CN109831046A - A kind of permanent magnetism spherical motor construction and electrifying method based on spheric harmonic function - Google Patents
A kind of permanent magnetism spherical motor construction and electrifying method based on spheric harmonic function Download PDFInfo
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Abstract
本发明涉及一种基于球谐函数的永磁球形电机结构设计与通电方法，该电机包括圆柱形定子线圈、圆柱形转子磁极两部分，对其关键参数即线圈底面中心球坐标的分量和磁极底面中心球坐标的分量进行设计，其中球坐标分量的取值范围分别是θR,θS∈[0,π]，包括：第一步：磁极底面中心球坐标的分量的确定；第二步：线圈底面中心球坐标的分量的确定；第三步：线圈通电方法的确定。
The invention relates to a structure design and energization method of a permanent magnet spherical motor based on spherical harmonic function. The motor includes two parts, a cylindrical stator coil and a cylindrical rotor magnetic pole. components and the spherical coordinates of the center of the bottom surface of the magnetic pole components, where the value ranges of the spherical coordinate components are θ R , θ S ∈ [0, π], respectively, Including: The first step: the spherical coordinates of the center of the bottom surface of the magnetic pole The determination of components; the second step: the spherical coordinates of the center of the bottom surface of the coil The determination of the component; the third step: the determination of the coil energization method.
Description
Technical field
The invention belongs to permanent magnetism spherical motor construction fields, more particularly to take spheric harmonic function as the permanent magnetism ball of reference
Shape motor.
Background technique
Domestic and foreign scholars have done many about the design and analysis of magneto globular motor stator, rotor structures at present
Work, about the research of its stator coil split-phase strategy, there has also been remarkable progress.For its structure, two classes can be divided into,
The movement of one class formation transfer is limited by angle, and rotor rotation and inclination separately consider, such structure is fixed using layer-stepping, turns
Minor structure, such as rotor equator layer one layer of permanent magnet pole of distribution, two sides respectively have one layer to stator coil under the line, the line of identical layer
The rotation of circle control rotor, the inclination of the coil control rotor of different layers.Relevant, some researchers turn to increase motor
Square and improve control stability, increase the stator coil number of plies and the rotor magnetic pole number of plies, propose outer-rotor structure and
New coil structure and rotor magnetic pole structure；In order to improve rotor motion range and operation characteristic, the items of motor are proposed
Mechanical dimension's optimisation strategy；For the ease of control, rotating coil and tilt coil are controlled respectively.Another class formation transfer fortune
It is dynamic to have a possibility that more, stator coil and rotor magnetic pole on symmetry and the spherical surface that the distribution in space has height
Uniformity guarantees movement without singular point.Such as regular polygon structure, stator coil and rotor magnetic pole be in spherical surface with it is polyhedral
It is overlapped rule arrangement, the symmetry with height.In the control method of these two types of structure permanent magnet globular motors, with reference to
The current reference equation that the basic theories of rotating electric machine is proposed, use the derivation algorithm based on dynamics and kinematical equation with
And various New Algorithms, all there is more complicated theoretical foundation, contacted seldom with the basic theories of traditional rotating electric machine.
Spheric harmonic function plays a significant role analyzing three-dimensional motor as one group of orthogonal basement in three-dimensional space.Into
One step, it can analyze the electromagnetic torque and control method of motor using this mathematical tool.For in the first class formation
Two-layer stratigraphic structure, researcher demonstrate the matching state of each order of ball harmonic wave；For the second class formation polyhedral structure permanent magnetism
Globular motor, the method that researcher exports coil stimulating using ball harmonic and reactive detection.Based on the above research achievement, it is believed that ball
Harmonic wave all has reference significance for the structure design and control strategy of permanent magnetism spherical motor.The present invention is on the studies above basis
On, based on the second class magneto globular motor structure, propose new stator coil and rotor magnetic pole on the spherical surface of space
Distribution Principles.
