Time-stepping Finite Element Research Articles

Performance Analysis of a Novel Magnetic-Geared Tubular Linear Permanent Magnet Machine

This paper presents a novel tubular linear permanent magnet machine for direct-drive applications, in which a magnetic gear is integrated with a tubular linear machine, aiming to improve the thrust force density and enhance the machine efficiency. The operating principle of the proposed machine is introduced and the machine design with improved thrust force density is presented and discussed. By using circuit-field-motion coupled time-stepping axisymmetric finite element method (FEM), the steady-state as well as transient performances of the machine are simulated. The FEM computation results are consistent with those obtained theoretically, hence verifying the validity of the machine design.

Design and Comparison of Vernier Permanent Magnet Machines

Vernier permanent magnet (VPM) machines can be utilized for direct drive applications by virtue of their high torque density and high efficiency. The purpose of this paper is to develop a general design guideline for split-slot low-speed VPM machines, generalize the operation principle, and illustrate the relationship among the numbers of the stator slots, coil poles, permanent magnet (PM) pole pairs, thereby laying a solid foundation for the design of various kinds of VPM machines. Depending on the PM locations, three newly designed VPM machines are reported in this paper and they are referred to as 1) rotor-PM Vernier machine, 2) stator-tooth-PM Vernier machine, and 3) stator-yoke-PM Vernier machine. The back-electromotive force (back-EMF) waveforms, static torque, and air-gap field distribution are predicted using time-stepping finite element method (TS-FEM). The performances of the proposed VPM machines are compared and reported.

Study on Electromagnetic Exciting Force Characteristics and Electromagnetic Noise of Permanent Magnet DC Motor

Electromagnetic exciting force is the key to generate electromagnetic noise. The characteristics of electromagnetic exciting force and the causing of electromagnetic noise were analyzed after the power was off for cooling fan Permanent Magnet DC (PMDC) motor. Time-stepping finite element method was selected to calculate its several parameters, such as air gap magnetic density harmonics generated by the stator and rotor, torque ripple and unbalanced magnetic pull at its different speed.Experiment on unloading vibration noise was carried out to confirm the validity of electromagnetic exciting force analysis. The results show: electromagnetic force amplitude keeps constant while the motor speed changing. Torque ripple decreases while the motor speed down. A kind of electromagnetic noise called howling noise produced by PMDC motor used in car cooling fan is mainly due to resonance. So the best way to eliminate this motor’s noise is to improve the order of electromagnetic waves and avoid the electromagnetic resonance.

Time-stepping finite element analysis on the influence of skewed rotors and different skew angles on the losses of squirrel cage asynchronous motors

To study the influence of skewed rotors and different skew angles on the losses of squirrel cage asynchronous motors, a 5.5-kW motor was taken as an example and the multi-sliced field-circuit coupled time stepping finite element method (T-S FEM) was used to analyze the axially non-uniform fundamental and harmonic field distribution characteristics at typical locations in the stator and rotor cores. The major conclusions are: firstly the skewed rotor exhibits a decrease in the harmonic copper losses caused by slot harmonic currents in the stator winding and rotor bars. Secondly, the skewed rotor shifts the non-uniform distribution of field in the axial direction, which leads to more severe saturation and an increase in iron losses. The heavier the load, the more pronounced the increase in iron losses. Furthermore, the influences of different skew angles on motor losses are studied systematically, with skew angles from 0.5 to 1.5 stator tooth pitch. It is found that the lowest total loss occurs at 0.8 stator tooth pitch, and the slot harmonics can be decreased effectively.

Electromagnetic Performance Analysis of a New Stator-Permanent-Magnet Doubly Salient Flux Memory Motor Using a Piecewise-Linear Hysteresis Model

The concept of flux memory is due to the nature that the magnetization level of the AlNiCo permanent magnet (AlNiCo-PM) in the motor can be regulated by a temporary dc current pulse and memorized automatically. In this paper, a new type of memory motor, namely the stator-permanent-magnet (stator-PM) doubly salient flux memory (DSFM) motor is proposed. The key is to incorporate both AlNiCo-PM and NdFeB-PM into the proposed memory motor. Thus, the resulting new memory motor can not only retain high power density, but also offer efficient air-gap flux control. To accurately analyze the stator-PM DSFM motor, a piecewise-linear hysteresis model is employed in the time-stepping finite element method. Both static and transient electromagnetic performances of the motor are given to verify the validity of the new method.

