CA1256499A - Device for measuring the induction in the air gap of a magnetic bearing - Google Patents
Device for measuring the induction in the air gap of a magnetic bearingInfo
- Publication number
- CA1256499A CA1256499A CA000514991A CA514991A CA1256499A CA 1256499 A CA1256499 A CA 1256499A CA 000514991 A CA000514991 A CA 000514991A CA 514991 A CA514991 A CA 514991A CA 1256499 A CA1256499 A CA 1256499A
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- Canada
- Prior art keywords
- small
- rotor
- notches
- poles
- stator
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Abstract
Device for measuring the induction in the air gap of a magnetic bearing ABSTRACT OF THE DISCLOSURE
This invention relates to a device for measuring the induction in the air gap of a magnetic bearing, which comprises an assembly of small notches of small width made in the longitudinal direction of the rotor and distributed on the periphery thereof, an assembly of small coils disposed in the end faces of the poles of the stator frame located opposite the rotor, parallel to said small notches, and means for detecting the alternating voltage induced in each small coil due to the passage of the small notches of the rotor opposite said small coils.
This invention relates to a device for measuring the induction in the air gap of a magnetic bearing, which comprises an assembly of small notches of small width made in the longitudinal direction of the rotor and distributed on the periphery thereof, an assembly of small coils disposed in the end faces of the poles of the stator frame located opposite the rotor, parallel to said small notches, and means for detecting the alternating voltage induced in each small coil due to the passage of the small notches of the rotor opposite said small coils.
Description
The present invention relates to a device for measuring the induction in the air yap of a magne-tic bearing comprising a rotor armature made of ferro-magnetic material, a stator constituted on the one hand by a frame made of ferromagnetic material defining a succession of poles and of notches in its part located opposite the rotor armature and, on the other hand, by electro-magnet coils disposed in the notches of said frame, and an air gap located between the rotor and the stator.
In an active magnetic bearing, the current for energizing the stator electro-magnets is controlled from the detection signals delivered by detectors which measure at every moment the displacements of the bearing rotor with respect to the stator, in order to maintain the rotor in a pre~etermined position.
The lifting force of a magnetic bearing is proportional to the square of the magnetic induction in the air gap of the bearing and to the useful active surface of the magnetic circuit of the bearing.
It is often useful to effect a precise measurement of the force of a bearing. This is the case, for example, when it is desired to measure the force of traction of a metal sheet resting on magnetic bearings.
In that case, the determination of the magnetic induction necessary for determining the lifting force is effected by a calculation which takes into account the result of different measure-ments, particularly of the air gap and the current for energizing the electro-magnets of the bearing.
However, this method cannot take into account the remanent field of the electro-magnets. The error thus introduced remains relatively small, but becomes ~, i~
appreciable for certain applications.
It is an object of an aspect of the present invention to remedy the above drawbacks and to effect a direct measurement of the induction in the air gap of a magnetic bearing, in order in particular ~o allow a precise determination of the force of attraction of the bearing.
It is an object of an aspect of the invention to allow a measurement of magnetic induction without it being necessary to employ measuring elements on the rotor and therefore to use commutators for taking signals which would be delivered by these measuring elements.
An aspect of the invention is as follows:
~ device for measuring the induction in the air gap of a magnetic bearing, comprising:
(a) a rotor armature made of ferromagnetic material;
(b) a stator, including--(i) a frame made of ferromagnetic material and defining a succession of poles having end faces, (ii) notches formed opposite the rotor armature, and (iii) electro-magnet coils disposed in the notches of said frame;
(c) an air gap located between the rotor armature and the stator;
(d) a plurality of small notches of small width made in the longitudinal direction of the rotor and distributed on the periphery thereof;
(e) a plurality of small coils disposed in the end faces of the poles opposite the rotor armature correspondin~ to said notches: and (f) means for detecting the alternating voltage induced in each small coil due to the passage of the small notches of the rotor opposite said small coils, which detected alternating voltage can be used to derive 2a ~ 2~ 9~
values of the induction in the portions of the air gap which are located opposite the end faces of the poles of the stator frame which support said small coils.
