CN116992723B - Motor dynamic magnetic network modeling method - Google Patents

Motor dynamic magnetic network modeling method Download PDF

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CN116992723B
CN116992723B CN202310965818.6A CN202310965818A CN116992723B CN 116992723 B CN116992723 B CN 116992723B CN 202310965818 A CN202310965818 A CN 202310965818A CN 116992723 B CN116992723 B CN 116992723B
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CN116992723A (en
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葛帅帅
晏敬鹏
杨曜泽
张志刚
石晓辉
王欢
祁文杰
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Chongqing University of Technology
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Abstract

The invention discloses a motor dynamic magnetic network modeling method, which belongs to the technical field of motor simulation modeling, and the method establishes and obtains a stator magnetic flux density distribution diagram and a rotor magnetic flux density distribution diagram according to a finite element model of a motor; according to the rotor magnetic flux density distribution diagram and the stator magnetic flux density distribution diagram, respectively obtaining the rotor magnetic conductance, the stator tooth magnetic conductance, the stator yoke magnetic conductance, the stator slot magnetic leakage magnetic conductance and the stator tooth end magnetic conductance of the motor; dividing an air gap region between a motor rotor and a motor stator by using a cross grid unit to obtain an air gap magnetic circuit; and performing air gap modeling on the motor motion process according to the air gap magnetic circuit to obtain an air gap modeling result, performing node analysis on a motor magnetic network to obtain a magnetic network model according to a motor magnetic network node algebraic equation set. The method solves the problems of overlapping errors, low modeling precision and complex calculation in the existing air gap motion modeling method.

Description

Motor dynamic magnetic network modeling method
Technical Field
The invention belongs to the technical field of motor simulation modeling, and particularly relates to a motor dynamic magnetic network modeling method.
Background
The permanent magnet synchronous motor is used as one of the core components of the new energy automobile, and the high-precision dynamic motor simulation model has very important significance for the research and development and performance optimization of the high-performance permanent magnet synchronous motor. The equivalent magnetic circuit method can consider nonlinear factors such as stator slotting, permanent magnet distribution and the like. Compared with the traditional dq axis model, the method can consider more nonlinear factors, is more flexible than a mathematical analysis model and is faster to calculate than a finite element model.
The existing technical scheme utilizes an equivalent magnetic circuit method to refine stator and rotor tooth magnetic circuits, and then steady-state simulation solves the steady-state electromagnetic characteristic of the motor. The existing other technical scheme utilizes an equivalent magnetic circuit method to establish a motion grid model between a stator and a rotor through an air gap, and carries out dynamic simulation on the motor to solve the dynamic electromagnetic characteristic of the motor. The air gap between the stator and the rotor of the motor is an important area for energy conversion, the equivalent magnetic resistance of the air gap is relatively large, the main magnetic potential drop occurs in the air gap, and the accuracy of the magnetic network model is relatively sensitive to the equivalent magnetic resistance of the air gap. Therefore, modeling of the air gap movement between the stator and the rotor of the motor is an extremely important ring when dynamic simulation analysis is carried out.
Motors are complex systems of multiple physical processes, multiple parameter coupling. The energy conversion is mainly the air gap between the stator and the rotor, and is also an important place for converting magnetic energy into mechanical energy. Therefore, the modeling of the relative motion of the stator and the rotor by the motor is particularly important. In the existing technology, the whole-step long-moving grid modeling method ignores the grid overlapping process, the connection of the magnetic network nodes is not changed along with the change of the rotor angle, which means that when the motor rotates by an angle smaller than half of the grid size, the network nodes are not changed, and partial simulation static state is lost when the rotating speed is lower, which also causes that the counter electromotive force is difficult to solve. The same node scalar magnetic potential interpolation dynamic grid modeling method also has overlapping errors, and the modeling method is equivalent to adding transverse flux guides inversely proportional to the distance on the moving surfaces of the stator and the rotor and connecting the transverse flux guides in series on the radial magnetic paths of the stator and the rotor to describe the transverse flow of magnetic fluxes, but the calculation accuracy is necessarily affected. Meanwhile, because the equivalent tangential flux guide which is connected in series is repeatedly inserted into the radial magnetic circuit of the air gap, and the change rate of the equivalent tangential flux guide is changed, larger high-frequency motion modeling errors can be generated, and the accuracy of a high-frequency harmonic influence result can be introduced when the counter electromotive force is solved.
Disclosure of Invention
Aiming at the defects in the prior art, the motor dynamic magnetic network modeling method provided by the invention solves the problems of overlapping errors, low modeling precision and complex calculation in the existing air gap motion modeling method.
In order to achieve the aim of the invention, the invention adopts the following technical scheme: a modeling method of a dynamic magnetic network of a motor comprises the following steps:
s1, establishing a finite element model of a motor, and simulating according to the finite element model of the motor to obtain a stator magnetic flux density distribution diagram and a rotor magnetic flux density distribution diagram;
s2, establishing a motor rotor magnetic circuit by adopting a cross grid unit according to a rotor magnetic flux density distribution diagram to obtain the motor rotor magnetic circuit;
s3, respectively establishing a motor stator tooth magnetic circuit, a motor stator yoke magnetic circuit and a motor stator slot leakage magnetic circuit by adopting a concentrated parameter method according to a stator magnetic flux density distribution diagram, and establishing a motor stator tooth end magnetic circuit by adopting a cross grid unit;
s4, calculating the magnetic conductance of the motor rotor, the magnetic conductance of the stator teeth, the magnetic conductance of the stator yoke, the magnetic conductance of the stator slots and the magnetic conductance of the stator teeth according to the magnetic circuit of the motor rotor, the magnetic circuit of the stator teeth of the motor, the magnetic circuit of the stator yoke, the magnetic circuit of the stator slots and the magnetic circuit of the stator teeth end parts of the motor;
S5, dividing an air gap region between a motor rotor and a motor stator by using a cross grid unit according to a finite element model of the motor to obtain an air gap magnetic circuit;
s6, performing air gap modeling in the motor motion process according to the air gap magnetic circuit to obtain an air gap modeling result;
and S7, analyzing nodes of the motor magnetic network according to the motor rotor flux guide, the stator tooth part flux guide, the stator yoke part flux guide, the stator slot flux guide, the stator tooth end part flux guide and the air gap modeling result, obtaining a motor magnetic network node algebraic equation set by using a Gaussian elimination method, obtaining a magnetic network model according to the motor magnetic network node algebraic equation set, and completing motor magnetic network modeling.
