CN111931406B - Method for establishing dynamic equivalent magnetic network model of axial permanent magnet magnetic suspension flywheel motor - Google Patents
Method for establishing dynamic equivalent magnetic network model of axial permanent magnet magnetic suspension flywheel motor Download PDFInfo
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Abstract
The invention discloses a method for establishing a dynamic equivalent magnetic network model of an axial permanent magnet magnetic suspension flywheel motor, which comprises the following steps: establishing a three-dimensional finite element model, obtaining the air gap magnetic force line distribution of an axial permanent magnet magnetic suspension flywheel motor, dividing the air gap magnetic force line distribution into three equivalent magnetic flux paths, and determining a critical angle based on a 'magnetic resistance minimum principle'; acquiring an equivalent magnetic network model of an air gap magnetic circuit, determining the rotation period of a rotor, dividing the period process into 7 areas, and acquiring the movement range of the rotor in each area; calculating the air gap permeabilities of the phase A and the phase B of the motor; and respectively and equivalently forming a magnetic resistance by the suspension iron core, the permanent magnet and the rotor yoke part of the radial magnetic circuit and the axial magnetic circuit, and acquiring a dynamic equivalent magnetic network model of the motor by combining air gap permeance. According to the invention, the continuously changed air gap flux guide and the permanent magnet, the suspension pole and the rotor yoke part flux guide are respectively calculated, the three-dimensional magnetic field of the axial permanent magnet magnetic suspension flywheel motor is simplified into a dynamic magnetic network, and the model precision and the calculation speed are improved.
Description
Technical Field
The invention relates to the technical field of magnetic suspension motors, in particular to a method for establishing a dynamic equivalent magnetic network model of an axial permanent magnet magnetic suspension flywheel motor.
Background
Since the 21 st century, environmental and energy problems faced by humans have prompted electric vehicles to enter a high-speed development stage. Compared with the traditional chemical storage battery, the flywheel energy storage device serving as the vehicle-mounted power battery has the advantages of high energy density, no excessive charge and discharge problem, quick charge, long service life and no pollution, accords with the development direction of the future energy strategy, and has great research significance.
The motor applied to the flywheel energy storage field mainly comprises an alternating current induction motor, a permanent magnet motor and a switched reluctance motor, wherein the induction motor has high efficiency, low price and convenient maintenance, but the rotor slip loss of the motor is large, and the rotating speed cannot be too high; the permanent magnet motor has high power density and good speed regulation performance, but has overlarge axial dimension and low critical rotation speed, limits the application field of the permanent magnet motor, and the magnetic bearing needs a certain number of coils, iron cores, sensors, control systems and the like, so the whole system has higher cost.
The magnetic suspension bearingless motor which is rising in recent years combines the dual advantages of a magnetic bearing and a switch reluctance motor, can simplify the system structure, improves the critical rotation speed and reliability, is used in the flywheel field, forms a magnetic suspension flywheel motor with unique advantages, is widely researched by students at home and abroad, and sequentially has radial split-phase, axial split-phase and other structures, wherein the axial split-phase structure realizes the electric/power generation function without additionally adding a magnetic bearing, and can realize radial four-degree-of-freedom suspension only by two sets of axially distributed suspension windings, thereby greatly improving the system integration level and the critical rotation speed, and is very suitable for flywheel energy storage suspension support and energy conversion systems.
In order to fully exploit the potential advantages of axial permanent magnet magnetically levitated flywheel motors, a wide range of application-specific parameter optimization methods are required, which require fast and accurate analysis tools capable of characterizing the design parameter variations. The method is used for evaluating a finite element analysis model, an analytic model and an equivalent magnetic network model of a basic analysis model of the motor, and the three models can be applied to modeling and optimization of the motor. The finite element analysis method has the characteristics of higher accuracy and flexible modeling, is widely applied to electromagnetic analysis of motors, has slower solving speed compared with the analytic method, but has higher difficulty in complex topology modeling and much lower solving accuracy than the finite element analysis method, and compared with the finite element analysis method, the equivalent magnetic network realizes the balance of the solving speed of the analytic method and the solving accuracy of the finite element analysis method.
The traditional equivalent magnetic network model only models a radial magnetic circuit of the motor, an effective model cannot be built for the motor with a complex structure, and the magnetic circuit topology description of the motor in motion is not accurate enough, so that the solving result of the model is not ideal. The magnetic flux paths of the axial permanent magnet magnetic suspension flywheel motor are distributed in three dimensions in space, and the air gap magnetic circuit topology of the motor in operation is continuously changed, so that the traditional equivalent magnetic network model is not applicable to the motor, and the equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor needs to be reestablished.
Disclosure of Invention
The invention aims to: aiming at the defects that an equivalent magnetic network model of an axial permanent magnet magnetic suspension flywheel motor is difficult to build and low in precision in the prior art, the invention discloses a method for building a dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor.
The technical scheme is as follows: in order to achieve the technical purpose, the invention adopts the following technical scheme.