Summary of the invention
The purpose of the present invention is to propose to a kind of design of novel permanent magnetic globular motor structure and electrifying methods.Scheme is as follows:
A kind of permanent magnetism spherical motor construction and electrifying method based on spheric harmonic function, which includes cylinder shape stator
Coil, cylindrical rotor magnetic pole two parts, to its key parameter, that is, coil bottom surface astrosphere coordinateComponent and magnetic pole
Bottom center's spherical coordinatesComponent is designed, and wherein the value range of spherical coordinates component is θ respectivelyR,θS∈ [0, π],And a kind of electrifying method is provided for this kind of structure design, include the steps that following:
Step 1: magnetic pole bottom center spherical coordinatesThe determination of component
(1) selection of order and degree of spherical harmonics is referred to: in view of the distributing homogeneity in magnetic field on spherical surface and single layer pole number
Half should be even number, only spheric harmonic functionWithProperly, it and selects in fact
Portion's image is as reference, wherein spheric harmonic functionIt is about space spherical coordinatesVariable and θ ∈ [0, π],The rank of function index l representative function, value range be l ∈ [0 ,+∞), function subscript m representative function time, take
Being worth range is m ∈ [0, l]；
(2) determination of position of magnetic pole: when rotor field, corresponding main harmonic order isWhen, rotor
Magnetic pole is distributed as in the positive hemisphere of Z axis, and spherical surface is divided into 2l parts along Z axis, and the l pole N is alternately arranged with the l pole S, negative in Z axis
Spherical surface is divided into 2l parts along Z axis by hemisphere, and the l pole N is alternately arranged with the l pole S, and is also replaced in the positive and negative semiaxis of Z axis
Arrangement is upper layer and lower layer heteropolarity；The spherical coordinates of each magnetic pole of first layer is respectively as follows:The second layer
The spherical coordinates of each magnetic pole is respectively as follows:Wherein k=0,1 ... 2l-1, θ 'RFor equationMinimum zero point,For equationMinimum zero point；
When rotor field, corresponding main harmonic order isWhen, rotor magnetic pole is distributed as will along Z axis
Spherical surface is divided into 2l parts, when the l pole N and the l pole S are alternately arranged layer under the line, and is in the positive and negative semiaxis identical polar of Z axis
The spherical coordinates of upper layer and lower layer same polarity, each magnetic pole of equator layer is respectivelyWherein k=0,1 ...
2l-1,For equationMinimum zero point；Uniformity is considered, by the magnetic pole of equator layer respectively to Z axis pros
It is replicated to negative direction movement, becomes two-layer；
Step 2: coil bottom surface astrosphere coordinateThe determination of component
It is that rotor magnetic pole is mobile to the positive and negative semiaxis of Z axis first, and is substituted with coil, such coil is named as " Z axis
Coil "；Two layers of the magnetic pole bottom centre spherical coordinates that followed by will be distributed over the positive and negative semiaxis of Z axis is rotated, and is rotated by 90 ° around X-axis
The coil positioned at the positive and negative semiaxis of Y-axis is obtained, " Y-axis coil " is named as；Followed by it will be distributed over two layers of magnetic pole of the positive and negative semiaxis of Z axis
Bottom centre's spherical coordinates is rotated, and is rotated by 90 ° to obtain the coil positioned at the positive and negative semiaxis of X-axis around Y-axis, is named as " X-axis line
Circle "；It is finally to merge 3 groups of coils, composition stator is whole；It is symmetrical about the centre of sphere with distribution of the coil on spherical surface and closes
Coordinate plane in rectangular coordinate system is symmetrical, need to only analyze the coil coordinate of one of quadrant, corresponding l rank spheric harmonic function
Rotor structure has three sides of the convex surface equilateral triangle that 1.5l coil is evenly distributed in first quartile on spherical surface
On；It is listed according to the distribution relation of each coil of above-mentioned first quartile containing coil position unknown numberEquation, solve obtain
Basic parameter
Step 3: the determination of coil electrifying method
(1) stator and rotor magnetic field harmonics coefficient analysis: ball harmonic wave is obtained about the symmetrical magnetic pole simulation calculation of the centre of sphere on rotor
Coefficient, it is known that then each position of magnetic pole passes through the rotation of ball harmonic wave, superposition obtains the corresponding ball harmonic constant of all magnetic poles, then really
Rotor motion profile obtains the ball harmonic constant of any position using the rotation of ball harmonic wave, extracts main order ball harmonic constant and constitutes
Rotor-position eigenmatrix CR(t), element is the function about time t in matrix；It is logical single about the symmetrical coil of the centre of sphere on stator
Position current simulations, which calculate, obtains corresponding harmonic constant, and the main order ball harmonic constant for extracting respective rotor constitutes stator coil position
Eigenmatrix KS, matrix element is constant；
(2) current equation: gone out using stator and rotor magnetic field proportional the characteristics of can produce constant torque and stator excitation
The theory of rotating excitation field proposes coefficient corresponding equation: KSI(t)=η CR(t), wherein KSFor stator coil position feature matrix, I(t)
For coil current matrix, η is torque factor, this constant is determined by desired output torque, CR(t)For rotor-position eigenmatrix；Most
Equation is solved eventually obtains each group coil current I(t)=η KS -1CR(t)。
Technical effect of the invention is as follows:
1. the new globular motor stator and rotor regularity of distribution, has references to the shape of Spatial Sphere harmonic wave, have in structure design aspect
There is novelty.
