winding configurations is also proposed in this paper. First, the motor structure and the influence of coil connections on torque and radial force are illustrated, and the fundamental radial force expressions of two diametrically opposite coils are derived. Afterward, two kinds of torque windings and four kinds of radial force windings for the motor are studied and the radial force models are derived accordingly. Following this, the radial force models are verified and the transient radial force and torque characteristics are investigated by finite element analysis. More importantly, an evaluation factor related to the winding copper losses is defined to evaluate the winding configurations. Finally, an optimal winding configuration is determined theoretically and a prototype motor is built to validate the effectiveness of the motor structure and the optimal winding configuration.

Modeling and Analysis of Hybrid Permanent Magnet Type Bearingless Motor

The traditional bearingless permanent magnet synchronous motor has complex decoupling control problems. To overcome the drawbacks above, a novel hybrid permanent magnet type bearingless motor (HPMTBM) is proposed in this paper, which has integrated the merits of hybrid excitation permanent magnet motor and magnetic bearings. The main advantages of this HPMTBM are the simple control mechanism and the low power consumption. First, the principle and theoretical background of this motor are introduced. Then, the mathematical models of radial suspension force and torque are established using Maxwell stress tensor method, and air-gap magnetic fields, radial suspension forces are calculated by finite-element analysis. Finally, the prototype motor is designed and constructed. The radial suspension forces and rotor radial displacements are tested. The simulation and experimental results show the feasibility of the proposed HPMTBM.

Design and experimental study on an ultrasonic bearing with bidirectional carrying capacity

Based on near-field acoustic levitation effect and piezoelectric drive theory, an ultrasonic bearing prototype with bidirectional carrying capability is designed and fabricated which is actuated by piezoelectric transducers. The ultrasonic bearing is able to support radial and axial loads simultaneously. Its axial load-carrying capacity relies on acoustic levitation force generated by the bearing lateral surfaces’ vibration. Its radial load capacity is derived from two parts: the acoustic levitation force excited by the bearing inner ring's vibration and the hydrodynamic pressure caused by high-speed rotation of the rotor. The axial and radial levitation force models are established to predict the bearing's load-carrying capacity. The starting friction torque of the bearing is about 1.76 μNm, and the running friction torque is less than 120 μNm when the bearing runs at a speed of 20,000 r/min. In the running performance experiments, the bearing shows good stability in rising and reduction stage within its limiting speed.

Research on Operation Principle and Control of Novel Hybrid Excitation Bearingless Permanent Magnet Generator

Under the condition of load changing, the magnetic field of traditional permanent magnet generators (PMG) is hard to be adjusted, and the mechanical bearings are significantly worn. To overcome the drawbacks above, a novel hybrid excitation bearingless permanent magnet generator (HEBPMG) is proposed in this paper, which has integrated the merits of hybrid excitation permanent magnet generators and magnetic bearings. Firstly, the structure and winding configuration of the HEBPMG are introduced, and then the principles of radial suspension and power generation are presented. The suspension principle as well as power generation principle is analyzed in this paper. Then, the flux linkage and induced voltage equations are derived, and the accurate mathematical model of radial suspension force is built based on the Maxwell tensor method. Subsequently, by means of the finite element analysis software-ANSYS Maxwell, the corresponding electromagnetic characteristics are analyzed to verify the correctness of the mentioned models. In addition, a compensation control strategy based on flux-linkage observation is proposed to solve the problems of unstable suspension force and generating voltage under variable load condition in this paper. Meanwhile, the corresponding control system is constructed and its feasibility is validated by simulation results. Finally, an experimental prototype of a 2.2 kW HEBPMG is tested. Experimental researches show that the HEBPMG can operate steadily under variable load condition and possess good suspension performance and power generation quality.

A novel integrated 4-DOF radial hybrid magnetic bearing for MSCMG

This paper proposes a novel integrated radial hybrid magnetic bearing (RHMB) for application with the small-sized magnetically suspended control moment gyroscope (MSCMG), which can control four degrees of freedom (4-DOFs), including two radial translational DOFs and two radial tilting DOFs, and provide the axial passive resilience. The configuration and working principle of the RHMB are introduced. Mathematical models of radial force, axial resilience and moment are established by using equivalent magnetic circuit method (EMCM), from which the radial force–radial displacement, radial force–current relationships are derived, as well as axial resilience–axial displacement, moment–tilting angle and moment–current. Finite element method (FEM) is also applied to analyze the performance and characteristics of the RHMB. The analysis results are in good agreement with that calculated by the EMCM, which is helpful in designing, optimizing and controlling the RHMB. The comparisons between the performances of the integrated 4-DOF RHMB and the traditional 4-DOF RHMB are made. The contrast results indicate that the proposed integrated 4-DOF RHMB possesses better performance compared to the traditional structure, such as copper loss, current stiffness, and tilting current stiffness.