A method for establishing a dynamic equivalent magnetic network model of an axial permanent magnet magnetic suspension flywheel motor is characterized by comprising the following steps of: the method comprises the following steps:
S1, dividing an air gap magnetic circuit: establishing a three-dimensional finite element model according to actual structural parameters of the axial permanent magnet magnetic levitation flywheel motor, acquiring air gap magnetic force line distribution of the axial permanent magnet magnetic levitation flywheel motor through finite element simulation, dividing a magnetic force line flowing path into an air gap magnetic circuit of three equivalent magnetic tubes, namely a rectangle, a rectangle plus 1/4 circle and a rectangle plus 1/4 circle, and determining critical angles of the rectangle plus 1/4 circle magnetic tube and the rectangular magnetic tube based on a magnetic resistance minimum principle;
S2, acquiring an equivalent magnetic network model of an air gap magnetic circuit in the rotation process of the rotor of the axial permanent magnet magnetic suspension flywheel motor according to the three equivalent magnetic flux pipes in the step S1, determining the rotation period of the rotor according to the change of the equivalent magnetic network model of the air gap magnetic circuit, and dividing the rotation period of the rotor into 7 areas;
S3, according to the critical angle obtained in the step S1, combining the 7 areas divided in the step S2 to obtain the movement range of the inner rotor in each area;
s4, according to the topological structure of the air gap equivalent magnetic network of each area obtained in the step S2, calculating air gap permeabilities of the A phase and the B phase of the axial permanent magnet magnetic levitation flywheel motor by combining the rotation range of the rotor in the step S3;
S5, according to the actual structure of the axial permanent magnet magnetic levitation flywheel motor, taking radial magnetic circuits and axial magnetic circuits of the axial permanent magnet magnetic levitation flywheel motor as research targets, respectively equivalent a magnetic resistance of a levitation iron core, a permanent magnet and a rotor yoke of the radial magnetic circuits and the axial magnetic circuits, and combining the air gap permeabilities of the phase A and the phase B obtained in the step S4 to obtain a dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor.
Preferably, according to the dynamic equivalent magnetic network model obtained in the step S5, with the magnetic conductance of the radial magnetic circuit as a research target, specific values of the levitation winding inductance, the counter electromotive force and the flux linkage of the axial permanent magnet magnetic levitation flywheel motor are directly calculated according to a basic formula of the magnetic circuit.
Preferably, the calculation formula of the inductance of the levitation winding is:
Wherein N is the number of turns of the suspension winding, G ry1 is the radial flux guide, G z is the total flux guide of the radial magnetic circuit, and G agapx is the air gap flux guide of the A phase region.
Preferably, in the step S2, the period of rotation of the rotor is 30 °.
Preferably, the critical angle calculation formula in step S1 is:
Wherein R rin is the inner diameter of the rotor teeth; r sout is the outer diameter of the suspension tooth; r ryin is the rotor yoke inner diameter.
Preferably, in the step S2, a period of rotation of the rotor of the axial permanent magnet magnetic levitation flywheel motor is divided into 7 areas according to the change of the air gap equivalent magnetic network model, and the specific process is as follows:
The region with uniformly distributed magnetic lines in the air gap magnetic circuit is equivalent to a magnetic tube based on an equivalent magnetic circuit method; dividing a period into 7 subregions according to the change condition of an air gap equivalent magnetic network model in a period of rotor rotation, and sequentially rotating the rotor from the region 1 to the region 7 when the rotor rotates in the period, wherein the air gap equivalent magnetic network topologies among the regions are different, and the resistance value of each magnetic tube in the region is changed along with the rotation of the rotor.
Preferably, in the step S1, the air gap magnetic circuit is divided into magnetic flux pipes with different shapes, the magnetic flux pipes are rectangular magnetic flux pipes, rectangular 1/4 circular magnetic flux pipes with rectangular strips, and the flux conductance calculation formulas of the three magnetic flux pipes are respectively:
The magnetic conductance of the rectangular magnetic tube is as follows:
The magnetic conductance of the rectangular 1/4 round magnetic tube is as follows:
the flux guide of the rectangular 1/4 circular magnetic tube is as follows:
Wherein h is the tooth height of the suspension tooth, delta is the average length of the rectangular part in each magnetic tube, X 1 is the width of the rectangular part in each magnetic tube, C 1 is the inner diameter of the circular magnetic circuit in each magnetic tube, and u 0 is the vacuum magnetic conductivity.
Preferably, in the step S5, a dynamic equivalent magnetic network model of the whole axial permanent magnetic levitation flywheel motor is obtained, and the specific process is as follows:
Acquiring air gap permeabilities in the phase A and the phase B, which are continuously changed in the rotating process of the rotor in the step S4, wherein the air gap permeabilities are three-dimensional permeabilities;
Respectively and equivalently using a permanent magnet, a suspension pole and a rotor yoke which have no change of magnetic conductance in the rotating process of the rotor as magnetic flux pipes, and calculating the radial and axial magnetic conductance of the corresponding axial permanent magnet magnetic suspension flywheel motor; the radial flux guide is generated by the yoke part of the rotor after the magnetic flux generated by the suspension pole winding passes through the radial magnetic circuit to form a closed loop; the axial flux guide is the flux guide generated by the yoke part of the rotor after the bias magnetic flux generated by the permanent magnet forms a closed loop through the axial magnetic circuit; combining the three-dimensional air gap flux guide and the radial and axial flux guides of the axial permanent magnet magnetic levitation flywheel motor, simplifying and equating the three-dimensional magnetic field of the axial permanent magnet magnetic levitation flywheel motor into a dynamic magnetic network, and further obtaining the overall dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor.