2. the corresponding electrifying method of new structure is the form of matrix multiple, but has one for the electric current of each coil
Fixed grouping relationship, for further controlling with reference significance.
Detailed description of the invention
Fig. 1: Y32 type rotor schematic diagram.
Fig. 2: Y44 type rotor schematic diagram.
Fig. 3: stator coil position derives.
Fig. 4: coil label schematic diagram.
Fig. 5: rotor field harmonic amplitude (modulus value).
Fig. 6: stator coil electric current.
Fig. 7: stator and rotor harmonics index contrast.
Specific embodiment
The invention proposes the novel permanent magnetic globular motor designs with outer-rotor structure, with reference to the accompanying drawings and examples
The present invention is described in detail.Specific implementation step of the present invention is as follows:
1, the selection of ball harmonic order
It is the order and number of the spheric harmonic function that can be used as structure design reference first.For same order spheric harmonic function, just
Secondary item and negative item parts have conjugate symmetry, therefore just secondary item parts are used only herein.When the order for determining spheric harmonic function
When with number, real part (re) and imaginary part (im) are of similar shape, but location is different.But they all may be used
Using the reference designed as structure, and real part is only selected herein.
In view of the distributing homogeneity in magnetic field on spherical surface, for l rank spheric harmonic function, only (l-1) and l item parts can be with
Reference as structure design, is then divided into 4 classes for spheric harmonic function according to the distribution in magnetic field:
(a) magnetic direction about the symmetrical two o'clock of the centre of sphere is directed to the centre of sphere (or outside ball), about XOY plane symmetrical two
The magnetic direction of point is directed to the centre of sphere (or outside ball), such as
(b) about the symmetrical two o'clock of the centre of sphere, it is a little directed toward the centre of sphere, another point is directed toward outside ball, about XOY plane symmetrical two
The magnetic direction of point is directed toward the centre of sphere, and another point is directed toward outside ball, such as
(c) about the symmetrical two o'clock of the centre of sphere, it is a little directed toward the centre of sphere, another point is directed toward outside ball, about XOY plane symmetrical two
The magnetic direction of point is directed toward the centre of sphere (or outside ball), such as
(d) it is directed toward the centre of sphere (or outside ball) about the magnetic direction of the symmetrical two o'clock of the centre of sphere, about the symmetrical two o'clock of XOY plane
Magnetic direction be directed toward the centre of sphere, and another point be directed toward ball outside, such as
Then, it is contemplated that the derivation method of stator coil position, stator coil need to be evenly distributed on spherical surface, only
(a) it may be used as the reference of motor construction with (b) two class spheric harmonic function.
