CN108595772A - A kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor - Google Patents

Abstract

A 2D magnetic circuit subdivision modeling method for a stator-rotor double permanent magnet vernier motor of the present invention includes dividing the complex magnetic field area and the regular magnetic field area of the motor, and performing diamond-shaped small grid subdivision and magnetic field analysis on the two areas respectively. The magnetic permeability equivalent of the circuit; improve the connection relationship of the magnetic permeability nodes at the boundaries of the two types of regions, build a complete 2D magnetic circuit subdivision model, and establish the magnetic permeability solution matrix equation in turn; construct the maximum difference between the magnetic permeability convergence factor and the motor tooth magnetic density The relational expression; solve the permeability matrix equation, and use the iterative algorithm to realize the fast solution of the matrix to obtain the magnetic flux and magnetic potential passing through each permeability node, and then calculate the flux density and permeability of each permeability, and according to the electromagnetic calculation constraints of the motor , can calculate the electromagnetic parameters such as the flux linkage of each phase of the motor, the back electromotive force of the winding, and finally compare with the results of the finite element method. The present invention is the first to carry out 2D magnetic circuit subdivision for the stator-rotor double permanent magnet vernier motor, and the provided scheme can provide reference research for this type of double permanent magnet motor.

Description

A 2D magnetic circuit subdivision modeling method for a stator and rotor double permanent magnet vernier motor

technical field

The invention relates to a 2D magnetic circuit subdivision modeling method of a stator-rotor double permanent magnet vernier motor, belonging to the field of electromagnetic field calculation.

Background technique

The stator and rotor double permanent magnet vernier motor utilizes the modulation effect of the modulating teeth on the spatial magnetic field, and has the characteristics of being able to output high torque at low speed, and is suitable for the field of agricultural machinery and equipment. Compared with the traditional permanent magnet vernier motor, the stator and rotor double permanent magnet vernier motor has improved the torque density. At the same time, the use of mixed magnetic materials not only reduces the cost of the motor, but also reduces the influence of thermal demagnetization of the motor rotor. The traditional permanent magnet vernier motor is divided into stator type and rotor type according to the position of the permanent magnet. The permanent magnet vernier motor is a stator and rotor double permanent magnet type, that is, there are permanent magnets on both the stator and the rotor of the motor. In the case of the same volume, the torque density of the motor is improved, and the space utilization ratio inside the motor is also improved.

At present, the commonly used analysis method for stator and rotor dual permanent magnet vernier motors is commercial finite element (Finite Element Analysis, FEA) software, which is widely used in various stages of motor design due to its high precision and easy operation. However, FEA software is based on the principle of full mesh division inside the motor, and the analysis is time-consuming and inefficient, so it is not suitable for the initial design stage of the motor. The 2D magnetic circuit subdivision modeling method combines the traditional magnetic circuit method and grid subdivision method. Its calculation principle is simple, the accuracy is high, and the simulation time is short, which brings high design efficiency. Through the 2D magnetic circuit subdivision modeling of the stator and rotor double permanent magnet vernier motor, the electromagnetic parameters such as the motor flux linkage, back EMF and torque can be quickly solved, and the high-efficiency design of the motor can be realized in the initial stage of research.

Contents of the invention

The purpose of the present invention is to provide a method for analyzing and solving the magnetic circuit model in the complex magnetic field of a stator-rotor double permanent magnet vernier motor, which mainly includes the grid subdivision of the magnetic permeance in the complex magnetic field area in the motor, the approximate permeance substitution of the regular magnetic field and Establishment of the permeability matrix model. Add the constraint of changing the convergence factor to the model for the fast convergence solution of the matrix.

In order to achieve the above object, the technical solution adopted in the present invention is: a 2D magnetic circuit subdivision modeling method of a stator-rotor double permanent magnet vernier motor, comprising the following steps:

Step 1, use the finite element software to divide the complex magnetic field area and the regular magnetic field area of the motor;

Step 2, establish the diamond-shaped small mesh division of the complex magnetic field area of the motor;

Step 3, establish the magnetic circuit permeance equivalent of the regular magnetic field area of the motor;

Step 4, improve the connection relationship of the permeance nodes at the boundaries of the two types of regions, construct a complete 2D magnetic circuit subdivision model, and establish the permeance solution matrix equations in turn;

Step 5, constructing the relational expression between the magnetic permeability convergence factor and the maximum difference of the motor tooth magnetic density;

Step 6, solving the permeance matrix equation, using an iterative algorithm to quickly solve the matrix to obtain the magnetic flux and magnetic potential passing through each permeance node, and then calculating the magnetic flux density and permeability of each permeance;

Step 7, according to the magnetic circuit parameters obtained in step 6, and according to the electromagnetic calculation constraints of the motor, the electromagnetic parameters such as the flux linkage of each phase of the motor and the back electromotive force of the winding can be calculated.