According to a particular feature of the invention, the small coils disposed in the poles of the stator frame and the small notches made on the periphery of the rotor are inclined with respect to the axis of rotation of the rotor.
According to another feature, which makes it possible to avoid a modulation of the induction measured, the distance between two adjacent small notches corresponds to the width of a pole of the stator frame.
The width of the sma]l coils disposed in the poles of the stator frame is substantially equal to the width of the small notches made on the periphery of the rotor.
In order not to affect the carrying capacity of the bearing whilst conserving a good sensitivity of measurement, the width of the small coils and of the small notches advantageously corresponds to about one tenth of the width of a pole of the stator frame.
According to a particular embodiment, the small coils are fixed by adhesion on the end faces of the poles of the stator frame.
According to another embodiment, the small coils are disposed in small notches made in the end faces of the poles of the stator frame.
The invention will be more readily understood on reading the following description with reference to the accompanying drawings, in which:
Fig. 1 is a schematic partial view in section perpendicular to the axis of an active, radial magnetic bearing incorporating the induction measuring device according to the invention.
Fig. 2 is a developed plan view of the outer surface of the rotor of the bearing of Fig.
1.
Fig. 3 is a view of poles of the stator of the bearing of Fig.l, along line III-III of Fig.
1.
Fig. 4 is a detailed view of a s-tator pole in section along line IV-IV of Fig. 3, and Fig. 5 is a variant embodiment of the stator pole of Fig. 4.
Referriny now to the drawings, Fig. 1 shows part of an active radial magnetic bearing cornprising a stator 1 constituted by a frame 10 defining notches 11 and pole pieces 12, and electro-rrlagnet windings 13 disposed around the pole pieces 12 in the notches 11. The frame 10 is formed by a stack of ferromagnetic plates perpendicularly to the axis of the bearing, i.e. parallel to -the plane of Fig. 1. The stator 1 is coaxial to a rotor 2 constituted by an armature 20 made of laminated ferromagnetic material, which defines with poles 12 an air gap of width E.
The basic structure of an active magnetic bearing is well known and wi]l not be described in detail. However, it will be noted that rotor 2 may be disposed either inside stator 1, as shown in Fig.
1, the outer cylindrical surface 21 of rotor 2 lying opposite the terminal surfaces 121 of the pole pieces 12 of the stator 1, or outside stator 1. In the latter case, the pole pieces 12 of stator 1 face outwardly and it is the inner cylindrical surface of the annular rotor which lies opposite the terminal surfaces of the pole pieces 12 of stator 1.
The carrying capacity of a magnetic bearing is proportional to the square of the magnetic induction in the air gap and to the useful active surface.
The useful active surface is constituted by the sum of the surfaces of the terminal faces of poles 12 of the stator magnetic circuit and is therefore propor-tional to diameter D of the rotor, to the air gap and to the width L of the magnetic bearing. I'he useful active surface being constant for a given magnetic bearing, the force of attraction of the bearing, which is the resultant of the forces of attraction of the different electro-magnets constituted by pairs of adjacent poles 12 of opposite polarities and the corresponding windinys, is therefore proportional to the magnetic induction in the air gap of the beariny.
In a magnetic bearing, the flux circuit of the electro-magnets is such that the major part of the energy of magnetization lies in the air gap.
If, furthermore, the relative permeabilities of the magnetic plates of the rotor and of the stator are high, it may be considered that, for a given air-gap, the magnetic induction is proportional to the intensity I of the current circulating in the windings 13 of the stator electro-magnets. In that case, by measuring the intensity I of the current for energization of the stator electro-magnets, combined with a precise measurement of the value of the air-gap, the force of attraction of the bearing can be determined. Such a measurement of force thus depends on an indirect determination of the value of the magnetic induction in the air gap. Despite its convenience, this method is not entirely satisfactory for certain applications, or necessitates the introduction of correction factors, and does not take into account the remanent field of the electro-magnets.
The magnetic bearing according to the inven-tion is thus equipped with a device for directly measuring the magnetic induction in the air-gap of the bearing, and consequently makes it possible-to determine the lifting force of the bearing in particu-larly reliable manner.
