CN110705088B - Permanent magnet motor modeling and electromagnetic performance calculating method based on magnetic network - Google Patents
Permanent magnet motor modeling and electromagnetic performance calculating method based on magnetic network Download PDFInfo
- Publication number
- CN110705088B CN110705088B CN201910920662.3A CN201910920662A CN110705088B CN 110705088 B CN110705088 B CN 110705088B CN 201910920662 A CN201910920662 A CN 201910920662A CN 110705088 B CN110705088 B CN 110705088B
- Authority
- CN
- China
- Prior art keywords
- magnetic
- subdivision
- node
- modeling
- permanent magnet
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Landscapes
- Permanent Field Magnets Of Synchronous Machinery (AREA)
- Iron Core Of Rotating Electric Machines (AREA)
Abstract
The invention discloses a permanent magnet motor modeling and electromagnetic performance calculating method based on a magnetic network, which comprises a motor stator, a rotor and an air gap modeling method: dividing a solution domain into different components according to the motion condition, generating a magnetic resistance model in a subdivision unit, adding a magnetomotive model generated by permanent magnet materials and current loading, connecting branches in the components in series and in parallel, following the magnetic field continuity theorem at a motion interface between the components, and realizing continuous and smooth distribution of magnetic flux in adjacent branches by a Lagrange interpolation method to obtain a node magnetic pressure equation of the whole motor; calculating a corresponding Jacobian matrix by adopting a Newton iteration method to obtain a faster model convergence rate; and verifying the accuracy of the model. The advantages are that: the method has the advantages that the universality of the modeling method is guaranteed by means of component division and unit subdivision, magnetic path analysis is not needed for different structures, the modeling efficiency is the same as that of a finite element, certain solving precision is guaranteed, and the method can be used as a tool for preliminary and rapid analysis of motor performance.
Description
Technical Field
The invention relates to a permanent magnet motor modeling and electromagnetic performance calculating method based on a magnetic network, and belongs to the field of electromagnetic field calculation.
Background
The equivalent magnetic circuit method has become an indispensable tool in the field of electromagnetic analysis, and is initially used for analyzing the saturation state of the motor, and is gradually applied to electromagnetic design due to the advantage of the equivalent magnetic circuit method in calculating speed. The equivalent magnetic circuit method gives consideration to the calculation speed of the traditional magnetic circuit method and the high flexibility of the finite element method, represents the magnetic circuit in the motor through a centralized parameter circuit model, for example, represents the magnetic resistance by using the resistance, and can flexibly adjust the resistance value according to the geometric parameters and the material properties of the actual model; meanwhile, the method can be used for analyzing the saturation condition in the motor. However, when the motor is used specifically, the motor needs to be designed and adjusted specifically according to the type and structure of the motor, so that the rapidity is ensured, and the accuracy is achieved, so that the application of the motor is limited to a certain extent. Main current motor finite element analysis software such as MotorCAD and ANSYS Maxwell is internally provided with a magnetic circuit model of a common motor type, the calculation speed is obviously improved compared with a finite element method, and novel motor topology analysis and calculation cannot be supported.
The invention introduces the mesh subdivision idea in the finite element method into the equivalent magnetic circuit method, generates a corresponding unit reluctance model for each subdivision unit, connects the subdivision units into a network, applies boundary conditions and motion conditions, further utilizes the continuous physical problem of mesh subdivision discretization, and solves the problem by a numerical method (the sentence is not connected with the front). The solving algorithm is usually based on kirchhoff current law to establish a node magnetic pressure equation, an algebraic system is constructed according to magnetic conductance and a node connection mode, a Newton iteration method is used for solving a nonlinear system, and a Lagrange interpolation algorithm is used for modeling a motion interface to solve the re-subdivision problem.
Disclosure of Invention
The invention aims to provide a permanent magnet motor modeling and electromagnetic performance analysis scheme based on a magnetic network, which mainly comprises modeling of a stator, a rotor and an air gap and a model solving algorithm based on a Newton iteration method, and can improve the universality of the existing method.
