CN115842496A - High-precision magnetic network modeling method suitable for hybrid stator permanent magnet vernier motor - Google Patents
High-precision magnetic network modeling method suitable for hybrid stator permanent magnet vernier motor Download PDFInfo
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Abstract
The invention discloses a high-precision magnetic network modeling method suitable for a hybrid stator permanent magnet vernier motor, which realizes the balance of model calculation time and calculation precision by adopting a method of combining an equivalent magnetic circuit model and a reluctance network model. For areas with complex magnetic flux distribution, such as air gaps and modulation tooth areas, a magnetoresistive network method is adopted for modeling, and modeling precision and dynamic analysis efficiency are improved. The mixed medium grid is introduced, the applicability of the model to motors with different topological structures is improved, the modeling difficulty and the workload are greatly reduced, the problem of irregular connection of a stator and an air gap node caused by transient simulation is avoided, and the simulation error is effectively reduced. And the magnetic conductivity is updated by adopting a cubic spline interpolation method, so that the iteration speed is accelerated, and the magnetic conductivity updating precision is improved. An orthogonal decomposition model and a harmonic decomposition method are introduced, the stator core loss is obtained through superposition, and the calculation error of a classical loss separation model is reduced.
Description
Technical Field
The invention relates to a high-precision magnetic network modeling method suitable for a hybrid stator permanent magnet vernier motor, and belongs to the field of electromagnetic field calculation.
Background
Due to the characteristics of low speed and large torque of the permanent magnet vernier motor, the permanent magnet vernier motor is widely applied to the fields of wind power generation, electric vehicles, ship propulsion and the like. Compared with the traditional permanent magnet vernier motor, the hybrid stator permanent magnet vernier motor has the advantages that multiple low-order harmonics are introduced into an air gap, so that the power factor of the motor is remarkably improved, and in addition, the design of multiple harmonics is favorable for increasing no-load counter electromotive force, so that the output torque of the motor is improved. By optimizing the thickness of the permanent magnet, the width of the armature teeth, the height of the modulation teeth and the pole arc coefficient of the permanent magnet, the output torque and the power factor of the motor can be effectively improved. In order to further research and analyze the efficiency of the motor, based on the magnetization mode of ferromagnetic materials, an orthogonal decomposition model is adopted, the rotating magnetization is equivalent to two alternating magnetic fields of radial direction and tangential direction, and according to a harmonic decomposition theory, a more accurate stator core loss result is obtained through superposition.
Finite Element Method (FEM) is commonly used for analyzing motor magnetic field due to its advantages of simple usage, strong versatility and high precision. However, due to the complex topological structure and magnetic field distribution of the permanent magnet vernier motor, very fine mesh subdivision is needed during finite element simulation, the solving process is very time-consuming, and in addition, the requirement on computer performance is very strict when the huge mesh scale is processed. The equivalent magnetic network method has the advantages of simple principle, small calculated amount, high simulation efficiency and high precision, can quickly analyze the electromagnetic characteristics of the motor, and is widely applied to the initial stage of various motor designs.
Disclosure of Invention
The invention aims to provide a high-precision magnetic network modeling method suitable for a magnetic field of a hybrid stator permanent magnet vernier motor, which mainly comprises an improved modeling method of a motor air gap and a modulation tooth region and a solving algorithm of a model. And combining the orthogonal decomposition model and the harmonic decomposition method with the constructed magnetic network model for accurately calculating the stator core loss.
In order to realize the purpose, the invention adopts the technical scheme that: a high-precision magnetic network modeling method suitable for a hybrid stator permanent magnet vernier motor comprises the following steps:
step 4, solving a nonlinear equation set by adopting a node magnetic potential method to obtain node magnetic potential and magnetic flux of each magnetic conductance unit, and further solving the magnetic density and the magnetic permeability of each magnetic conductance unit;
Further, the hybrid stator permanent magnet vernier motor is a five-phase motor with 20 slots/46 poles, and comprises a rotor, a stator and an air gap; the rotor is cylindrical, the permanent magnet body is attached to the inner wall of the rotor, the rare earth neodymium iron boron material and the radial magnetizing mode are adopted, NS poles are alternately arranged in the circumferential direction, the pole arc coefficient is set to be 0.86, the high power factor and the large torque output are obtained, meanwhile, the using amount of the permanent magnet is saved, the permanent magnet flux leakage is reduced, and the installation difficulty of the permanent magnet is reduced; the stator comprises modulation teeth, stator teeth, an armature winding and a yoke part, wherein the stator teeth are formed by staggered arrangement of the armature teeth and fault-tolerant teeth and respectively adopt a split tooth structure and a slotted structure, and the armature winding is designed as a fractional slot concentrated winding; the rotor and the stator are both made of silicon steel sheets DW465_50; the air gap is located between the stator and the rotor, has the thickness of 0.5mm, and is the main field for magnetic field energy exchange.