The beneficial effects of the invention are as follows: according to the invention, air gap modeling is performed in the motor motion process, and the purpose of high-efficiency dynamic simulation analysis is achieved under the same modeling precision; according to the invention, the flux guide units are continuously subdivided while the air gap unit nodes are not increased, the flux guide of one grid is divided into two flux guides connecting the left node and the right node according to the actual overlapping degree of the adjacent units, and the node equation dimension is reduced under the same simulation precision; the invention can better process the superposition of the flux guiding units, can effectively reduce the calculation error caused by the superposition of the flux guiding units when the grid quantity is properly selected, and is more accurate for solving the simulation result of the back electromotive force.
Further, the cross-shaped grid unit in the step S2 is a grid unit formed by connecting two radial flux guides and two tangential flux guides in a cross shape to one point.
The beneficial effects of the above-mentioned further scheme are: the cross grid unit can effectively simulate the radial and tangential magnetic flux flow of one unit; meanwhile, the cross grid unit can flexibly grid the rotor according to the structure and the position of the permanent magnet, and the arrangement of the grid unit is not considered.
Further, in the step S4, there are three cases of the rotor flux guide and the stator tooth end flux guide:
the first case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are cuboid, and then the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
wherein G is Re_1 The magnetic conductance of the motor rotor when the cross grid unit is cuboid represents the radial magnetic conductance or tangential magnetic conductance in the cuboid cross grid unit; g Re_2 The stator tooth end magnetic conductance when the cross grid unit is cuboid represents radial magnetic conductance or tangential magnetic conductance in the cuboid cross grid unit; w (w) Re The length of the magnetic flux path of the rectangular cross grid unit in the magnetic circuit of the motor rotor; mu (mu) Re Is the magnetic permeability of the motor rotor; h is a Re The magnetic flux path section of the rectangular cross grid unit in the motor rotor magnetic circuit is wide; l (L) Re The magnetic flux path section of the rectangular cross grid unit in the motor rotor magnetic circuit is long; w (w) Re ' is the length of the magnetic flux path of the cuboid cross-shaped grid unit in the stator tooth end magnetic circuit; mu (mu) Re ' is the magnetic permeability of the stator tooth end; h is a Re ' is the width of the magnetic flux path section of the cuboid cross-shaped grid unit in the stator tooth end magnetic circuit; l (L) Re ' is the length of the magnetic flux path section of the cuboid cross-shaped grid unit in the stator tooth end magnetic circuit;
the second case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are trapezoidal bodies, so that the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
wherein G is Tr,t_1 When the cross grid unit is a trapezoid body, tangential flux in the flux guide of the motor rotor; g Tr,t_2 When the cross grid unit is a trapezoid body, tangential flux in the flux at the end part of the stator tooth; g Tr,r_1 When the cross grid unit is a trapezoid body, radial flux in the flux guide of the motor rotor; g Tr,r_2 When the cross grid unit is a trapezoid body, radial flux guide in the flux guide of the end part of the stator tooth; l (L) Tr In the magnetic circuit of the rotor of the motor The thickness of the trapezoid cross grid cells; mu (mu) Tr Is the magnetic permeability of the motor rotor; h is a Tr Is the height of a trapezoid cross grid unit in a motor rotor magnetic circuit; w (w) Tr,2 The upper bottom of the trapezoid cross grid unit in the magnetic circuit of the motor rotor; w (w) Tr,1 Is the lower bottom of a trapezoid cross grid unit in a motor rotor magnetic circuit; l (L) Tr ' is the thickness of the trapezoidal cross grid unit in the magnetic circuit at the end part of the stator tooth; mu (mu) Tr ' is the magnetic permeability of the stator tooth end; h is a Tr ' is the height of the trapezoidal cross grid unit in the magnetic circuit at the end part of the stator teeth; w (w) Tr,2 ' is the upper bottom of a trapezoid cross grid unit in a magnetic circuit at the end part of the stator tooth; w (w) Tr,1 ' is the lower bottom of a trapezoid cross grid unit in the magnetic circuit at the end part of the stator teeth; ln is a logarithmic function with a base of natural constant; (. Cndot. -1 Is the inverse of the matrix;
the third case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are semi-cylindrical, and the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
G Se,r_1 ＝πL Se *μ Se
G Se,r_2 ＝πL Se '*μ Se '
wherein G is Se,t_1 When the cross grid unit is a semi-cylinder, tangential flux in the flux guide of the motor rotor; g Se,t_2 When the cross grid unit is a semi-cylinder, tangential flux guiding in the flux guiding of the end part of the stator tooth; g Se,r_1 When the cross grid unit is a semi-cylinder, radial flux in the flux guide of the motor rotor; g Se,r_2 When the cross grid unit is a semi-cylinder, radial flux guide in the flux guide of the end part of the stator tooth; r is the radius of a semi-cylindrical cross grid unit in a motor rotor magnetic circuit;μ Se is the magnetic permeability of the motor rotor; l (L) Se Is the height of a semi-cylindrical cross grid unit in a motor rotor magnetic circuit; s is S y The cross section area of the side arc of the semi-cylindrical cross grid unit in the magnetic circuit of the motor rotor; y is a differential variable of a side arc of a semi-cylindrical cross grid unit in a motor rotor magnetic circuit; r' is the radius of the semi-cylindrical cross grid unit in the magnetic circuit of the end part of the stator tooth; mu (mu) Se ' is the magnetic permeability of the stator tooth end; l (L) Se ' is the height of the semi-cylindrical cross grid unit in the magnetic circuit of the end part of the stator tooth; s is S y' ' is the cross-sectional area of the side arc of the semi-cylindrical cross grid unit in the magnetic circuit of the end part of the stator tooth; y' is a differential variable of a side arc of a semi-cylindrical cross grid unit of the magnetic circuit at the end part of the stator tooth; d is the differential sign.
The beneficial effects of the above-mentioned further scheme are: the reasonable equivalent grid shape can enable the flux-guide calculation of the cross grid unit to be simpler and more accurate, and the modeling precision is improved.
Further, in the step S4, the stator tooth flux guide, the stator yoke flux guide and the stator slot flux leakage flux guide are respectively:
Wherein G is Re_1 ' is stator tooth flux guide; g Re_2 ' is stator yoke flux guide; g Re_3 ' is stator slot leakage flux guide; w (w) Re_1 ' is the length of the flux path of the concentrated parameter grid in the motor stator tooth magnetic circuit; mu (mu) Re_1 ' is the magnetic permeability of the motor stator teeth; h is a Re_1 ' is the width of the magnetic flux path cross section of the concentrated parameter grid in the motor stator tooth magnetic circuit; l (L) Re_1 ' as motor statorThe length of the magnetic flux path section of the concentrated parameter grid in the tooth magnetic circuit; w (w) Re_2 ' is the length of the flux path of the concentrated parameter grid in the motor stator yoke magnetic circuit; mu (mu) Re_2 ' is the magnetic permeability of the motor stator yoke; h is a Re_2 ' is the width of the flux path cross section of the concentrated parameter grid in the motor stator yoke magnetic circuit; l (L) Re_2 ' is the length of the magnetic flux path cross section of the concentrated parameter grid in the magnetic circuit of the motor stator yoke; w (w) Re_3 ' is the length of the flux path of the concentrated parameter grid in the leakage magnetic circuit of the motor stator slot; mu (mu) Re_3 ' is the magnetic permeability of the motor stator slot leakage; h is a Re_3 ' is the width of the magnetic flux path section of the concentrated parameter grid in the leakage magnetic circuit of the motor stator slot; l (L) Re_3 ' is the length of the magnetic flux path cross section of the concentrated parameter grid in the leakage magnetic circuit of the motor stator slot.
