WO2006030824A1 - 磁気軸受制御装置 - Google Patents
磁気軸受制御装置 Download PDFInfo
- Publication number
- WO2006030824A1 WO2006030824A1 PCT/JP2005/016930 JP2005016930W WO2006030824A1 WO 2006030824 A1 WO2006030824 A1 WO 2006030824A1 JP 2005016930 W JP2005016930 W JP 2005016930W WO 2006030824 A1 WO2006030824 A1 WO 2006030824A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- rotor shaft
- sensor
- sensitivity
- correction value
- detected
- Prior art date
Links
Classifications
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0444—Details of devices to control the actuation of the electromagnets
- F16C32/0446—Determination of the actual position of the moving member, e.g. details of sensors
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C32/00—Bearings not otherwise provided for
- F16C32/04—Bearings not otherwise provided for using magnetic or electric supporting means
- F16C32/0406—Magnetic bearings
- F16C32/044—Active magnetic bearings
- F16C32/0474—Active magnetic bearings for rotary movement
- F16C32/0489—Active magnetic bearings for rotary movement with active support of five degrees of freedom, e.g. two radial magnetic bearings combined with an axial bearing
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2231/00—Running-in; Initial operation
-
- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2360/00—Engines or pumps
- F16C2360/44—Centrifugal pumps
- F16C2360/45—Turbo-molecular pumps
Definitions
- the present invention relates to a magnetic bearing control device, and more particularly to a magnetic bearing control device capable of accurately detecting a rotor shaft displacement abnormality even when there are variations in the sensor itself or when there is an error in sensor mounting during stator assembly. About.
- These semiconductors are manufactured by doping impurities into a semiconductor substrate to impart electrical properties, forming a fine circuit pattern on the semiconductor substrate, and laminating them.
- the turbo molecular pump not only evacuates the chamber, but also exhausts these process gases into the chamber. Also used.
- the turbo-molecular pump prevents the electron beam from being refracted due to the presence of dust or the like in equipment such as an electron microscope. Used.
- Such a turbo molecular pump is composed of a turbo molecular pump main body for sucking and exhausting gas from a channel such as a semiconductor manufacturing apparatus or an electron microscope, and a control device for controlling the turbo molecular pump main body. !
- FIG. 5 shows a longitudinal sectional view of the turbo molecular pump main body.
- the turbo molecular pump main body 100 has an intake port at the upper end of a cylindrical outer cylinder 127. 101 is formed. Inside the outer cylinder 127, there is a rotating body 103 in which a plurality of rotor blades 102a, 102b, 102c ′, etc., formed by a turbine blade for sucking and exhausting gas are formed radially and in multiple stages around the periphery. Is provided.
- a rotor shaft 113 is attached to the center of the rotating body 103, and the rotor shaft 113 is levitated and supported in the air and controlled in position by, for example, a 5-axis control magnetic bearing.
- the upper radial electromagnet 104 In the upper radial electromagnet 104, four electromagnets are arranged in pairs in the X axis and the Y axis and in the + direction and in one direction (not shown, but if necessary, the electromagnet 104X + , 104X—, 104Y +, 104Y—).
- an upper radial sensor 107 having four electromagnet forces in close proximity to and corresponding to the upper radial electromagnet 104 is provided.
- the upper radial direction sensor 107 is configured to detect a radial displacement of the rotating body 103 and send it to the control device 200.
- this control device 200 on the basis of the displacement signal detected by the upper radial sensor 107, the upper radial electromagnet 104 is excited and controlled by the PID adjustment function, and the upper radial position of the rotor shaft 113 is controlled. Adjust.
- the rotor shaft 113 is formed of a high magnetic permeability material (such as iron) and is attracted by the magnetic force of the upper radial electromagnet 104. Such adjustment is performed independently in the X-axis direction and the heel axis direction.
- the lower radial electromagnet 105 and the lower radial sensor 108 are arranged in the same manner as the upper radial electromagnet 104 and the upper radial sensor 107, and the lower radial position of the rotor shaft 113 is set. Adjustments are made in the same way as the upper radial position (the lower radial electromagnet 105 is also referred to as electromagnets 105X +, 105X-, 105 ⁇ +, 105- as required).
- the axial electromagnets 106 A and 106 B are arranged with a disk-shaped metal disk 111 provided at the lower part of the rotor shaft 113 sandwiched vertically.
- the metal disk 111 is made of a high permeability material such as iron.
- An axial sensor 109 is provided to detect the axial displacement of the rotor shaft 113, and the axial displacement signal is sent to the control device 200.