Further, in the step 1, since the magnetic field distribution of the rotor yoke, the stator pole shoe, the stator teeth and the stator yoke is uniform, and the magnetic lines of force are ordered, the rotor yoke, the stator pole shoe, the stator teeth and the stator yoke can be equivalent to a unidirectional magnetic conductance unit according to the magnetic flux path; the rotor yoke is evenly divided into corresponding magnetic conductance units according to the number of the permanent magnets, and the cross section of each unit is in a fan shape; the stator pole shoe is divided into two magnetic conductance units which are symmetrical about the center line of the armature tooth according to the flow direction of magnetic flux, and the section of each unit is approximately in a right-angle trapezoid shape; the section of the stator tooth magnetic conduction unit is rectangular; the stator yoke is uniformly divided into corresponding magnetic conductance units according to the number of stator teeth, and the section of each unit is in a fan shape; the permanent magnet is equivalent to a magnetic conductance and magnetomotive force series structure; according to the law of full current, the energized winding is equivalent to an armature magnetomotive force source and is connected with the armature tooth flux guide in series.
In the step 2, the hybrid stator permanent magnet vernier motor adopts a stator structure combining slotting and split teeth, compared with the traditional permanent magnet vernier motor, multi-order harmonics are introduced into an air gap and are influenced by permanent magnet leakage flux and tooth tip leakage flux, the magnetic field distribution of the air gap and a modulation tooth area is particularly complex, the magnetic force line distribution and the iron core saturation degree are comprehensively considered, and a magnetoresistive network method is adopted to model the air gap and the modulation tooth area. The air gap model is similar to the finite element grid generation method and comprises a large number of cross-shaped grid units, wherein the number of the air gap grid units is 1840 and is a common multiple of the number of poles and the number of grooves so as to provide enough modeling precision. All grid units have the same size and the determined air gap magnetic conductance, and only the change of the node connection relation between the air gap and the stator needs to be considered, so that the efficiency of dynamic analysis of the model is improved, the complex magnetic conductance boundary determination and magnetic conductance calculation of an equivalent magnetic circuit method are avoided, the defect that the tangential magnetic flux cannot be considered in the equivalent magnetic circuit method is overcome, and the model precision is further improved.
Under the influence of the topological structure of the motor, the air gap and the grid of the modulation tooth area are overlapped, and better connectivity is lacked. By introducing the mixed medium grid, the modulation tooth area can be divided into grid units with the same size along the circumferential direction, so that the node connection relation of the stator and the air gap is determined, the problem of irregular connection of the two nodes caused by transient simulation is solved, simulation errors are reduced, and in addition, the universality of an equivalent magnetic network model is enhanced by applying the mixed medium grid, so that the optimal design of the motor is facilitated.
Further, in the step 4, consideration is given toMatlab has the advantage of calculating a large-scale matrix, and a magnetic conductance matrix equation is solved in Matlab by adopting a node magnetomotive method: f = G -1 Φ, where F is the magnetomotive matrix, G is the permeance matrix, and Φ is the magnetic flux matrix. And carrying out nonlinear iteration by adopting a Newton iteration method, wherein the magnetic flux density B is an iteration variable, and in order to accelerate the iteration convergence speed, the magnetic flux density B is corrected as follows: b is co ＝aB (k-1) +(1-a)B (k) Wherein B is co Correction value for the k-th iteration magnetic flux density, B (k-1) The magnetic density of the k-1 iteration, B (k) The magnetic density of the kth iteration is, a is a relaxation factor and is set to be 0.5; after all node magnetic potentials of the model are obtained, the magnetic density B of each magnetic conduction unit can pass through B = delta F ele ·G ele /S ele Is calculated as where Δ F ele Is the magnetic potential drop of the magnetic conductance unit, G ele Is a flux guide of a flux guide unit, S ele Effective sectional area of the magnetic conduction unit; the magnetic permeability is obtained by inquiring a B-H curve, and because the number of discrete sample points in the magnetization curve directly influences the calculation precision of the magnetic permeability, a cubic spline interpolation method is introduced to improve the smoothness of the B-H curve, so that the calculation precision of the magnetic permeability is improved, and the iterative convergence speed is further improved.
In the formula, H ele And u new Magnetic field strength and magnetic permeability of the updated magnetically conductive element respectively, (H) n ,B n ) And (H) n+1 ,B n+1 ) Two adjacent sample points on the B-H curve.