Preferably, the expression formula of the radial magnetic conductance and the axial magnetic conductance in a period of the motor rotor is as follows:
Wherein, G ry1 is radial magnetic conductance, G ry2 is axial magnetic conductance, u 0 is vacuum magnetic permeability, u r is relative magnetic permeability of the rotor core, h is tooth height of the suspension teeth, l e is rotor yoke thickness, w r is rotor tooth width, R rout is outer diameter of the rotor, and R rin is inner diameter of the rotor teeth.
The beneficial effects are that:
1. the invention calculates the radial magnetic circuit and the axial magnetic circuit of the axial permanent magnet magnetic suspension flywheel motor respectively, simplifies the magnetic force line distribution of the motor according to the actual parameters of the axial permanent magnet magnetic suspension flywheel motor, calculates the air gap flux guide which is continuously changed and the permanent magnet, the suspension pole and the rotor yoke part flux guide respectively, simplifies the three-dimensional magnetic field of the axial permanent magnet magnetic suspension flywheel motor into a dynamic magnetic network, establishes a dynamic equivalent magnetic network model of the whole axial permanent magnet magnetic suspension flywheel motor, and improves the model precision, the modeling speed and the calculating speed.
2. According to the method, the continuously-changing air gap flux guide in the rotor movement process is calculated independently, a periodic process is divided into 7 areas according to the periodic change of the air gap magnetic circuit topology in the axial permanent magnet magnetic suspension flywheel motor rotor operation process, and then the air gap flux guide is calculated for each area.
3. The dynamic equivalent magnetic network model of the whole axial permanent magnet magnetic suspension flywheel motor can predict the electromagnetic property of the motor, can directly calculate specific numerical values of the inductance, counter electromotive force and magnetic linkage of the suspension winding of the motor, and reduces the calculation resources in the early stage of motor design.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of an air gap magnetic circuit split of an electric machine;
FIG. 3 is a schematic illustration of an air gap equivalent to an atypical flux tube during rotor motion;
FIG. 4 is a schematic diagram of the air gap flux path and equivalent magnetic circuit of region 1;
FIG. 5 is a schematic diagram of the air gap flux path and equivalent magnetic circuit of region 2;
FIG. 6 is a schematic diagram of the air gap flux path and equivalent magnetic circuit of region 3;
FIG. 7 is a schematic diagram of the air gap flux path and equivalent magnetic circuit of region 4;
FIG. 8 is a schematic diagram of an equivalent magnetic network for a pair of poles of a motor during a cycle;
FIG. 9 is a structural parameter of the novel axial permanent magnet magnetic levitation flywheel motor optimized by the invention;
FIG. 10 is a schematic diagram of a three-dimensional finite element model of an axial permanent magnet magnetic levitation flywheel motor constructed by the invention;
Wherein, 1 is a flywheel, 2 is a torque pole, 3 is a magnetic conduction sleeve, 4 is a magnetism isolating ring, 5 is a torque winding, 6 is a suspension pole, 7 is a rotor pole, 8 is a phase, 9 is a phase B, 10 is a permanent magnet, 11 is a rotating shaft, 12 is a suspension winding, 13 is an outer rotor iron core, and 14 is an inner stator iron core;
FIG. 11 is a flux linkage comparison graph of finite element analysis and model of an axial permanent magnet magnetic levitation flywheel motor;
FIG. 12 is a graph of a comparison of motor finite element analysis with computational resources of a model;
FIG. 13 is a graph comparing finite element analysis of a motor with model levitation winding back EMF;
fig. 14 is a finite element analysis versus model levitation winding inductance diagram for an axial permanent magnet magnetically levitated flywheel motor.
Detailed Description
The present invention will be described in further detail below with reference to the drawings and examples for the purpose of enhancing the understanding of the present invention. The invention discloses a method for establishing a dynamic equivalent magnetic network model of an axial permanent magnet magnetic suspension flywheel motor, which is shown in the attached figure 1 and comprises the following steps:
Firstly, establishing a three-dimensional finite element model according to actual structural parameters of an axial permanent magnet magnetic levitation flywheel motor, acquiring air gap magnetic force line distribution of the axial permanent magnet magnetic levitation flywheel motor through finite element simulation, dividing a magnetic force line flowing path into an air gap magnetic circuit of three equivalent magnetic tubes, namely a rectangle, a rectangle plus 1/4 circle and a rectangle plus 1/4 circle, and determining critical angles of the rectangle plus 1/4 circle magnetic tube and the rectangular magnetic tube based on a 'magnetic resistance minimum principle';
Step two, obtaining an equivalent magnetic network model of an air gap magnetic circuit in the rotation process of the rotor of the axial permanent magnet magnetic suspension flywheel motor according to the three equivalent magnetic flux pipes in the step one, determining the rotation period of the rotor according to the change of the equivalent magnetic network model of the air gap magnetic circuit, and dividing the rotation period of the rotor into 7 areas; as can be seen from practical situations, the movement period of the rotor is 30 °, i.e. the magnetic circuit change of the air gap portion of one revolution of the rotor comprises 12 periods, one period every 30 °.
