CN111931406A - Method for establishing dynamic equivalent magnetic network model of axial permanent magnetic suspension flywheel motor - Google Patents
Method for establishing dynamic equivalent magnetic network model of axial permanent 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 magnetic suspension flywheel motor, which comprises the following steps: establishing a three-dimensional finite element model, acquiring air gap magnetic line distribution of an axial permanent magnetic suspension flywheel motor, dividing the air gap magnetic line distribution into three air gap magnetic circuits of equivalent flux tubes, and determining a critical angle based on a 'minimum reluctance principle'; obtaining an equivalent magnetic network model of an air gap magnetic circuit, determining the rotation period of the rotor, dividing the period process into 7 areas, and obtaining the motion range of the rotor in each area; calculating the air gap permeance of the phase A and the phase B of the motor; the suspension iron cores, the permanent magnets and the rotor yoke parts of the radial magnetic circuit and the axial magnetic circuit are respectively equivalent to form a magnetic resistance, and a dynamic equivalent magnetic network model of the motor is obtained by combining air gap magnetic conductance. The invention respectively calculates the constantly changing air gap magnetic conductance and the permanent magnet, the suspension pole and the rotor yoke part magnetic conductance, simplifies the three-dimensional magnetic field of the axial permanent magnet magnetic suspension flywheel motor into a dynamic magnetic network, and improves the model precision and the calculation speed.
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 facing 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 charging, long service life and no pollution, conforms to the direction of future energy strategic development, 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 the axial size is overlarge, the critical rotating speed is low, the application field is limited, and the magnetic bearing needs a certain number of coils, iron cores, sensors, a control system and the like, so the cost of the whole system is higher.
The magnetic suspension bearingless motor which is started in recent years combines the dual advantages of the magnetic bearing and the switched reluctance motor, can simplify the system structure and improve the critical rotating speed and reliability, is used in the field of the flywheel to form the magnetic suspension flywheel motor with unique advantages, is widely researched by domestic and foreign scholars, and sequentially has the structures of radial phase splitting, axial phase splitting and the like, wherein the axial phase splitting structure can realize the radial four-degree-of-freedom suspension only by two sets of suspension windings which are axially distributed without additionally arranging the magnetic bearing while realizing the electric/power generation function, thereby greatly improving the system integration level and the critical rotating speed, and being very suitable for a flywheel energy storage suspension support and energy conversion system.
In order to fully exploit the potential advantages of axial permanent-magnet magnetic levitation flywheel motors, it is necessary to be able to perform extensive, application-specific parameter optimization methods, which require fast and accurate analysis tools, which can characterize the characteristics of the design parameter variations. The basic analysis model for evaluating the motor comprises a finite element analysis model, an analytic model and an equivalent magnetic network model, 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 the motor, and has a lower solving speed compared with an analytic method, but has higher difficulty for complex topology modeling and much lower solving accuracy compared with the finite element analysis method, and in contrast, the equivalent magnetic network realizes the balance between the solving speed of the analytic method and the solving accuracy of the finite element analysis method.
The traditional equivalent magnetic network model is only used for modeling a radial magnetic circuit of a motor, an effective model cannot be built for the motor with a complex structure, and the topological description of the magnetic circuit 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 topology of an air gap magnetic circuit of the motor in operation is changed continuously, so that the traditional equivalent magnetic network model is not applicable to the motor any more, and therefore the equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor needs to be reestablished.
Disclosure of Invention
The purpose of the invention is as follows: the invention discloses a dynamic equivalent magnetic network model building method of an axial permanent magnetic suspension flywheel motor, which aims at the defects of difficult building of an equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor and lower precision in the prior art.
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 magnetic suspension flywheel motor is characterized by comprising the following steps: 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 magnetic suspension flywheel motor, obtaining air-gap magnetic line distribution of the axial permanent magnetic suspension flywheel motor through finite element simulation, dividing a magnetic line flowing path into air-gap magnetic paths of three equivalent magnetic flux tubes of a rectangle, a rectangle plus 1/4 circle and a rectangle plus 1/4 circular ring, and determining a critical angle between the rectangle plus 1/4 circular magnetic flux tube and the rectangular magnetic flux tube based on a 'magnetic resistance minimum principle';
s2, obtaining an equivalent magnetic network model of an air gap magnetic circuit in the rotation process of the rotor of the axial permanent magnetic suspension flywheel motor according to the three equivalent flux tubes 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 process of the rotor into 7 areas;
s3, acquiring the motion range of the rotor in each area according to the critical angle obtained in the step S1 by combining the 7 divided areas in the step S2;
s4, calculating the air gap permeance of the A phase and the B phase of the axial permanent magnet magnetic suspension flywheel motor according to the topological structure of the equivalent magnetic network of the air gap of each region obtained in the step S2 and by combining the rotation range of the rotor in the step S3;
and S5, according to the actual structure of the axial permanent magnet magnetic suspension flywheel motor, taking the radial and axial magnetic circuits of the axial permanent magnet magnetic suspension flywheel motor as research targets, enabling the suspension iron cores, the permanent magnets and the rotor yoke parts of the radial magnetic circuit and the axial magnetic circuit to respectively form a magnetic resistance in an equivalent mode, and combining the A-phase and B-phase air gap magnetic conductances obtained in the step S4 to obtain a dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor.