This induction measuring device essentially comprises an assembly of small coils 32 placed on the stator 1 and cooperating with small notches 31 made on the cylindrical surface 21 of the armature 20 of the rotor which defines the air gap 4 of the -6- ~56~9 bearing. Each terminal Eace 121 oE a pole piece 12 of the stator 1 comprises a small coil 32 and the number of the small notches 31 made on the rotor
In an active magnetic bearing, the current for energizing the stator electro-magnets is controlled from the detection signals delivered by detectors which measure at every moment the displacements of the bearing rotor with respect to the stator, in order to maintain the rotor in a pre~etermined position.
The lifting force of a magnetic bearing is proportional to the square of the magnetic induction in the air gap of the bearing and to the useful active surface of the magnetic circuit of the bearing.
It is often useful to effect a precise measurement of the force of a bearing. This is the case, for example, when it is desired to measure the force of traction of a metal sheet resting on magnetic bearings.
In that case, the determination of the magnetic induction necessary for determining the lifting force is effected by a calculation which takes into account the result of different measure-ments, particularly of the air gap and the current for energizing the electro-magnets of the bearing.
However, this method cannot take into account the remanent field of the electro-magnets. The error thus introduced remains relatively small, but becomes ~, i~
appreciable for certain applications.
It is an object of an aspect of the present invention to remedy the above drawbacks and to effect a direct measurement of the induction in the air gap of a magnetic bearing, in order in particular ~o allow a precise determination of the force of attraction of the bearing.
It is an object of an aspect of the invention to allow a measurement of magnetic induction without it being necessary to employ measuring elements on the rotor and therefore to use commutators for taking signals which would be delivered by these measuring elements.
An aspect of the invention is as follows:
~ device for measuring the induction in the air gap of a magnetic bearing, comprising:
(a) a rotor armature made of ferromagnetic material;
(b) a stator, including--(i) a frame made of ferromagnetic material and defining a succession of poles having end faces, (ii) notches formed opposite the rotor armature, and (iii) electro-magnet coils disposed in the notches of said frame;
(c) an air gap located between the rotor armature and the stator;
(d) a plurality of small notches of small width made in the longitudinal direction of the rotor and distributed on the periphery thereof;
(e) a plurality of small coils disposed in the end faces of the poles opposite the rotor armature correspondin~ to said notches: and (f) means for detecting the alternating voltage induced in each small coil due to the passage of the small notches of the rotor opposite said small coils, which detected alternating voltage can be used to derive 2a ~ 2~ 9~
values of the induction in the portions of the air gap which are located opposite the end faces of the poles of the stator frame which support said small coils.
According to a particular feature of the invention, the small coils disposed in the poles of the stator frame and the small notches made on the periphery of the rotor are inclined with respect to the axis of rotation of the rotor.
According to another feature, which makes it possible to avoid a modulation of the induction measured, the distance between two adjacent small notches corresponds to the width of a pole of the stator frame.
The width of the sma]l coils disposed in the poles of the stator frame is substantially equal to the width of the small notches made on the periphery of the rotor.
In order not to affect the carrying capacity of the bearing whilst conserving a good sensitivity of measurement, the width of the small coils and of the small notches advantageously corresponds to about one tenth of the width of a pole of the stator frame.
According to a particular embodiment, the small coils are fixed by adhesion on the end faces of the poles of the stator frame.
According to another embodiment, the small coils are disposed in small notches made in the end faces of the poles of the stator frame.
The invention will be more readily understood on reading the following description with reference to the accompanying drawings, in which:
Fig. 1 is a schematic partial view in section perpendicular to the axis of an active, radial magnetic bearing incorporating the induction measuring device according to the invention.
Fig. 2 is a developed plan view of the outer surface of the rotor of the bearing of Fig.
1.
Fig. 3 is a view of poles of the stator of the bearing of Fig.l, along line III-III of Fig.
1.
Fig. 4 is a detailed view of a s-tator pole in section along line IV-IV of Fig. 3, and Fig. 5 is a variant embodiment of the stator pole of Fig. 4.