The beneficial effects of the above-mentioned further scheme are: the stator slot is equivalent to a rectangular slot, so that the calculation of the slot flux leakage guide is easier, the magnetic flux distribution and the structure of the stator tooth part and the stator yoke part are simpler, the number of nodes in a magnetic network model can be effectively reduced by adopting a concentrated parameter grid, the model calculation efficiency can be improved, and the calculation amount is reduced.
Further, the step S6 specifically includes:
s601, calculating the flux guide of the air gap flux guide grid unit according to the air gap magnetic circuit:
wherein G is Re "is the flux guide of the air gap flux guide grid unit; w (w) Re "is the length of the flux path of the air-gap flux-guide grid cell in the air-gap magnetic circuit; mu (mu) Re "is the magnetic permeability of the air gap flux guide grid unit in the air gap magnetic circuit; h is a Re "is the width of the flux path cross section of the air-gap flux-guiding grid cell in the air-gap magnetic circuit; l (L) Re "is the length of the magnetic flux path cross section of the air gap flux guide grid unit in the air gap magnetic circuit;
s602, performing air gap modeling on an air gap magnetic circuit in a motor motion process according to the flux guide of the air gap flux guide grid unit to obtain an air gap modeling result:
wherein G is N Modeling results for air gap movement; g n,R Radial flux guides connected with grid nodes at the lower right side when the air gap flux guide grid units are overlapped due to the movement of the air gap flux guide grid units; g n,L Radial flux guides connected with grid nodes at the lower left side when the air gap flux guide grid units are overlapped due to the movement of the air gap flux guide grid units; beta is the ratio of the remainder of the rotation angle of the motor rotor and 2 pi to the interval angle between the divided air gap flux guide grid units, and represents the actual overlapping degree of adjacent units; g n The radial flux guide value of the upper half part of the air gap flux guide grid unit in the flux guide of the air gap flux guide grid unit is; θ is the rotation angle of the motor rotor; delta theta is the air gap flux guiding unit interval angle; mod (·) is a remainder function.
The beneficial effects of the above-mentioned further scheme are: the air gap flux guide is a function of the rotor movement angle, and when the rotor movement angle is changed at will, the size of the flux guide is changed, so that the flux guide in a magnetic flux path is changed, and the air gap flux guide in the motor movement process can be obtained through an air gap modeling result; the node equation dimension can be reduced under the same simulation precision by continuously subdividing the flux guide units while the air gap unit nodes are not increased, so that the purpose of high-efficiency dynamic simulation analysis is achieved; the flux guiding units can be better processed to overlap, calculation errors caused by the overlapping of the flux guiding units can be effectively reduced when the number of grids is properly selected, and the simulation result of back electromotive force can be solved more accurately.
Further, the step S7 specifically includes:
s701, analyzing nodes of a motor magnetic network according to the motor rotor flux, the stator tooth flux, the stator yoke flux, the stator slot flux leakage, the stator tooth end flux and the air gap flux, and obtaining a motor magnetic network node algebraic equation set by using a Gaussian elimination method:
Wherein Λ is a motor magnetic network node algebraic equation set; g 1,n The magnetic flux guide is between the 1 st node position and the n th node position, and is a motor rotor magnetic flux guide or a motor stator magnetic flux guide or an air gap magnetic flux guide, wherein the motor stator magnetic flux guide comprises a stator tooth part magnetic flux guide, a stator yoke part magnetic flux guide, a stator slot magnetic flux guide and a stator tooth end part magnetic flux guide; g n,n A flux guide connected for the nth node position; u (U) n Magnetomotive force for the nth node position; f (F) n Flux generated for the excitation source at the nth node location; n is the number of nodes;
s702, obtaining the flux density of a flux guiding unit according to an algebraic equation set of a motor magnetic network node:
wherein B is the magnetic flux density of the magnetic conduction unit; g is magnetic conductance; u (U) i The magnetic potential of the grid node i; u (U) j The magnetic potential of the grid node j; s is the cross sectional area of the air gap flux guide grid unit between the grid node i and the grid node j;
s703, interpolating on a B-H curve of the ferromagnetic material according to the magnetic flux density of the magnetic conduction unit to obtain the magnetic conductivity of the iron core;
and S704, judging whether a termination condition is met according to the magnetic conductivity of the iron core, if so, obtaining a magnetic network model, completing the modeling of the magnetic network of the motor, otherwise, updating the magnetic conductivity of the motor rotor, the magnetic conductivity of the motor stator tooth part, the magnetic conductivity of the motor stator yoke part, the magnetic conductivity of the motor stator slot leakage and the magnetic conductivity of the stator tooth end part to values of the magnetic conductivity of the iron core, and returning to the step S4.
The beneficial effects of the above-mentioned further scheme are: and establishing an algebraic equation set of the motor magnetic network node, preparing for calculating the magnetic permeability of the iron core, and finishing updating of the magnetic permeability, thereby realizing modeling of the motor magnetic network.
Further, the termination condition in step S704 is that the error of the result of two continuous core permeability calculation is less than 5%, and the expression of the error of the result of core permeability calculation is:
wherein Lu is the error of the calculation result of the magnetic permeability of the iron core;is the magnetic conductivity of the iron core; />The magnetic permeability of the iron core is the last step.
The beneficial effects of the above-mentioned further scheme are: the nonlinear factor of motor magnetic saturation is considered, and the magnetic conductivity of the rotor core under different magnetic flux densities can be better simulated by calculating the error of the magnetic conductivity calculation result of the iron core.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a concentrated parameter flux guiding unit according to an embodiment of the invention.
Fig. 3 is a schematic diagram of a cross-shaped grid magnetically permeable unit according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of motor stator and rotor magnetic network unit division in the embodiment of the invention.
FIG. 5 is a schematic diagram of a division of a CS-M grid air gap flux guide unit for an inter-rotor air gap of a motor in accordance with an embodiment of the present invention.
Fig. 6 is a schematic diagram of magnetic flux guides of a motor rotor according to an embodiment of the present invention, wherein the magnetic paths of the motor rotor are divided into different shapes.