Preferably, according to the dynamic equivalent magnetic network model obtained in the step S5, with the permeance of the radial magnetic circuit as a research target, specific values of the levitation winding inductance, the back electromotive force, and the flux linkage of the axial permanent magnet levitation flywheel motor are directly calculated according to the basic formula of the magnetic circuit.
Preferably, the calculation formula of the inductance of the levitation winding is as follows:
where N is the number of turns of the levitation winding, Gry1Is radial flux guide, GzIs the total flux guide of the radial magnetic circuit.
Preferably, in step S2, the period of the rotor rotation is 30 °.
Preferably, the critical angle calculation formula in step S1 is:
wherein R isrinIs the rotor tooth inside diameter; rsoutThe outer diameter of the suspension tooth; rryinIs the inner diameter of the yoke part of the rotor.
Preferably, in the step S2, a cycle of rotation of the rotor of the axial permanent magnet magnetic suspension flywheel motor is divided into 7 regions according to a change of the air gap equivalent magnetic network model, and the specific process includes:
the region with uniformly distributed magnetic lines of force in the air gap magnetic circuit is equivalent to a flux tube based on an equivalent magnetic circuit method; a period is divided into 7 sub-regions according to the change condition of an air gap equivalent magnetic network model in the period of rotor rotation, when the rotor rotates in the period, the rotor rotates from the region 1 to the region 7 in sequence, the topology of the air gap equivalent magnetic network among the regions is different, and the resistance value of each flux tube in the region changes along with the rotation of the rotor.
Preferably, in the step S1, the air-gap magnetic circuit is divided into flux tubes with different shapes, the flux tubes are rectangular flux tubes, rectangular strip 1/4 circular flux tubes and rectangular strip 1/4 circular flux tubes, and the magnetic conductance calculation formulas of the three types of flux tubes are respectively:
the permeance of the rectangular flux tube is:
the permeance of the rectangular band 1/4 round flux tube is:
the magnetic conductance of the rectangular band 1/4 circular magnetic flux tube is:
wherein h is the tooth height of the suspension teeth, the average length of the rectangular part in each flux tube, and X1Is the width of the rectangular part in each flux tube, C1Is the inner diameter u of the circular magnetic circuit in each flux tube0Is a vacuum magnetic permeability.
Preferably, the step S5 is to obtain a dynamic equivalent magnetic network model of the whole axial permanent magnet magnetic suspension flywheel motor, and the specific process includes:
acquiring air gap permeance 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 permeance is three-dimensional permeance;
respectively and equivalently setting permanent magnets, suspension poles and rotor yokes, of which the magnetic conductances are not changed in the rotation process of the rotor, as flux tubes, and calculating the radial and axial magnetic conductances of the corresponding axial permanent magnet magnetic suspension flywheel motor; the radial magnetic conductance is the magnetic conductance generated by the yoke part of the rotor after magnetic flux generated by the suspension pole winding passes through a radial magnetic circuit to form a closed loop; the axial magnetic conductance is the magnetic conductance generated by the yoke part of the rotor after bias magnetic flux generated by the permanent magnet passes through an axial magnetic circuit to form a closed loop; and simplifying the three-dimensional magnetic field of the axial permanent magnetic suspension flywheel motor into a dynamic magnetic network by combining the three-dimensional air gap magnetic conductance and the radial and axial magnetic conductances of the axial permanent magnetic suspension flywheel motor, thereby obtaining the overall dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor.
Preferably, the radial flux guide and the axial flux guide are expressed in the following formula within one period of the rotor of the motor:
wherein G isry1Is radial flux guide, Gry2Is axially magnetically permeable, u0Is a vacuum permeability of urIs the relative magnetic permeability of the rotor core, h is the tooth height of the suspended teeth, leIs the rotor yoke thickness, wrIs the rotor tooth width, RroutIs the outer diameter of the rotor, RrinThe inner diameter of the rotor teeth.