A novel approach to evaluate the equivalent dynamic stiffness of guy clusters in telecommunication masts under ground excitation

Telecommunication structures are essential components of communication and post-disaster networks and critically important facilities require reliable earthquake-resistant design procedures in seismically active regions. Calculation of the nonlinear seismic response of tall guyed masts using detailed time-step finite element methods is far more complex than linear response spectrum analysis that is routinely used in structural engineering practice. It is recognized that detailed computational procedures are not always necessary, in particular when the goal of the analysis is to provide a global earthquake-resistant design check on a regular structure with predictable response: this is when rational simplified methods are called upon to calculate the seismic demand. However, up until now, no such method exists for tall guyed masts that can account for the dynamic cable–mast interactions which dominate seismic effects in these structures. In the study reported here, the writers explore the dynamic behavior of guy cables under harmonic and seismic support ground motion through detailed computational modeling and propose a novel frequency-dependent method to evaluate the equivalent dynamic stiffness of guy clusters. This development will contribute efficiently towards a new robust rational model of general applicability for simplified seismic analysis of tall guyed telecommunication masts. Detailed numerical simulations involving 57 guy cables from eight existing towers with varying heights of 150–607 m were used in the study. A mathematical procedure was developed to replace the nonlinear time-variant cable stiffness with an equivalent linear frequency-dependent spring/mass system, based on the response spectrum of individual guy cables and the frequency content of the seismic excitation. Comparison of the main response indicators of these equivalent models and the detailed nonlinear finite element analysis results confirmed the reasonable and consistent engineering accuracy of the proposed simplified method with considerable savings in analysis effort.

Time-Stepping Finite Element Analysis of Distribution Transformers Performance under Unbalanced Voltage and Load

In this article, a distribution transformer is analyzed under unbalanced voltage and unbalanced load. The transformer is modeled using the time-stepping finite element method, considering all geometrical and physical characteristics. To analyze precisely the occurrence of unbalanced voltage and load in transformer, spectral analysis of the secondary current is essential. To this, the frequency spectrum of the secondary current, obtained using the time-stepping finite element method, is calculated. It is shown that the unbalanced voltage or unbalanced load in the distribution transformer adds to the amplitude of harmonic components considerably; however, its incremental rate has a decreasing pattern. The amplitude of the harmonic components for the two unbalanced cases are compared, and it is shown that the unbalanced voltage has more effect upon the increase of the amplitude of the harmonic components compared to the unbalanced load. Meanwhile, the performance of the distribution transformer under balanced and unbalanced voltage and load is studied. The performance of the transformer when the load and supply are balanced compared to the case in which voltage or load is unbalanced indicates that the unbalanced load only causes the copper loss to increase, while the unbalanced voltage not only increases copper loss but also adds to the core loss. It is also shown that unbalanced voltage increases the copper loss more than an unbalanced load. Simulation results are verified by experimental results.

On the lumped lorentz force approximation for modeling the motion of free metallic particles

The force acting upon a free metallic particle in an alternating electric field will determine its motion and ultimately allow for the estimation of the risk imposed due to dielectric failure of the high voltage equipment. Existing models approximate the force with Lorentz' law and consider the charge resting upon the surface as being lumped into a point charge at the center of the particle during its motion. The model proposed in this paper demonstrates a time stepped electrostatic Finite Element Method to calculate these forces, therefore taking into account the charge distribution upon the surface of the particle. The use of this model is seen to have a significant effect upon the motion of the particle under certain conditions.

Thermal Analysis of Canned Induction Motor for Coolant Pump Considering the Eddy Current Loss in Cans

This paper describes thermal analysis of canned induction motor for coolant pump considering eddy current loss. The electromagnetic field of a canned motor was analyzed by using the time-step finite element method, and the eddy loss was obtained. Equivalent circuit considering can loss was developed and the equitation to calculate can loss was derived from theory of conventional motor. Using the loss from electromagnetic analysis as heat source of temperature field, thermal analysis was conducted by three dimensional finite element analyses. The simulation results show good agreement with experiment data, which indicates that this method has good accuracy and reliability for dealing with thermal behavior of canned motor.