Referriny now to the drawings, Fig. 1 shows part of an active radial magnetic bearing cornprising a stator 1 constituted by a frame 10 defining notches 11 and pole pieces 12, and electro-rrlagnet windings 13 disposed around the pole pieces 12 in the notches 11. The frame 10 is formed by a stack of ferromagnetic plates perpendicularly to the axis of the bearing, i.e. parallel to -the plane of Fig. 1. The stator 1 is coaxial to a rotor 2 constituted by an armature 20 made of laminated ferromagnetic material, which defines with poles 12 an air gap of width E.
The basic structure of an active magnetic bearing is well known and wi]l not be described in detail. However, it will be noted that rotor 2 may be disposed either inside stator 1, as shown in Fig.
1, the outer cylindrical surface 21 of rotor 2 lying opposite the terminal surfaces 121 of the pole pieces 12 of the stator 1, or outside stator 1. In the latter case, the pole pieces 12 of stator 1 face outwardly and it is the inner cylindrical surface of the annular rotor which lies opposite the terminal surfaces of the pole pieces 12 of stator 1.
The carrying capacity of a magnetic bearing is proportional to the square of the magnetic induction in the air gap and to the useful active surface.
The useful active surface is constituted by the sum of the surfaces of the terminal faces of poles 12 of the stator magnetic circuit and is therefore propor-tional to diameter D of the rotor, to the air gap and to the width L of the magnetic bearing. I'he useful active surface being constant for a given magnetic bearing, the force of attraction of the bearing, which is the resultant of the forces of attraction of the different electro-magnets constituted by pairs of adjacent poles 12 of opposite polarities and the corresponding windinys, is therefore proportional to the magnetic induction in the air gap of the beariny.
In a magnetic bearing, the flux circuit of the electro-magnets is such that the major part of the energy of magnetization lies in the air gap.
If, furthermore, the relative permeabilities of the magnetic plates of the rotor and of the stator are high, it may be considered that, for a given air-gap, the magnetic induction is proportional to the intensity I of the current circulating in the windings 13 of the stator electro-magnets. In that case, by measuring the intensity I of the current for energization of the stator electro-magnets, combined with a precise measurement of the value of the air-gap, the force of attraction of the bearing can be determined. Such a measurement of force thus depends on an indirect determination of the value of the magnetic induction in the air gap. Despite its convenience, this method is not entirely satisfactory for certain applications, or necessitates the introduction of correction factors, and does not take into account the remanent field of the electro-magnets.
The magnetic bearing according to the inven-tion is thus equipped with a device for directly measuring the magnetic induction in the air-gap of the bearing, and consequently makes it possible-to determine the lifting force of the bearing in particu-larly reliable manner.
This induction measuring device essentially comprises an assembly of small coils 32 placed on the stator 1 and cooperating with small notches 31 made on the cylindrical surface 21 of the armature 20 of the rotor which defines the air gap 4 of the -6- ~56~9 bearing. Each terminal Eace 121 oE a pole piece 12 of the stator 1 comprises a small coil 32 and the number of the small notches 31 made on the rotor
2 is equal to the total number of small coils 32 and therefore of the poles of stator 1.
The small coils 32 and the small notches 31 are disposed lengthwise of the bearing (Figs.
2 and 3), but are inclined by the same angle ~ with respect to the axis of rotation X'X of the bearing, similarly to the notches made in the rotor of an induction motor which are inclined with respect to the axis of rotation of this rotor.
The distance d which separates two successive notches 31 of the rotor is equal to the width 1 of a pole 12 of the stator 1. In this way, any phenomenon of modulation of -the signal delivered by the small coils 32 is avoided.
In operation, upon each passage of a small notch 31 beneath a small coil 32, an alternating voltage is induced in this small coil 32. Taking into account the fact that the geometrical characteris-tics of each small coil 32 are well determined, the alternating voltage produced upon passage of a notch 31 beneath the coil 32 is proportional to the magnetic induction in the air gap 4.
By taking the signals available at the terminals of the different small coils 32 disposed on the different poles 12 of the stator 1 when the rotation of rotor 2 causes notches 31 to pass opposite said small coils 32, a value proportional to -the magnetic induction B may thus be obtained and the value of the force of the beari.ng may be deduced therefrom.