Has the advantages that:
1. the invention respectively calculates the radial and axial magnetic circuits of the axial permanent magnetic suspension flywheel motor, simplifies the magnetic line distribution of the motor according to the actual parameters of the axial permanent magnetic suspension flywheel motor, respectively calculates the constantly changed air gap magnetic conductance and the permanent magnet, the suspension pole and the rotor yoke part magnetic conductance, simplifies the three-dimensional magnetic field of the axial permanent magnetic suspension flywheel motor into a dynamic magnetic network, establishes the integral dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor, and improves the model precision, the modeling speed and the calculation speed.
2. The invention separately calculates the air gap permeance which constantly changes in the rotor motion process, divides a period process into 7 areas according to the periodic change of the topology of an air gap magnetic circuit in the operation process of the rotor of the axial permanent magnetic suspension flywheel motor, and further calculates the air gap permeance for each area.
3. The dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor built by the invention can predict the electromagnetic property of the motor, can directly calculate the specific values of the inductance, the counter electromotive force and the flux 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 a method of the present invention;
FIG. 2 is a schematic view of the air-gap magnetic circuit division of the machine;
FIG. 3 is a schematic view of an air gap equivalent in shape to an atypical flux tube during rotor motion;
FIG. 4 is a schematic view of the air gap flux path and equivalent magnetic circuit of region 1;
FIG. 5 is a schematic view of the air gap flux path and equivalent magnetic circuit of region 2;
figure 6 is a schematic view of the air gap flux path and equivalent magnetic circuit of region 3;
figure 7 is a schematic view 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 one pair of poles of the motor during a cycle;
FIG. 9 shows the structural parameters of the novel axial permanent magnet magnetic suspension flywheel motor optimized by the present invention;
FIG. 10 is a schematic structural diagram of a three-dimensional finite element model of an axial permanent magnet magnetic suspension 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 an A phase, 9 is a B phase, 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 magnetic flux linkage comparison graph of a finite element analysis and a model of an axial permanent magnet magnetic levitation flywheel motor;
FIG. 12 is a diagram of a comparison of computational resources of a finite element analysis and a model of an electric machine;
FIG. 13 is a graph comparing the back EMF of the levitation winding of the finite element analysis and model of the motor;
FIG. 14 is a graph comparing the inductance of the suspension winding of the model and the finite element analysis of the axial permanent magnet magnetic suspension flywheel motor.
Detailed Description
For a better understanding of the present invention, reference will now be made in detail to the present invention, examples of which are illustrated in the accompanying drawings. The invention discloses a method for establishing a dynamic equivalent magnetic network model of an axial permanent magnetic suspension flywheel motor, which comprises the following steps as shown in the attached figure 1:
step one, establishing a three-dimensional finite element model according to actual structural parameters of an axial permanent magnetic suspension flywheel motor, obtaining air-gap magnetic line distribution of the axial permanent magnetic suspension flywheel motor through finite element simulation, dividing a magnetic line flowing path into air-gap magnetic paths of three equivalent magnetic flux tubes of a rectangle, a rectangle plus 1/4 circle and a rectangle plus 1/4 circular ring, and determining a critical angle between the rectangle plus 1/4 circular magnetic flux tube and the rectangular magnetic flux tube based on a 'magnetic resistance minimum principle';
step two, acquiring an equivalent magnetic network model of an air gap magnetic circuit in the rotating process of the rotor of the axial permanent magnetic suspension flywheel motor according to the three equivalent magnetic flux tubes in the step one, determining the rotating period of the rotor according to the change of the equivalent magnetic network model of the air gap magnetic circuit, and dividing the rotating period process of the rotor into 7 areas; according to practical conditions, the movement period of the rotor is 30 degrees, namely, the magnetic circuit change of the air gap part of one rotation of the rotor comprises 12 periods, and one period is provided every 30 degrees.
Step three, according to the critical angle obtained in the step one, combining 7 areas divided in the process of one period of the rotation of the rotor in the step two to obtain the motion range of the rotor in each area;
step four, calculating the air gap permeance of the A phase and the B phase of the axial permanent magnetic suspension flywheel motor according to the equivalent magnetic network model of the air gap magnetic circuit obtained in the step two and by combining the motion range of the rotor in the step three;
and step five, according to the actual structure of the axial permanent magnetic suspension flywheel motor, taking the radial and axial magnetic circuits of the axial permanent magnetic suspension flywheel motor as research targets, enabling the suspension iron cores, the permanent magnets and the rotor yoke parts of the radial magnetic circuit and the axial magnetic circuit to respectively form a magnetic resistance in an equivalent mode, and combining the A-phase air gap magnetic conductance and the B-phase air gap magnetic conductance obtained in the step four to obtain a dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor.