Further, in the step 5, the magnetic permeability of each magnetic permeability unit is updated according to a cubic spline interpolation method, and a magnetic permeability matrix is recalculated; considering that a ferromagnetic material has two magnetization modes of alternating magnetization and rotating magnetization, in order to calculate the stator core loss more accurately, an orthogonal decomposition model is adopted, the rotating magnetization is regarded as two alternating magnetic fields in the radial direction and the tangential direction, and the core losses generated by the harmonic waves in the radial direction and the tangential direction are superposed to obtain the stator core loss according to a harmonic wave decomposition theory, so that the error of a classical loss separation model is reduced.
The invention has the following beneficial effects:
1. the method combines the equivalent magnetic circuit model and the reluctance network model, and models the magnetic flux distribution regular region by the equivalent magnetic circuit method, thereby greatly reducing the node number of the equivalent magnetic network model, reducing the calculation time and improving the analysis efficiency of the model. In addition, the reluctance network method fully considers the local magnetic saturation of the stator core, the magnetic leakage of the permanent magnet and the magnetic leakage of the modulated tooth tip, and effectively improves the model precision.
2. According to the invention, by introducing the mixed medium grid into the modulation tooth region, the region can be divided into grid units with the same size along the circumferential direction, the universality of an equivalent magnetic network model is improved, and the method has good portability for permanent magnet vernier motors with different modulation tooth structures. In addition, the application of the mixed medium grid also determines the node connection relation between the stator and the air gap, thereby avoiding the problem of irregular connection of the two nodes caused by transient simulation and reducing simulation errors.
3. The air gap area adopts the cross grid subdivision, thereby avoiding the complex magnetic conductance boundary determination and magnetic conductance calculation of an equivalent magnetic circuit method. In addition, because the grid cells in the air gap have the same geometric size, the air gap flux guide does not change along with the change of the position of the rotor, and the dynamic analysis of the model can be realized only by changing the node connection relation between the air gap and the stator.
4. The magnetic conductance units divided in the model are in fan-shaped, trapezoidal and rectangular regular shapes, the magnetic conductance calculation formula is simple, and the requirement on simplified treatment of a complex magnetic field is met.
5. The magnetic conductance of ferromagnetic material is updated generally by adopting a linear interpolation method, the number of discrete samples in a magnetization curve directly influences the update precision of the magnetic conductance, and when a motor is supersaturated, iteration by adopting the linear interpolation method is difficult to converge and oscillation easily occurs. The cubic spline interpolation method inserts a cubic function between adjacent B values, so that the smoothness of a B-H curve is improved, the iterative oscillation frequency can be effectively improved, the iterative convergence speed is accelerated, and the updating precision of the magnetic conductivity is improved.
Drawings
Fig. 1 (a) is a topological structure of a hybrid stator permanent magnet vernier motor according to an embodiment of the present invention;
fig. 1 (b) is a dimension label of a hybrid stator permanent magnet vernier motor according to an embodiment of the present invention;
FIG. 2 is a magnetic flux distribution rule area equivalent magnetic network model according to an embodiment of the present invention;
FIG. 3 is an equivalent magnetic network model of the air gap and modulated tooth regions of an embodiment of the present invention;
FIG. 4 is a mixed media grid cell employed in an embodiment of the present invention;
FIG. 5 is a flowchart of an iterative process according to an embodiment of the present invention;
FIG. 6 (a) shows the distribution of three positions of stator cores A, B and C;
FIG. 6 (b) is a magnetic flux density waveform of the stator core at different positions;
FIG. 6 (c) is a stator pole shoe equivalent magnetic network improved model;
FIG. 6 (d) is a comparison of simulation results for a stator core loss separation model and a stator core loss improvement model;
FIG. 7 (a) is a five-phase no-load flux linkage simulation waveform;
FIG. 7 (b) is a five-phase load flux linkage simulation waveform;
FIG. 7 (c) is an air gap flux density simulation waveform;
FIG. 7 (d) is a frequency domain decomposition of air gap flux density;
FIG. 7 (e) is an electromagnetic torque simulation waveform;
FIG. 7 (f) is a simulated waveform of average torque as a function of current;
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
In order to be able to illustrate the advantages of the present invention more briefly, the following detailed description is made in conjunction with a specific hybrid stator permanent magnet vernier motor: fig. 1 (a) is a topological structure diagram of the motor, wherein 1 is a rotor, 2 is a surface-mounted permanent magnet, 3 is a modulation tooth, 4 is an armature tooth, 5 is a fault-tolerant tooth, 6 is a stator, and 7 is an armature winding; the embodiment of the invention is a five-phase motor with 20 slots/46 poles, which comprises a rotor, a stator and an air gap; the rotor is cylindrical, the permanent magnet body is attached to the inner wall of the rotor, the rare earth neodymium iron boron material and the radial magnetizing mode are adopted, NS poles are alternately arranged in the circumferential direction, the pole arc coefficient is set to be 0.86, the high power factor and the large torque output are obtained, meanwhile, the using amount of the permanent magnet is saved, the permanent magnet flux leakage is reduced, and the installation difficulty of the permanent magnet is reduced; the stator comprises modulation teeth, stator teeth, an armature winding and a yoke part, wherein the stator teeth are formed by staggered arrangement of the armature teeth and fault-tolerant teeth and respectively adopt a split tooth structure and a slotted structure, and the armature winding is designed as a fractional slot concentrated winding; the rotor and the stator are both made of silicon steel sheets DW465_50; the air gap is positioned between the stator and the rotor, has the thickness of 0.5mm, and is the main place for magnetic field energy exchange; fig. 1 (b) shows the dimensions of the motor.