FIG. 7 is a schematic diagram of a method for modeling air gap movement based on grid cells and a flux guide in an embodiment of the invention.
FIG. 8 is a diagram of a full-step dynamic mesh motion modeling method and a flux guide according to an embodiment of the present invention.
FIG. 9 is a diagram of a moving grid modeling method and magnetic flux guide for node scalar magnetic potential interpolation in an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
As shown in fig. 1, in one embodiment of the present invention, a method for modeling a dynamic magnetic network of an electric machine includes the steps of:
s1, establishing a finite element model of a motor, and simulating according to the finite element model of the motor to obtain a stator magnetic flux density distribution diagram and a rotor magnetic flux density distribution diagram;
S2, establishing a motor rotor magnetic circuit by adopting a cross grid unit according to a rotor magnetic flux density distribution diagram to obtain the motor rotor magnetic circuit;
s3, respectively establishing a motor stator tooth magnetic circuit, a motor stator yoke magnetic circuit and a motor stator slot leakage magnetic circuit by adopting a concentrated parameter method according to a stator magnetic flux density distribution diagram, and establishing a motor stator tooth end magnetic circuit by adopting a cross grid unit;
s4, calculating the magnetic conductance of the motor rotor, the magnetic conductance of the stator teeth, the magnetic conductance of the stator yoke, the magnetic conductance of the stator slots and the magnetic conductance of the stator teeth according to the magnetic circuit of the motor rotor, the magnetic circuit of the stator teeth of the motor, the magnetic circuit of the stator yoke, the magnetic circuit of the stator slots and the magnetic circuit of the stator teeth end parts of the motor;
s5, dividing an air gap region between a motor rotor and a motor stator by using a cross grid unit according to a finite element model of the motor to obtain an air gap magnetic circuit;
s6, performing air gap modeling in the motor motion process according to the air gap magnetic circuit to obtain an air gap modeling result;
and S7, analyzing nodes of the motor magnetic network according to the motor rotor flux guide, the stator tooth part flux guide, the stator yoke part flux guide, the stator slot flux guide, the stator tooth end part flux guide and the air gap modeling result, obtaining a motor magnetic network node algebraic equation set by using a Gaussian elimination method, obtaining a magnetic network model according to the motor magnetic network node algebraic equation set, and completing motor magnetic network modeling.
In this embodiment, the technical problems to be solved by the present invention are as follows: processing the flux guiding unit overlapping process; partial simulation static state is lost when the rotating speed is low; the simulation results such as the solved counter electromotive force and the like have lower precision due to difficult counter electromotive force solution or higher high-frequency motion modeling errors; if the modeling precision of the motor air gap is improved, the nodes of the grid are necessarily increased, and the dimension of the node equation set is increased, so that the calculated amount is increased.
The cross-shaped grid unit in the step S2 is a grid unit formed by cross-shaped connection of two radial magnetic permeabilities and two tangential magnetic permeabilities to one point.
As shown in fig. 3 and 6, in the step S4, there are three cases of the rotor flux and the stator tooth end flux:
the first case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are cuboid, and then the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
wherein G is Re_1 The magnetic conductance of the motor rotor when the cross grid unit is cuboid represents the radial magnetic conductance or tangential magnetic conductance in the cuboid cross grid unit; g Re_2 The stator tooth end magnetic conductance when the cross grid unit is cuboid represents radial magnetic conductance or tangential magnetic conductance in the cuboid cross grid unit; w (w) Re The length of the magnetic flux path of the rectangular cross grid unit in the magnetic circuit of the motor rotor; mu (mu) Re For electric motor rotorsMagnetic permeability of (2); h is a Re The magnetic flux path section of the rectangular cross grid unit in the motor rotor magnetic circuit is wide; l (L) Re The magnetic flux path section of the rectangular cross grid unit in the motor rotor magnetic circuit is long; w (w) Re ' is the length of the magnetic flux path of the cuboid cross-shaped grid unit in the stator tooth end magnetic circuit; mu (mu) Re ' is the magnetic permeability of the stator tooth end; h is a Re ' is the width of the magnetic flux path section of the cuboid cross-shaped grid unit in the stator tooth end magnetic circuit; l (L) Re ' is the length of the magnetic flux path section of the cuboid cross-shaped grid unit in the stator tooth end magnetic circuit;
the second case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are trapezoidal bodies, so that the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
wherein G is Tr,t_1 When the cross grid unit is a trapezoid body, tangential flux in the flux guide of the motor rotor; g Tr,t_2 When the cross grid unit is a trapezoid body, tangential flux in the flux at the end part of the stator tooth; g Tr,r_1 When the cross grid unit is a trapezoid body, radial flux in the flux guide of the motor rotor; g Tr,r_2 When the cross grid unit is a trapezoid body, radial flux guide in the flux guide of the end part of the stator tooth; l (L) Tr The thickness of the trapezoid cross grid unit in the magnetic circuit of the motor rotor; mu (mu) Tr Is the magnetic permeability of the motor rotor; h is a Tr Is electric powerThe height of the trapezoid cross grid unit in the magnetic circuit of the machine rotor; w (w) Tr,2 The upper bottom of the trapezoid cross grid unit in the magnetic circuit of the motor rotor; w (w) Tr,1 Is the lower bottom of a trapezoid cross grid unit in a motor rotor magnetic circuit; l (L) Tr ' is the thickness of the trapezoidal cross grid unit in the magnetic circuit at the end part of the stator tooth; mu (mu) Tr ' is the magnetic permeability of the stator tooth end; h is a Tr ' is the height of the trapezoidal cross grid unit in the magnetic circuit at the end part of the stator teeth; w (w) Tr,2 ' is the upper bottom of a trapezoid cross grid unit in a magnetic circuit at the end part of the stator tooth; w (w) Tr,1 ' is the lower bottom of a trapezoid cross grid unit in the magnetic circuit at the end part of the stator teeth; ln is a logarithmic function with a base of natural constant; (. Cndot. -1 Is the inverse of the matrix;
the third case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are semi-cylindrical, and the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
G Se,r_1 ＝πL Se *μ Se
G Se,r_2 ＝πL Se '*μ Se '
wherein G is Se,t_1 When the cross grid unit is a semi-cylinder, tangential flux in the flux guide of the motor rotor; g Se,t_2 When the cross grid unit is a semi-cylinder, tangential flux guiding in the flux guiding of the end part of the stator tooth; g Se,r_1 When the cross grid unit is a semi-cylinder, radial flux in the flux guide of the motor rotor; g Se,r_2 When the cross grid unit is a semi-cylinder, radial flux guide in the flux guide of the end part of the stator tooth; r is the radius of a semi-cylindrical cross grid unit in a motor rotor magnetic circuit; mu (mu) Se Is the magnetic permeability of the motor rotor; l (L) Se Is a semi-cylindrical cross shape in a magnetic circuit of a motor rotorThe height of the grid cells; s is S y The cross section area of the side arc of the semi-cylindrical cross grid unit in the magnetic circuit of the motor rotor; y is a differential variable of a side arc of a semi-cylindrical cross grid unit in a motor rotor magnetic circuit; r' is the radius of the semi-cylindrical cross grid unit in the magnetic circuit of the end part of the stator tooth; mu (mu) Se ' is the magnetic permeability of the stator tooth end; l (L) Se ' is the height of the semi-cylindrical cross grid unit in the magnetic circuit of the end part of the stator tooth; s is S y' ' is the cross-sectional area of the side arc of the semi-cylindrical cross grid unit in the magnetic circuit of the end part of the stator tooth; y' is a differential variable of a side arc of a semi-cylindrical cross grid unit of the magnetic circuit at the end part of the stator tooth; d is the differential sign.