Stator Harmonic Currents in VSI-Fed Synchronous Motors With Multiple Three-Phase Armature Windings

Electric motors equipped with multiple three-phase windings are often used for the advantages they offer in terms of reliability, performance, and inverter power segmentation. When the windings are fed by independent voltage-source inverters (VSIs), circulation harmonic currents can occur in stator phases. If the motor is an induction machine, circulation currents are known to originate form transient imbalances in the applied voltages due to inverter switching. This paper investigates the problem when a synchronous machine is used and shows how additional (and possibly major) sources for circulation currents can arise in this case (even with a round-rotor design) due to the nonsinusoidal air-gap flux distribution. The phenomenon is illustrated for a 45-MW quadruple three-phase synchronous motor supplied by four medium-voltage (MV) multilevel VSIs. Its circulation currents are predicted with two alternative methods, i.e., analytically and from time-stepping finite-element simulation. The results obtained in both ways are shown to well match measurement results collected on the actual motor during full-load system testing.

A study on characteristics of rotor losses for IPMSM considering slot-pole combination

In this paper, we investigated the effect of slot-pole combi nation on rotor loss in interior permanent magnet synchronous machine (IPMSM) with distributed armature windings. In order to study the characteristics of the rotor los ses, two machines for high-speed operation such as electric vehicle were designed. One is fractional slot winding and the other is conventional one. Based on 2-D time-stepped finite element m ethod (FEM) we analyzed both iron loss and eddy-current loss in the permanent magnet of the machines according to their driving conditions. From the analysis results, it was shown that rotor iron loss and eddy-current loss of PM of machine employing fractional slot-winding is definitely large at load condition .

Two-dimensional time-stepping finite element analysis of a three-phase electric arc furnace

This paper presents two-dimensional (2D) transient finite element solutions of an 100 MVA three-phase electric arc furnace (EAF). In practice, it was observed that there were a few high-voltage arcs between upper side of high-carrying current electrodes and EAF roof. To specify the operation and performance of this EAF, a 2D time-stepping finite element method (FEM) program was developed and induced voltages between the roof and the electrodes at different load conditions were predicted. In addition, the effective value of induced voltages between the roof, electrodes, and water pipes by which the roof was being cooled was measured. The results obtained using the FEM simulations proved that in unbalanced and asymmetrical operations of this EAF, high-voltage arcing may occur.

Shape Optimization of Rotating Machines Using Time-Stepping Adaptive Finite Element Method

A time-stepping adaptive finite element method is proposed for shape optimization of rotating machines. In the proposed method, different mesh-generation procedures are applied to the core and the other regions for the purpose of the iron-loss calculation. A technique for automatically separating and connecting the stator and rotor meshes is also introduced for the rotation of the rotor. The proposed method is applied for shape optimizations of permanent magnet motors to achieve the loss reduction. The necessity and usefulness of the proposed method are verified.

Reduction of Numerical Errors of Time-Stepping Finite Element Analysis for Dynamic Simulation of Electric Machines

The time-stepping finite element method (TS-FEM) can couple the magnetic field, electric circuit and mechanical torque balance equations together and has been widely used to simulate the dynamic characteristics of electric machines. Despite its heavy computational burden, the accuracy of TS-FEM is still limited by a host of practical constraints. Also, it is difficult to accurately model the sliding surface of the stator mesh and the rotor mesh in rotating electric machines. In this paper, a curvilinear element to approximate the curved geometry of sliding surface is presented to increase the computational accuracy. To reduce the numerical error of the derivative quantities, a modified nonlinear iterative formulation is adopted. To reduce the computing time, an adaptive time step size algorithm is also proposed. The proposed strategy and algorithm are verified by the FEM examples as reported in this paper.