2, the determination of magnetic pole approximate location
For each order ball harmonic wave, the relationship of the distribution of distribution shape and rotor magnetic pole in space is as follows: a side
Face, considers the uniformity that ball harmonic wave is distributed in spherical surface, and magnetic pole can be non-cylindrical abnormity magnetic pole, be also possible to cylinder-shaped magnetic pole；
On the other hand, the just secondary item of ball harmonic wave same order and negative item have symmetric relation, therefore need to only consider just secondary item.Rotor magnetic pole point
Cloth rule is as follows:
(a) when rotor field, corresponding main harmonic order isWhen, rotor magnetic pole is distributed as in Z axis
Spherical surface is divided into 2l parts along Z axis by positive hemisphere, and the l pole N is alternately arranged with the l pole S, in the negative hemisphere of Z axis, along Z axis by ball
Face is divided into 2l parts, and the l pole N is alternately arranged with the l pole S, and it is different in the positive and negative semiaxis of Z axis to be also alternately arranged i.e. upper layer and lower layer
Polarity.The spherical coordinates of each magnetic pole of first layer is respectively
The spherical coordinates of each magnetic pole of the second layer is respectively as follows:
(b) when rotor field, corresponding main harmonic order isWhen, rotor magnetic pole is distributed as along Z
Spherical surface is divided into 2l parts, when the l pole N and the l pole S are alternately arranged layer under the line, and in the positive and negative semiaxis same pole of Z axis by axis
Property, that is, upper layer and lower layer same polarity, the spherical coordinates of each magnetic pole of equator layer is respectively
In practice in order to which uniformity becomes two by the magnetic pole of equator layer respectively to Z axis positive direction and the mobile duplication of negative direction
Laminar, specific coordinate are needed through optimization realization, and such rotor structure can also generate identical main order harmonic.
3, the determination of magnetic pole exact position
And spherical coordinates parameter aboveDetermination, on the one hand, can according to ball harmonic wave be distributed determine its peak value at
Spherical coordinates；On the other hand, the concept of optimization can be introduced, so that magnetic pole distribution is closest with main harmonic number, and its
His harmonic amplitude is minimum.By the above-mentioned rotor magnetic pole regularity of distribution, it was specifically described by taking two kinds of harmonic structures as an example below
Journey.
(a) be first upper layer and lower layer heteropolarity rotor structure, illustrate by taking Y32 type rotor as an example, Y32 order ball harmonic wave solution
Analyse expression formula are as follows:
Its image is as in Figure 2-4, and the peak value on the direction θ can be found out by following formula:
Minimum zero point is taken, can be obtainedItsPeak value on direction can be found out by following formula:
Minimum zero point is taken, can be obtainedSo the coordinate of permanent magnet pole shown in such as Fig. 1 (b) or (c) are as follows:
(b) the followed by rotor structure of upper layer and lower layer same polarity, illustrates, Y44 order ball harmonic wave solution by taking Y44 type rotor as an example
Analyse expression formula are as follows:
Wherein θ=[0, π],Its image is as shown in Figure 2-5.Its peak value on the direction θ can pass through following formula
It finds out:
Minimum zero point is taken, can be obtainedItsPeak value on direction can be found out by following formula:
Minimum zero point is taken, can be obtainedSo when magnetic pole is distributed one layer under the line, as shown in Fig. 2 (b), each magnetic pole
Coordinate are as follows:
When magnetic pole distribution two layers totally of two sides under the line, as shown in Fig. 2 (c), the coordinate of each magnetic pole are as follows:
Wherein θ1 RIt needs to realize by optimization and solve.
4, coil position is substantially estimated
Based on above-mentioned rotor magnetic pole analysis of distribution process, the stator coil regularity of distribution is proposed, and with Y32 type rotor knot
Structure illustrates for deriving Y32 type stator structure.
As shown in figure 3, the first step is that rotor magnetic pole is mobile to the positive and negative semiaxis of Z axis, and substituted, that is, corresponded to coil
Stator coil is placed in the place of rotor magnetic pole, altogether 8 coils, one group is symmetrically divided into according to the centre of sphere, such 4 groups of coils name
For " z axis circle "；Second step is to will be distributed over two layers of magnetic pole bottom centre spherical coordinates of the positive and negative semiaxis of Z axis to be rotated, around X-axis
It is rotated by 90 ° to obtain the coil positioned at the positive and negative semiaxis of Y-axis, is named as " Y-axis coil "；Third step is to will be distributed over the positive and negative semiaxis of Z axis
Two layers of magnetic pole bottom centre spherical coordinates rotated, be rotated by 90 ° to obtain the coil positioned at the positive and negative semiaxis of X-axis, name around Y-axis
For " X-axis coil "；4th step is to synthesize 3 groups of coils, and composition stator is whole.Pictorial diagram in Fig. 3 is the lower semisphere of stator ball,
Episphere can be by symmetrically obtaining.