Step three, according to the critical angle obtained in the step one, combining 7 areas divided in the rotation period process of the rotor in the step two to obtain the movement range of the rotor in each area;
step four, according to the equivalent magnetic network model of the air gap magnetic circuit obtained in the step two, calculating air gap permeabilities of the A phase and the B phase of the axial permanent magnet magnetic suspension flywheel motor by combining the movement range of the rotor in the step three;
And fifthly, according to the actual structure of the axial permanent magnet magnetic levitation flywheel motor, taking radial magnetic circuits and axial magnetic circuits of the axial permanent magnet magnetic levitation flywheel motor as research targets, respectively and equivalently forming a magnetic resistance by a levitation iron core, a permanent magnet and a rotor yoke part of the radial magnetic circuits and the axial magnetic circuits, and combining the air gap permeabilities of the phase A and the phase B obtained in the step four to obtain a dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor.
Examples
In the first step, as shown in fig. 9, the motor structural parameters include rotor outer diameter, rotor inner diameter, air gap length, stator outer diameter, axial length, rotor yoke height, torque pole yoke height, suspension pole yoke height, permanent magnet outer diameter, permanent magnet inner diameter, permanent magnet thickness, torque pole arc, suspension pole arc, rotor pole arc, number of suspension winding turns and number of torque winding turns. The schematic structural diagram of the three-dimensional finite element model of the axial permanent magnet magnetic suspension flywheel motor is shown in fig. 10, the position relation between a suspension pole 6 and a rotor pole 7 is shown in fig. 10, and the schematic diagram of air gap magnetic circuit segmentation of the motor is shown in fig. 2. In fig. 2: τ is the pole pitch of the floating teeth; alpha is the rotor tooth width, both of which represent length in terms of angle. θ is the angle through which the rotor rotates, θ=ωt, ω is the rotor angular velocity, and the initial position angle θ=0°, defined as the position where the pole axis of the floating pole 6 coincides with the pole axis of the rotor pole 7. According to the principle of minimum reluctance, when the rotor starts to rotate from the initial position angle θ=0°, most of the magnetic flux flows from the levitation tooth surface into the rotor tooth surface and a small part flows into the rotor tooth surface and the rotor yoke. When the path length of the magnetic flux flowing into the rotor tooth side is greater than the path length of the magnetic flux flowing into the rotor yoke, the angle corresponding to the arc defining the point to the adjacent rotor tooth side is the critical angle of the magnetic circuit, denoted by gamma, and the expression of gamma is shown as formula (1):
Wherein: r rin is the inner diameter of the rotor teeth; r sout is the outer diameter of the suspension tooth; r ryin is the rotor yoke inner diameter.
The magnetic circuit of the air gap part in the rotor rotating process is equivalent to three magnetic tubes, as shown in fig. 3, the magnetic tube in the left diagram is rectangular, the flux guiding calculation formula is shown in formula (2), the magnetic tube in the middle diagram in fig. 3 is rectangular with a 1/4 circle magnetic tube, the flux guiding calculation formula is shown in formula (3), the magnetic tube in the right diagram is rectangular with a 1/4 circle magnetic tube, and the flux guiding calculation formula is shown in formula (4):
Wherein h is the tooth height of the suspension tooth, delta is the average length of an air gap, X 1 is the width of each magnetic tube, C 1 is the inner diameter of a circular magnetic circuit, and u 0 is the vacuum magnetic conductivity.
In the second step, the region with more uniform magnetic force line distribution in the air gap magnetic circuit is equivalent to a magnetic tube based on an equivalent magnetic circuit method; dividing a period into 7 subregions according to the change condition of an air gap equivalent magnetic network model in a period of rotor rotation, and sequentially rotating from the region 1 to the region 7 when the rotor rotates in the period, namely rotating the current rotor tooth at the suspension tooth to the next rotor tooth; and (3) determining that the air gap equivalent magnetic network topologies among the areas are different according to the air gap equivalent magnetic network model obtained in the step two, wherein the resistance value of each magnetic tube in each area changes along with the rotation of the rotor. Because the A-phase and B-phase structures of the motor are similar and differ only by 15 degrees in the direction of rotation, the A-and B-phase air gap permeance calculation process is similar and detailed below regarding the specific calculation process of the air gap permeance of a pair of poles of the motor in the A-phase.