Quantitative Comparison of Novel Vernier Permanent Magnet Machines

In this paper, a novel direct-drive double rotor Vernier panent magnet (DR-VPM) machine is proposed and analyzed. The key of the design is to incorporate two concentric rotors and the Vernier structure within one permanent magnet (PM) machine, while keeping the machine volume and slot number unchanged. The main merits of this proposed machine are its compact structure, improved torque density, reduced stator end winding length, and reduced copper loss. The operating principle of the machine is discussed and its steady and transient performances are analyzed using circuit-field-motion coupled time-stepping finite element method (CFM-TS-FEM). A dual-excitation PM Vernier (DE-VPM) machine and a single outer rotor PM Vernier (SR-VPM) machine are designed and compared with this proposed Vernier PM machine using CFM-TS-FEM. Comparison results as reported are used to confirm and validate the advantageous performance of the proposed machine.

Eddy-Current Analysis of Double-Stator Inset-Type Permanent Magnet Brushless Machines

In this paper, a new multi-pole double-stator inset-type permanent magnet (PM) machine is proposed for low-speed direct-drive applications. In the outer stator, a fractional-slot concentrated winding is adopted to reduce the slot number and stator yoke height, hence saving the space and improving the torque density. In the inner stator, a vernier structure is used to reduce the winding slots and enlarge the slot area to accommodate more conductors, hence fully utilizing the inner stator space. Consequently, the torque density is improved, and the cogging torque is reduced. Since the machine structure is so unique while its operating principle is so distinct, a nodal method based network-field coupled time-stepping finite element method (NF-TS-FEM) is newly developed. The corresponding modeling and analysis are simpler and more convenient than its loop method based counterpart. The analysis of eddy-current loss in both of the PMs is conducted. The performance of the proposed machine is verified by the proposed NF-TS-FEM.

Dynamic Demagnetization Computation of Permanent Magnet Motors Using Finite Element Method With Normal Magnetization Curves

A time-stepping finite element method (FEM) to simulate the transient operations of permanent magnet (PM) motors is presented. It uses only the normal magnetization curves to address the effects of irreversible demagnetization of PM materials. An effective algorithm to implement the methodology with nonlinear iteration is presented. A formulation of Newton-Raphson method using the true Jacobian matrix which is applicable to any type of elements and any order of elements with anisotropy materials is derived. A matrix method is introduced to express space vectors and the FEM formulation can be conveniently deduced.

Design and Analysis of a HTS Vernier PM Machine

This paper proposes a novel high-temperature superconductor (HTS) vernier permanent-magnet machine which can offer low-speed high-torque operation under line frequency. The key is to newly introduce the flux-modulation poles which modulate the high-speed rotating field in the stator to become the low-speed rotating field in the airgap. Also, the use of HTS armature windings can greatly reduce the power loss and improve the power density. By using the time-stepping finite element method, the machine performances are analyzed. Hence, the validity of the proposed machine is verified.

A Novel Direct-Drive Dual-Structure Permanent Magnet Machine

By incorporating the merits of fractional-slot concentrated windings and Vernier machine structure, a new multi-pole dual-structure permanent magnet (PM) machine is proposed for low speed, direct-drive applications in this paper. In the outer stator, a fractional-slot concentrated winding is adopted to reduce the slot number and stator yoke height, hence saving space and improving torque density. In the inner stator, a Vernier structure is used to reduce the winding slots, thereby enlarging the slot area to accommodate more conductors, thus the inner stator space is fully utilized. Consequently, the merits of these two structures can be ingeniously integrated into one compact PM machine and the torque density is improved, cogging torque is reduced and the control flexibility with two sets of independent stator windings is increased. By using time-stepping finite element method with curvilinear elements for moving between the stator and the rotor, the steady state and transient performances of the PM machine are simulated and the validity of proposed dual-structure PM machine is verified.

Loss Analysis of Permanent Magnet Hybrid Brushless Machines With and Without HTS Field Windings

This paper presents and implements the power loss analysis of a new kind of permanent magnet hybrid brushless (PMHB) machines with and without using high-temperature superconductor (HTS) field windings. The circuit-field-torque time-stepping finite element method together with experiential equations is developed to perform power loss analysis of the PMHB machine. Experimentation is carried out to verify the proposed loss analysis.