Examples
In the first step, the structural parameters of the motor are as shown in fig. 9, and the structural parameters of the motor include the outer diameter of the rotor, the inner diameter of the rotor, the length of the air gap, the outer diameter of the stator, the axial length, the height of the rotor yoke, the height of the torque pole yoke, the height of the levitation pole yoke, the outer diameter of the permanent magnet, the inner diameter of the permanent magnet, the thickness of the permanent magnet, the arc of the torque pole, the arc of the levitation pole, the arc of the rotor pole, the number of. The structural schematic diagram of the three-dimensional finite element model of the axial permanent magnet magnetic suspension flywheel motor is shown in the attached drawing 10, the position relationship between the suspension pole 6 and the rotor pole 7 is shown in the attached drawing 10, and the schematic diagram of the air gap magnetic circuit division of the motor is shown in the attached drawing 2. In the attached fig. 2: tau is the suspension tooth pole distance; α is the rotor tooth width, both expressed in degrees as length. θ is the angle of the rotor, θ is ω t, ω is the angular speed of the rotor, and the initial position angle θ is 0 °, which is defined as the position where the pole axis of the levitation pole 6 and the pole axis of the rotor pole 7 coincide. According to the principle of minimum reluctance, when the rotor starts to rotate from the initial position angle θ of 0 °, most of the magnetic flux flows from the floating tooth surface into the rotor tooth surface, and a small portion flows into the rotor tooth surface and the rotor yoke. When the path length of the magnetic flux flowing into the rotor tooth flank is longer than the path length of the magnetic flux flowing into the rotor yoke, the magnetic flux flows into the rotor yoke, an angle corresponding to an arc from the point to the adjacent rotor tooth flank is defined as a critical angle of a magnetic circuit, and is expressed by gamma, and then the expression of gamma is expressed by the formula (1):
in the formula: rrinIs the rotor tooth inside diameter; rsoutThe outer diameter of the suspension tooth; rryinIs the inner diameter of the yoke part of the rotor.
The magnetic circuit of the air gap part in the rotation process of the rotor is equivalent to three shapes of flux pipes, as shown in fig. 3, the shape of the flux pipe in the left figure is a rectangular flux pipe, the calculation formula of the magnetic conductance is shown in formula (2), the shape of the flux pipe in the middle figure of fig. 3 is a rectangular flux pipe with 1/4 circles, the calculation formula of the magnetic conductance is shown in formula (3), the shape of the flux pipe in the right figure is a rectangular flux pipe with 1/4 circles, and the calculation formula of the magnetic conductance is shown in formula (4):
wherein h is the tooth height of the suspended tooth, the average length of the air gap, and X1Is the width of each flux tube, C1Is the inner diameter u of the circular magnetic circuit0Is a vacuum magnetic permeability.
In the second step, the region with more uniform magnetic force line distribution in the air gap magnetic circuit is equivalent to a flux tube based on an equivalent magnetic circuit method; dividing a period into 7 sub-regions according to the change condition of an air gap equivalent magnetic network model in the period of rotor rotation, and sequentially rotating from the region 1 to the region 7 when the rotor rotates in the period, namely the process that the current rotor tooth at the suspension tooth rotates to the next rotor tooth; and determining that the air gap equivalent magnetic network topologies among the regions are different according to the air gap equivalent magnetic network model obtained in the step two, wherein the resistance values of the flux tubes in the regions are changed along with the rotation of the rotor. Because the A phase and the B phase of the motor are similar in structure and are different by 15 degrees in the rotating direction, the calculation processes of the A-phase air gap permeance and the B-phase air gap permeance are similar, and the detailed description is given below on the specific calculation process of the air gap permeance of one pair of poles of the motor in the A phase.