- the axial electromagnets 106A and 106B are subjected to excitation control by a PID adjustment function based on the axial displacement signal.
- the axial electromagnet 106A The metal disk 111 is attracted upward, and the axial electromagnet 106B attracts the metal disk 111 downward.
- the rotor shaft 113 is magnetically levitated in the axial direction and is held in a non-contact manner in the space. Yes.
- the motor 121 includes a plurality of magnetic poles arranged circumferentially so as to surround the rotor shaft 113.
- Each magnetic pole is controlled by the control device 200 so as to rotationally drive the rotor shaft 113 through an electromagnetic force acting between the rotor shaft 113 and the magnetic pole.
- a rotation speed sensor (not shown) is incorporated in the motor 121, and the rotation speed of the rotor shaft 113 is detected by the detection signal of the rotation speed sensor.
- a phase sensor (not shown) is attached in the vicinity of the lower radial direction sensor 108 to detect the phase of rotation of the rotor shaft 113.
- the position of the magnetic pole is detected by using the detection signals of the phase sensor and the rotational speed sensor together.
- the fixed blade 123 is also formed so as to be inclined by a plane force perpendicular to the axis of the rotor shaft 113 by a predetermined angle, and to the inside of the outer cylinder 127, and the step of the rotor blade 102. It is arranged in the wrong place.
- One end of the fixed wing 123 is supported while being inserted between a plurality of stacked fixed wing spacers 125a, 125b, 125c.
- the fixed wing spacer 125 is a ring-shaped member, and is made of, for example, a metal such as aluminum, iron, stainless steel, copper, or an alloy containing these metals as components.
- An outer cylinder 127 is fixed to the outer periphery of the fixed wing spacer 125 with a slight gap therebetween.
- a base part 129 is disposed at the bottom of the outer cylinder 127, and the lower part of the fixed wing spacer 125 and the base
- a threaded spacer 131 is disposed between the sleeve portions 129.
- An exhaust port 133 is formed in the lower portion of the threaded spacer 131 in the base portion 129 and communicates with the outside.
- the threaded spacer 131 is a cylindrical member made of a metal such as aluminum, copper, stainless steel, iron, or an alloy composed of these metals, and has a spiral screw on its inner peripheral surface. A plurality of grooves 131a are formed.
- the direction of the spiral of the thread groove 131a is a direction in which molecules of the exhaust gas move toward the exhaust port 133 when the molecules of the exhaust gas move in the rotational direction of the rotating body 103.
- a rotating blade 102d is suspended at the lowermost part following the rotating blades 102a, 102b, 102c '.
- the outer peripheral surface of the rotating blade 102d is cylindrical and protrudes toward the inner peripheral surface of the threaded spacer 131, and is separated from the inner peripheral surface of the threaded spacer 131 by a predetermined gap. Are close to each other.
- the base portion 129 is a disk-like member that forms the base portion of the turbo molecular pump main body 100, and is generally made of a metal such as iron, aluminum, or stainless steel.
- the base part 129 physically holds the turbomolecular pump body 100 and also has the function of a heat conduction path, so it has rigidity such as iron, aluminum and copper, has high thermal conductivity, and uses metal. I hope it is.
- the exhaust gas sucked from the intake port 101 passes between the rotary blade 102 and the fixed blade 123 and is transferred to the base portion 129. At this time, the temperature of the rotor blades 102 rises due to frictional heat generated when the exhaust gas contacts the rotor blades 102, conduction of heat generated by the motor 121, etc., but this heat is generated by the radiation or gas of the exhaust gas. It is transmitted to the fixed wing 123 side by conduction by molecules.
- the fixed blade spacer 125 is joined to each other at the outer periphery, and externally receives heat received by the fixed blade 123 from the rotor blade 102, frictional heat generated when exhaust gas contacts the fixed blade 123, and the like. Communicate to.
- the exhaust gas transferred to the base portion 129 is sent to the exhaust port 133 while being guided by the screw groove 13 la of the threaded spacer 131.
- the threaded spacer 131 is disposed on the outer periphery of the rotating blade 102d and the thread groove 131a is formed on the inner peripheral surface of the threaded spacer 131.
- a thread groove may be formed on the outer peripheral surface of the rotor blade 102d, and a spacer having a cylindrical inner peripheral surface may be disposed around the screw groove.
- the gas suctioned from the intake port 101 is an electrical component side configured by a motor 121, a lower radial electromagnet 105, a lower radial sensor 108, an upper radial electromagnet 104, an upper radial sensor 107, and the like.
- the electrical component is covered with a stator column 122 so that the electrical component does not enter the interior, and the interior of the electrical component is maintained at a predetermined pressure with a purge gas.