5, coil exact position derives
As shown in figure 4, carrying out label according to being symmetrically divided into 12 groups about the centre of sphere to 24 coils.Wherein symbol indicates electricity
Positive direction is flowed, "+" indicates that magnetic field deviates from the centre of sphere when coil leads to unitary current, and "-" indicates that magnetic field is directed toward when coil leads to unitary current
The centre of sphere.
Next it needs to carry out specific location accurately to derive, it is normal for determining that the bottom center of stator coil is distributed in radius
On the spherical surface of value, each coil coordinate isThen the coil of first quartile under rectangular coordinate system is analyzed
The coil coordinate of position, other quadrants can be obtained by symmetry: each coil spherical coordinates component of first quartile meets following
Relationship is overlooked from Z+ axis, and coil should be equally distributed:
As shown in figure 4, rectangular co-ordinate (the x of each group coilv,yv,zv)S, v=1 ... 12, straight line, that is, X and Y locating for coil
Coordinate, according to the corresponding relationship of rotation, the 1st group, the 5th group and the 6th group of coordinate should meet:
1st group of coil and the 5th group of coil angle in the plane that they are constituted are 45 °, similarly the 5th group of coil and the 6th
Group coil, the 5th group of coil and the 6th group of coil also meet such relationship:
In conclusion the θ component of the 1st and 5 group of coil can be obtained in conjunction with the transformational relation of spherical coordinate system and rectangular coordinate system
Coordinate:
θ1 S=0.53, θ5 S=1.2
It finally can get the angle component of the position spherical coordinates of 12 groups of coils:
And for the rotor structure of upper and lower same polarity, such as Y44 shape rotor structure, corresponding stator coil position is also according to upper
The discussion in face is derived, but for coil be symmetrically grouped according to the centre of sphere when, it is same when determining electric current positive direction
Group coil leads to unitary current, and magnetic field should all be directed toward the centre of sphere.
6, stator and rotor magnetic field harmonics coefficient analysis
(a) rotor magnetic pole harmonic constant: ideally, when Y32 type rotor magnetic pole is polymorphic structure, magnetic field only generates 3
Rank ball harmonic wave, but to cylinder-shaped magnetic pole in this article, contains other order harmonics in actual magnetic field, for the ease of analysis,
The influence for ignoring other order ball harmonic waves, only analyzes its third order products.
Firstly, be located at Z axis on about symmetrical two double magnetic poles being magnetized along Z axis negative direction of the centre of sphere, in space
3 order harmonics coefficient of magnetic flux density radial component are as follows:
Using the superposition theorem of rotation transformation and magnetic field, 3 order harmonics coefficient of Y32 type rotor field is as follows:
Rotor rotates ZYZ Eulerian angles, and the coefficient under stator coordinate changes:
The polarity of rotor magnetic pole position combination magnetic pole is obtained into Eulerian angles:
It can to sum up obtain:
As shown in figure 5, the magnetic field to Y32 type rotor carries out finite element analysis, corresponding ball harmonic constant is solved.It is different from
Ideally Y32 type rotor only generates 3 order harmonics, there are other order harmonics in air gap when magnetic pole is cylindrical,
His order harmonic is mainly 7 order harmonics, but it is lower compared to the amplitude of 3 order harmonics, therefore ignores the ball harmonic wave of higher order time
Part.3 ranks and 7 exponent parts also need to be only considered when finally to the comparison of stator and rotor magnetic field harmonics amplitude.