GagapxAir-gap permeance of phase A, GbgapxAir-gap permeance of phase B, permeance GxAnd magnetic resistance RxThe conversion relationship is as follows: gx＝1/Rx. As shown in fig. 4, the left diagram of fig. 4 shows the actual magnetic flux path, and the right diagram shows the equivalent magnetic path. The region 1 is a rectangular path from the initial position of the inner rotor to one side of the rotation direction of the rotor without the suspension teeth to the yoke part of the rotor, the rotation range of the rotor is more than or equal to 0 and less than theta/24-gamma, and the calculation formula of the air gap magnetic conductance in the region 1 is as follows:
wherein G is11For the intersection of the suspended teeth with the current rotor teethAir gap permeance of the stack, G12And G14For the air gap permeance of the current rotor tooth edge path, as can be seen in FIG. 4, G12And G14The flux tube flux guides are respectively a rectangle and 1/4 circles from two sides of the current rotor tooth to the suspension tooth; g13And G15Air gap permeance being a straight path from the floating tooth to the current rotor yoke portion on both sides, i.e. a rectangular flux tube permeance on both sides, GrtBeing the flux-guide of a single rotor tooth, GstA core flux guide being a suspended pole.
In the area 2, the rotor rotates from the final position of the area 1 until no edge magnetic flux flows into the side face of the rotor on the left side of the suspension tooth, and the rotation range of the rotor is pi/24-gamma < theta and is not more than pi/24. When the rotor rotates in the area 2, the straight path on the left side of the floating tooth is longer than the magnetic flux path flowing into the side face of the rotor tooth, so that the magnetic flux of the straight path on the left side of the floating pole is not generated, namely the equivalent rectangular magnetic flux tube, the length of the curved path of the large air gap on the right side of the floating tooth is smaller than that of the rectangular path, but the shape of the path is different from that of the curved path on the left side of the floating tooth, and the path is in a ring-shaped magnetic path. The inner circle radius of the curved path is continuously reduced along with the rotation of the rotor until the inner circle radius is reduced to zero when the left edge line of the next rotor tooth is coincident with the right edge line of the suspension tooth, and the equivalent magnetic circuit of the part is shown as figure 5, wherein G26The representative flux tube is actually a rectangle plus an 1/4 circular ring, and here, for convenience of representation, it is represented in fig. 5 in the shape of 1/4 circular ring, and the calculation formula adopts formula (4). The calculation formula of the air gap magnetic conductance in the region 2 is as follows:
wherein G is21Air gap permeance at the overlapping part of the floating tooth and the current rotor tooth, G22And G25For the air gap permeance of the current rotor tooth edge path, as can be seen in FIG. 5, G22And G25The flux tube flux guides are respectively a rectangle and 1/4 circles from two sides of the current rotor tooth to the suspension tooth; g23The air gap flux guide which is a straight path of the floating teeth to the rotor yoke,i.e. rectangular flux-tube permeance, G24And G26Flux-tube flux-guides G of a rectangular and 1/4 circular ring between the two sides of the next rotor tooth and the floating tooth respectivelyrtBeing the flux-guide of a single rotor tooth, GstA core flux guide being a suspended pole.
When the rotor rotates to the range of the area 3, the shape of the curve path on the left side of the suspension tooth changes, adjacent rotor teeth move to the position where a part of tooth poles are overlapped with the suspension teeth, the condition that one suspension tooth is opposite to a pair of adjacent rotor teeth occurs, the rotor movement range is pi/24 < theta and is not more than pi/24 + gamma, and the air gap equivalent magnetic network is shown in fig. 6. The calculation formula of the air gap magnetic conductance in the region 3 is as follows:
wherein G is31Air gap permeance at the overlapping part of the floating tooth and the current rotor tooth, G35Air gap permeance at the overlap of the floating tooth with the next rotor tooth, G32And G37For the air gap permeance of the current rotor tooth edge path, as can be seen in FIG. 6, G32And G37The flux tube flux guides are respectively a rectangle and 1/4 circles from two sides of the current rotor tooth to the suspension tooth; g34And G36The gap permeance for the next rotor tooth edge path, G, can be seen in FIG. 634And G36The flux tube flux guides are respectively a rectangle and 1/4 circles from two sides of the next rotor tooth to the suspension tooth; g33Air gap permeance being a straight path from the floating tooth to the yoke of the rotor, i.e. rectangular flux tube permeance, GrtBeing the flux-guide of a single rotor tooth, GstA core flux guide being a suspended pole.