Further, the stator and rotor double permanent magnet vernier motor is a three-phase motor with 12 slots/28 poles, which is divided into four parts: stator, air gap, rotor and rotating shaft; the stator includes stator yoke, stator teeth, stator slots, electrical The permanent magnet array at the armature winding and the pole shoe, the armature slot shape is a flat-bottomed slot, the armature winding adopts a centralized winding method, and the span is 4 stator slots; the stator permanent magnet material is NdFe35, at each pole shoe of the stator There are 2 notches, each equipped with a Halbach permanent magnet array, each Halbach permanent magnet array is composed of a main permanent magnet with radial impulse magnetization in the middle and auxiliary permanent magnets with tangential impulse magnetization on both sides, which can effectively improve the air gap magnetic field Distribution status; the rotor is cylindrical, with slots on the surface to install surface-embedded permanent magnets, the permanent magnet material is ferrite Y30, and the cross-section of surface-embedded permanent magnets is trapezoidal, evenly distributed in the circumferential direction of the rotor; the stator core and rotor The material of the iron core is silicon steel sheet DW540_50; the air gap is between the stator and the rotor, and the thickness of the air gap is 0.5mm; the motor shaft is made of non-magnetic material, is a solid cylinder, and is coaxially connected with the rotor.

Further, in the step 1, according to the simulation results of the finite element software, the complex magnetic field distribution area of the motor is mainly concentrated in a range of the permanent magnets on both sides of the stator and rotor, including the air gap, the stator pole shoe and the rotor tooth area; the motor law The magnetic field distribution area includes the stator yoke and teeth, and the rotor yoke area. Since the magnetization directions of the permanent magnets on both sides are fixed, the internal magnetic field distribution of the permanent magnets is also regular.

Further, in the step 2, the double permanent magnet vernier motor of the stator and rotor is composed of a Halbach permanent magnet array and a single permanent magnet in the direction of magnetization. The bilateral permanent magnet distribution is relatively complicated in structure, resulting in a range of the stator and rotor and the air gap. The magnetic field distribution is complex. Therefore, the entire complex magnetic field distribution area is subdivided into small diamond-shaped grids, and each small grid area is equivalent to a magnetic permeability;

Furthermore, the specific process of subdividing the complex magnetic field distribution area is as follows: according to the actual design size of the motor, considering the magnetic flux leakage at the air gap between the pole pieces, the stator pole pieces include the air gap between the pole pieces, the air gap between the stator and the rotor, and the rotor teeth. The part adopts the method of grid division with different layers to obtain a suitable subdivision model, and establishes the permeance connection relationship in each grid according to the subdivision results.

Further, the specific process of step 3 is as follows: the permeance model modeling of the stator yoke, teeth, and rotor yoke adopts the traditional method, and each stator tooth, the stator yoke between the teeth, the rotor yoke, and each The permanent magnet blocks are regarded as an overall permeance, and are connected to the permeance nodes in each area in turn according to the magnetic field distribution law.

Further, the specific process of step 4 is: the equivalent permeance of the main permanent magnet in the Halbach permanent magnet array at the pole shoe and the permeance of the auxiliary permanent magnets on both sides, the permeance of the upper pole shoe and the lower air gap respectively The permeance of the auxiliary permanent magnet and the permeance of the rotor permanent magnet are connected correspondingly with the permeance of the adjacent split grid; the permeance of the subdivided area at the junction of the stator and the air gap is connected correspondingly according to the quantitative relationship; the permeance of the rotor teeth is connected with the The connection relationship of the air gap permeance needs to be updated continuously during the rotation of the motor.