Any time, rotor relative initial position rotate Eulerian angles (α, beta, gamma)tWhen, Distribution of Magnetic Field in space
Ball harmonic constant can be obtained by ball harmonic wave rotation transformation:
Real part, the imaginary part for separating spherical harmonic coefficient, constitute new matrix:
(b) stator field harmonic constant: in the corresponding stator of Y32 rotor structure, the twin coil on Z axis is according to above
The positive direction, the ball harmonic constant in the magnetic field that logical unitary current motivates are as follows:
And then in the way of rotation superposition, 3 order harmonics coefficient matrix of stator coil excitation field under unitary current is obtained:
The position Eulerian angles of its coil u are represented byAnd u=1,2 ... 12.By 3 order harmonics
Coefficient matrix K ' separates real part, the imaginary part of spherical harmonic coefficient, constitutes new matrix:
The structure studied herein is permanent magnet material in addition to magnetic pole, and coil is outside enamel-cover wire material, other are plastics material
Matter, so meeting the superposition theorem in magnetic field in air gap.Any current value I(t)Motivate 3 order harmonic component of lower peripheral surface radial direction flux density
Are as follows:
7, coil electrifying method
For the Y32 type momentum spherical structure and magnetic field analysis being analyzed above as a result, using stator and rotor magnetic field is proportional can
The characteristics of to generate constant torque and stator excitation go out the theory of rotating excitation field, obtain equation:
KSI(t)=η CR(t)
Wherein I(t)For current matrix, KSFor stator coil position feature matrix, when the stator coil of magneto globular motor
Position is determining, then KSIt determines, rotor-position eigenmatrix CRChanging with rotor-position and changes, torque factor η is constant, according to
Required torque is adjusted, and when torque factor is big, stator coil institute galvanization is big；When torque factor is small, stator coil institute
Galvanization is small.
It solves equation and obtains I(t)=KS -1ηCR(t), the current expression of each group coil has certain relationship, but unlike that
Relationship after common rotating electric machine, amplitude, the phase of each group coil are as complexity, and expression formula is complex, is not
Simple delayed phase relationship.
8, simulating, verifying
Rotor motion track selected first, following formula be 3 group rotor skimulated motion tracks Eulerian angles expression and torque because
Son:
Rotor is equivalent to rotate around Y-axis.Calculated electric current is as shown in Figure 6.As can be seen from the figure it is rotated around fixing axle
Each group coil current have biggish correlation, also more meet with actual analysis result, rotor rotates about the z axis, in correspondence
Four coils in portion should also be 90 electrical angles of difference for the theory according to common rotating electric machine, the two more meets.
At the selected t=0.2s moment, 12 groups of coil current values under the track such as Fig. 6 are corresponded to, stator is emulated in ANSOFT
Static magnetic field, then calculate corresponding each order harmonics coefficient, it carried out with the rotor field harmonic constant at corresponding moment pair
Than.Corresponding main 3 rank of order harmonic of rotor has been selected herein, and has selected higher 7 subharmonic in other harmonic waves, between them
Comparison it is as shown in Figure 7.By in figure it can be seen that 3 rank ball harmonic amplitude parts be completely coincident, illustrate stator produce with
Rotor motion and the rotating excitation field moved；And it is mutually weaker for 7 rank ball harmonic amplitudes, influence of the gap to motor control is
Torque ripple is generated, weakening it influences to need to account for from pole dimension design etc., this gap is only shown herein,
For the reference of optimization design in future.
Claims (1)
1. a kind of permanent magnetism spherical motor construction and electrifying method based on spheric harmonic function, which includes cylinder shape stator line
Circle, cylindrical rotor magnetic pole two parts, to its key parameter, that is, coil bottom surface astrosphere coordinateComponent and magnetic pole bottom
Face center spherical coordinatesComponent is designed, and wherein the value range of spherical coordinates component is θ respectivelyR,θS∈ [0, π],And a kind of electrifying method is provided for this kind of structure design, include the steps that following:
Step 1: magnetic pole bottom center spherical coordinatesThe determination of component
(1) refer to the selection of order and degree of spherical harmonics: in view of the distributing homogeneity in magnetic field on spherical surface and single layer pole number one
It partly should be even number, only spheric harmonic functionWithProperly, and its real part figure is selected
As reference, wherein spheric harmonic functionIt is about space spherical coordinatesVariable and θ ∈ [0, π],The rank of function index l representative function, value range be l ∈ [0 ,+∞), function subscript m representative function time, take
Being worth range is m ∈ [0, l]；