In order to realize the purpose, the technical scheme of the invention is as follows: a permanent magnet motor modeling and electromagnetic performance calculation method based on a magnetic network comprises the following steps:
and 3, selecting proper subdivision densities in the part along the radial direction R and the tangential direction theta, and performing consistent subdivision. The characteristic of the consistent subdivision is that adjacent subdivision units share a common vertex, namely, the vertex of one subdivision unit is not positioned on the side of the other subdivision unit. The method comprises the following steps of recommending that a rectangle is used as a basic subdivision unit, and ensuring that each subdivision unit only has one material attribute in the subdivision process;
step 5, generating a corresponding magnetic permeability and a magnetic permeability-magnetic field strength partial derivative value for each subdivision unit, generating a corresponding connection matrix, a branch magnetic permeability-node magnetic voltage partial derivative and a branch magnetic potential value for each component, and generating a component node magnetic voltage equation and a component jacobian matrix;
step 7, solving an iterative formula to obtain node magnetic pressure, then calculating a branch magnetic field strength value, and repeating the steps 5, 6 and 7 until the correction is smaller than a required value;
the invention has the following beneficial effects:
1. the method generates the unit reluctance model based on the subdivision grids, has good structural adaptability, and is favorable for improving the universality of the calculation method;
2. according to the method, different components are divided according to the motion condition of a solution domain, and the components are decoupled with each other, so that on one hand, different subdivision densities and modeling modes are allowed to be adopted, and on the other hand, when the position of the motion component is changed, the regeneration of a magneto-resistance model is avoided, and the modeling flexibility and the calculation speed are improved;
3. the current magnetic potential model fully considers the influence of different winding modes on the magnetic potential model, and ensures that the ampere loop law is followed in any loop, namely each physical quantity in the magnetic circuit model complies with the physical constraint in the actual model;
4. the node magnetic pressure, the magnetic field intensity calculated by the node magnetic pressure and the magnetic steel stress intensity calculated by the node magnetic pressure are values under the physical coordinates of the node, and a corresponding distribution map can be directly generated.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
FIG. 1 is a surface mount permanent magnet synchronous machine topology according to an embodiment of the present invention;
FIG. 2 is a schematic view of a surface-mounted permanent magnet synchronous motor stator subdivision according to an embodiment of the present invention;
FIG. 3 is a schematic subdivision view of a surface-mounted permanent magnet synchronous motor rotor according to an embodiment of the present invention;
FIG. 4 is a diagram of a subdivision unit magneto-resistance model according to an embodiment of the present invention;
FIG. 5 is a permanent magnetic potential model of a subdivision unit according to an embodiment of the present invention;
FIG. 6 is a subdivision unit current magnetic potential model according to an embodiment of the present invention;
FIG. 7 is a model of a moving interface according to an embodiment of the present invention;
FIG. 8 (a) is an air gap radial magnetic induction distribution for an embodiment of the present invention;
FIG. 8 (b) is an air gap circumferential magnetic induction distribution of an embodiment of the present invention;
FIG. 8 (c) is a magnetic flux linkage diagram according to an embodiment of the present invention;
FIG. 8 (d) is a back emf distribution diagram of an embodiment of the invention;
fig. 8 (e) is a torque variation diagram of the embodiment of the present invention.
Detailed Description
The technical solution of the present invention will be described in detail with reference to the accompanying drawings in the following embodiments.
In order to more simply and clearly illustrate the beneficial effects of the present invention, the following description is made in detail in conjunction with a specific surface-mount permanent magnet synchronous motor: fig. 1 is a topological structure diagram of the motor, and the embodiment of the invention is an 18-slot/6-pole three-phase motor, which is divided into four parts, namely a stator, a rotor, an air gap and a rotating shaft: the stator comprises a yoke part, stator teeth, armature grooves and an armature winding, the armature winding is wound in a distributed mode, and the span is 3 armature grooves; the rotor is cylindrical and is provided with a surface-mounted permanent magnet, and the permanent magnet is made of rare earth neodymium iron boron.
And 2, setting an area from the outer diameter of the motor to 1.2 times of the outer diameter of the motor as an air area so as to consider the magnetic leakage effect.