The width a of a notch 31 corresponds to _7_ ~2t~9~
the width b of a coil 32. Notch and coil wid-ths a, b are advantageous]y chosen which correspond to about one tenth of the width 1 of a pole 12. This makes it possible not to reduce substantially the carrying capacity of the bearing whilst leading to voltages induced at the terminals of the small coils 32 which are sufficiently high to ensure a reliable and sensi-tive measurement of induction.
Each small coil 32 may be inserted in small notches 132 made in the terminal face 121 of the pole pieces 12 of the stator (Fig. 4). However, accor-ding to a variant embodiment, the small coils 32, of which the thickness is much less than the width E of the average air gap 4, are simply connected to the terminal faces 121 of the pole pieces 12 and are fixed on these faces 121 for example via a small layer of adhesive 232. Fixation of the small measuring coils 32 is facilitated by the fact that tne diameter of a magnetic bearing at the level of the air gap 4 is generally relatively large.
It will be noted that the device described hereinbefore requires no rotating contact insofar as all the coils are placed on the stator 1, whether it is question of the windings 13 of electro-magnets of the bearing or of the small coils 32 for taking signals~ Consequently, practical embodiment is particu-larly simple and very reliable.
A magnetic bearing equipped with the induc-tion measuring device according to the invention may be used for example within the framework of the application described in French Patent Application No. 83 18435 filed on November 18, 1983 and entitled:
"Device for measuring the longitudinal voltage of a strip of material". In this application, which 5Ei~
may concern for exarnple the measurement o:E the forces of traction in a rolling mill, the rneasuremen-t o:f the induction in the air gap of a bearing according to the present invention may be replaced by the measure-ment of the current in the windings of the activemagnetic bearing serving as force detector in order to deliver a signal as a function of the effect of traction exerted on the strip of material in abutment on a roller mounted on said active magnetic bearing.
The small coils 32 and the small notches 31 are disposed lengthwise of the bearing (Figs.
2 and 3), but are inclined by the same angle ~ with respect to the axis of rotation X'X of the bearing, similarly to the notches made in the rotor of an induction motor which are inclined with respect to the axis of rotation of this rotor.
The distance d which separates two successive notches 31 of the rotor is equal to the width 1 of a pole 12 of the stator 1. In this way, any phenomenon of modulation of -the signal delivered by the small coils 32 is avoided.
In operation, upon each passage of a small notch 31 beneath a small coil 32, an alternating voltage is induced in this small coil 32. Taking into account the fact that the geometrical characteris-tics of each small coil 32 are well determined, the alternating voltage produced upon passage of a notch 31 beneath the coil 32 is proportional to the magnetic induction in the air gap 4.
By taking the signals available at the terminals of the different small coils 32 disposed on the different poles 12 of the stator 1 when the rotation of rotor 2 causes notches 31 to pass opposite said small coils 32, a value proportional to -the magnetic induction B may thus be obtained and the value of the force of the beari.ng may be deduced therefrom.
The width a of a notch 31 corresponds to _7_ ~2t~9~
the width b of a coil 32. Notch and coil wid-ths a, b are advantageous]y chosen which correspond to about one tenth of the width 1 of a pole 12. This makes it possible not to reduce substantially the carrying capacity of the bearing whilst leading to voltages induced at the terminals of the small coils 32 which are sufficiently high to ensure a reliable and sensi-tive measurement of induction.
Each small coil 32 may be inserted in small notches 132 made in the terminal face 121 of the pole pieces 12 of the stator (Fig. 4). However, accor-ding to a variant embodiment, the small coils 32, of which the thickness is much less than the width E of the average air gap 4, are simply connected to the terminal faces 121 of the pole pieces 12 and are fixed on these faces 121 for example via a small layer of adhesive 232. Fixation of the small measuring coils 32 is facilitated by the fact that tne diameter of a magnetic bearing at the level of the air gap 4 is generally relatively large.
It will be noted that the device described hereinbefore requires no rotating contact insofar as all the coils are placed on the stator 1, whether it is question of the windings 13 of electro-magnets of the bearing or of the small coils 32 for taking signals~ Consequently, practical embodiment is particu-larly simple and very reliable.