Unbalanced Magnetic Forces Due to Rotor Eccentricity in a Toroidally Wound BLDC Motor

A common source of noise and vibrations in a permanent-magnetic synchronous motor is the radial forces due to rotor eccentricity. In this paper, we present entirely analytical models for the radial forces resulting from the eccentricity in a toroidally wound brushless dc motor by applying the perturbation theory. The air-gap magnetic field with eccentricity is first obtained. Then, the radial forces are obtained by integrating the Maxwell stress tensor. The radial force models are verified against the finite-element analysis (FEA). It is found that the maximum mismatch between the results by the model and by FEA is <2%, which confirms the validity of the model.

STUDY ON RADIAL SUSPENSION FORCE OF SINGLE WINDING BEARINGLESS INDUCTION MOTOR BASED ON TWO-FUNDAMENTAL WAVE METHOD

The radial suspension force with a new structure of a bearingless induction motor based on single winding is researched. Compared to the conventional double-winding structure of bearingless induction motor, torque and suspension forces are produced with a single-winding system. Bearingless induction motor is a nonlinear, multi-variable and strong coupling system. It is difficult to obtain an accurate mathematical model on the radial suspension force. So the research method about radial suspension force of a single-winding bearingless induction motor is proposed, based on two fundamentals. Firstly, a new structure and operation principle of a single-winding bearingless induction motor is introduced. Then the air gap flux density distribution of the single-winding bearingless induction motor is analyzed in detail. The accurate mathematical model of radial suspension force is deduced by using two-fundamental wave method and Maxwell's stress tensor method. Secondly, according to the transient analysis of the single-winding bearingless induction motor in which its speed is 6000 r/min by finite element method (FEM), the component of radial suspension force in x-axis and y-axis is obtained by FEM simulation analysis. The calculation results used by FEM and the theoretical calculation results of mathematical model used by two-fundamental wave method have been compared. Thirdly, an experimental prototype is produced, and suspension experiment of prototype is carried out. Then measured result of radial suspension force is analyzed. The analysis results show that the prototype has excellent suspension characteristics, and the mathematical model of radial suspension force based on two-fundamental wave method has low error and high precision.

Mathematical Model of Radial Suspending Force for a New Stator-Permanent Magnet Bearingless Machine

In this paper, a new stator-permanent magnet (PM) bearingless machine (SPMBM) is proposed. Its suspending windings, armature windings, and PMs are in the stator, while no PMs or windings are in the rotor. However, it is the focus in establishing an accurate mathematical model of radial suspension force to levitate the rotor stably by directly and effectively controlling the rotor eccentric displacement. First, operating principle and air-gap flux density distributions of the SPMBM are analyzed in detail. Then, an accurate mathematical model of radial suspension force is deduced by the Maxwell stress tensor method, and it is verified by the 2-D finite-element method (FEM). Results are consistent both by the radial suspension force mathematical models of the SPMBM and FEM.

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.

Study on radial suspension forces of bearingless permanent magnet slice motor based on accurate inductance model

An accurate mathematical model of radial suspension forces for a bearingless permanent magnet slice motor (BPMSM) is of great significance to levitate the rotor stably and to improve the control accuracy of radial suspension force. In this paper, after a brief introduction on the suspension principle of the BPMSM, the accurate inductance model of two sets of stator windings (torque windings and bearing windings) is deduced. Based on the accurate inductance model and taking rotor eccentricity into account, a complete and precise mathematical model of radial suspension forces of the BPMSM is obtained. In order to confirm the validity and feasibility of this mathematical model, the experiments are carried out on a 4kW prototype of the BPMSM. The experimental results show that the control system designed by using this method has high control accuracy of radial suspension force, strong capability of resisting disturbance, and good static and dynamic performance.

Real-time tool wear monitoring in milling using a cutting condition independent method

This paper describes a new method to monitor end milling tool wear in real-time by tracking force model coefficients during the cutting process. The behavior of these coefficients are shown to be independent from the cutting conditions and correlated with the wear state of the cutting tool. The tangential and radial force model coefficients are normalized and combined into a single parameter for wear monitoring. A number of experiments with different workpiece materials are run to investigate the feasibility of tool wear monitoring using this method. We show that this method can be used in real-time to track tool wear and detect the transition point from the gradual wear region to the failure region in which the rate of wear accelerates.

Coating thickness and coverage effects on the forces between silica nanoparticles in water.

The structure and interactions of coated silica nanoparticles have been studied in water using molecular dynamics simulations. For 5 nm diameter amorphous silica nanoparticles, we studied the effects of varying the chain length and grafting density of polyethylene oxide on the nanoparticle coating's shape and on nanoparticle-nanoparticle effective forces. For short ligands of length n = 6 and n = 20 repeat units, the coatings are radially symmetric while for longer chains (n = 100) the coatings are highly anisotropic. This anisotropy appears to be governed primarily by chain length, with coverage playing a secondary role. For the largest chain lengths considered, the strongly anisotropic shape makes fitting to a simple radial force model impossible. For shorter ligands, where the coatings are isotropic, we found that the force between pairs of nanoparticles is purely repulsive and can be fit to the form (R/2r(core) - 1)(-b) where R is the separation between the center of the nanoparticles, r(core) is the radius of the silica core, and b is measured to be between 2.3 and 4.1.