And 3, selecting proper subdivision densities in the part along the radial direction R and the tangential direction theta, and performing consistent subdivision. The characteristic of the consistent subdivision is that adjacent subdivision units share a common vertex, namely, the vertex of one subdivision unit is not positioned on the side of the other subdivision unit. The method is recommended to use rectangles as basic subdivision units, each subdivision unit only has one material property in the subdivision process, and the method is approximate to the irregular boundary by improving subdivision density.
Fig. 2 and 3 are schematic partial views of the stator and rotor parts of the motor in this embodiment, and the unit partial views at only one pole pitch are shown for convenience of description, and the length of the air gap is enlarged to some extent. According to the requirement, the stator and the rotor can adopt different subdivision densities.
And 4, adding nodes on the motion interface for each subdivision unit along the extension direction of the motion interface, and setting the initial magnetic field intensity of the subdivision unit with nonlinear material property as any point value in a linear region of a BH curve.
And 5, generating corresponding magnetic permeability and a magnetic permeability-magnetic field strength partial derivative value for each subdivision unit, generating a corresponding connection matrix, branch magnetic permeability-node voltage partial derivative and branch magnetic potential value for each component, and generating a component node magnetic pressure equation and a component Jacobian matrix.
Fig. 4 is a subdivision unit used in the embodiment of the present invention, and a calculation formula of the magnetic resistance of the subdivision unit is as follows:
in the formula R r Is a subdivision cell radial reluctance, R θ The circumferential magnetic resistance of the subdivision unit is represented, the dimensions of the subdivision unit are shown in figure 4, d is the axial length of the motor, and mu is the magnetic permeability of a material corresponding to the subdivision unit.
Fig. 5 is a subdivision unit permanent magnetic potential model used in the embodiment of the present invention, where voltage source type magnetic potential is used, the remanence of the permanent magnet needs to be orthogonally decomposed according to the magnetization direction thereof, and in this example, radial magnetization is used, so the remanence does not contain circumferential component, and the formula is directly used:
in the formula of U PM For subdivision of the unit radial permanent-magnet potential, B r Is the remanence of the permanent magnet.
Fig. 6 is a current magnetic potential model used in the embodiment of the present invention, and according to the winding distribution mode, the air gap magnetic potential distribution of each phase winding is considered, in this embodiment, a distributed winding is adopted, and the winding span is 3 slots, so that the generated air gap magnetic potential can be considered approximately as a trapezoidal wave, and the waveform of the a-phase winding can be determined by formula (3):
in the formula SA A As a function of the A-phase air gap magnetomotive force distribution, position coordinate x begA+ ,x endA+ ,x begA -,x endA- As identified in FIG. 6, N A Is the number of turns of the coil, I A Is the instantaneous value of phase a current.
The three-phase air gap magnetic potential synthesis magnetic potential is as follows:
SA s (x)＝SA A (x)+SA B (x)+SA C (x) (4)
the air gap magnetic potential is considered to be generated by the radial voltage source type magnetic potential of each subdivision unit on the stator tooth and the slot, so the air gap magnetic potential is positioned at x for the central node t The magnetic potential of the subdivision unit of (3) is calculated by the formula (5):
in the formulaU MMF Is the radial current magnetic potential of the subdivision unit H c Is the depth of the stator slot. All the subdivision units distributed to the current magnetic potential are collectively referred to as a current domain and comprise stator slots and stator teeth.
The connection matrix is used for describing the connection condition of the nodes and the branches in the network, and the magnetic conductance in the coefficient matrix of the node magnetic pressure equation can be separated by using the connection matrix, so that the jacobian matrix is conveniently solved, and therefore, the node magnetic pressure equation described by using the connection matrix is as follows:
CPC T V＝-CPU (6)
in the formula, C is a connection matrix, P is a branch magnetic potential matrix, V is a node magnetic voltage, U is a branch magnetic potential which consists of a permanent magnetic potential and a current magnetic potential, the subdivision unit is not made of a permanent magnetic material and is not in a current domain, and the four branch magnetic potentials of the subdivision unit are 0.
The Newton iteration method has the iteration formula as follows:
V k+1 ＝V k -J -1 F(V k ) (7)
wherein
F(V k )＝CP(V k )C T V k +CP(V k )U (8)
Operator in formula
Representing elemental multiplication between matrices.