FIG. 2 is a schematic diagram of a uniform magnetic field distribution region model according to an embodiment of the present invention; the rotor yoke part is uniformly divided into 46 magnetic conductance units according to the number of surface-mounted permanent magnets and the magnetization center line of the permanent magnets, and the sections of the magnetic conductance units are fan-shaped; the magnetic leakage conductance between the stator tooth grooves is extremely small and can be ignored; because the stator teeth have a regular topological structure and magnetic flux distribution, the stator teeth can be equivalent to a single magnetic conductance unit, and the section of the unit is rectangular; the stator yoke is uniformly divided into 20 magnetic conduction units according to the number of stator teeth and the central line of the stator teeth, and the sections of the magnetic conduction units are fan-shaped; the stator pole shoe is divided into two magnetic conductance units according to the flow direction of magnetic flux, the magnetic conductance units are symmetrical about the central line of the armature tooth, and the cross section of each unit is in a right-angled trapezoid shape; the magnetic conductance calculation formula of the rotor yoke portion is as follows:
in the formula, G ry To the rotor yoke permeance, N pm Number of permanent magnets, u 0 And u r Vacuum permeability and relative permeability, W ry Is the rotor yoke width, R ri Is the rotor inner diameter, h pm Is the permanent magnet height; stator tooth permeameterThe calculation formula is as follows:
in the formula, G st Is stator tooth flux guide, W st And W sy Width of stator teeth and stator yoke, L respectively d Is the axial length of the motor, R st Is the stator tooth radius; the stator yoke permeance calculation formula is:
in the formula, G sy To the stator yoke permeance, N slot Number of stator slots, R si Is the stator inner diameter; the calculation formula of the stator pole shoe magnetic conductance is as follows:
in the formula, G sh For stator pole shoe permeance, theta sho Radian, R, corresponding to the outside diameter of the pole shoe sho Is the outer diameter of the pole shoe, h 0 Height of pole shoe, h 1 Is the wedge height.
In the embodiment of the invention, the permanent magnet is equivalent to a magnetomotive force and magnetic conductance series structure, a large amount of permanent magnet leakage flux exists in an air gap in consideration of the multi-pole logarithm and surface-mounted permanent magnet structure of the permanent magnet vernier motor, and the air gap is divided by a large amount of cross-shaped grids, so that the interpolar leakage flux of the permanent magnet does not need to be considered independently, and the corresponding calculation formulas of the magnetomotive force and the magnetic conductance of the permanent magnet are as follows:
in the formula F pm Is a permanent magnet magnetomotive force, G pm Is a permanent magnet flux guide, B r Is remanence of permanent magnet, mu 0 Is a vacuum permeability, mu pm Is a permanent magnet phaseFor magnetic permeability, w pm And l pm The width and length of the permanent magnet respectively; the winding is designed as a fractional-slot concentrated winding, and according to a full current law, the line integral of a magnetic field intensity vector along any closed line is equal to the current algebraic sum of the enclosed areas of the closed loop lines; because the magnetic flux route that the circular telegram conductor produced all passes through on the armature tooth, consequently place equivalent magnetomotive force on the armature tooth, the direction is decided according to right hand spiral rule, and its size is:
in the formula, F s Is the winding magnetomotive force, H is the magnetic field strength, l is the magnetic flux closed path, N s I is the armature winding number of turns, i is the armature winding current.
And 2, establishing an equivalent magnetic network model of an air gap and a modulation tooth area.
In the embodiment of the invention, the schematic diagram of an equivalent magnetic network model of an air gap and a modulation tooth area is shown in fig. 3, in order to improve the air gap modeling precision, the air gap model adopts a grid generation method similar to a finite element to divide the air gap into a large number of cross-shaped grid units, and the grid division process strictly follows the following principle: (1) all the cross-shaped grid cells have the same size; (2) The number of the cross grid units is controlled within the range of 1500-2000; (3) The radial arrangement of the cross grid units does not exceed two layers, the grid units with the same size have determined air gap magnetic conductance, so that the complex magnetic conductance calculation caused by the influence of the position of a rotor is avoided, and meanwhile, the dynamic analysis of the motor can be quickly realized only by changing the node connection relation of the stator and the air gap; all grid units have the same size and determined air gap magnetic conductance, and only the change of the node connection relation between an air gap and a stator needs to be considered; the complex magnetic conductance boundary determination and magnetic conductance calculation of the equivalent magnetic circuit method are avoided, the defect that the tangential magnetic flux cannot be considered in the equivalent magnetic circuit method is overcome, and the model precision is further improved; when the number of the grid layers in the air gap exceeds two layers, the model precision is not obviously improved, therefore, in order to balance the time counting and the calculation precision of the model, the air gap is subdivided by adopting a single-layer cross-shaped grid unit, and the air gap magnetic conductance calculation formula is as follows:
in the formula G t_air And G r_air Air-gap tangential and radial permeance, N air Number of air gap grid cells, W air Is the air gap width, R so The outer diameter of the stator; in order to avoid sudden change of the connection relation between the stator and the air gap node caused by transient simulation of an equivalent magnetic network model, a mixed medium grid is introduced, and a modulation tooth area is divided into grid units with the same size along the circumferential direction, so that the connection relation between the stator and the air gap node is determined, and the aim of reducing simulation errors is fulfilled; the mixed medium grid unit is shown in fig. 4, and the corresponding magnetic conductance calculation formula is as follows:
where Gr and Gt are the radial and tangential permeances of the mixed-media grid cell, u i Is the magnetic permeability of the iron core, g is the height of the grid unit of the mixed medium, R is the inner diameter of the grid unit of the mixed medium, since u i >>u 0 Therefore, the flux guide formula of the mixed medium grid can be respectively simplified as follows:
And 3, constructing a complete magnetic network model.
The magnetic flux distribution rule area model, the air gap and the modulation tooth area model of the embodiment of the invention are connected through the air nodes to form a complete magnetic network model, and each node of the equivalent magnetic network model is numbered, wherein the total number of the nodes is 6668.
And 4, establishing and solving a magnetic conductance matrix equation.
Based on the similarity between the circuit and the magnetic circuit, the circuit analysis method, such as kirchhoff's voltage law and kirchhoff's current law, is also suitable for solving the equivalent magnetic network model, so as to simplify the magnetic circuit analysis, and the magnetic conductance matrix equation can be expressed as:
F＝G -1 ·Φ (10)
in the formula:
F＝[F(1),F(2),....,F(n)] T
Φ＝[Φ(1),Φ(2),....,Φ(n)] T
Based on the Matlab platform, the magnetic flux density between the node i and the node j can be calculated as:
in the formula, B new For new magnetic density values, F (i) and F (j) are the magnetic potentials of the node i and the node j respectively, G (i, j) is the magnetic conductance between the node i and the node j, and S ij Is the cross-sectional area of the grid cell between node i and node j, W ele Is the grid cell width; the magnetic conductance matrix equation (10) is a nonlinear equation, a newton iteration method is required for nonlinear iteration, in this embodiment, the magnetic flux density is used as an iteration variable, and the influence of the magnetic flux density calculation result in the previous iteration step on the magnetic flux density calculation result in the current iteration step is considered, and the iteration format is as follows:
B co ＝aB pre +(1-a)B new (12)
in the formula B pre The magnetic density value obtained in the previous iteration step; according to B co Updating magnetic conductivity, and adopting cubic spline interpolation for a B-H curve:
an iterative process flow diagram is shown in fig. 5.
And 5, applying the stator core loss improvement model.
And (5) reserving the magnetic permeability of the nonlinear magnetic guiding unit obtained in each iteration step in the step (4), recalculating the magnetic guiding matrix, performing the next iteration operation, presetting an error limit and iteration times in order to prevent the iteration from entering a dead loop, and once a stopping condition is met, namely B co The iteration ends when the following relationship is satisfied:
in the formula, B co (k+1) And B co (k) Respectively taking the magnetic flux density values after the k +1 th correction and the k-th correction, setting epsilon as an error limit to be 0.0001 to ensure that iteration is sufficiently converged, and if the inequality is true, entering the next rotor position by the equivalent magnetic network model and carrying out iteration operation again; the stator core loss and the rotor core loss of the motor obtained through finite element calculation are respectively 45W and 2W, and the stator core loss is far greater than the rotor core loss in numerical value, so that the prediction and analysis capability of the equivalent magnetic network model on the loss characteristic of the motor can be improved by adopting the stator core loss improvement model; because the change law and the amplitude size of the different regional position magnetic flux density of iron core are different, consequently, divide into stator core: four parts of a modulation tooth, a pole shoe, a stator tooth (armature tooth and fault-tolerant tooth) and a stator yoke; in addition, considering that the ferromagnetic material is influenced by the rotating magnetization, an orthogonal decomposition model is introduced, and the rotating magnetic field is regarded asTwo alternating magnetic fields, radial and tangential, are shown in fig. 6 (B), which is the magnetic flux density waveform of three points a, B, C on the stator core in fig. 6 (a) that change with time in an electrical period, it can be found that the radial magnetic density amplitude at the point a of the stator pole shoe is 0.63T, the tangential magnetic density amplitude is 0.99T, therefore, both alternating magnetization and rotating magnetization have influence on the stator pole shoe. The radial flux density amplitude at the point B of the armature teeth is 1.54T, and the tangential flux density amplitude is 0.01T, so that the magnetization mode of the armature teeth can be approximately regarded as alternating magnetization, and the influence of the rotating magnetization on the point can be ignored. The radial magnetic density amplitude at the point C of the fault-tolerant teeth is 1.07T, and the tangential magnetic density amplitude is 0.02T, so that the magnetization mode of the fault-tolerant teeth can be approximately alternate magnetization. Based on the analysis, an equivalent magnetic circuit method and a reluctance network method are respectively adopted for modeling the stator teeth and the stator pole shoes. Fig. 6 (c) shows an improved stator pole shoe model, in which the stator pole shoe is divided into three parts, and the magnetic conductance calculation formula corresponding to each part is as follows:
in the formula, G r_left And G t_right Radial and tangential permeance, G, of zone I respectively r_mid And G t_mid Radial and tangential permeance, R, of zone II shi And R sho Respectively the inner and outer diameters of the pole shoe, theta 1 Is the radian measure, theta, corresponding to the height in the region I 2 And theta 3 Respectively corresponding radians of the middle lower bottom and the upper bottom of the area II，h 0 Height of pole shoe, h 1 Is the slot wedge height; the magnetic flux density waveforms of all the regions are approximate to sine waves, but higher harmonics with different degrees exist, and according to the Fourier decomposition theory, any periodic function can be decomposed into superposition of a limited number of simple harmonic functions with different amplitudes and frequencies, and in addition, because the iron core is simultaneously influenced by the amplitude and the frequency of the magnetic density, the loss caused by the higher harmonics cannot be ignored; and superposing the iron core loss generated by each harmonic after decomposition to obtain the stator iron core loss, wherein based on the classical loss separation model, the stator iron core loss improvement model adopts the following formula:
in the formula, P fe Is the stator core loss density, K h 、K c And K e Hysteresis loss coefficient, eddy current loss coefficient and additional loss coefficient, f is motor frequency, k is harmonic order, B kr And B kt Radial flux density and tangential flux density amplitudes of the k-th harmonic respectively; comparing the stator core loss model and the finite element calculation results before and after improvement respectively in fig. 6 (d), it can be observed that the stator core loss improvement model calculation results are closer to the finite element calculation results, the calculation efficiency of the model is ensured on the premise of increasing less nodes and grid unit numbers, and meanwhile, the equivalent magnetic network model core loss calculation accuracy is remarkably improved.
And 7, comparing, analyzing and calculating errors among results.
To verify the accuracy of the modeling method of the embodiment of the present invention, fig. 7 (a) to 7 (f) are error comparisons of the equivalent magnetic network calculation result and the finite element calculation result.
Fig. 7 (a) shows the no-load flux linkage waveform of the motor, the equivalent magnetic network calculation result is highly consistent with the finite element calculation result, and the accuracy and the effectiveness of the equivalent magnetic network model are verified. Fig. 7 (b) shows the load flux linkage waveform of the motor (the current amplitude is 10A), and the equivalent magnetic network model and the finite element calculation result are still very close.
Fig. 7 (c) and 7 (d) are the simulation waveform and frequency domain decomposition result of the air gap flux density, respectively, and it can be found that the error of the magnetic network in comparison with the finite element is smaller on the simulation waveform and each harmonic amplitude, and because the stator adopts a mixed structure of split teeth and slots, a plurality of low-order working harmonics are introduced into the air gap, and the power factor and the output torque of the motor are effectively improved.
Fig. 7 (e) compares the output torque of the motor, and it can be seen that the output torque waveform obtained by the equivalent magnetic network and the finite element calculation is almost consistent, wherein, the magnetic network is based on the virtual work principle, and the output torque calculation formula can be expressed as:
in the formula, T e To output torque, p r Is the pole pair number psi of the permanent magnet d And psi q Are respectively a quadrature-direct axis flux linkage, I d And I q Respectively, the AC-DC axis current, W the magnetic field energy, and theta e And theta m Rotor position in electrical and mechanical degrees, respectively; considering d ψ d /dθ e 、dψ q /dθ e And dW/d θ m There is no contribution to the average torque, so the average torque equation can be simplified as:
in the formula, T avg Is the average torque; fig. 7 (f) shows the average torque of the motor at different winding currents, and it is easy to find that the equivalent magnetic network and the finite element calculation result are very close to each other, and better accuracy is achieved.
In conclusion, the high-precision magnetic network modeling method suitable for the hybrid stator permanent magnet vernier motor adopts a method of combining an equivalent magnetic circuit model and a reluctance network model, and realizes the balance of model timing and calculation precision. The topological structure and the magnetic field distribution of the motor are comprehensively considered, and an equivalent magnetic circuit method is adopted to model a magnetic flux distribution regular region, so that the model analysis time is reduced. For areas with complex magnetic flux distribution, such as air gaps and modulation tooth areas, a magnetoresistive network method is adopted for modeling, the leakage flux of the permanent magnet and the tooth tip is fully considered, the complex magnetic conductance boundary determination and magnetic conductance calculation of an equivalent magnetic circuit method are overcome, and the modeling precision and the dynamic analysis efficiency are improved. By introducing the mixed medium grid, the applicability of the model to motors with different topological structures is improved, the modeling difficulty and the workload are greatly reduced, the problem of irregular connection of a stator and an air gap node caused by transient simulation is solved, and the simulation error is effectively reduced. And the magnetic conductivity is updated by adopting a cubic spline interpolation method, so that the iteration speed is accelerated, and the magnetic conductivity updating precision is improved. Considering that the ferromagnetic material is influenced by rotating magnetization, an orthogonal decomposition model and a harmonic decomposition method are introduced and superposed to obtain the stator core loss, so that the calculation error of a classical loss separation model is reduced. And comparing the magnetic network calculation result with the finite element calculation result, and verifying the accuracy of the model. The invention firstly implements magnetic network modeling for the hybrid stator permanent magnet vernier motor, and the scheme can provide reference for the later research of the magnetic network modeling of the motor.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (7)
1. A high-precision magnetic network modeling method suitable for a hybrid stator permanent magnet vernier motor is characterized by comprising the following steps:
step 1, establishing a magnetic flux distribution rule area equivalent magnetic network model;
step 2, establishing an equivalent magnetic network model of an air gap and a modulation tooth area;
step 3, constructing a complete magnetic network model and establishing a magnetic conductance matrix equation;
step 4, solving a nonlinear equation set by adopting a node magnetic potential method to obtain node magnetic potential and magnetic flux of each magnetic conductance unit, and further solving the magnetic density and the magnetic permeability of each magnetic conductance unit;
step 5, reserving the magnetic conductivity of each magnetic conduction unit obtained in the step 4, and resetting the magnetic conduction matrix according to the magnetic conductivity; an orthogonal decomposition model and a harmonic decomposition method are introduced, the stator core loss is obtained through superposition, and the error of a classical loss separation model is reduced.
2. The high-precision magnetic network modeling method suitable for the hybrid stator permanent magnet vernier motor according to claim 1, wherein the hybrid stator permanent magnet vernier motor is a 20 slot/46 pole five-phase motor, and comprises three parts, namely a rotor, a stator and an air gap; the rotor is cylindrical, the surface of the permanent magnet is attached to the inner wall of the rotor, a rare earth neodymium iron boron material and a radial magnetizing mode are adopted, NS poles are alternately arranged in the circumferential direction, the pole arc coefficient is set to be 0.86, the stator comprises modulation teeth, stator teeth, an armature winding and a yoke part, wherein the stator teeth are formed by staggered arrangement of armature teeth and fault-tolerant teeth and respectively adopt a split tooth and slotted structures, and the armature winding is designed as a fractional slot concentrated winding; the rotor and the stator are both made of silicon steel sheets DW465_50; the air gap is located between the stator and the rotor, has the thickness of 0.5mm, and is the main field for magnetic field energy exchange.