A magnetic bearing equipped with the induc-tion measuring device according to the invention may be used for example within the framework of the application described in French Patent Application No. 83 18435 filed on November 18, 1983 and entitled:
"Device for measuring the longitudinal voltage of a strip of material". In this application, which 5Ei~
may concern for exarnple the measurement o:E the forces of traction in a rolling mill, the rneasuremen-t o:f the induction in the air gap of a bearing according to the present invention may be replaced by the measure-ment of the current in the windings of the activemagnetic bearing serving as force detector in order to deliver a signal as a function of the effect of traction exerted on the strip of material in abutment on a roller mounted on said active magnetic bearing.
Claims (8)
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. A device for measuring the induction in the air gap of a magnetic bearing, comprising:
(a) a rotor armature made of ferromagnetic material;
(b) a stator, including--(i) a frame made of ferromagnetic material and defining a succession of poles having end faces, (ii) notches formed opposite the rotor armature, and (iii) electro-magnet coils disposed in the notches of said frame;
(c) an air gap located between the rotor armature and the stator;
(d) a plurality of small notches of small width made in the longitudinal direction of the rotor and distributed on the periphery thereof;
(e) a plurality of small coils disposed in the end faces of the poles opposite the rotor armature corresponding to said notches; and (f) means for detecting the alternating voltage induced in each small coil due to the passage of the small notches of the rotor opposite said small coils, which detected alternating voltage can be used to derive values of the induction in the portions of the air gap which are located opposite the end faces of the poles of the stator frame which support said small coils.
(a) a rotor armature made of ferromagnetic material;
(b) a stator, including--(i) a frame made of ferromagnetic material and defining a succession of poles having end faces, (ii) notches formed opposite the rotor armature, and (iii) electro-magnet coils disposed in the notches of said frame;
(c) an air gap located between the rotor armature and the stator;
(d) a plurality of small notches of small width made in the longitudinal direction of the rotor and distributed on the periphery thereof;
(e) a plurality of small coils disposed in the end faces of the poles opposite the rotor armature corresponding to said notches; and (f) means for detecting the alternating voltage induced in each small coil due to the passage of the small notches of the rotor opposite said small coils, which detected alternating voltage can be used to derive values of the induction in the portions of the air gap which are located opposite the end faces of the poles of the stator frame which support said small coils.
2. The device of claim 1, wherein the small coils disposed in the poles of the stator frame and the small notches made on the periphery of the rotor are inclined with respect to the axis of rotation of the rotor.
3. The device of claim 1, wherein the distance between two adjacent small notches corresponds to the width of a pole of the stator frame.
4. The device of claim 1, wherein the width of the small coils disposed in the poles of the stator frame is substantially equal to the width of the small notches made on the periphery of the rotor.
5. The device of claim 4, wherein the width of the small coils and of the small notches corresponds to about one tenth of the width of a pole of the stator frame.
6. The device of claim 1, wherein the small coils are fixed by adhesion on the end faces of the poles of the stator frame.
7. The device of claim 1, wherein the small coils are disposed in small notches made in the end faces of the poles of the stator frame.
8. The device of claim 1, wherein the device is capable of measuring the force of traction in rolling mills.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CA000514991A CA1256499A (en) | 1986-07-30 | 1986-07-30 | Device for measuring the induction in the air gap of a magnetic bearing |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CA000514991A CA1256499A (en) | 1986-07-30 | 1986-07-30 | Device for measuring the induction in the air gap of a magnetic bearing |
Publications (1)
Publication Number | Publication Date |
---|---|
CA1256499A true CA1256499A (en) | 1989-06-27 |
Family
ID=4133656
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CA000514991A Expired CA1256499A (en) | 1986-07-30 | 1986-07-30 | Device for measuring the induction in the air gap of a magnetic bearing |
Country Status (1)
Country | Link |
---|---|
CA (1) | CA1256499A (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN112557901A (en) * | 2020-12-01 | 2021-03-26 | 重庆邮电大学 | Precise micro-motor detection device and method based on multiphase magnetoelectric induction |
-
1986
- 1986-07-30 CA CA000514991A patent/CA1256499A/en not_active Expired
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN112557901A (en) * | 2020-12-01 | 2021-03-26 | 重庆邮电大学 | Precise micro-motor detection device and method based on multiphase magnetoelectric induction |
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