G agapx is the air gap flux guide of A phase, G bgapx is the air gap flux guide of B phase, and the conversion relation between the flux guide G x and the magnetic resistance R x is as follows: g x＝1/Rx. As shown in fig. 4, the actual magnetic flux path is shown in the left diagram of fig. 4, and the equivalent magnetic circuit is shown in the right diagram. The area 1 is a rectangular path from the initial position rotation of the inner rotor to the rotor rotation direction side without occurrence of floating teeth to the rotor yoke part, the rotor rotation range is more than or equal to 0 and less than pi/24-gamma, and the air gap flux conductivity calculation formula in the area 1 is as follows:
Wherein, G 1δ1 is the air gap flux guide of the overlapped part of the suspension tooth and the current rotor tooth, G 1δ2 and G 1δ4 are the air gap flux guides of the current rotor tooth edge path, and as can be seen from figure 4, G 1δ2 and G 1δ4 are the magnetic flux tube flux guides of the rectangle plus 1/4 circle from the two sides of the current rotor tooth to the suspension tooth respectively; g 1δ3 and G 1δ5 are air gap permeabilities of the levitation teeth to the straight paths on both sides of the current rotor yoke, i.e., rectangular flux guides on both sides, G rt is permeabilities of the individual rotor teeth, and G st is core permeabilities of the levitation poles.
In zone 2, the rotor rotates from the final position of zone 1 until no more fringe magnetic flux flows into the rotor tooth flank to the left of the floating tooth, and the rotor rotation range is pi/24-gamma < theta less than or equal to pi/24. When the rotor rotates in the area 2, the left straight path of the floating tooth is longer than the magnetic flux path flowing into the tooth side of the rotor, so that the left side of the floating pole is not provided with the magnetic flux of the straight path, namely an equivalent rectangular magnetic tube, and the curve path length of the large air gap on the right side of the floating tooth is smaller than the rectangular path length, but the shape of the curve path is different from that of the curve path on the left side of the floating tooth, and the curve path is a ring magnetic circuit. As the rotor rotates, the radius of the inner circle of the curved path continuously decreases until the radius of the inner circle decreases to zero when the left edge line of the next rotor tooth is coincident with the right edge line of the floating tooth, and the equivalent magnetic circuit is shown in fig. 5, wherein the magnetic flux tube denoted by G 2δ6 is actually rectangular plus 1/4 ring, and is shown in fig. 5 as a 1/4 ring shape for convenience of representation, and the formula (4) is adopted as the calculation formula. The air gap flux guide calculation formula in the area 2 is as follows:
Wherein, G 2δ1 is the air gap flux guide of the overlapped part of the suspension tooth and the current rotor tooth, G 2δ2 and G 2δ5 are the air gap flux guides of the current rotor tooth edge path, and as can be seen from figure 5, G 2δ2 and G 2δ5 are the magnetic flux tube flux guides of the rectangle plus 1/4 circle from the two sides of the current rotor tooth to the suspension tooth respectively; g 2δ3 is the air gap flux guide of the straight line path from the suspension tooth to the rotor yoke, namely, the rectangular flux guide, G 2δ4 and G 2δ6 are the flux guide of the rectangular plus 1/4 circular ring between the two sides of the next rotor tooth and the suspension tooth, G rt is the flux guide of the single rotor tooth, and G st is the iron core flux guide of the suspension pole.
When the rotor rotates to the range of the area 3, the shape of the left curved path of the suspension teeth changes, the adjacent rotor teeth move to the position where part of tooth poles overlap with the suspension teeth, the situation that one suspension tooth is opposite to a pair of adjacent rotor teeth occurs, the rotor movement range is pi/24 < theta less than or equal to pi/24+gamma, and the air gap equivalent magnetic network is shown in figure 6. The air gap flux guide calculation formula in the area 3 is as follows:
Wherein, G 3δ1 is the air gap flux guide of the overlapping part of the floating tooth and the current rotor tooth, G 3δ5 is the air gap flux guide of the overlapping part of the floating tooth and the next rotor tooth, G 3δ2 and G 3δ7 are the air gap flux guides of the edge paths of the current rotor tooth, and as can be seen from the figure 6, G 3δ2 and G 3δ7 are the flux tube flux guides of the rectangle plus 1/4 circle from the two sides of the current rotor tooth to the floating tooth respectively; g 3δ4 and G 3δ6 are air gap permeabilities of the next rotor tooth edge paths, and as can be seen in FIG. 6, G 3δ4 and G 3δ6 are magnetic flux tube permeabilities of a rectangle plus 1/4 circle from both sides of the next rotor tooth to the floating tooth, respectively; g 3δ3 is the air gap permeance of the straight path of the floating teeth to the rotor yoke, i.e., the rectangular flux tube permeance, G rt is the permeance of a single rotor tooth, and G st is the core permeance of the floating pole.