3. The modeling method for the high-precision magnetic network applicable to the hybrid stator permanent magnet vernier motor according to claim 1, wherein in the step 1, as the magnetic fields of the rotor yoke, the stator pole shoe, the stator teeth and the stator yoke are uniformly distributed and the magnetic lines of force are ordered, the magnetic network can be equivalent to a unidirectional magnetic conductance unit according to the magnetic flux path; the rotor yoke is evenly divided into corresponding magnetic conductance units according to the number of the permanent magnets, and the cross section of each unit is in a fan shape; the stator pole shoe is divided into two magnetic conductance units which are symmetrical about the center line of the armature tooth according to the flow direction of magnetic flux, and the cross section of each unit is approximately in a right trapezoid shape; the section of the stator tooth magnetic conductance unit is rectangular; the stator yoke is uniformly divided into corresponding magnetic conductance units according to the number of stator teeth, and the section of each unit is in a fan shape; the permanent magnet is equivalent to a magnetic conductance and magnetomotive force series structure; according to the ampere rule, the electrified winding is equivalent to an armature magnetomotive force source and is connected with the armature tooth flux guide in series.
4. The method according to claim 1, wherein in step 2, the hybrid stator permanent magnet vernier motor adopts a stator structure combining slotting and split teeth, and adopts a reluctance network method to model air gap and modulation tooth regions, and comprises a large number of cross-shaped grid units, the number of the air gap grid units is 1840 which is a common multiple of the number of poles and slots to provide sufficient modeling accuracy, all the grid units have the same size and determined air gap permeance, and only the change of the node connection relationship between the air gap and the stator needs to be considered; under the influence of a topological structure of the motor, the air gap and the grid of the modulation tooth area are overlapped and lack of good connectivity, and the modulation tooth area can be divided into grid units with the same size along the circumferential direction by introducing a mixed medium grid, so that the node connection relation of the stator and the air gap is determined.
5. The modeling method for the high-precision magnetic network of the hybrid stator permanent magnet vernier motor according to claim 1, wherein in the step 3, the air gap is divided by adopting a cross grid unit, the upper radial flux guide of the air gap flux guide is connected with the permanent magnet, and the lower radial flux guide is connected with the modulation tooth area, so that a complete equivalent magnetic network model is formed; and numbering equivalent magnetic network model nodes, and establishing a magnetic conductance matrix equation according to kirchhoff voltage law in view of the similarity of a magnetic circuit and a circuit.
6. The method for modeling a high-precision magnetic network applicable to a hybrid stator permanent magnet synchronous motor according to claim 1, wherein in step 4, considering that Matlab has the advantage of calculating a large-scale matrix, a node magnetomotive method is adopted in Matlab to solve a magnetic conductance matrix equation: f = G -1 Phi, where F is a magnetomotive matrix, G is a flux guide matrix, and phi is a magnetic flux matrix, a newton iteration method is used for nonlinear iteration, and a magnetic flux density B is an iteration variable, and in order to accelerate the iteration convergence speed, the magnetic flux density B is corrected to: b is co ＝aB (k-1) +(1-a)B (k) Wherein B is co Correction value for the k-th iteration magnetic density, B (k-1) The magnetic density of the k-1 iteration, B (k) The magnetic density of the kth iteration is, a is a relaxation factor and is set to be 0.5; after all node magnetic potentials of the model are obtained, the magnetic flux density B of each magnetic conduction unit can pass through B = delta F ele ·G ele /S ele Is calculated to be where Δ F ele Is the magnetic potential drop of the magnetic conductance unit, G ele Is a flux guide of a flux guide unit, S ele Effective sectional area of the magnetic conductance unit; the magnetic permeability is obtained by inquiring a B-H curve, and because the number of discrete sample points in the magnetization curve directly influences the calculation precision of the magnetic permeability, a cubic spline interpolation method is introduced to improve the smoothness of the B-H curve, so that the calculation precision of the magnetic permeability is improved, and the iterative convergence speed is further improved;
wherein H ele And u new Magnetic field strength and magnetic permeability of the updated magnetically conductive element respectively, (H) n ,B n ) And (H) n+1 ,B n+1 ) Two adjacent sample points on the B-H curve.
7. The modeling method for the high-precision magnetic network model of the hybrid stator permanent magnet vernier motor according to claim 1, wherein in the step 5, the magnetic permeability matrix is recalculated according to the magnetic permeability of each magnetic permeability unit updated by a cubic spline interpolation method; considering that a ferromagnetic material has two magnetization modes of alternating magnetization and rotating magnetization, in order to calculate the stator core loss more accurately, an orthogonal decomposition model is adopted, the rotating magnetization is regarded as two alternating magnetic fields in the radial direction and the tangential direction, and the core losses generated by the harmonic waves in the radial direction and the tangential direction are superposed to obtain the stator core loss according to a harmonic wave decomposition theory, so that the error of a classical loss separation model is reduced.
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