Average Air Gap Flux Research Articles

Modeling and optimization of a novel multi-DOF electromagnetic driven spherical motion generator

This paper introduces a new spherical motion generator and presents a method for modeling its magnetic field and analyzing its moments. The generator employs an electromagnetic drive of a spherical motor as its driving method and utilizes a spherical parallel manipulator to execute the spherical motion. The combination of these two technologies offers several advantages, including a large workspace and high motion accuracy. The equivalent magnetizing current method is used in the magnetic field modeling and the average air-gap flux density is optimized to achieve a better magnetic field distribution, and the accuracy of the analytical model is verified by finite element simulations and experiments.

Analytical modeling and performance evaluation of an adjustable permanent magnet linear eddy current brake with mechanical magnetic adjuster

A novel mechanical flux-adjusting permanent magnet linear eddy current brake with high performance and its nonlinear analytical model are proposed. The innovative point lies in attaching an additional mechanical magnetic adjuster directly above the interior permanent magnet bar, which can achieve flexible adjustment of the air-gap flux and improve the generation capacity of the braking force and its regulation range. Considering the importance of the analytic model in practical design, the average air-gap flux density and eddy current density are estimated based on the equivalent magnetic circuit method and Ampere’s law, where the critical flux-weakening effect and leakage flux effect are calculated quantitatively. Then a practical theoretical model of braking force is derived based on the energy conversion and verified by the 3D finite-element method. Through analysis of the magnitude and regulation range of the braking force in a given range of speed, the advantages of the device and the electromagnetic force model are proved separately. Moreover, design suggestions for selecting the key geometrical parameters are further given, which offer useful information for pre-design and optimization.

Boundary-Free Analytic Magnetic Field Calculations Including Soft Iron and Permanent Magnets Using an Iterative Discretization Technique

An extremely fast magnetostatic magnetic field modeling method is developed that includes nonlinear relative permeabilities (or “magnetic saturation”) of soft magnetic materials with nonuniform magnetization. The model assumes regions of linearity within the material in order to apply analytic equations and superposition. This article presents the general theory and method for 3-D geometries, along with a 2-D axisymmetric example case study that is of interest for tubular linear actuator (or motor) design. The case study maximizes the average air-gap flux of an axially magnetized pole piece and shows a close correlation of the internal and external magnetic flux densities with a finite element analysis. This demonstrates the method as suitable for large parametric searches of topologies, toward the optimization of electrical machines, linear actuators, transformers, or more general 3-D electromagnetic problems.

Equivalent Magnetic Circuit Analysis of Doubly Salient PM Machine With Π-Shaped Stator Iron Core Segments

An equivalent magnetic circuit (EMC) analytical method for a 3-phase doubly salient permanent magnet (DSPM) machine with Π-shaped stator iron core segments (Π-core DSPM machine) is presented in this paper. This method is based on the airgap field modulation theory. First, the airgap permeance of the doubly salient machine is calculated, based on which the influence of slotting on modulation effect is analyzed. Then, an EMC model of this machine is established according to its main magnetic field distribution. Considering the slotting effect on the average airgap flux density, Carter's coefficient is used to calculate the equivalent airgap length and the airgap magnetomotive force (MMF). Subsequently, the flux density is calculated, which allows the calculation of no-load electromotive force (EMF) and also on-load torque. In addition, the relationship between machine performances and key dimensions can be obtained by analytical expressions without complicated finite element analysis (FEA). Analytical results are validated by both the 2-dimension FEA and experimental results.

An analytical approach and finite element evaluation of leakage fluxes of the PMs in a non-slotted axial flux permanent magnet machine

PurposeConsideration of leakage fluxes in the preliminary design stage of a machine is important for accurate determination of machine dimensions and prediction of performance characteristics. This paper aims to obtain some equations for calculating the average air gap flux density, the flux density within the magnet and the air gap leakage flux factor.Design/methodology/approachA detailed magnetic equivalent circuit (MEC) is presented for a TORUS-type non-slotted axial flux permanent magnet (TORUS-NS AFPM) machine. In this MEC, the leakage flux occurring between two adjacent magnets and the leakage fluxes taking place between the magnet and rotor iron at the interpolar, inner and outer edges of the magnets are considered. According to the proposed MEC and by using flux division law, some equations are extracted. A three-dimensional finite element method (FEM) is used to evaluate the proposed analytical equations. The study machine is a 3.7 kW and 1,400 rpm TORUS-NS AFPM machine.FindingsThe air gap leakage flux factor, the average air gap flux density and the flux density within the magnet are calculated using the proposed equations and FEM. All the results of FEM confirm the excellent accuracy of the proposed analytical method.Originality/valueThe new equations presented in this paper can be applied for leakage flux evaluating purposes.

Analytical prediction of optimal split ratio of consequent‐pole permanent magnet machines

For consequent-pole permanent magnet (CPM) machines, the permanent magnet (PM)-arc ratio and split ratio have great influence on the output torque. This study establishes general relationship of the output torque/torque density with PM-arc ratio and split ratio considering the effects of slot/pole number combinations and the tooth-tips. In addition, both the optimal PM-arc ratio and split ratio for maximising the torque density are analytically derived and confirmed by finite-element analysis. It is found that the optimal PM-arc ratio is determined by the ratio of the airgap length to the PM thickness. It is demonstrated that the optimal split ratio depends on the ratio of average airgap flux density below one slot to maximum flux density in the stator iron k B γ and the number of slots for the slots per pole q ≤ 1 .5 or the number of poles for q > 1 .5 . Moreover, it is found that the optimal split ratio decreases with the ratio k B γ , which depends on the PM thickness and PM-arc ratio, and it is reduced when the effect of the stator tooth-tips is taken into consideration. The experimental results on the 12-slot/10-pole CPM machine are given to verify these analyses.

MAGNETOSTATIC FIELD ANALYSIS OF DC COMMUTATOR MOTORS WITH GEAR-TEETH ON THE ROTOR

This paper presents the open-circuit magnetostatic field analysis of a DC commutator motor by applying 1-D and 2-D equivalent magnetic circuit methods. For the 1-D and 2-D equivalent magnetic circuit method, the average air-gap flux density of a DC commutator motor and magnetic flux in every node are derived respectively, and the validity is verified by the finite-element analysis. The Carter’s coefficient is applied to model the permeance of the slot and gear-teeth space. The differences of the air-gap flux density are 3.21% and 3.06% for 1-D and 2-D methods, respectively. The flux linkages, back-EMF constants, cogging torques, electromagnetic torques, and torque ripples of the two gear profiles with feasible number of teeth integrated on the rotor are analyzed to verify the effects of gear profiles. The result shows that the gear-teeth integrated on the motor act as dummy slots, which reduce the cogging torque and torque ripple by 92.02% and 50.14 %, respectively.

Permanently split capacitor motor-study of the design parameters

Abstract Paper analyzes the influence of various design parameters on torque of permanently split capacitor motor. Motor analytical model is derived and it is used for calculating the performance characteristics of basic motor model. The acquired analytical model is applied in optimization software that uses genetic algorithms (GA) as an optimization method. Optimized motor model with increased torque is derived by varying three motor parameters in GA program: winding turns ratio, average air gap flux density and motor stack length. Increase of torque has been achieved for nominal operation but also at motor starting. Accuracy of the derived models is verified by Simulink. The acquired values of several motor parameters from transient characteristics of Simulink models are compared with the corresponding values obtained from analytical models of both motors, basic and optimized. Numerical analysis, based on finite element method (FEM), is also performed for both motor models. As a result of the FEM analysis, magnetic flux density in motor cross-section is calculated and adequate conclusions are derived in relation to core saturation and air gap flux density in both motor models.

Physical Mechanism of Eddy Current Demagnetizing Effect for Eddy Current Brake

This article researches both the mathematical relation between the braking force of eddy current brake and the speed of the moving conductor and the relationship between the average air-gap flux density and the velocity of the moving conductor respectively which result in the ambiguity of the physical mechanism of eddy current demagnetizing effect. The theoretical methods for obtaining the distribution of the excitation magnetic field, the eddy current magnetic field and the air gap magnetic field of eddy current brake were presented. Then the impacts of the excitation magnetic field and eddy current magnetic field on the distribution of air gap magnetic field were got through contrastive analysis and then the physical mechanism of eddy current demagnetizing effect is obtained. Finally, the influence of the eddy current demagnetizing effect on the design and control of eddy current brake was discussed in depth. The correctness of these theoretical calculations was validated by experiments on the retarder synthetic performance test bench or the finite element numerical calculation.

Analytical optimisation of external rotor permanent magnet machines

This study presents an analytical model for optimising the maximum torque per volume in external rotor permanent magnet (PM) machines, in which the maximum achievable airgap flux density depends on the split ratio of airgap diameter to outer diameter and the stator slot area is a function of split ratio, airgap flux density, and stator split ratio of stator diameter at slot bottom to airgap diameter. The optimal split ratio, stator split ratio and airgap flux density are derived analytically with/without considering that the maximum achievable airgap flux density is limited by the split ratio. In addition, the influence of airgap flux density distributions, slot and pole numbers, slot shapes, tooth-tips, end-windings, rotor yoke and inner diameter on the optima is discussed. The analytical analyses are validated by both finite element and experimental results. It is shown that the torque density of external rotor PM machines is maximum when the average airgap flux density is slightly lower than half of the maximum flux density in the stator.

Parameters and Steady State Characteristics Analysis of PMLSM

Permanent magnet linear synchronous motor (PMLSM) has many advantages; it has been used in the industry. Electromagnetic parameters and steady state characteristics are the focus analysis of PMLSM. Based on a permanent magnet linear synchronous motor for horizontal motion system, according to the magnetic field unified equation, the thesis has given the formulas of the average airgap flux density, harmonic analysis diagram of the air-gap magnetic field, the formulas of no-load leakage flux coefficient, no-load back electromotive force and the thrust in steady-state operation. The thrust-angle curve and structure parameters on the influence of the thrust are also analyzed, then the value of these parameters are computed according to the formula, the simulation curves to the parameters are given based on the finite element method. Two methods for the parameters are consistent with the experimental data, which also prove the correctness of the calculation methods and results.

Analytical Modeling of Open-Circuit Air-Gap Field Distributions in Multisegment and Multilayer Interior Permanent-Magnet Machines

We present a simple lumped magnetic circuit model for interior permanent-magnet (IPM) machines with multisegment and multilayer permanent magnets. We derived analytically the open-circuit air-gap field distribution, average air-gap flux density, and leakage fluxes. To verify the developed models and analytical method, we adopted finite-element analysis (FEA). We show that for prototype machines, the errors between the FEA and analytically predicted results are <1% for multisegment IPM machines and <2% for multilayer IPM machines. By utilizing the developed lumped magnetic circuit models, the IPM machines can be optimized for maximum fundamental and minimum total harmonic distortion of the air-gap flux density distribution.

Development of Hybrid Type Combined Motor-Bearing without Bias Permanent Magnet.

A segmented permanent magnet rotor is proposed to generate sinusoidal flux density for motor torque. It also provides bias flux for HB type motor-bearing without using additional bias permanent magnet. Hence the construction of combined motor-bearing is simpler and reliable. First, the concept of the proposed HB type combined motor-bearing is introduced. Then the radial force is analyzed to be proportional to the average air gap flux density, even though the air gap flux includes some opposite pole parts. Finally, the experimental setup is made to confirm the capability of the proposed motor. It can run up to 12 000 rev/min and record 0.15 N. m/A torque constant with 9.8 N/A radial levitation force. The levitation is very stable with high performance to practical application.

EXPERIENCE WITH DIRECT AND INDIRECT SEARCH METHODS APPLIED TO CAGE INDUCTION MOTOR DESIGN OPTIMIZATION

Abstract In the present paper low cost cage induction motor design problem is approached using direct search methods, which do not require to calculate the derivatives of the function, and indirect method-a penalty function approach. Induction motor design is considered as a nonlinear, multivariable constrained optimisation problem with ampere conductors per meter, ratios stack length to pole pitch and stator slot depth to width, stator core depth, average air-gap flux density, and stator and rotor winding current densities as variables. The constraints are imposed on the thermal ratings of the machine and on performance indices- Results for same capacity motor with different optimization techniques are tabulated and compared.

Optimization techniques applied to induction motor design—A comparative study

This paper deals with the optimized design of cage induction motors considering cost of active materials as the objective function and performance quantities as constraints. All the expressions involved are highly nonlinear and constraints are of inequality type. Three different optimization methods have been used, i.e. Incremental Search Method, Rosenbrock's method and Complex-Box method, to obtain the optimum design. The explicit independent variables considered are ampere conductors/ m, stator stack length to pole pitch and slot depth to slot width ratios, stator core depth, average air gap flux density and stator and rotor winding current densities. Finally, a comparative study of these methods is presented.

Induction motor design optimization using constrained Rosenbrock method (hill algorithm)

In the present work an optimum design of polyphase cage induction motor using Rosenbrock's method is put forth. The optimization programme considers the cost of active materials as an objective function and temperature rise and other performance items as constraints. The variables chosen are ampere conductors/m, ratios of stack length to pole pitch and stator slot depth to width, stator core depth (cm), average air gap flux density (wb/m 2) and stator and rotor winding current densities (A/mm 2).