Further, in the step 5, in the step 5, the magnetic permeability of the iron core permeance is corrected when solving, and the iterative formula is: μ ^(k) = k ₁ × μ ^(k-1) + (1 -k ₁ )×μ ^(k) , where k ₁ satisfies 0<k ₁ <1. However, due to the iterative calculation of the magnetic permeability, the difference of the magnetic density of the teeth will be generated △B=max{B _i ^(k) -B _i-1 ^(k) }, where i is the number of teeth of the motor stator, which is 12. The value of k ₁ changes according to the calculated value of ΔB, k ₁ =k ₂ ×ΔB, and k ₂ is 0.008.

Further, in the step 6, the constraint formula of the magnetic circuit permeance model is Ф=F·G; the matrix of Ф is established for the upper and lower positions of the permanent magnet and the winding, and the G matrix is established for the magnetic circuit permeance in the motor at the same time, and iterative Method, query the B-H curve parameters, use the update iteration calculation of the magnetic permeability to a stable value, that is, when △B≤0.5%, the magnetic potential of each node can be obtained.

Further, in step 7, according to the magnetic potential of each node obtained by solving the magnetic circuit matrix, the magnetic flux flowing through the stator teeth of the motor at a moment in the electrical angle cycle can be obtained. Recalculate the next rotor position, so as to obtain the flux linkage Ф of each tooth in an electrical angle cycle, and obtain the electromagnetic parameters such as the three-phase magnetic flux and induced electromotive force of the motor.

The present invention has the following beneficial effects:

1. In the modeling of the present invention, the magnetic saturation and magnetic flux leakage caused by the stator permanent magnets and rotor permanent magnets on both sides of the air gap are fully taken into account, so that it is close to the principle of the FEA method and helps to improve the accuracy of model calculation.

2. In the present invention, the regular magnetic circuit performs the equivalent of the magnetic circuit permeance according to the regular range of the magnetic field lines. At the same time, because the internal magnetic field of the motor is symmetrical, the magnetic circuit permeance at its symmetrical position also has a high similarity, without reducing Accurate while improving the simplicity of model programming.

3. In the present invention, the complex magnetic field divides the size of the permeable grid according to the structural parameters of the iron core. Since the motor stator and rotor have different structures at different positions, three different grids are used for subdivision, thereby effectively reducing grid inconsistencies. errors caused by matching.

4. Completed the procedure of adjusting the convergence factor with the change of the maximum error value. Compared with the traditional algorithm, it is unnecessary to use a constant constant as the convergence factor all the time, and the iteration of the matrix solution can be completed more quickly.

Description of drawings

Fig. 1 is the 2D structural diagram of motor used in the present invention;

Fig. 2 is the magnetic flux analysis diagram of motor used in the present invention;

Fig. 3 is a structural diagram of the magnetization direction of the permanent magnet of the motor;

Fig. 4 is the structural diagram of the magnetic network model of band grid subdivision of the present invention;

Fig. 5 is a partial enlarged structural diagram of the magnetic network model with mesh division of the present invention;

Fig. 6 is the structural diagram of the magnetic field complex region of the magnetic network model with grid division in the present invention;

Fig. 7 is a schematic diagram of comparison of single-phase no-load magnetic flux between finite element software and magnetic network model with grid subdivision.

Fig. 8 is a flowchart of the modeling method of the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention.

In order to explain the beneficial effects of the present invention more simply and clearly, a detailed description will be given below in conjunction with a specific stator-rotor double permanent magnet vernier motor: Fig. 1 is a topological structure diagram of the motor, in which 1 is the stator yoke, 2-1 is the stator teeth; 2-2 is the pole shoes of the stator teeth; 2-3 is the air gap between the pole shoes of the stator teeth; 3 is the winding; 4-1 is the rotor yoke; 4-2 is the permanent magnet of the rotor , 4-3 is the rotor teeth, 5-1 is the first permanent magnet of the stator Halbach permanent magnet array, 5-2 is the second permanent magnet of the stator Halbach permanent magnet array, 5-3 is the third permanent magnet of the stator Halbach permanent magnet array , 6 is the air gap between the stator and the rotor; the embodiment of the present invention is a three-phase motor with 12 slots/28 poles, which is divided into four parts: the stator, the rotor, the air gap and the rotating shaft; the stator includes a stator yoke, a stator tooth, and a stator slot , The armature winding and the permanent magnet array at the pole shoes, the armature slot shape is a flat-bottomed slot, the armature winding adopts a centralized winding method, and the span is 4 stator slots; the stator permanent magnet material is NdFe35, in each pole of the stator There are 2 notches on the shoe, each equipped with a Halbach permanent magnet array, each Halbach permanent magnet array is composed of a main permanent magnet with radial impulse magnetization in the middle and auxiliary permanent magnets with tangential impulse magnetization on both sides, which can effectively improve the air gap The distribution of the magnetic field; the rotor is cylindrical, and the surface is slotted to install surface-embedded permanent magnets. The permanent magnet material is ferrite Y30, and the cross-section of the surface-embedded permanent magnets is trapezoidal, evenly distributed in the circumferential direction of the rotor; the stator core And the material of the rotor core is silicon steel sheet DW540_50;