When the rotor rotates in the area 4, the edge flux guide G 4δ6、G4δ7 does not change, the rest part of the air gap magnetic resistance does not change, the flux linkage of the suspension winding tends to a constant value in the area, the rotor operates in the range of pi/24+gamma < theta less than or equal to pi/8-gamma, and the equivalent magnetic network is shown in figure 7. The air gap flux guide calculation formula in the area 4 is as follows:
Wherein, G 4δ1 is the air gap flux guide of the overlapping part of the floating tooth and the current rotor tooth, G 4δ5 is the air gap flux guide of the overlapping part of the floating tooth and the next rotor tooth, G 4δ2 and G 4δ7 are the air gap flux guides of the edge paths of the current rotor tooth, and as can be seen from the figure 7, G 4δ2 and G 4δ7 are the flux tube flux guides of the rectangle plus 1/4 circle from the two sides of the current rotor tooth to the floating tooth respectively; g 4δ4 and G 4δ6 are air gap permeabilities of the next rotor tooth edge paths, and as can be seen in FIG. 7, G 4δ4 and G 4δ6 are magnetic flux tube permeabilities of a rectangle plus 1/4 circle from both sides of the next rotor tooth to the floating tooth, respectively; g 4δ3 is the air gap permeance of the straight path of the floating teeth to the rotor yoke, i.e., the rectangular flux tube permeance, G rt is the permeance of a single rotor tooth, and G st is the core permeance of the floating pole.
In the rotor rotation range corresponding to the suspension pole in one period of the motor, according to the half period condition, the areas 5, 6 and 7 are symmetrical with the areas 3, 2 and 1 respectively, and the calculation formulas of the air gap permeance of the areas are in one-to-one correspondence, namely G agap5＝Gagap3,Gagap6＝Gagap2,Gagap7＝Gagap1.
According to the method, the continuously-changing air gap flux guide in the rotor movement process is calculated independently, a periodic process is divided into 7 areas according to the periodic change of the air gap magnetic circuit topology in the axial permanent magnet magnetic suspension flywheel motor rotor operation process, and then the air gap flux guide is calculated for each area.
And fifthly, according to the actual structure of the axial permanent magnet magnetic levitation flywheel motor, taking radial magnetic circuits and axial magnetic circuits of the axial permanent magnet magnetic levitation flywheel motor as research targets, respectively and equivalently forming a magnetic resistance by a levitation iron core, a permanent magnet and a rotor yoke part of the radial magnetic circuits and the axial magnetic circuits, and combining the air gap permeabilities of the phase A and the phase B obtained in the step four to obtain a dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor. The permanent magnet, the suspension pole and the rotor yoke part of which the magnetic conductance is not changed in the process of the movement of the motor rotor are respectively equivalent to a magnetic tube, and the radial and axial magnetic permeabilities of the corresponding axial permanent magnet magnetic suspension flywheel motor are calculated: in the magnetic circuit, the two magnetic resistances are in series connection. After the magnetic flux flows into the rotor from the air gap, the magnetic flux generated by the suspension winding forms a closed loop through a radial magnetic circuit, the equivalent magnetic resistance of the part of the rotor yoke is represented by R ry1, the bias magnetic flux generated by the permanent magnet forms a closed loop through an axial magnetic circuit, and the equivalent magnetic resistance of the part of the rotor yoke is represented by R ry2. As shown in fig. 8.
Through the series of conversion and simplification, the three-dimensional magnetic field of the axial permanent magnet magnetic suspension flywheel motor can be represented by a dynamic magnetic network. As shown in fig. 8: r agapx is the air gap magnetic resistance of the A phase, R bgapx is the air gap magnetic resistance of the B phase, R sta is the iron core magnetic resistance of the A phase suspension pole, R stb is the iron core magnetic resistance of the B phase suspension pole, R pm is the magnetic resistance of the axial magnetizing permanent magnet, F pm is the magnetomotive force of the axial magnetizing permanent magnet, and F sα is the magnetomotive force of the suspension winding.
The calculation formula of each amount in fig. 8 is:
Gpm＝u0upm·π(lpmo 2-lpmi 2)/hpm (13)
Fpm＝(Brm·hpm)/(u0·upm) (14)
Fsα＝N·isα (15)
Wherein: u 0 is vacuum magnetic permeability, u r is relative magnetic permeability of a rotor core, h is tooth height of a suspension tooth, l e is rotor yoke thickness, w r is rotor tooth width, w s is suspension tooth width, l s is sum of suspension tooth and yoke length, l r is rotor tooth thickness, u pm is relative magnetic permeability of an axial magnetization permanent magnet, l pmo is outer diameter of the axial magnetization permanent magnet, l pmi is inner diameter of the axial magnetization permanent magnet, h pm is thickness of the axial magnetization permanent magnet, B rm is remanence of the axial magnetization permanent magnet, i sα is winding current of a suspension winding, and N is number of turns of the suspension winding.
The invention calculates the radial magnetic circuit and the axial magnetic circuit of the axial permanent magnet magnetic suspension flywheel motor respectively, simplifies the magnetic force line distribution of the motor according to the actual parameters of the axial permanent magnet magnetic suspension flywheel motor, calculates the air gap flux guide which is continuously changed and the permanent magnet, the suspension pole and the rotor yoke part flux guide respectively, simplifies the three-dimensional magnetic field of the axial permanent magnet magnetic suspension flywheel motor into a dynamic magnetic network, establishes a dynamic equivalent magnetic network model of the whole axial permanent magnet magnetic suspension flywheel motor, and improves the model precision, the modeling speed and the calculating speed.