(2) determination of position of magnetic pole: when rotor field, corresponding main harmonic order isWhen, rotor magnetic pole
It being distributed as in the positive hemisphere of Z axis, spherical surface is divided into 2l parts along Z axis, the l pole N is alternately arranged with the l pole S, in the negative hemisphere of Z axis,
Spherical surface is divided into 2l parts along Z axis, the l pole N is alternately arranged with the l pole S, and is also alternately arranged i.e. in the positive and negative semiaxis of Z axis
Upper layer and lower layer heteropolarity；The spherical coordinates of each magnetic pole of first layer is respectively as follows:Each magnetic pole of the second layer
Spherical coordinates is respectively as follows:Wherein k=0,1 ... 2l-1, θ 'RFor equationMinimum zero point,For equationMinimum zero point；
When rotor field, corresponding main harmonic order isWhen, rotor magnetic pole is distributed as spherical surface along Z axis
2l parts, when the l pole N and the l pole S are alternately arranged layer under the line are divided into, and is up and down in the positive and negative semiaxis identical polar of Z axis
The spherical coordinates of two layers of same polarity, each magnetic pole of equator layer is respectivelyWherein k=0,1 ... 2l-1,For equationMinimum zero point；Consider uniformity, by the magnetic pole of equator layer respectively to Z axis positive direction and
The mobile duplication of negative direction, becomes two-layer；
Step 2: coil bottom surface astrosphere coordinateThe determination of component
It is that rotor magnetic pole is mobile to the positive and negative semiaxis of Z axis first, and is substituted with coil, such coil is named as " z axis
Circle "；Two layers of the magnetic pole bottom centre spherical coordinates that followed by will be distributed over the positive and negative semiaxis of Z axis is rotated, and is rotated by 90 ° around X-axis
To the coil for being located at the positive and negative semiaxis of Y-axis, it is named as " Y-axis coil "；Followed by it will be distributed over two layers of magnetic pole bottom of the positive and negative semiaxis of Z axis
Portion center spherical coordinates is rotated, and is rotated by 90 ° to obtain the coil positioned at the positive and negative semiaxis of X-axis around Y-axis, is named as " X-axis coil "；
It is finally to merge 3 groups of coils, composition stator is whole；It is about the centre of sphere symmetrically and about straight with distribution of the coil on spherical surface
Coordinate plane in angular coordinate system is symmetrical, need to only analyze the coil coordinate of one of quadrant, the rotor of corresponding l rank spheric harmonic function
Structure has on three sides of the convex surface equilateral triangle that 1.5l coil is evenly distributed in first quartile on spherical surface；Root
It lists according to the distribution relation of each coil of above-mentioned first quartile containing coil position unknown numberEquation, solve obtain it is basic
Parameter
Step 3: the determination of coil electrifying method
(1) ball harmonic series stator and rotor magnetic field harmonics coefficient analysis: are obtained about the symmetrical magnetic pole simulation calculation of the centre of sphere on rotor
Number, it is known that then each position of magnetic pole passes through the rotation of ball harmonic wave, superposition obtains the corresponding ball harmonic constant of all magnetic poles, then determines
Rotor motion track obtains the ball harmonic constant of any position using the rotation of ball harmonic wave, extracts main order ball harmonic constant composition and turns
Sub- position feature Matrix CR(t), element is the function about time t in matrix；Lead to unit about the symmetrical coil of the centre of sphere on stator
Current simulations, which calculate, obtains corresponding harmonic constant, and the main order ball harmonic constant for extracting respective rotor constitutes stator coil position spy
Levy matrix KS, matrix element is constant；
(2) current equation: go out to rotate using stator and rotor magnetic field proportional the characteristics of can produce constant torque and stator excitation
The principle in magnetic field proposes coefficient corresponding equation: KSI(t)=η CR(t), wherein KSFor stator coil position feature matrix, I(t)For line
Loop current matrix, η are torque factor, this constant is determined by desired output torque, CR(t)For rotor-position eigenmatrix；Finally ask
It solves equation to obtain each group coil current I(t)=η KS -1CR(t)。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910042911.3A CN109831046B (en) | 2019-01-17 | 2019-01-17 | Permanent magnet spherical motor structure design and power-on method based on spherical harmonic function |
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| CN110955960A (en) * | 2019-11-11 | 2020-04-03 | 天津大学 | Analysis method of cogging torque of permanent magnet spherical motor based on equivalent magnetic circuit method |
| CN111585409A (en) * | 2020-06-24 | 2020-08-25 | 山西睿智健科技有限公司 | Spherical universal motor |
| CN118914946A (en) * | 2024-10-09 | 2024-11-08 | 潍坊新力超导磁电科技有限公司 | Gradient coil nonlinearity analysis method based on spherical surface measurement |
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