The edge permeance G of the rotor in the region 446、G47The variation does not occur, the rest part of the air gap magnetic resistance does not change, the magnetic linkage of the suspension winding tends to a constant value in the area, the rotor in the area operates in the range of pi/24 + gamma < theta and not more than pi/8-gamma, and the equivalent magnetic network is shown in figure 7. The calculation formula of the air gap magnetic conductance in the region 4 is as follows:
wherein G is41Air gap permeance at the overlapping part of the floating tooth and the current rotor tooth, G45Air gap permeance at the overlap of the floating tooth with the next rotor tooth, G42And G47For the air gap permeance of the current rotor tooth edge path, as can be seen in FIG. 7, G42And G47The flux tube flux guides are respectively a rectangle and 1/4 circles from two sides of the current rotor tooth to the suspension tooth; g44And G46The gap permeance for the next rotor tooth edge path, G, can be seen in FIG. 744And G46The flux tube flux guides are respectively a rectangle and 1/4 circles from two sides of the next rotor tooth to the suspension tooth; g43Air gap permeance being a straight path from the floating tooth to the yoke of the rotor, i.e. rectangular flux tube permeance, GrtBeing the flux-guide of a single rotor tooth, GstA core flux guide being a suspended pole.
In the rotor rotation range corresponding to the suspension pole in one period of the motor, according to the half-period condition, it can be known that the regions 5, 6 and 7 are respectively symmetrical to the regions 3, 2 and 1, and the calculation formulas of the air gap permeance are in one-to-one correspondence, namely Gagap5＝Gagap3，Gagap6＝Gagap2，Gagap7＝Gagap1。
The invention separately calculates the air gap permeance which constantly changes in the rotor motion process, divides a period process into 7 areas according to the periodic change of the topology of an air gap magnetic circuit in the operation process of the rotor of the axial permanent magnetic suspension flywheel motor, and further calculates the air gap permeance for each area.
And step five, according to the actual structure of the axial permanent magnetic suspension flywheel motor, taking the radial and axial magnetic circuits of the axial permanent magnetic suspension flywheel motor as research targets, enabling the suspension iron cores, the permanent magnets and the rotor yoke parts of the radial magnetic circuit and the axial magnetic circuit to respectively form a magnetic resistance in an equivalent mode, and combining the A-phase and B-phase air gap magnetic conductances obtained in the step four to obtain a dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor. Moving the rotor of the machineIn the process, the permanent magnet with unchanged magnetic conductance, the suspension pole and the rotor yoke are equivalent to a flux tube respectively, and the radial and axial magnetic conductances of the corresponding axial permanent magnet magnetic suspension flywheel motor are calculated as follows: in the magnetic circuit, the two parts of the magnetic resistance are in series relation. After 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, and the equivalent magnetic resistance of the part of the rotor yoke uses Rry1That is, the bias magnetic flux generated by the permanent magnet forms a closed loop through the axial magnetic circuit, and the equivalent magnetic resistance of the rotor yoke of the part is represented by Rry2To indicate. 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: ragapxAir gap reluctance of phase A, RbgapxAir gap reluctance of phase B, RstaIron core reluctance of A-phase suspension pole, RstbIron core reluctance of B-phase suspension pole, RpmFor magnetic reluctance of axially-charged permanent magnets, FpmMagnetomotive force of axially-charged permanent magnets, FsαIs the magnetomotive force of the suspension winding.
The calculation formula for each quantity in fig. 8 is:
Gpm＝u0upm·π(lpmo 2-lpmi 2)/hpm (13)
Fpm＝(Brm·hpm)/(u0·upm) (14)
Fsα＝N·isα (15)
in the formula: u. of0Is a vacuum permeability of urIs the relative magnetic permeability of the rotor core, h is the tooth height of the suspended teeth, leIs the rotor yoke thickness, wrIs the rotor tooth width, wsFor suspending tooth width, /)sIs the sum of the lengths of the floating teeth and the yoke part, lrIs the rotor tooth thickness, upmFor the relative permeability of axially-magnetized permanent magnets, /)pmoFor axially magnetizing the outer diameter of the permanent magnet, /)pmiFor axially magnetizing the inner diameter of the permanent magnet, hpmThickness of the axially magnetized permanent magnet, BrmRemanence of permanent magnets for axial magnetization, isαThe winding current of the suspension winding is shown, and N is the number of turns of the suspension winding.
The invention respectively calculates the radial and axial magnetic circuits of the axial permanent magnetic suspension flywheel motor, simplifies the magnetic line distribution of the motor according to the actual parameters of the axial permanent magnetic suspension flywheel motor, respectively calculates the constantly changed air gap magnetic conductance and the permanent magnet, the suspension pole and the rotor yoke part magnetic conductance, simplifies the three-dimensional magnetic field of the axial permanent magnetic suspension flywheel motor into a dynamic magnetic network, establishes the integral dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor, and improves the model precision, the modeling speed and the calculation speed.