As the branch magnetic conductance is influenced by the magnetic conductance of the subdivision unit, for a nonlinear material, the magnetic conductance is determined by the magnetic field intensity, and the magnetic field intensity is a function of the node magnetic pressure, the partial derivative of the branch magnetic conductance to the node magnetic pressure is calculated by the formulas (10) and (11):
wherein B represents the total number of branches, N represents the total number of nodes, l bi 、S bi 、l bj 、S bj The length and the area of the branch b in the subdivision unit i and the length and the area of the branch in the subdivision unit j are respectively.
FIG. 7 is a schematic diagram of a kinematic interface linking algorithm used in an embodiment of the present invention along which a rotor component moves, the set of stator points { mn ] on the interface being determined by step 4 s } i And rotor point set { mn r } i In an electromagnetic field, the normal component of the magnetic induction at the interface is continuous and the tangential direction of the magnetic field strength is continuous, considering the use of a scalar magnetic potential, for point i at the interface there are:
v ri ＝v si (12)
B nri ＝B nsi (13)
wherein: v. of si And v ri Magnetic potential of point i on the stator side and rotor side, B, respectively nsi And B nri The normal components of the magnetic induction at point i on the stator side and the rotor side, respectively.
Without loss of generality, assume that the point i has a corresponding node mn on the rotor side ri And the stator side is not. Then the closest point mn can be selected on the stator side ri N +1 nodes are interpolation points, and v is obtained by using a Lagrange interpolation method si ，B nsi The equations (12), (13) can be rewritten as:
wherein: l j Is the lagrange interpolation coefficient and n is the interpolation degree. If m nodes are connected to a certain node, the normal magnetic induction intensity of the certain node to a certain plane can be calculated by the formula (16):
wherein theta is ki Is branch b mi The angle to the plane.
And 7, solving an iterative formula to obtain node magnetic pressure, then calculating a node magnetic field strength value, and repeating the steps 5, 6 and 7 until the correction is smaller than the required value.
The branch magnetic field strength is calculated by formula (17):
in the formula I b Is the length of branch b.
The branch magnetic induction is calculated by the formula (18):
in the formula R b Is the branch reluctance, S b Is a branch b Cross-sectional area of (a).
And 8, analyzing and comparing simulation results.
In order to verify the accuracy of the modeling method of the embodiment of the invention, simulation results of air gap radial magnetic induction, air gap circumferential magnetic induction, flux linkage, back emf and torque are respectively given in fig. 8 (a) - (e), and are compared with the finite element simulation result for verification.
Claims (7)
1. A permanent magnet motor modeling and electromagnetic performance calculation method based on a magnetic network is characterized by comprising the following specific steps:
step 1, setting a position 1/2 of an air gap as a motion interface for a single-rotor motor, dividing a solution domain into a group of stator and rotor components, setting a second motion interface at a position 1/2 of a second air gap for a double-rotor motor, and dividing the solution domain into 2 groups of stator and rotor components;
step 2, setting an area from the outer diameter of the motor to 1.2 times of the outer diameter of the motor as an air area;
step 3, selecting proper subdivision density in the part along two directions of the radial direction R and the tangential direction theta, and performing consistent subdivision;
step 4, adding nodes on the motion interface for each subdivision unit along the extension direction of the motion interface, and setting the initial magnetic field intensity of the subdivision unit with the nonlinear material property as the value of any point in the linear area of the BH curve;
step 5, generating corresponding magnetic conductivity and a magnetic field strength partial derivative value of the magnetic conductivity for each subdivision unit, generating a corresponding connection matrix, branch magnetic conductivity, node magnetic pressure partial derivative of the branch magnetic conductivity and node magnetic pressure and branch magnetic potential value for each component, and generating a component node magnetic pressure equation and a component Jacobian matrix;
step 6, using a Lagrange interpolation algorithm on the motion interface, assembling the node magnetic pressure equation of each component into the node magnetic pressure equation of the solution domain, and assembling the component Jacobian matrix into the solution domain Jacobian matrix;
and 7, solving an iterative formula to obtain node magnetic pressure, then calculating a node magnetic field strength value, and repeating the steps 5, 6 and 7 until the correction is smaller than a required value.