According to the dynamic equivalent magnetic network model obtained in the step S5, the magnetic conductance of the radial magnetic circuit is taken as a research target, the specific values of the levitation winding inductance, the counter electromotive force and the flux linkage of the axial permanent magnet magnetic levitation flywheel motor are directly calculated according to the basic formula of the magnetic circuit, and simulation verification is carried out below.
Simulation verification:
In order to further illustrate the effectiveness of the dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor built by the invention, the flux linkage pair of the motor with the modeling type (EMN) of the invention is shown in the figure 11, and from the figure analysis, the flux linkage result obtained by the invention is basically consistent with the finite element analysis result from the whole period.
The Finite Element Analysis (FEA) and the modeling type (EMN) solving of the motor consume resources as shown in figure 12, and compared with the finite element analysis method, the method can obviously reduce the calculation resources in the early stage of motor design.
In order to further verify the effectiveness of the dynamic equivalent magnetic network model of the built axial permanent magnet magnetic suspension flywheel motor, the suspension winding flux linkage, the counter electromotive force and the inductance obtained by finite element simulation are introduced for comparison, and the invention calculates through formulas (16), (17) and (18).
Ψ＝N·U·Gz (16)
Wherein, ψ is the flux linkage of the levitation winding, N is the number of turns of the levitation winding, U is the magnetomotive force of the levitation winding, e is the counter electromotive force of the levitation winding, G z is the total flux guide of the radial magnetic circuit, and G agapx is the air gap flux guide of the A phase region x. The dynamic equivalent magnetic network model of the whole axial permanent magnet magnetic suspension flywheel motor can predict the electromagnetic property of the motor, can directly calculate specific numerical values of the inductance, counter electromotive force and magnetic linkage of the suspension winding of the motor, and reduces the calculation resources in the early stage of motor design.
Comparison results referring to fig. 11, 13 and 14, the comparison of the finite element analysis FEA of the motor and the floating inductance back electromotive force of the model EMN of the present invention is shown in fig. 13, and the comparison of the finite element analysis FEA of the motor and the floating winding inductance of the model EMN of the present invention is shown in fig. 14. It can be seen that: compared with the finite element analysis result, the model has higher calculation speed, and avoids the defect of low precision of the traditional equivalent magnetic circuit method.
In summary, the technical scheme provided by the invention has the following beneficial effects:
(1) Based on a dynamic equivalent magnetic network model formed by a traditional equivalent magnetic circuit method, modeling is conducted aiming at the condition that the air gap magnetic circuit topology and the magnetic resistance of each magnetic tube are changed along with the rotation of a rotor in the rotation process of the rotor, the solving precision of the built model is greatly improved, and the dynamic modeling in the early stage of motor design is achieved.
(2) The traditional equivalent magnetic circuit model only considers the radial magnetic circuit of the motor, the motor magnetic circuit with a more complex structure cannot be accurately described, the solving precision of the model is low, and the dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor not only can accurately describe the three-dimensional magnetic circuit of the motor, but also can accurately express the magnetic resistance change condition of each region in the motor rotation process.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (8)
1. A method for establishing a dynamic equivalent magnetic network model of an axial permanent magnet magnetic suspension flywheel motor is characterized by comprising the following steps of: the method comprises the following steps:
S1, dividing an air gap magnetic circuit: establishing a three-dimensional finite element model according to actual structural parameters of the axial permanent magnet magnetic levitation flywheel motor, acquiring air gap magnetic force line distribution of the axial permanent magnet magnetic levitation flywheel motor through finite element simulation, dividing a magnetic force line flowing path into an air gap magnetic circuit of three equivalent magnetic tubes, namely a rectangle, a rectangle plus 1/4 circle and a rectangle plus 1/4 circle, and determining critical angles of the rectangle plus 1/4 circle magnetic tube and the rectangular magnetic tube based on a magnetic resistance minimum principle;
S2, acquiring an equivalent magnetic network model of an air gap magnetic circuit in the rotation process of the rotor of the axial permanent magnet magnetic suspension flywheel motor according to the three equivalent magnetic flux pipes in the step S1, determining the rotation period of the rotor according to the change of the equivalent magnetic network model of the air gap magnetic circuit, and dividing the rotation period of the rotor into 7 areas;
S3, according to the critical angle obtained in the step S1, combining the 7 areas divided in the step S2 to obtain the movement range of the inner rotor in each area;
s4, according to the topological structure of the air gap equivalent magnetic network of each area obtained in the step S2, calculating air gap permeabilities of the A phase and the B phase of the axial permanent magnet magnetic levitation flywheel motor by combining the rotation range of the rotor in the step S3;
S5, according to the actual structure of the axial permanent magnet magnetic levitation flywheel motor, taking radial magnetic circuits and axial magnetic circuits of the axial permanent magnet magnetic levitation flywheel motor as research targets, respectively and equivalently forming a magnetic resistance by a levitation iron core, a permanent magnet and a rotor yoke part of the radial magnetic circuits and the axial magnetic circuits, and combining the air gap permeabilities of the phase A and the phase B obtained in the step S4 to obtain a dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor;
in the step S5, a dynamic equivalent magnetic network model of the whole axial permanent magnet magnetic suspension flywheel motor is obtained, and the specific process is as follows:
Acquiring air gap permeabilities in the phase A and the phase B, which are continuously changed in the rotating process of the rotor in the step S4, wherein the air gap permeabilities are three-dimensional permeabilities;
Respectively and equivalently using a permanent magnet, a suspension pole and a rotor yoke which have no change of magnetic conductance in the rotating process of the rotor as magnetic flux pipes, and calculating the radial and axial magnetic conductance of the corresponding axial permanent magnet magnetic suspension flywheel motor; the radial flux guide is generated by the yoke part of the rotor after the magnetic flux generated by the suspension pole winding passes through the radial magnetic circuit to form a closed loop; the axial flux guide is the flux guide generated by the yoke part of the rotor after the bias magnetic flux generated by the permanent magnet forms a closed loop through the axial magnetic circuit;
Combining the three-dimensional air gap flux guide and the radial and axial flux guides of the axial permanent magnet magnetic levitation flywheel motor, simplifying and equating the three-dimensional magnetic field of the axial permanent magnet magnetic levitation flywheel motor into a dynamic magnetic network, and further obtaining the overall dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor.
2. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor according to claim 1, which is characterized by comprising the following steps: and (3) according to the dynamic equivalent magnetic network model obtained in the step (S5), taking the magnetic conductance of the radial magnetic circuit as a research target, and directly calculating specific values of the levitation winding inductance, the counter electromotive force and the flux linkage of the axial permanent magnet magnetic levitation flywheel motor according to a basic formula of the magnetic circuit.
3. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor according to claim 2, wherein the calculation formula of the levitation winding inductance is as follows:
Wherein N is the number of turns of the suspension winding, G ry1 is the radial flux guide, G z is the total flux guide of the radial magnetic circuit, and G agapx is the air gap flux guide of the A phase region.
4. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor according to claim 1, which is characterized by comprising the following steps: in the step S2, the period of rotation of the rotor is 30 °.
5. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor according to claim 1, which is characterized by comprising the following steps: the critical angle calculation formula in the step S1 is as follows:
Wherein, gamma is a critical angle, and R rin is the inner diameter of the rotor teeth; r sout is the outer diameter of the suspension tooth; r ryin is the rotor yoke inner diameter.
6. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor according to claim 1, which is characterized by comprising the following steps: in the step S2, a period of rotation of the rotor of the axial permanent magnet magnetic levitation flywheel motor is divided into 7 areas according to the change of the air gap equivalent magnetic network model, and the specific process is as follows:
The region with uniformly distributed magnetic lines in the air gap magnetic circuit is equivalent to a magnetic tube based on an equivalent magnetic circuit method; dividing a period into 7 subregions according to the change condition of an air gap equivalent magnetic network model in a period of rotor rotation, and sequentially rotating the rotor from the region 1 to the region 7 when the rotor rotates in the period, wherein the air gap equivalent magnetic network topologies among the regions are different, and the resistance value of each magnetic tube in the region is changed along with the rotation of the rotor.
7. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor according to claim 1, which is characterized by comprising the following steps: in the step S1, the air gap magnetic circuit is divided into magnetic flux pipes with different shapes, the shape of the magnetic flux pipe is a rectangular magnetic flux pipe, a rectangular 1/4 circular magnetic flux pipe and a rectangular 1/4 circular magnetic flux pipe, and the flux conductivity calculation formulas of the three magnetic flux pipes are respectively as follows:
The magnetic conductance of the rectangular magnetic tube is as follows:
The magnetic conductance of the rectangular 1/4 round magnetic tube is as follows:
the flux guide of the rectangular 1/4 circular magnetic tube is as follows:
Wherein h is the tooth height of the suspension tooth, delta is the average length of the rectangular part in each magnetic tube, X 1 is the width of the rectangular part in each magnetic tube, C 1 is the inner diameter of the circular magnetic circuit in each magnetic tube, and u 0 is the vacuum magnetic conductivity.
8. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic levitation flywheel motor according to claim 1, which is characterized by comprising the following steps: the expression formula of the radial magnetic conductance and the axial magnetic conductance in one period of the motor rotor is as follows:
Wherein, G ry1 is radial magnetic conductance, G ry2 is axial magnetic conductance, u 0 is vacuum magnetic permeability, u r is relative magnetic permeability of the rotor core, h is tooth height of the suspension teeth, l e is rotor yoke thickness, w r is rotor tooth width, R rout is outer diameter of the rotor, and R rin is inner diameter of the rotor teeth.
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| CN113392557B (en) * | 2021-06-18 | 2023-08-11 | 南京工程学院 | Method for establishing axial split-phase magnetic suspension flywheel motor suspension force model |
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