In this embodiment, as shown in fig. 4, the magnetic paths of the motor stator and rotor are first divided. Before dividing the magnetic circuit, a finite element model of the motor is established for simulation to obtain a distribution diagram of magnetic flux density of a stator and a rotor, and then the magnetic circuit of the motor stator and the rotor is divided according to the distribution diagram. The stator area is composed of stator teeth, stator teeth ends, stator yokes and stator slot leaks. The stator tooth part and the stator yoke part have single magnetic flux paths, the stator tooth part and the stator yoke part are modularized by using the concentrated parameter grid, and the node number is reduced while the precision is not influenced. The stator tooth end, the rotor and the air gap adopt a cross grid to model the magnetic circuit because of the complex structure and magnetic density distribution. Because the rotor, stator tooth ends and air gaps are complex in structure and magnetic circuit distribution, the flux guide is generally equivalent to three shapes when the flux guide is calculated: cuboid, trapezoid body, semi-cylinder.
In the step S4, the stator tooth flux guide, the stator yoke flux guide and the stator slot flux leakage flux guide are respectively:
wherein G is Re_1 ' is stator tooth flux guide; g Re_2 ' is stator yoke flux guide; g Re_3 ' is stator slot leakage flux guide; w (w) Re_1 ' is the length of the flux path of the concentrated parameter grid in the motor stator tooth magnetic circuit; mu (mu) Re_1 ' is the magnetic permeability of the motor stator teeth; h is a Re_1 ' is the width of the magnetic flux path cross section of the concentrated parameter grid in the motor stator tooth magnetic circuit; l (L) Re_1 ' is the length of the magnetic flux path cross section of the concentrated parameter grid in the motor stator tooth magnetic circuit; w (w) Re_2 ' is the length of the flux path of the concentrated parameter grid in the motor stator yoke magnetic circuit; mu (mu) Re_2 ' is the magnetic permeability of the motor stator yoke; h is a Re_2 ' is the width of the flux path cross section of the concentrated parameter grid in the motor stator yoke magnetic circuit; l (L) Re_2 ' is the length of the magnetic flux path cross section of the concentrated parameter grid in the magnetic circuit of the motor stator yoke; w (w) Re_3 ' is the length of the flux path of the concentrated parameter grid in the leakage magnetic circuit of the motor stator slot; mu (mu) Re_3 ' is the magnetic permeability of the motor stator slot leakage; h is a Re_3 ' is the width of the magnetic flux path section of the concentrated parameter grid in the leakage magnetic circuit of the motor stator slot; l (L) Re_3 ' is the length of the magnetic flux path cross section of the concentrated parameter grid in the leakage magnetic circuit of the motor stator slot.
As shown in fig. 2, in the present embodiment, since the central parameter grids divided in the stator tooth portion, the stator yoke portion, and the stator slot drain are equally rectangular, the flux guide may be calculated by using a flux guide calculation formula in a rectangular cross grid unit.
The step S6 specifically includes:
s601, calculating the flux guide of the air gap flux guide grid unit according to the air gap magnetic circuit:
wherein G is Re "is the flux guide of the air gap flux guide grid unit; w (w) Re Magnetic circuit being air gap flux guide grid unit in air gap magnetic circuitThe length of the diameter; mu (mu) Re "is the magnetic permeability of the air gap flux guide grid unit in the air gap magnetic circuit; h is a Re "is the width of the flux path cross section of the air-gap flux-guiding grid cell in the air-gap magnetic circuit; l (L) Re "is the length of the magnetic flux path cross section of the air gap flux guide grid unit in the air gap magnetic circuit;
s602, performing air gap modeling on an air gap magnetic circuit in a motor motion process according to the flux guide of the air gap flux guide grid unit to obtain an air gap modeling result:
wherein G is N Modeling results for air gap movement; g n,R Radial flux guides connected with grid nodes at the lower right side when the air gap flux guide grid units are overlapped due to the movement of the air gap flux guide grid units; g n,L Radial flux guides connected with grid nodes at the lower left side when the air gap flux guide grid units are overlapped due to the movement of the air gap flux guide grid units; beta is the ratio of the remainder of the rotation angle of the motor rotor and 2 pi to the interval angle between the divided air gap flux guide grid units, and represents the actual overlapping degree of adjacent units; g n The radial flux guide value of the upper half part of the air gap flux guide grid unit in the flux guide of the air gap flux guide grid unit is; θ is the rotation angle of the motor rotor; delta theta is the air gap flux guiding unit interval angle; mod (·) is a remainder function.
In this embodiment, the purpose of air gap modeling during motor movement of the air gap magnetic circuit is to simulate the change of flux guide in the air gap magnetic circuit caused by the change of relative positions of the stator and the rotor during motor movement. Because the motor movement can cause the change of the air gap flux, the air gap modeling in the motor movement process is to obtain the air gap flux when the rotor rotates to different positions, simulate the air gap magnetic circuit under the motor movement, establish the foundation for the magnetic network node equation of the subsequent air gap part, and obtain the corresponding more accurate air gap flux under the rotor rotation angle at each moment. The air gap magnetic circuit simulation under the motor motion is more accurate, and a foundation is established for a magnetic network node equation of a subsequent air gap part.
As shown in fig. 5 and 7, in this embodiment, the air gap area between the stator and the rotor of the motor is divided into a certain number of cross-shaped grid (CS-M) cell grids with the same size. Since the meshing in the air gap region is small enough and large enough, each mesh can be equivalent to a simple rectangular parallelepiped mesh, and then the radial and tangential permeabilities of each mesh cell can be calculated from the rectangular parallelepiped cross-shaped mesh cell calculation formula. After the flux guide of the air gap flux guide grid unit is calculated, the CS-M air gap flux guide grid unit is split, so that the radial air gap flux guide in the grid unit and the distance between the air gap flux guide grid units are in a relation. The air gap flux guide grid unit established in this way is equivalent to a local flux guide unit which does not change with the movement angle of the rotor. When the divided air gap mesh sizes are identical, the radial flux guide value of the CS-M mesh becomes a function of the rotor movement angle.
As shown in fig. 8 and 9, in the present embodiment, the main air gap motion modeling methods currently include a full-step moving grid motion modeling method and a node scalar magnetic potential interpolation moving grid modeling method. The whole-step moving grid motion modeling method is a local application of a magnetic resistance minimum method, and in the process of magnetic conduction unit motion overlapping, the magnetic conduction unit nodes closest to each other are connected. When the mesh size is exactly the same, it can be described as a function of rotor movement angle as shown in the following equation:
as can be seen from the formula, only when the rotor movement angle is greater than half of the interval angle of the flux guide unit, the stator and rotor nodes connected by the grid can be changed, and the whole-step moving grid movement modeling method is equivalent to a step-change flux guide when the rotor moves.
The dynamic grid modeling method of the node scalar magnetomotive force interpolation is to interpolate and calculate the adjacent node scalar magnetomotive forces of the stator and rotor motion surfaces according to the interval angle, and the method is shown in the following formula:
the dynamic grid modeling method of node scalar magnetic potential interpolation calculates the magnetic conductance to change along with the rotor motion, the magnetic conductance is maximum and the change rate is also maximum when the grid staggering is smaller, and the magnetic conductance is minimum and the change rate is also minimum when the upper grid and the lower grid are about to be completely staggered.
The step S7 specifically includes:
s701, analyzing nodes of a motor magnetic network according to the motor rotor flux, the stator tooth flux, the stator yoke flux, the stator slot flux leakage, the stator tooth end flux and the air gap flux, and obtaining a motor magnetic network node algebraic equation set by using a Gaussian elimination method:
wherein Λ is a motor magnetic network node algebraic equation set; g 1,n The magnetic flux guide is between the 1 st node position and the n th node position, and is a motor rotor magnetic flux guide or a motor stator magnetic flux guide or an air gap magnetic flux guide, wherein the motor stator magnetic flux guide comprises a stator tooth part magnetic flux guide, a stator yoke part magnetic flux guide, a stator slot magnetic flux guide and a stator tooth end part magnetic flux guide; g n,n A flux guide connected for the nth node position; u (U) n Magnetomotive force for the nth node position; f (F) n Flux generated for the excitation source at the nth node location; n is the number of nodes;
s702, obtaining the flux density of a flux guiding unit according to an algebraic equation set of a motor magnetic network node:
wherein B is the magnetic flux density of the magnetic conduction unit; g is magnetic conductance; u (U) i The magnetic potential of the grid node i; u (U) j Is netThe magnetic potential of lattice node j; s is the cross sectional area of the air gap flux guide grid unit between the grid node i and the grid node j;
s703, interpolating on a B-H curve of the ferromagnetic material according to the magnetic flux density of the magnetic conduction unit to obtain the magnetic conductivity of the iron core;
And S704, judging whether a termination condition is met according to the magnetic conductivity of the iron core, if so, obtaining a magnetic network model, completing the modeling of the magnetic network of the motor, otherwise, updating the magnetic conductivity of the motor rotor, the magnetic conductivity of the motor stator tooth part, the magnetic conductivity of the motor stator yoke part, the magnetic conductivity of the motor stator slot leakage and the magnetic conductivity of the stator tooth end part to values of the magnetic conductivity of the iron core, and returning to the step S4.
In this embodiment, the magnetic network model may be solved by using an electric field law, and the sum of the output fluxes and the sum of the input fluxes are zero as known from kirchhoff current law. Assuming that the air gap node is 120, a node algebraic equation is created by taking the first air gap node as an example, as shown in the following formula:
(-G st1 -G r1 -G 1,R -G 1,L -G t120 -G t2 )U air1 +G st1 U st1 +G r1 U ro1 +G t120 U air120 +G t2 U air2 ＝0
wherein G is st1 G is the radial flux guide of the stator teeth r1 Is the radial flux guide of an air gap; g 1,R ，G 1,L Calculating left and right radial magnetic permeabilities of the connecting air gap nodes for the air gap motion modeling method; g t120 ，G t2 Tangential permeabilities to the left and right of the first air gap node, respectively; u (U) air1 Magnetomotive force for a first air gap node; u (U) air120 Magnetomotive force of a node to the left of the first air gap node; u (U) air2 Magnetomotive force of a node to the right of an air gap node; u (U) st1 Magnetomotive force of a stator tooth node connected to the first air gap node; u (U) ro1 Magnetomotive force of the outer layer node of the rotor is connected for the first air gap node. Writing it in the form of a matrix:
In summary, node analysis is performed on the whole magnetic network of the motor to obtain a node algebraic equation set:
solving by using Gaussian elimination method. Since the motor is a dynamic simulation process, the nonlinear factor of magnetic saturation needs to be considered, so that the magnetic flux density of the flux guiding unit needs to be calculated, as shown in the following formula:
wherein B is the magnetic flux density of the magnetic conduction unit; g is magnetic conductance; u (U) i The magnetic potential of the grid node i; u (U) j The magnetic potential of the grid node j; s is the cross-sectional area of the air gap flux guiding grid cell between grid node i and grid node j.
After B is calculated, the magnetic permeability of the iron core can be obtained by interpolation on the B-H curve of the ferromagnetic materialEach time step adopts an iterative mode to iterate the permeability calculated by the time step to the permeability of the iron core with the last step. The end condition of the iterative process is that the core permeability converges within a set error range, which can be expressed as:
and stopping iteration if and only if the error of the continuous twice calculation results of all the nonlinear flux guiding units in the cyclic process is less than 5%, thereby calculating the saturation degree of different iron core areas of the stator and the rotor of the motor in the current state. And then the magnetic flux is returned to the magnetic flux calculating part to update the magnetic flux value so as to realize the dynamic change of the magnetic saturation degree of the magnetic network model. Programming the modeling flow through Matlab/Simulink, and then performing comparative analysis through the method, the whole-step long-moving grid motion modeling method and the moving grid modeling method of node scalar magnetic potential interpolation, as shown in fig. 7, 8 and 9, to verify the beneficial effects achieved by the proposed method.
The termination condition in step S704 is that the error of the result of two continuous core permeability calculation is less than 5%, and the expression of the result error of core permeability calculation is:
wherein Lu is the error of the calculation result of the magnetic permeability of the iron core;is the magnetic conductivity of the iron core; />The magnetic permeability of the iron core is the last step.
The beneficial effects of the invention are as follows:
(1) the rotor structure complexity of the permanent magnet synchronous motor is far greater than that of the rotor of the asynchronous motor, and the invention can achieve the purpose of high-efficiency dynamic simulation analysis under the same modeling precision when the flux guide grids are established at the air gaps.
(2) The method provided by the invention can calculate the air gap flux guide in the motor movement process, and the size of the air gap flux guide is changed when the rotor movement angle is changed randomly because the air gap flux guide is a function of the rotor movement angle, so that the flux guide in a magnetic flux path is changed.
(3) The method provided by the invention continues to subdivide the flux guide units while not increasing the air gap unit nodes, and divides the flux guide of one grid into two flux guides connected with the left node and the right node according to the actual overlapping degree of adjacent units, so that the node equation dimension can be reduced under the same simulation precision.
(4) The invention can better process the superposition of the flux guiding units, can effectively reduce the calculation error caused by the superposition of the flux guiding units when the grid quantity is properly selected, and is more accurate for solving the simulation result of the back electromotive force.

Claims (5)

1. The motor dynamic magnetic network modeling method is characterized by comprising the following steps of:
s1, establishing a finite element model of a motor, and simulating according to the finite element model of the motor to obtain a stator magnetic flux density distribution diagram and a rotor magnetic flux density distribution diagram;
s2, establishing a motor rotor magnetic circuit by adopting a cross grid unit according to a rotor magnetic flux density distribution diagram to obtain the motor rotor magnetic circuit;
s3, respectively establishing a motor stator tooth magnetic circuit, a motor stator yoke magnetic circuit and a motor stator slot leakage magnetic circuit by adopting a concentrated parameter method according to a stator magnetic flux density distribution diagram, and establishing a motor stator tooth end magnetic circuit by adopting a cross grid unit;
s4, calculating the magnetic conductance of the motor rotor, the magnetic conductance of the stator teeth, the magnetic conductance of the stator yoke, the magnetic conductance of the stator slots and the magnetic conductance of the stator teeth according to the magnetic circuit of the motor rotor, the magnetic circuit of the stator teeth of the motor, the magnetic circuit of the stator yoke, the magnetic circuit of the stator slots and the magnetic circuit of the stator teeth end parts of the motor;
s5, dividing an air gap region between a motor rotor and a motor stator by using a cross grid unit according to a finite element model of the motor to obtain an air gap magnetic circuit;
s6, performing air gap modeling in the motor motion process according to the air gap magnetic circuit to obtain an air gap modeling result; the step S6 specifically includes:
S601, calculating the flux guide of the air gap flux guide grid unit according to the air gap magnetic circuit:
wherein G is Re "is the flux guide of the air gap flux guide grid unit; w (w) Re "is the length of the flux path of the air-gap flux-guide grid cell in the air-gap magnetic circuit; mu (mu) Re "is the magnetic permeability of the air gap flux guide grid unit in the air gap magnetic circuit; h is a Re Grid sheet for air gap flux guide in air gap magnetic circuitThe width of the flux path cross section of the element; l (L) Re "is the length of the magnetic flux path cross section of the air gap flux guide grid unit in the air gap magnetic circuit;
s602, performing air gap modeling on an air gap magnetic circuit in a motor motion process according to the flux guide of the air gap flux guide grid unit to obtain an air gap modeling result:
wherein G is N Modeling results for air gap movement; g n,R Radial flux guides connected with grid nodes at the lower right side when the air gap flux guide grid units are overlapped due to the movement of the air gap flux guide grid units; g n,L Radial flux guides connected with grid nodes at the lower left side when the air gap flux guide grid units are overlapped due to the movement of the air gap flux guide grid units; beta is the ratio of the remainder of the rotation angle of the motor rotor and 2 pi to the interval angle between the divided air gap flux guide grid units, and represents the actual overlapping degree of adjacent units; g n The radial flux guide value of the upper half part of the air gap flux guide grid unit in the flux guide of the air gap flux guide grid unit is; θ is the rotation angle of the motor rotor; delta theta is the air gap flux guiding unit interval angle; mod (Ω) is a remainder function;
S7, analyzing nodes of a motor magnetic network according to motor rotor flux, stator tooth flux, stator yoke flux, stator slot flux leakage, stator tooth end flux and air gap modeling results, obtaining a motor magnetic network node algebraic equation set by using a Gaussian elimination method, obtaining a magnetic network model according to the motor magnetic network node algebraic equation set, and completing motor magnetic network modeling; the step S7 specifically includes:
s701, analyzing nodes of a motor magnetic network according to the motor rotor flux, the stator tooth flux, the stator yoke flux, the stator slot flux leakage, the stator tooth end flux and the air gap flux, and obtaining a motor magnetic network node algebraic equation set by using a Gaussian elimination method:
wherein Λ is a motor magnetic network node algebraic equation set; g 1,n The magnetic flux guide is between the 1 st node position and the n th node position, and is a motor rotor magnetic flux guide or a motor stator magnetic flux guide or an air gap magnetic flux guide, wherein the motor stator magnetic flux guide comprises a stator tooth part magnetic flux guide, a stator yoke part magnetic flux guide, a stator slot magnetic flux guide and a stator tooth end part magnetic flux guide; g n,n A flux guide connected for the nth node position; u (U) n Magnetomotive force for the nth node position; f (F) n Flux generated for the excitation source at the nth node location; n is the number of nodes;
S702, obtaining the flux density of a flux guiding unit according to an algebraic equation set of a motor magnetic network node:
wherein B is the magnetic flux density of the magnetic conduction unit; g is magnetic conductance; u (U) i The magnetic potential of the grid node i; u (U) j The magnetic potential of the grid node j; s is the cross sectional area of the air gap flux guide grid unit between the grid node i and the grid node j;
s703, interpolating on a B-H curve of the ferromagnetic material according to the magnetic flux density of the magnetic conduction unit to obtain the magnetic conductivity of the iron core;
and S704, judging whether a termination condition is met according to the magnetic conductivity of the iron core, if so, obtaining a magnetic network model, completing the modeling of the magnetic network of the motor, otherwise, updating the magnetic conductivity of the motor rotor, the magnetic conductivity of the motor stator tooth part, the magnetic conductivity of the motor stator yoke part, the magnetic conductivity of the motor stator slot leakage and the magnetic conductivity of the stator tooth end part to values of the magnetic conductivity of the iron core, and returning to the step S4.
2. The method of modeling a dynamic magnetic network of an electric motor according to claim 1, wherein the cross-shaped grid cell in step S2 is a grid cell formed by two radial flux guides and two tangential flux guides cross-connected to a point.
3. The method of modeling a dynamic magnetic network of a motor according to claim 1, wherein in the step S4, there are three cases of the rotor flux and the stator tooth end flux:
The first case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are cuboid, and then the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
wherein G is Re_1 The magnetic conductance of the motor rotor when the cross grid unit is cuboid represents the radial magnetic conductance or tangential magnetic conductance in the cuboid cross grid unit; g Re_2 The stator tooth end magnetic conductance when the cross grid unit is cuboid represents radial magnetic conductance or tangential magnetic conductance in the cuboid cross grid unit; w (w) Re The length of the magnetic flux path of the rectangular cross grid unit in the magnetic circuit of the motor rotor; mu (mu) Re Is the magnetic permeability of the motor rotor; h is a Re The magnetic flux path section of the rectangular cross grid unit in the motor rotor magnetic circuit is wide; l (L) Re The magnetic flux path section of the rectangular cross grid unit in the motor rotor magnetic circuit is long; w (w) Re ' is the length of the magnetic flux path of the cuboid cross-shaped grid unit in the stator tooth end magnetic circuit; mu (mu) Re ' is the magnetic permeability of the stator tooth end; h is a Re ' is the width of the magnetic flux path section of the cuboid cross-shaped grid unit in the stator tooth end magnetic circuit; l (L) Re ' magnetic flux path section for rectangular cross grid unit in stator tooth end magnetic circuit The length of the face;
the second case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are trapezoidal bodies, so that the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
wherein G is Tr,t_1 When the cross grid unit is a trapezoid body, tangential flux in the flux guide of the motor rotor; g Tr,t_2 When the cross grid unit is a trapezoid body, tangential flux in the flux at the end part of the stator tooth; g Tr,r_1 When the cross grid unit is a trapezoid body, radial flux in the flux guide of the motor rotor; g Tr,r_2 When the cross grid unit is a trapezoid body, radial flux guide in the flux guide of the end part of the stator tooth; l (L) Tr The thickness of the trapezoid cross grid unit in the magnetic circuit of the motor rotor; mu (mu) Tr Is the magnetic permeability of the motor rotor; h is a Tr Is the height of a trapezoid cross grid unit in a motor rotor magnetic circuit; w (w) Tr,2 The upper bottom of the trapezoid cross grid unit in the magnetic circuit of the motor rotor; w (w) Tr,1 Is the lower bottom of a trapezoid cross grid unit in a motor rotor magnetic circuit; l (L) Tr ' is the thickness of the trapezoidal cross grid unit in the magnetic circuit at the end part of the stator tooth; mu (mu) Tr ' is the magnetic permeability of the stator tooth end; h is a Tr ' trapezoidal cross grid list in magnetic circuit at end part of stator toothThe meta is high; w (w) Tr,2 ' is the upper bottom of a trapezoid cross grid unit in a magnetic circuit at the end part of the stator tooth; w (w) Tr,1 ' is the lower bottom of a trapezoid cross grid unit in the magnetic circuit at the end part of the stator teeth; ln is a logarithmic function with a base of natural constant; (omega) -1 Is the inverse of the matrix;
the third case is: the cross grid units in the motor rotor magnetic circuit and the stator tooth end magnetic circuit are semi-cylindrical, and the motor rotor magnetic conductance and the stator tooth end magnetic conductance are respectively:
G Se,r_1 ＝πL Se *μ Se
G Se,r_2 ＝πL Se '*μ Se '
wherein G is Se,t_1 When the cross grid unit is a semi-cylinder, tangential flux in the flux guide of the motor rotor; g Se,t_2 When the cross grid unit is a semi-cylinder, tangential flux guiding in the flux guiding of the end part of the stator tooth; g Se,r_1 When the cross grid unit is a semi-cylinder, radial flux in the flux guide of the motor rotor; g Se,r_2 When the cross grid unit is a semi-cylinder, radial flux guide in the flux guide of the end part of the stator tooth; r is the radius of a semi-cylindrical cross grid unit in a motor rotor magnetic circuit; mu (mu) Se Is the magnetic permeability of the motor rotor; l (L) Se Is the height of a semi-cylindrical cross grid unit in a motor rotor magnetic circuit; s is S y The cross section area of the side arc of the semi-cylindrical cross grid unit in the magnetic circuit of the motor rotor; y is a differential variable of a side arc of a semi-cylindrical cross grid unit in a motor rotor magnetic circuit; r' is the radius of the semi-cylindrical cross grid unit in the magnetic circuit of the end part of the stator tooth; mu (mu) Se ' is the magnetic permeability of the stator tooth end; l (L) Se ' as stator teethThe height of the semi-cylindrical cross grid unit in the end magnetic circuit; s is S y’ ' is the cross-sectional area of the side arc of the semi-cylindrical cross grid unit in the magnetic circuit of the end part of the stator tooth; y' is a differential variable of a side arc of a semi-cylindrical cross grid unit of the magnetic circuit at the end part of the stator tooth; d is the differential sign.
4. The method of modeling a dynamic magnetic network of an electric machine according to claim 1, wherein the stator tooth flux guide, the stator yoke flux guide and the stator slot flux guide in step S4 are respectively:
wherein G is Re_1 ' is stator tooth flux guide; g Re_2 ' is stator yoke flux guide; g Re_3 ' is stator slot leakage flux guide; w (w) Re_1 ' is the length of the flux path of the concentrated parameter grid in the motor stator tooth magnetic circuit; mu (mu) Re_1 ' is the magnetic permeability of the motor stator teeth; h is a Re_1 ' is the width of the magnetic flux path cross section of the concentrated parameter grid in the motor stator tooth magnetic circuit; l (L) Re_1 ' is the length of the magnetic flux path cross section of the concentrated parameter grid in the motor stator tooth magnetic circuit; w (w) Re_2 ' is the length of the flux path of the concentrated parameter grid in the motor stator yoke magnetic circuit; mu (mu) Re_2 ' is the magnetic permeability of the motor stator yoke; h is a Re_2 ' is the width of the flux path cross section of the concentrated parameter grid in the motor stator yoke magnetic circuit; l (L) Re_2 ' is the length of the magnetic flux path cross section of the concentrated parameter grid in the magnetic circuit of the motor stator yoke; w (w) Re_3 ' as a collection in leakage magnetic circuit of stator slot of motorThe length of the flux path of the medium parameter grid; mu (mu) Re_3 ' is the magnetic permeability of the motor stator slot leakage; h is a Re_3 ' is the width of the magnetic flux path section of the concentrated parameter grid in the leakage magnetic circuit of the motor stator slot; l (L) Re_3 ' is the length of the magnetic flux path cross section of the concentrated parameter grid in the leakage magnetic circuit of the motor stator slot.
5. The method of modeling a dynamic magnetic network of a motor according to claim 1, wherein the termination condition in step S704 is that the error of the core permeability calculation result is less than 5% in two consecutive times, and the expression of the core permeability calculation result error is:
wherein Lu is the error of the calculation result of the magnetic permeability of the iron core;is the magnetic conductivity of the iron core; />The magnetic permeability of the iron core is the last step.
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