2. The method for modeling the permanent magnet motor and calculating the electromagnetic performance based on the magnetic network according to claim 1, wherein the method comprises the following steps: the steps 1 to 3 are used as a first part for subdividing the solution domain to provide the size and material parameters for the steps 4 to 7.
3. The method for modeling the permanent magnet motor and calculating the electromagnetic performance based on the magnetic network according to claim 2, wherein the method comprises the following steps: and 4, the step 4 to the step 7 are used as a second part for calculating the electromagnetic distribution of the solution domain, the calculation method adopts a Newton iteration method, and the required size and material parameters are provided by the first part.
4. The method for modeling the permanent magnet motor and calculating the electromagnetic performance based on the magnetic network according to claim 2, wherein: the moving interface of the step 1 needs to be arranged at 1/2 of the air gap.
5. The method for modeling the permanent magnet motor and calculating the electromagnetic performance based on the magnetic network according to claim 2, wherein the method comprises the following steps: the consistency subdivision in the step 3 is characterized in that adjacent subdivision units share a common vertex, namely, the vertex of one subdivision unit is not located on the side of the other subdivision unit, and each subdivision unit is ensured to only have one material attribute in the subdivision process.
6. The method for modeling the permanent magnet motor and calculating the electromagnetic performance based on the magnetic network according to claim 3, wherein the method comprises the following steps: the jacobian matrix J in step 5 has the following form:
in the formula, C is a connection matrix, P is a branch magnetic potential matrix, V is node magnetic voltage, and U is branch magnetic potential.
Wherein:
wherein B represents the total number of branches, N represents the total number of nodes, and l bi 、S bi 、l bj 、S bj The length and the area of the branch b in the subdivision unit i and the length and the area of the branch in the subdivision unit j are respectively.
7. The method for modeling the permanent magnet motor and calculating the electromagnetic performance based on the magnetic network according to claim 3, wherein the method comprises the following steps: the moving interface of the step 6 is processed by adopting the following method:
set of stator points on the interface as { mn s } i The rotor point set is { mn r } i (ii) a In the electromagnetic field, the normal component of the magnetic induction intensity on the interface is continuous, and the tangential direction of the magnetic field intensity is continuous, so that the point i on the interface has
v ri ＝v si (4)
B nri ＝B nsi (5)
Wherein: v. of si And v ri Magnetic potential of point i on the stator side and rotor side, respectively, B nsi And B nri The normal components of the magnetic induction at the stator side and the rotor side, respectively, of point i;
without loss of generality, assume that the point i has a corresponding node mn on the rotor side ri And the stator side does not; selecting the closest point mn on the stator side ri N +1 nodes are interpolation points, and v is obtained by using a Lagrange interpolation method si ，B nsi The values of (5) and (4) are rewritten as:
wherein: l. the j Is the lagrange interpolation coefficient, n is the interpolation times; if m nodes are connected to a certain node, the normal magnetic induction intensity of the certain node to a certain plane is calculated by the formula (8):
wherein theta is ki Is branch b mi The angle to the plane.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910920662.3A CN110705088B (en) | 2019-09-27 | 2019-09-27 | Permanent magnet motor modeling and electromagnetic performance calculating method based on magnetic network |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910920662.3A CN110705088B (en) | 2019-09-27 | 2019-09-27 | Permanent magnet motor modeling and electromagnetic performance calculating method based on magnetic network |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110705088A CN110705088A (en) | 2020-01-17 |
| CN110705088B true CN110705088B (en) | 2022-11-18 |
Family
ID=69197764
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910920662.3A Active CN110705088B (en) | 2019-09-27 | 2019-09-27 | Permanent magnet motor modeling and electromagnetic performance calculating method based on magnetic network |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110705088B (en) |
Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111709167B (en) | 2020-05-27 | 2021-07-20 | 江苏大学 | Multi-objective optimization parameterized equivalent magnetic network modeling method for permanent magnet motor |
| CN112228619A (en) * | 2020-10-14 | 2021-01-15 | 哈尔滨工程大学 | Magnetic circuit calculation method for high-speed electromagnetic valve |
| CN112347676B (en) * | 2020-11-10 | 2022-07-05 | 湖南大学 | Method, device and system for rapidly calculating loss of motor stator winding |
| CN114386199B (en) * | 2022-01-20 | 2023-11-10 | 重庆大学 | High-temperature-resistant shielding type synchronous reluctance motor copper loss reduction optimization design rapid method |
| CN116992723B (en) * | 2023-07-31 | 2024-01-16 | 重庆理工大学 | Motor dynamic magnetic network modeling method |
| CN118395805B (en) * | 2024-06-17 | 2024-08-30 | 湖南迈曦软件有限责任公司 | Hysteresis problem solving method based on stable node smoothness finite element method |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107565782A (en) * | 2017-08-31 | 2018-01-09 | 江苏大学 | A kind of equivalent magnetic network analysis method of mixed rotor permagnetic synchronous motor |
| CN108595772A (en) * | 2018-03-26 | 2018-09-28 | 江苏大学 | A kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor |
-
2019
- 2019-09-27 CN CN201910920662.3A patent/CN110705088B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107565782A (en) * | 2017-08-31 | 2018-01-09 | 江苏大学 | A kind of equivalent magnetic network analysis method of mixed rotor permagnetic synchronous motor |
| CN108595772A (en) * | 2018-03-26 | 2018-09-28 | 江苏大学 | A kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor |
Non-Patent Citations (1)
| Title |
|---|
| 集中绕组外转子永磁同步发电机非线性变网络磁路分析;程明等;《东南大学学报(自然科学版)》;20060420(第02期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110705088A (en) | 2020-01-17 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110705088B (en) | Permanent magnet motor modeling and electromagnetic performance calculating method based on magnetic network | |
| EP3660522B1 (en) | Method for evaluating electromagnetic performace of permanent-magnet machines | |
| Parviainen et al. | Modeling of axial flux permanent-magnet machines | |
| CN107565782B (en) | A kind of equivalent magnetic network analysis method of mixed rotor permanent magnet synchronous motor | |
| Liu et al. | Nonlinear equivalent magnetic network of a linear permanent magnet vernier machine with end effect consideration | |
| Lubin et al. | Two-dimensional analytical calculation of magnetic field and electromagnetic torque for surface-inset permanent-magnet motors | |
| Wu et al. | A hybrid field model for open-circuit field prediction in surface-mounted PM machines considering saturation | |
| Ding et al. | A novel mesh-based equivalent magnetic network for performance analysis and optimal design of permanent magnet machines | |
| Zhou et al. | Nonlinear equivalent magnetic circuit analysis for linear flux-switching permanent magnet machines | |
| CN108595772B (en) | 2D magnetic circuit subdivision modeling method for stator and rotor double-permanent-magnet vernier motor | |
| Touati et al. | Experimental investigation and optimization of permanent magnet motor based on coupling boundary element method with permeances network | |
| Dianati et al. | Analytical design of axial-flux induction motors | |
| CN108539934A (en) | It is a kind of asymmetry Magnetic Circuit permanent magnet-type motor modeling with demagnetization method for analyzing performance | |
| Saied et al. | New approach to cogging torque simulation using numerical functions | |
| Somesan et al. | Sizing-designing procedure of the permanent magnet flux-switching machine based on a simplified analytical model | |
| Chen et al. | Calculation of inductances with 3-D FEM for SRM with segmental rotors and fully-picthed windings | |
| Ali et al. | Cogging torque Mitigation for PMSM using stator slots design and Magnets skewing | |
| CN107862167B (en) | Switched reluctance motor modeling method considering instantaneous iron loss | |
| CN115842496A (en) | High-precision magnetic network modeling method suitable for hybrid stator permanent magnet vernier motor | |
| Qu et al. | Analysis and modeling of airgap & zigzag leakage fluxes in a surface-mounted-PM machine | |
| Zhang | An efficient modeling of air gap and nonlinear analysis of magnetic equivalent circuit for large turbogenerators under no-load condition | |
| Si et al. | Development of the equivalent magnetic circuit model for a surface-interior permanent magnet synchronous motor | |
| Bhashini et al. | Magnetic equivalent circuit for surface-mounted PM motor | |
| Kazem et al. | Finite Element Analysis of Shaded Pole Motor Based on Maxwell2D | |
| Zhang et al. | Nonlinear magnetic network models for flux-switching permanent magnet machines |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |