CN104269947A - Method for optimizing magnetic suspension permanent magnet planar motor magnetic steel array parameter - Google Patents
Method for optimizing magnetic suspension permanent magnet planar motor magnetic steel array parameter Download PDFInfo
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- CN104269947A CN104269947A CN201410492590.4A CN201410492590A CN104269947A CN 104269947 A CN104269947 A CN 104269947A CN 201410492590 A CN201410492590 A CN 201410492590A CN 104269947 A CN104269947 A CN 104269947A
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- magnetic
- close
- voltage amplitude
- fundamental voltage
- steel
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K1/00—Details of the magnetic circuit
- H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
- H02K1/12—Stationary parts of the magnetic circuit
- H02K1/17—Stator cores with permanent magnets
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K41/00—Propulsion systems in which a rigid body is moved along a path due to dynamo-electric interaction between the body and a magnetic field travelling along the path
- H02K41/02—Linear motors; Sectional motors
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K2201/00—Specific aspects not provided for in the other groups of this subclass relating to the magnetic circuits
- H02K2201/18—Machines moving with multiple degrees of freedom
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K2213/00—Specific aspects, not otherwise provided for and not covered by codes H02K2201/00 - H02K2211/00
- H02K2213/03—Machines characterised by numerical values, ranges, mathematical expressions or similar information
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- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Physics & Mathematics (AREA)
- Chemical & Material Sciences (AREA)
- Combustion & Propulsion (AREA)
- Electromagnetism (AREA)
- Soft Magnetic Materials (AREA)
- Permanent Field Magnets Of Synchronous Machinery (AREA)
Abstract
The invention discloses a method for optimizing the magnetic suspension permanent magnet planar motor magnetic steel array parameter. An average fundamental wave amplitude is used for setting the expected gas flux density, and a mathematic model of the expected gas flux density is set up; average fundamental wave amplitudes on different levels are used for calculating the expected flux density overall average fundamental wave amplitude in an effective magnetic field space height range, and a gas flux density harmonic model is used for calculating the average relative mean square error of the practical flux density and the expected gas flux density; the magnetic steel parameter is determined based on the principle that the expected flux density overall average fundamental wave amplitude should be as large as possible, and the average relative mean square error of the practical flux density should be as small as possible, an optimizing result can effectively restrain higher harmonics, and especially, second harmonics are restrained greatly.
Description
Technical field
The invention belongs to Electric Drive technical field, particularly relate to the design and optimization of magnetic suspension permanent magnet planar motor, be specially adapted to parameter designing and the optimization of the permanent-magnet planar motor adopting Halbach magnetic steel array (Halbach magnetic steel array).
Background technology
Moving-coil type magnetic suspension permanent magnet planar motor rotor is coil array, and stator is permanent magnet array.Stator permanent magnet array adopts Halbach arrangement mode to combine by main magnet steel and secondary magnet steel.During work, pass into corresponding electric current to mover coil, the magnetic field interaction that this electric current and stator Halbach permanent magnet array produce to produce required thrust and torque, therefore, the size of stator field and the generation of sine to thrust and torque particularly important.The air gap flux density of Halbach magnetic steel array is three-dimensional periodic distribution, the fundamental voltage amplitude of the close each axial component of sustained height magnetic is all not identical with relative harmonic content, the fundamental voltage amplitude of the close each axial component of differing heights magnetic is not identical with relative harmonic content yet, and this air-gap field just made is particularly complicated.Usually the half that secondary magnet steel width is main magnet steel width is got at present, although 3 times and multiple subharmonic that this parameter coordination can suppress magnetic close well, undesirable to the inhibition of other high order harmonic component, especially poor to the inhibition of 2 subharmonic.Magnetic close 3 times and multiple subharmonic thereof on thrust and torque impact very little, and 2 subharmonic on thrust and torque ripple impact comparatively large, so must be suppressed it.
Summary of the invention
2 subharmonic and the poor defect of high order harmonic component effect is suppressed for existing magnetic suspension permanent magnet planar motor stator permanent magnet array, a kind of method of magnetic suspension permanent magnet planar motor magnetic steel array parameter optimization is proposed, make magnetic suspension permanent magnet planar motor restrained effectively high order harmonic component, especially have stronger inhibitory action to 2 subharmonic.
For achieving the above object, the technical solution adopted in the present invention is: the stator of magnetic suspension permanent magnet planar motor is permanent magnetic steel array, adopts Halbach arrangement mode to combine, comprise the following steps by main magnet steel and secondary magnet steel;
(1) Halbach type magnetic steel array magnetic system of coordinates is set up
with
, coordinate system
initial point be positioned at main magnet steel center,
axle,
axle is vertical with main magnet steel limit respectively, coordinate system
for coordinate system
around
axle is rotated counterclockwise
the coordinate system of rear gained,
place is strong side, magnetic field;
Utilize magnetic field, Halbach magnetic steel array strong side at coordinate system
under the close harmonic-model of magnetic
, obtain magnetic field, Halbach magnetic steel array strong side at coordinate system
under the close vector of magnetic
, calculate the average fundamental voltage amplitude on the differentiated levels of distance magnetic steel array surface
, by average fundamental voltage amplitude
build magnetic close expectation first-harmonic model
;
(2) according to the described average fundamental voltage amplitude on differentiated levels
calculate at effective magnetic field spatial altitude
the close overall average fundamental voltage amplitude of expectation magnetic in scope
;
(3) according to the close harmonic-model of described magnetic
try to achieve the close i.e. close vector of magnetic of actual magnetic of magnetic steel array
's
,
with
axial component
, according to described magnetic close expectation first-harmonic model
try to achieve and expect that magnetic is close namely
's
,
,
axial component
, thus try to achieve the close average relative mean square deviation close with expectation magnetic of actual magnetic
;
(4) by close for described expectation magnetic overall average fundamental voltage amplitude
, described actual magnetic close with expect the close average relative mean square deviation of magnetic
discretization, makes the close overall average fundamental voltage amplitude of described expectation magnetic
with ratio
relation curve and described average relative mean square deviation
with
relation curve, according to the close overall average fundamental voltage amplitude of described expectation magnetic
should large as far as possible and described average relative mean square deviation
principle that should be little as far as possible determines main magnet steel width
with secondary magnet steel width
,
for total magnet steel width.
Compared with prior art, the invention has the beneficial effects as follows:
(1) because different magnet steel parameter coordination is comparatively large on the impact of the close distribution of magnetic around magnet steel, optimum results of the present invention can restrained effectively high order harmonic component, especially has stronger inhibitory action to 2 subharmonic.
(2) Cost optimization is low, does not need other auxiliary equipment.
(3) complexity and the accuracy of algorithm has been taken into account, rationally reliably.
Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.
Accompanying drawing explanation
Fig. 1 is the front view of magnetic suspension permanent magnet planar motor stator permanent magnet array;
Fig. 2 is the vertical view of Fig. 1, and stator permanent magnet array adopts Halbach to be arranged in a combination by main magnet steel and secondary magnet steel;
In Fig. 1 and Fig. 2:
for total magnet steel width,
be the width of main magnet steel,
for secondary magnet steel width,
for pole span;
Fig. 3 is
axially expect the close overall average fundamental voltage amplitude of magnetic
and
the close average relative mean square deviation close with expectation magnetic of axial actual magnetic
with
relation curve;
In Fig. 3:
for the ratio of secondary magnet steel width and main magnet steel width; Curve 1 is
with
relation curve, curve 2 is
with
relation curve.
Fig. 4 is
axially expect the close overall average fundamental voltage amplitude of magnetic
with
the close average relative mean square deviation close with expectation magnetic of axial actual magnetic
with
relation curve;
In Fig. 4:
for the ratio of secondary magnet steel width and main magnet steel width; Curve 1 is
with
relation curve, curve 2 is
with
relation curve.
Embodiment
The present invention adopts average fundamental voltage amplitude to set expectation air gap flux density, sets up the Mathematical Modeling expecting air gap flux density; Utilizing the close overall average fundamental voltage amplitude of expectation magnetic within the scope of the average fundamental voltage amplitude calculating effective magnetic field spatial altitude on differentiated levels, calculating the close average relative mean square deviation with expecting air gap flux density of actual magnetic by air gap flux density harmonic-model; According to the principle determination magnet steel parameter of " expect that the close overall average fundamental voltage amplitude of magnetic should be large as far as possible, the close average relative mean square deviation close with expecting magnetic of actual magnetic should be little as far as possible ".Specific as follows:
As depicted in figs. 1 and 2, the stator of magnetic suspension permanent magnet planar motor is permanent magnetic steel array, this stator permanent magnet array adopts Halbach arrangement mode to combine by main magnet steel and secondary magnet steel, is the Halbach magnetic steel array being arranged as one-sided strengthening form by the magnet steel that two kinds of volumes are different.Large magnet steel is main magnet steel, and main magnet steel cross section is in square, and little magnet steel is secondary magnet steel, and secondary magnet steel cross section is rectangle, and the length of secondary magnet steel is equal with the cross section length of side of main magnet steel, and two kinds of magnet thicknesses are identical; Main magnet steel is identical with the secondary magnet steel magnetization, alignment and the direction of magnetization is orthogonal, and the non-magnet material that gap magnetic permeability is identical with air is filled.The close side of magnetic field magnetic of such formation is very strong, and opposite side is then more weak.Only utilize the side that the close distribution of magnetic is strong during application, magnet steel parameter coordination is very large to the close distribution influence of the magnetic around magnet steel, can be optimized according to the harmonic-model that magnetic is close to it.
Set up Halbach type magnetic steel array magnetic system of coordinates
with
, coordinate system
initial point be positioned at main magnet steel center, its
axle,
axle is vertical with main magnet steel limit respectively, coordinate system
for coordinate system
around
axle is rotated counterclockwise
the coordinate system of rear gained;
place is strong side, magnetic field.From coordinate system
to coordinate system
transformation matrix of coordinates be:
， (1)
Its inverse matrix is:
， (2)
In formula:
.
Permanent magnetic steel presses the uniform magnetization of prescribed direction shown in Fig. 1, and magnetic steel array infinitely extends in horizontal plane, disregards edge effect, and magnet steel overall width is
, main magnet steel width is
, secondary magnet steel width is
, magnet thickness is
, pole span
, magnetic field, Halbach magnetic steel array strong side is at coordinate system
the close harmonic-model of lower magnetic be:
， (3)
Wherein,
for at coordinate system
the close harmonic-model of magnetic in magnetic field, middle Halbach magnetic steel array strong side,
,
,
for at coordinate system
the coordinate figure of the close calculation level of middle magnetic,
for the relative permeability of magnet steel,
for the remanent magnetism of magnet steel,
,
be
,
harmonic order axially,
， (4)
， (5)
， (6)
， (7)
， (8)
， (9)
By close for magnetic calculation level at coordinate system
in coordinate figure adopt coordinate transform obtain at coordinate system
in coordinate figure, and being substituted into formula (3), to calculate this magnetic close
axle,
axle and
axial component, then press close for the magnetic of this point
axle,
axle and
axle decompose can this magnetic close
,
with
axial component, can obtain magnetic field, Halbach magnetic steel array strong side at coordinate system
the close harmonic-model of lower magnetic, computing formula is as follows:
， (10)
Wherein,
for at coordinate system
the close vector of magnetic in magnetic field, middle Halbach magnetic steel array strong side,
with
be respectively the close vector of magnetic
's
,
with
axial component,
,
,
for at coordinate system
the coordinate figure of the close calculation level of middle magnetic.
Based on the close harmonic-model of above-mentioned magnetic
, the present invention first utilizes the close harmonic-model of magnetic
calculate the average fundamental voltage amplitude on the differentiated levels of distance magnetic steel array surface, and build the close expectation first-harmonic model of magnetic thus.Definition
, when
during for certain value, the fundamental voltage amplitude of the close each axial component of magnetic is only
(
) function.Discussion territory is set to
with
,
be effective magnetic field spatial altitude, exceed
magnetic field highly then very weak can not work is considered.When
during for certain value, the average fundamental voltage amplitude that magnetic steel array produces magnetic field is
, and have:
(11)
In formula,
with
be respectively
one timing
,
with
the average amplitude of the close component first-harmonic of axial magnetic,
with
be respectively
certain but
(
) asynchronous
,
with
the close component fundamental voltage amplitude of axial magnetic.
By the average fundamental voltage amplitude in magnetic field
building magnetic close expectation first-harmonic model is
, can obtain:
(12)
Wherein,
with
be respectively and expect the close vector of magnetic
's
,
with
axial component.
The present invention calculates the close overall average fundamental voltage amplitude of expectation magnetic within the scope of effective magnetic field spatial altitude again according to the average fundamental voltage amplitude on differentiated levels.If the close overall average fundamental voltage amplitude of the expectation magnetic in room for discussion is
, can obtain:
(13)
Wherein,
with
respectively
,
with
axially expect the close overall average fundamental voltage amplitude of magnetic.
The close actual magnetic for magnetic steel array of magnetic that then the present invention tries to achieve with the harmonic-model that magnetic is close is close, i.e. the close vector of magnetic
's
,
with
axial component
, the magnetic of trying to achieve with the expectation first-harmonic model that magnetic is close is close for expecting that magnetic is close namely
's
,
,
axial component
, try to achieve the close average relative mean square deviation close with expectation magnetic of actual magnetic further.If the close average relative mean square deviation close with expecting magnetic of actual magnetic is in room for discussion
, can obtain:
(14)
Wherein,
respectively
,
with
the average relative mean square deviation of axle,
be respectively the close vector of magnetic
's
,
with
axial component,
be respectively and expect the close vector of magnetic
's
,
with
axial component,
be respectively
one timing
,
with
the average amplitude of the close component first-harmonic of axial magnetic.
Finally, formula (13) is expected the close overall average fundamental voltage amplitude of magnetic by the present invention
and the close average relative mean square deviation close with expectation magnetic of formula (14) actual magnetic
discretization is to adopt numerical method to calculate respectively, according to the principle determination magnet steel parameter of " expect that the close overall average fundamental voltage amplitude of magnetic should be large as far as possible, the close average relative mean square deviation close with expecting magnetic of actual magnetic should be little as far as possible ".
Territory will be discussed
with
press
,
with
axially be divided into respectively
,
with
equal portions, can obtain formula (13), (14) discretization respectively:
(15)
(16)
The ratio defining secondary magnet steel width and main magnet steel width is
, make and expect the close average fundamental voltage amplitude of magnetic
with
relation curve and average relative mean square deviation
with
relation curve, according to the optimization major-minor magnet steel width parameter of " expect that magnetic close overall average fundamental voltage amplitude should be large as far as possible, the close average relative mean square deviation close with expecting magnetic of actual magnetic should be little as far as possible ", thus determine main magnet steel width
with secondary magnet steel width
.
With a specific design case, the invention will be further described below:
When
time, made by formula (15), (16) and expect the close average fundamental voltage amplitude of magnetic
with
relation curve and average relative mean square deviation
with
relation curve, as shown in Figures 2 and 3.According to the principle determination magnet steel parameter of " expect that the close overall average fundamental voltage amplitude of magnetic should be large as far as possible, the close average relative mean square deviation close with expecting magnetic of actual magnetic should be little as far as possible ", as shown in dotted line in Fig. 2 and Fig. 3, get
, namely
.
Claims (5)
1. a method for magnetic suspension permanent magnet planar motor magnetic steel array parameter optimization, the stator of magnetic suspension permanent magnet planar motor is permanent magnetic steel array, adopts Halbach arrangement mode to combine, it is characterized in that comprising the following steps by main magnet steel and secondary magnet steel;
(1) Halbach type magnetic steel array magnetic system of coordinates is set up
with
, coordinate system
initial point be positioned at main magnet steel center,
axle,
axle is vertical with main magnet steel limit respectively, coordinate system
for coordinate system
around
axle is rotated counterclockwise
the coordinate system of rear gained,
place is strong side, magnetic field;
Utilize magnetic field, Halbach magnetic steel array strong side at coordinate system
under the close harmonic-model of magnetic
, obtain magnetic field, Halbach magnetic steel array strong side at coordinate system
under the close vector of magnetic
, calculate the average fundamental voltage amplitude on the differentiated levels of distance magnetic steel array surface
, by average fundamental voltage amplitude
build magnetic close expectation first-harmonic model
;
(2) according to the described average fundamental voltage amplitude on differentiated levels
calculate at effective magnetic field spatial altitude
the close overall average fundamental voltage amplitude of expectation magnetic in scope
;
(3) according to the close harmonic-model of described magnetic
try to achieve the close i.e. close vector of magnetic of actual magnetic of magnetic steel array
's
,
with
axial component
, according to described magnetic close expectation first-harmonic model
try to achieve and expect that magnetic is close namely
's
,
,
axial component
, thus try to achieve the close average relative mean square deviation close with expectation magnetic of actual magnetic
;
(4) by close for described expectation magnetic overall average fundamental voltage amplitude
, described actual magnetic close with expect the close average relative mean square deviation of magnetic
discretization, makes the close overall average fundamental voltage amplitude of described expectation magnetic
with ratio
relation curve and described average relative mean square deviation
with
relation curve, according to the close overall average fundamental voltage amplitude of described expectation magnetic
should large as far as possible and described average relative mean square deviation
principle that should be little as far as possible determines main magnet steel width
with secondary magnet steel width
,
for total magnet steel width.
2. the method for magnetic suspension permanent magnet planar motor magnetic steel array parameter optimization according to claim 1, is characterized in that:
In step (1), the close harmonic-model of described magnetic:
，
,
,
for at coordinate system
the coordinate figure of the close calculation level of middle magnetic,
for the relative permeability of magnet steel,
for the remanent magnetism of magnet steel,
,
be respectively
,
harmonic order axially,
,
，
，
，
，
，
，
；
Described average fundamental voltage amplitude:
，
with
be respectively
one timing
,
with
the average amplitude of the close component first-harmonic of axial magnetic, when
during for certain value, the fundamental voltage amplitude of the close each axial component of magnetic is
(
) function,
with
be respectively
certain but
(
) asynchronous
,
with
the close component fundamental voltage amplitude of axial magnetic;
Described magnetic close expectation first-harmonic model
.
3. the method for magnetic suspension permanent magnet planar motor magnetic steel array parameter optimization according to claim 2, is characterized in that: in step (2), the close overall average fundamental voltage amplitude of described expectation magnetic:
。
4. the method for magnetic suspension permanent magnet planar motor magnetic steel array parameter optimization according to claim 3, is characterized in that: in step (3), described average relative mean square deviation:
。
5. the method for magnetic suspension permanent magnet planar motor magnetic steel array parameter optimization according to claim 4, is characterized in that: in step (4), will
with
press
,
with
axially be divided into respectively
,
with
equal portions, the close overall average fundamental voltage amplitude of described expectation magnetic
, average relative mean square deviation
discretization obtains respectively:
.
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|---|---|---|---|
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107819391A (en) * | 2017-10-30 | 2018-03-20 | 中国石油大学(华东) | A kind of novel permanent magnetic array and planar motor |
| CN111665723A (en) * | 2020-06-19 | 2020-09-15 | 深圳大学 | Control method of planar motor based on track gradient soft constraint |
| CN112311192A (en) * | 2020-10-20 | 2021-02-02 | 江苏科技大学 | Logistics device based on magnetic suspension planar motor and control method thereof |
| CN114352616A (en) * | 2021-12-31 | 2022-04-15 | 哈尔滨工业大学 | Halbach array assembling method for magnetic levitation moving table |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5633545A (en) * | 1995-12-06 | 1997-05-27 | International Business Machines Corporation | Disk drive in-hub radial-gap spindle motor with coils generating axial fields |
| JP5040441B2 (en) * | 2007-05-24 | 2012-10-03 | 日産自動車株式会社 | Electric motor |
| CN101610054B (en) * | 2009-07-21 | 2011-02-16 | 清华大学 | Planar motor adopting three-dimensional permanent magnet array |
| CN102097982B (en) * | 2011-02-24 | 2013-06-05 | 华中科技大学 | Permanent-magnet synchronous magnetic suspension planar motor |
-
2014
- 2014-09-24 CN CN201410492590.4A patent/CN104269947B/en active Active
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107819391A (en) * | 2017-10-30 | 2018-03-20 | 中国石油大学(华东) | A kind of novel permanent magnetic array and planar motor |
| CN107819391B (en) * | 2017-10-30 | 2023-07-07 | 中国石油大学(华东) | Permanent magnet array and planar motor |
| CN111665723A (en) * | 2020-06-19 | 2020-09-15 | 深圳大学 | Control method of planar motor based on track gradient soft constraint |
| CN111665723B (en) * | 2020-06-19 | 2022-09-20 | 深圳大学 | Control method of planar motor based on track gradient soft constraint |
| CN112311192A (en) * | 2020-10-20 | 2021-02-02 | 江苏科技大学 | Logistics device based on magnetic suspension planar motor and control method thereof |
| CN114352616A (en) * | 2021-12-31 | 2022-04-15 | 哈尔滨工业大学 | Halbach array assembling method for magnetic levitation moving table |
| CN114352616B (en) * | 2021-12-31 | 2022-07-19 | 哈尔滨工业大学 | Halbach array assembling method for magnetic levitation moving table |
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|---|---|
| CN104269947B (en) | 2016-11-30 |
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Effective date of registration: 20211223 Address after: 212200 GANGLONG road science and technology innovation center, Yangzhong Development Zone, Zhenjiang City, Jiangsu Province Patentee after: Yangzhong Guanjie Technology Innovation Co.,Ltd. Address before: 212200 No. 239 Chunliu North Road, Sanmao street, Yangzhong City, Zhenjiang City, Jiangsu Province Patentee before: Zhenjiang Top Management Consulting Co.,Ltd. Effective date of registration: 20211223 Address after: 212200 No. 239 Chunliu North Road, Sanmao street, Yangzhong City, Zhenjiang City, Jiangsu Province Patentee after: Zhenjiang Top Management Consulting Co.,Ltd. Address before: Zhenjiang City, Jiangsu Province, 212013 Jingkou District Road No. 301 Patentee before: JIANGSU University |