According to the dynamic equivalent magnetic network model obtained in the step S5, specific values of the inductance, the back electromotive force, and the flux linkage of the levitation winding of the axial permanent magnetic levitation flywheel motor are directly calculated according to the basic formula of the magnetic circuit with the permeance of the radial magnetic circuit as a research target, and simulation verification is performed below.
Simulation verification:
to further illustrate the effectiveness of the dynamic equivalent magnetic network model of the axial permanent magnetic levitation flywheel motor built by the invention, a Finite Element Analysis (FEA) of the motor and a flux linkage pair of the model built by the invention (EMN) are shown in fig. 11, and it can be known from the graph analysis that the flux linkage result obtained by the invention is basically consistent with the finite element analysis result in the whole period.
The resource consumed by Finite Element Analysis (FEA) of the motor and the solution of the model (EMN) built by the invention is shown in fig. 12, and it can be seen from the figure that compared with the finite element analysis method, the invention can obviously reduce the calculation resource in the early stage of motor design.
In order to further verify the effectiveness of the dynamic equivalent magnetic network model of the axial permanent 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 calculation is carried out according to the formulas (16), (17) and (18).
Ψ＝N·U·Gz (16)
Where Ψ is the flux linkage of the suspension winding, N is the number of turns of the suspension winding, U is the magnetomotive force of the suspension winding, e is the back electromotive force of the suspension winding, and GzTotal magnetic conductance, G, of radial magnetic circuitsagapxThe air gap permeance in phase a region x. The dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor built by the invention can predict the electromagnetic property of the motor, can directly calculate the specific values of the inductance, the counter electromotive force and the flux linkage of the suspension winding of the motor, and reduces the calculation resources in the early stage of motor design.
Referring to fig. 11, 13 and 14, the finite element analysis FEA of the motor is compared with the back electromotive force of the levitation inductance of the model EMN built by the invention as shown in fig. 13, and the finite element analysis FEA of the motor is compared with the levitation winding inductance of the model EMN built by the invention as shown in fig. 14. It can be seen that: compared with a finite element analysis result, the model has higher calculation speed, and the defect of low precision of the traditional equivalent magnetic circuit method is avoided.
In summary, the invention adopting the above technical scheme has the following beneficial effects:
(1) a dynamic equivalent magnetic network model formed based on a traditional equivalent magnetic circuit method is modeled aiming at the condition that the topology of an air gap magnetic circuit and the magnetic resistance of each flux tube change along with the rotation of a rotor in the rotation process of the rotor, so that the solving precision of the established model is greatly improved, and the dynamic modeling in the early stage of motor design is realized.
(2) The traditional equivalent magnetic circuit model only considers the radial magnetic circuit of the motor, the magnetic circuit of the motor with a complex structure can not be accurately described, the solving precision of the model is low, and the axial permanent magnetic suspension flywheel motor dynamic equivalent magnetic network model 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 rotation process of the motor.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A method for establishing a dynamic equivalent magnetic network model of an axial permanent magnetic suspension flywheel motor is characterized by comprising the following steps: 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 magnetic suspension flywheel motor, obtaining air-gap magnetic line distribution of the axial permanent magnetic suspension flywheel motor through finite element simulation, dividing a magnetic line flowing path into air-gap magnetic paths of three equivalent magnetic flux tubes of a rectangle, a rectangle plus 1/4 circle and a rectangle plus 1/4 circular ring, and determining a critical angle between the rectangle plus 1/4 circular magnetic flux tube and the rectangular magnetic flux tube based on a 'magnetic resistance minimum principle';
s2, obtaining an equivalent magnetic network model of an air gap magnetic circuit in the rotation process of the rotor of the axial permanent magnetic suspension flywheel motor according to the three equivalent flux tubes 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 process of the rotor into 7 areas;
s3, acquiring the motion range of the rotor in each area according to the critical angle obtained in the step S1 by combining the 7 divided areas in the step S2;
s4, calculating the air gap permeance of the A phase and the B phase of the axial permanent magnet magnetic suspension flywheel motor according to the topological structure of the equivalent magnetic network of the air gap of each region obtained in the step S2 and by combining the rotation range of the rotor in the step S3;
and S5, according to the actual structure of the axial permanent magnet magnetic suspension flywheel motor, taking the radial and axial magnetic circuits of the axial permanent magnet magnetic suspension flywheel motor as research targets, enabling the suspension iron cores, the permanent magnets and the rotor yoke parts of the radial magnetic circuit and the axial magnetic circuit to respectively form a magnetic resistance in an equivalent mode, and combining the A-phase and B-phase air gap magnetic conductances obtained in the step S4 to obtain a dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor.
2. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor according to claim 1, wherein the method comprises the following steps: and according to the dynamic equivalent magnetic network model obtained in the step S5, directly calculating specific values of the inductance, the back electromotive force and the flux linkage of the suspension winding of the axial permanent magnetic suspension flywheel motor according to a basic formula of the magnetic circuit by taking the magnetic conductance of the radial magnetic circuit as a research target.
3. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor according to claim 2, wherein the calculation formula of the suspension winding inductance is as follows:
where N is the number of turns of the levitation winding, Gry1Is radial flux guide, GzIs the total flux guide of the radial magnetic circuit.
4. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor according to claim 1, wherein the method comprises the following steps: in step S2, the period of the rotor rotation is 30 °.
5. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor according to claim 1, wherein the method comprises the following steps: the formula for calculating the critical angle in step S1 is:
wherein gamma is the critical angle, RrinIs the rotor tooth inside diameter; rsoutThe outer diameter of the suspension tooth; rryinIs the inner diameter of the yoke part of the rotor.
6. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor according to claim 1, wherein the method comprises the following steps: in the step S2, a cycle of rotation of the rotor of the axial permanent-magnet magnetic suspension flywheel motor is divided into 7 regions 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 of force in the air gap magnetic circuit is equivalent to a flux tube based on an equivalent magnetic circuit method; a period is divided into 7 sub-regions according to the change condition of an air gap equivalent magnetic network model in the period of rotor rotation, when the rotor rotates in the period, the rotor rotates from the region 1 to the region 7 in sequence, the topology of the air gap equivalent magnetic network among the regions is different, and the resistance value of each flux tube in the region changes along with the rotation of the rotor.
7. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor according to claim 1, wherein the method comprises the following steps: in the step S1, the air-gap magnetic circuit is divided into flux tubes of different shapes, the flux tubes are rectangular flux tubes, rectangular strip 1/4 circular flux tubes and rectangular strip 1/4 circular flux tubes, and the flux guide calculation formulas of the three types of flux tubes are respectively:
the permeance of the rectangular flux tube is:
the permeance of the rectangular band 1/4 round flux tube is:
the magnetic conductance of the rectangular band 1/4 circular magnetic flux tube is:
wherein h is the tooth height of the suspension teeth, the average length of the rectangular part in each flux tube, and X1Is the width of the rectangular part in each flux tube, C1Is the inner diameter u of the circular magnetic circuit in each flux tube0Is a vacuum magnetic permeability.
8. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor according to claim 1, wherein the method comprises the following steps: the step S5 is to obtain a dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor as a whole, and the specific process is as follows:
acquiring air gap permeance 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 permeance is three-dimensional permeance;
respectively and equivalently setting permanent magnets, suspension poles and rotor yokes, of which the magnetic conductances are not changed in the rotation process of the rotor, as flux tubes, and calculating the radial and axial magnetic conductances of the corresponding axial permanent magnet magnetic suspension flywheel motor; the radial magnetic conductance is the magnetic conductance generated by the yoke part of the rotor after magnetic flux generated by the suspension pole winding passes through a radial magnetic circuit to form a closed loop; the axial magnetic conductance is the magnetic conductance generated by the yoke part of the rotor after bias magnetic flux generated by the permanent magnet passes through an axial magnetic circuit to form a closed loop;
and simplifying the three-dimensional magnetic field of the axial permanent magnetic suspension flywheel motor into a dynamic magnetic network by combining the three-dimensional air gap magnetic conductance and the radial and axial magnetic conductances of the axial permanent magnetic suspension flywheel motor, thereby obtaining the overall dynamic equivalent magnetic network model of the axial permanent magnetic suspension flywheel motor.
9. The method for establishing the dynamic equivalent magnetic network model of the axial permanent magnet magnetic suspension flywheel motor according to claim 8, wherein the method comprises the following steps: the expression formula of the radial magnetic conduction and the axial magnetic conduction in a period of the motor rotor is as follows:
wherein G isry1Is radial flux guide, Gry2Is axially magnetically permeable, u0Is a vacuum permeability of urIs the relative magnetic permeability of the rotor core, h is the tooth height of the suspended teeth, leIs the rotor yoke thickness, wrIs the rotor tooth width, RroutIs the outer diameter of the rotor, RrinThe inner diameter of the rotor teeth.
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