The flow chart shown in Figure 8 is divided into the following steps to achieve:

Step 1, use the finite element software to divide the complex magnetic field area and the regular magnetic field area of the motor.

Fig. 2 is an analysis diagram of the magnetic force lines in the magnetic field of the motor according to the embodiment of the present invention. In the motor model, the complex areas of the motor magnetic field are mainly concentrated in the three parts of the stator tooth pole shoe, the air gap and the rotor teeth. The shape of this area is inconsistent, the magnetic force line trend is complex and irregular, and it is easy to generate inter-tooth magnetic flux leakage and looping magnetic force lines; The area where the motor magnetic field is simple is mainly concentrated in the three parts of the stator yoke, stator teeth and rotor yoke. The shape of this position is relatively regular, and the trend of the magnetic force lines is regular. They are basically facing the same direction, and the number of magnetic force lines on one magnetic circuit remains unchanged. , At the same time, the flux leakage conductance of the stator armature slot is extremely small, and it is not easy to generate flux leakage.

Step 2, establish the subdivision of diamond-shaped small meshes in the complex magnetic field region of the motor.

Fig. 4 is a complete 2D magnetic circuit subdivision model of the embodiment of the present invention, and Fig. 6 is a schematic diagram of a small diamond-shaped grid subdivision of the enlarged complex magnetic field region of the motor; according to the actual motor design size and considering the magnetic flux leakage at the air gap between the pole pieces, For the stator pole pieces including the air gap between the pole pieces, the air gap between the stator and the rotor, and the rotor teeth, different layers of grids are used to obtain a suitable subdivision model, and according to the subdivision results, the Permeable connection relationship. The area where the magnetic field of the stator part is complex is the air gap 2-3 between the stator tooth pole piece 2-2 and the pole piece. In the stator pole piece 2-2 of each tooth of the motor, two sets of permanent magnets using the Halbach array are embedded, consisting of the first permanent magnet 5-1, the second permanent magnet 5-2 and the third permanent magnet 5-3 . Due to the embedded Halbach permanent magnet array, the grid in the pole shoe is distributed according to the position, and is connected with the left side of the second permanent magnet 5-2, the top of the first permanent magnet 5-1 and the right side of the third permanent magnet 5-3 . At the same time, because the overall magnetization direction is downward, the second permanent magnet 5-2 and the third permanent magnet 5-3 are connected with the upper point of the first permanent magnet 5-1. At the same time, there is an air gap 2-3 between the pole piece and the pole piece. Because the magnetic field at the pole shoe is complex, the direction of the magnetic force line is chaotic and there is magnetic flux leakage, the pole shoe is divided into small grids, and the height and width of the grid are equal to l ₁ . From the bottom to the top of the pole shoe 2-2, it is divided into 5 layers of rectangular grids. Since the magnetization direction of the permanent magnet array is fixed, the grid at the position of the permanent magnet is excluded, and the traditional method is used for the permanent magnet. All are a whole magnetic permeance, and the height of the permanent magnet array is 4l ₁ . Therefore, the pole shoe 2-2 grid division has 5 rows, the first row is composed of 28 grids, and each of the following four rows is composed of 12 grids, which are divided into three sections by permanent magnets, and each section has 4 grids grid. The air gaps 2-3 between the pole shoes also use 5 rows of grids of the same size, each row is composed of 3 grids, and the two sides are respectively connected to the adjacent pole shoe grids.

The air gap is an important place for energy exchange, and it is also the most complex area of the magnetic field. Through reasonable design, the air gap 6 is divided into three layers, each row has 1800 grids forming a ring, and the height and width of the grids are equal to l3. At the same time, the grid size of the air gap 6 is approximately 1/5 of the grid size of the stator pole piece 2-2, that is, the lowest layer grid of each pole piece 2-2 and the air gap 2-3 between the pole pieces, the connection network 5 air gap grids within grid width. For the Halbach permanent magnet array, since the tangentially magnetized permanent magnets in practice do not form magnetic force lines downward, the second permanent magnet 5-2 and the third permanent magnet 5-3 are not connected to the grid of the air gap 6, only the second permanent magnet 5-2 The lower end of a permanent magnet 5-1 is connected to the grids of the air gaps 6 within the width of the first permanent magnet 5-1.

The complex magnetic field area of the rotor part is the rotor teeth 4-3 and the rotor permanent magnet 4-2. For the rotor tooth part 4-3, because the magnetic field in this part is complex and the distribution of the magnetic force lines is irregular, the rotor tooth part 4-3 is meshed, and the mesh width and height are equal to l ₂ . Inside the rotor tooth part 4-3, the grid division method of 4 rows and 5 columns is adopted. Since the boundary of the rotor tooth part 4-3 is not completely radial and has a certain offset angle, the permeance grid in each row Add one to the boundary of , the equivalent tangential permeance calculated according to the area ratio of the cut mesh of the rotor tooth boundary. Similarly, since the magnetization direction of the rotor permanent magnet 4-2 is downward, and the magnetization direction is fixed and there is basically no deviation, the traditional magnetic circuit model is adopted for the rotor permanent magnet 4-2, and the upper end of the rotor permanent magnet 4-2 is connected to the left and right sides. The upper three rows of the rotor teeth 4-3 on both sides are connected. Since the rotor teeth 4-3 and the rotor permanent magnets 4-2 are close to the bottom of the rotor teeth, there are some loops of magnetic force lines, so by designing under the rotor permanent magnets 4-2 and the rotor teeth 4-3, continue to add a layer and rotor Grids with the same mesh size of the tooth portion are used to lay out the loop magnetic circuit between the tooth portion and the permanent magnet. The lower end of the equivalent magnetic conductance of the rotor permanent magnet 4-2 is connected to the grid within the width range of the permanent magnet, and the grid of the rotor teeth 4-3 is sequentially connected to the next layer of grid.

The permeance calculation formula is as follows:

Step 3, establish the magnetic circuit permeance equivalent of the regular magnetic field region of the motor.

For the stator part of the motor, since the magnetic force lines of the stator yoke part 1 and the stator tooth part 2-1 move smoothly and there is no circular magnetic force line, the traditional method is used to model the magnetic permeability model of these two places, and the distance between each stator tooth and the teeth The stator yokes are respectively regarded as a whole magnetic conductance, and are connected in sequence. Since the stator pole piece of the motor is meshed, the permeance model of the stator tooth part 2-1 is connected to the 28 grids in the first row of the corresponding tooth bottom pole piece 2-2.

The rotor yoke 4-1 of the motor is similar to the stator yoke 1, its magnetic flux path is tangentially flowing, and it is smooth without loops, so the connection between each rotor tooth 4-1 and the adjacent rotor permanent magnet 4-2 Part 4-1 of the rotor yoke adopts a traditional magnetic circuit model, which is equivalent to a whole magnetic conductance, and a total of 56 yoke magnetic conductances are connected to form a ring of the rotor yoke.

Step 4: Improve the connection relationship of the permeance nodes at the boundaries of the two types of regions, construct a complete 2D magnetic circuit subdivision model, and establish the permeance solution matrix equations in turn.

The equivalent permeance of the main permanent magnet in the Halbach permanent magnet array at the pole shoe is respectively connected with the permeance of the secondary permanent magnets on both sides, the permeance of the upper pole shoe and the lower air gap, and the permeance of the auxiliary permanent magnet is connected with the rotor permanent The magnetic permeance of the magnets is connected correspondingly with the permeance of the adjacent subdivided grid; for the air gap 6, since the rotor rotates relative to the stator, the stator pole piece 2-2, the stator pole piece air gap 2-3 and the first permanent magnet 5 The connection between -1 and the air gap 6 is fixed, while the connection between the rotor and the air gap changes with the rotation angle. Therefore, determining the connection method between the rotor and the air gap is the key to establishing the rotating magnetic network model. When the rotor is in different positions, the first row of 4 grids of the rotor teeth 4-3 are respectively connected with the air gap grids in the corresponding range, and there are about 6 to 7 air gap grids are connected to it. The rotor permanent magnet 4-2 is also connected to the air gap grid in the corresponding range. Since the rotor permanent magnet 4-2 is modeled with a traditional magnetic circuit, it covers a large air gap range. In the range of the rotor permanent magnet 4-2 There are about 32 air gaps 6 grids connected to it. Whenever the rotor rotates through a set angle, the rotor permanent magnet 4-2 and all the rotor teeth 4-3 grids will rotate this angle along the Z axis, and the size of the coverage area remains the same, but the air gap in the coverage area connected to it 6 Grid nodes change. When the rotor rotates through different angles, the permeance of the subdivided area at the junction of the stator and the air gap is connected correspondingly according to the quantitative relationship; the connection relationship between the permeance of the rotor teeth and the permeance of the air gap needs to be continuously updated during the rotation of the motor. The grids of the rotor teeth 4-3 and the grids of the rotor permanent magnets 4-2 to the grids of the air gap 6 are connected in different order to update the node connection relationship between the rotor and the air gap.

Connect the magnetic circuit permeance nodes of stator, air gap and rotor according to step 1, step 2, step 3 and step 4, a complete 2D magnetic circuit subdivision model can be constructed, and the permeance solution matrix equation can be established in turn. The calculation formula is as follows:

G·F=Q (2)

In the formula:

and

F＝[F(1) ... F(7672)] ^T

Q＝[Q(1) ... Q(7672)] ^T

The node magnetic potential F satisfies:

F＝G ^-1 ·Q (3)

In the MATLAB environment, directly use the following formula to solve:

F＝G\Q (4)

The magnetic density calculation formula is:

In the formula, B represents the magnetic density, s and t are the nodes at both ends of the permeable, and S is the effective cross-sectional area of the permeable region.

Step 5, constructing the relational expression between the magnetic permeability convergence factor and the maximum difference of the motor tooth magnetic density;

The solution process of matrix equation (2) is a non-linear iterative process, which needs to be solved by a non-linear iterative algorithm, and the formula of the Newton iterative method used is:

μ ^(k) =k ₁ ×μ ^(k-1) +(1-k ₁ )×μ ^(k) (6)

In the formula, the magnetic permeability μ is an iterative calculation parameter, k ₁ is a coefficient, and k is the number of iterations; where k ₁ satisfies 0<k ₁ <1. However, due to the iterative calculation of the magnetic permeability, the difference of the magnetic density of the teeth will be generated △B=max{B _i ^(k) -B _i-1 ^(k) }, where i is the number of teeth of the motor stator, which is 12. The value of k ₁ changes according to the calculated value of ΔB, k ₁ =k ₂ ×ΔB, and k ₂ is 0.008. By connecting the tooth magnetic density calculation difference △B with the coefficient k ₁ , a functional relationship that changes with iterations is generated. When the difference is large, the coefficient takes a larger value, so that the calculation result is greatly affected by the previous calculation; When the difference is small, the coefficient value is small, so that the calculation result is less affected by the previous calculation. Accelerate the iteration speed of the entire program and improve efficiency.

Step 6, solve the permeability matrix equation, use the iterative algorithm to realize the rapid solution of the matrix to obtain the magnetic flux and magnetic potential passing through each permeability node, and then calculate the flux density and permeability of each permeability; the constraint formula of the magnetic circuit permeability model Ф=F G; establish a Ф matrix for the upper and lower positions of the permanent magnet and the winding, and at the same time establish a G matrix for the magnetic circuit permeability in the motor, and use the iterative method to query the parameters of the B-H curve, and use the updated iterative calculation of the magnetic permeability to a stable value.

According to the permeability matrix equation established in step 4, linear interpolation is used for the B-H curve at the same time:

When the tooth magnetic density B satisfies the following conditional formula, it means that an iterative calculation is completed:

In the formula, ζ is the maximum error value, and its value is 0.5%;

Step 7, according to the magnetic circuit parameters obtained in step 6, and according to the electromagnetic calculation constraints of the motor, the electromagnetic parameters such as the flux linkage of each phase of the motor, the back electromotive force of the winding, and the output torque can be calculated.

According to the magnetic position of each node obtained by solving the magnetic circuit matrix, the magnetic flux flowing through the stator teeth of the motor at a moment in the electrical angle period can be obtained, and the next rotor position can be calculated again, so that the magnetic flux of each tooth in an electrical angle period can be obtained Chain Ф, based on which the electromagnetic parameters such as three-phase magnetic flux and induced electromotive force of the motor can be obtained, which can be used to calculate the output torque of the motor in the case of load. In order to verify the accuracy and reliability of the 2D magnetic circuit subdivision modeling method of a stator-rotor double permanent magnet vernier motor proposed by the present invention, the simulation results are shown in Fig. 7, and compared with the results obtained by finite element commercial software for verification.

As shown in Figure 7, it is a comparison diagram of single-phase magnetic flux analyzed by commercial finite element software and equivalent magnetic network model analyzed by multi-grid. A1 in the figure is the single-phase no-load magnetic The flux waveform, B1 is the single-phase no-load flux waveform obtained by multi-grid equivalent magnetic network model. It can be seen that the high actuarial precision and accuracy are guaranteed under the condition of low calculation and analysis time consumption of the equivalent magnetic network specialty.

To sum up, a 2D magnetic circuit subdivision modeling method of a stator-rotor double permanent magnet vernier motor according to the present invention includes dividing the complex magnetic field area and the regular magnetic field area of the motor, and performing diamond-shaped small mesh sectioning on the two areas respectively The division is equivalent to the magnetic permeability of the magnetic circuit; the connection relationship of the magnetic permeability nodes at the boundary of the two types of regions is improved, a complete 2D magnetic circuit subdivision model is constructed, and the matrix equation for the magnetic permeability solution is established in turn; the magnetic permeability convergence factor and the magnetic density of the motor teeth are constructed The relational expression of the maximum difference, in order to improve the speed of matrix solution, in order to optimize the design; solve the permeance matrix equation, use the iterative algorithm to realize the fast solution of the matrix to obtain the magnetic flux and magnetic potential passing through each permeance node, and then calculate the permeance Magnetic flux density and permeability, and according to the electromagnetic calculation constraints of the motor, the electromagnetic parameters such as the flux linkage of each phase of the motor and the back electromotive force of the winding can be calculated, and finally compared with the results of the finite element method. The present invention is the first to carry out 2D magnetic circuit subdivision for the stator-rotor double permanent magnet vernier motor, and the provided scheme can provide reference research for this type of double permanent magnet motor.

Although the present invention has been disclosed above with preferred embodiments, the embodiments are not intended to limit the present invention. Any equivalent change or modification made without departing from the spirit and scope of the present invention shall fall within the scope of protection defined by the appended claims of this application.

Claims (9)

1. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor, which is characterized in that include the following steps：

Step 1, motor complexity field region and rule field region are divided using finite element software；

Step 2, the diamond shape small grid subdivision of motor complexity field region is established；

Step 3, the magnetic circuit magnetic conductance for establishing motor rule field region is equivalent；

Step 4, magnetic conductance node connection relation at two class zone boundaries is improved, complete 2D magnetic circuits subdivision model is built, establishes successively Magnetic conductance solution matrix equation；

Step 5, the relational expression of magnetic conductivity convergence factor and motor teeth portion flux density maximum difference is built；

Step 6, magnetic conductance matrix equation is solved, realizes that the rapid solving of matrix is obtained through each magnetic conductance node using iterative algorithm Magnetic flux and magnetic potential, and then calculate the magnetic flux density and magnetic conductivity of each magnetic conductance；

Step 7, it according to the magnetic circuit parameters solved in step 6, calculates and constrains according to motor electromagnetic, each phase magnetic of motor can be calculated The electromagnetic parameters such as chain, winding counter electromotive force.

2. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor according to claim 1, feature It is, the double permanent magnetism vernier motors of the rotor are the three phase electric machine of the pole of 12 slots/28, are divided into stator, air gap, rotor and shaft four Part；Include stator yoke, stator teeth, stator slot, armature winding and pole shoe permanent magnet array in stator, armature flute profile is flat Kerve, for armature winding using centralized winding method, span is 4 stator slots；Stator permanent magnet material is NdFe35, in stator Each pole shoe has 2 notches, and there are one Halbach permanent magnet arrays, each Halbach permanent magnet arrays are rushed each dress by intermediate radial The secondary permanent magnet that the main permanent magnet of magnetic and both sides tangentially rush magnetic is constituted；Rotor is cylindrical shape, and installation table of slotting on surface is embedding forever Magnet, permanent magnet material are ferrite Y30, and the embedding permanent magnet cross section of table is trapezoidal, is evenly distributed on rotor circumference direction；Stator The material of iron core and rotor core is silicon steel sheet DW540_50；Between stator and rotor, air gap thickness is air gap 0.5mm；Machine shaft is made of un-conducted magnetic material, is solid cylindrical, and connect with rotor coaxial.

3. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor according to claim 2, feature It is, in the step 1, according to the simulation result of finite element software, motor complexity Distribution of Magnetic Field region focuses primarily upon fixed turn In one segment limit of sub- two-sided permanent magnet body, including at air gap, stator pole shoes and rotor teeth portion region；Motor rule Distribution of Magnetic Field area Domain includes stator yoke and teeth portion, rotor yoke region, since both sides permanent magnet magnetizing direction has been fixed, permanent magnet inner magnet Field distribution is also that rule is distributed.

4. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor according to claim 2, feature It is, the detailed process to complicated Distribution of Magnetic Field domain mesh is：According to real electrical machinery design size, consider between pole shoe at air gap Leakage field, air gap air gap, rotor, rotor teeth portion use the side of different number of plies mesh generations including pole shoe between stator pole shoes Formula establishes according to subdivision result the magnetic conductance connection relation in each grid to obtain suitable subdivision model.

5. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor according to claim 2, feature It is, the detailed process of the step 3 is：Tradition side is used to the magnetic conductance model modeling of stator yoke and teeth portion, rotor yoke Each stator tooth, the stator yoke of between cog, rotor yoke and each permanent magnet blocks are respectively seen as a whole magnetic conductance, and press by formula According to Distribution of Magnetic Field rule, it is sequentially connected magnetic conductance node in each region.

6. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor according to claim 2, feature It is, the detailed process of the step 4 is：The equivalent magnetic conductance of main permanent magnet is respectively with two in pole shoe Halbach permanent magnet arrays Side pair permanent magnet magnetic conductance, upside pole shoe are connected with magnetic conductance at the air gap of downside, secondary permanent magnet magnetic conductance and rotor permanent magnet magnetic conductance It is corresponding with adjacent subdivision grid magnetic conductance to be connected；The magnetic conductance of stator and air gap intersection divided region is corresponded to according to quantitative relation to be connected It connects；Rotor teeth portion magnetic conductance and the connection relation of air-gap permeance needs are constantly updated in motor rotation process.

7. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor according to claim 1, feature It is, in the step 5, when solution is modified the magnetic conductivity of iron core magnetic conductance, and iterative formula is：μ^(k)=k₁× μ^(k-1)+(1-k₁)×μ^(k), wherein k₁Meet 0<k₁<1, and since the iterative calculation of magnetic conductivity will produce the difference △ of teeth portion flux density B=max { B_i ^(k)-B_i-1 ^(k), wherein i is the motor stator number of teeth, is 12, k₁Value according to the calculated value of △ B change and change, k₁=k₂× △ B, k₂Take 0.008.

8. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor according to claim 1, feature It is, in the step 6, magnetic circuit magnetic conductance model constraint formulations are Ф=FG；The upper and lower position of permanent magnet and winding is established The matrix of Ф, while G matrix is established to magnetic circuit magnetic conductance in motor, and iterative method is used, BH curve parameter is inquired, magnetic conductance is utilized When the update of rate is iterated to calculate to stationary value, i.e. △ B≤0.5%, you can obtain the magnetic potential of each node.

9. a kind of 2D magnetic circuit subdivision modeling methods of the double permanent magnetism vernier motors of rotor according to claim 1, feature It is, in the step 7, according to each node magnetic potential for solving the acquisition of magnetic circuit matrix, one can be obtained in the electrical angle period The motor stator tooth at moment flows through magnetic flux, calculates again next rotor-position, so obtains an electrical angle period The magnetic linkage Ф of each tooth, obtains the electromagnetic parameters such as motor three-phase magnetic flux, induced electromotive force accordingly, and carrying situation if band can be used for Calculate motor output torque.