- a pipe (not shown) is provided in the base portion 129, and the purge gas is introduced through this pipe.
- the introduced purge gas is sent to the exhaust port 133 through the clearance between the protective bearing 120 and the rotor shaft 113, between the rotor and the stator of the motor 121, and between the stator column 122 and the rotor blade 102.
- the process gas may be introduced into the chamber at a high temperature in order to increase the reactivity.
- these process gases are cooled and reach a certain temperature, they become solid and products may be deposited in the exhaust system. Then, this kind of process gas force S becomes a low temperature in the turbo molecular pump main body 100 and becomes solid, and adheres to and accumulates in the turbo molecular pump main body 100.
- the solid product for example, A1C1
- V is attached to the outer periphery of the base portion 129, etc., and a heater or an annular water cooling tube 149 is attached, and for example, not shown on the base portion 129 !, Warm A temperature sensor (for example, a thermistor) is embedded, and based on the signal from this temperature sensor, the heating of the heater and the cooling by the water-cooled pipe 149 (hereinafter TMS) are controlled so as to keep the temperature of the base part 129 at a constant high temperature (set temperature). TMS; Temperature Management System) is being carried out.
- TMS Temperature Management System
- Patent Document 1 has been proposed in order to stably float the magnetic levitation state to the target position even if such variations exist.
- Patent Document 1 Japanese Patent No. 2700904
- the above-described method is a force that can be accurately controlled under the condition that the sensor sensitivity is always constant.
- the sensitivity of the sensor includes, for example, individual differences in the sensor, errors in the gap detection circuit, cable length It varies depending on factors such as changes.
- FIG. 7 shows the relationship between the mechanical position of the rotor shaft 113 and the electrical level at which an abnormality can be detected when the sensor sensitivity changes in this way.
- the inner diameter of the protective bearing 120 is restricted to the range of 125 m force + 125 ⁇ m.
- the abnormal detection voltage IV or IV is detected when the mechanical position of the rotor shaft 113 is 100 ⁇ m or -100 ⁇ m. It becomes like this.
- the present invention has been made in view of such a conventional problem, and if there is a variation in the sensor itself, even if there is an error in the sensor mounting at the time of assembling the stator, the rotor shaft displacement abnormality can be accurately detected.
- An object of the present invention is to provide a magnetic bearing control device capable of detection. Means for solving the problem
- the present invention provides a rotor shaft, a protective bearing disposed around the rotor shaft, a position sensor that detects a radial direction or an axial position of the rotor shaft, and a position sensor that detects the rotor shaft.
- An electric sensitivity of a signal detected by the position sensor with respect to a mechanical position of the rotor shaft inside the protective bearing and an electromagnet that adjusts the radial direction or the axial direction position of the rotor shaft based on the determined position is predetermined.
- Correction value calculation means for calculating a correction value necessary for achieving the reference sensitivity, and position correction means for correcting the position signal detected by the position sensor with the correction value calculated by the correction value calculation means. Prepared and configured.
- a correction value necessary for the electrical sensitivity of the signal detected by the position sensor with respect to the mechanical position of the rotor shaft inside the protective bearing to be a predetermined reference sensitivity is calculated.
- adjustment of the position of the rotor shaft by the electromagnet is performed by the position correction. It is performed based on the position signal corrected by the means.
- the position of the rotor shaft is adjusted based on the position signal whose sensitivity has been corrected. For this reason, it is possible to easily control the center position of the port shaft to the center position of the protective bearing. Therefore, the magnetic levitation position control is performed with extremely high accuracy.
- the correction value calculation means is provided, when a position sensor having a variation in individual differences is used, a detection circuit difference, a cable length difference V, etc. Even if there is an error or the like that occurs due to the error, the rotor shaft displacement abnormality can be accurately detected by the position signal whose sensor sensitivity is adjusted. Similarly, even if there is an error in sensor mounting during stator assembly, abnormal displacement of the rotor shaft can be detected accurately.
- FIG. 1 is a block diagram of a magnetic bearing control device according to an embodiment of the present invention.
- FIG. 2 is a flowchart for explaining the operation of this embodiment.
- FIG. 3 Diagram showing how the rotor shaft is moved to the right from the inner diameter center of the protective bearing
- FIG.4 Diagram showing how the rotor shaft is moved to the left from the center of the inner diameter of the protective bearing
- FIG. 7 is a diagram showing the relationship between the mechanical position of the rotor shaft and the electrical level at which an abnormality can be detected.
- FIG. 1 is a block diagram of a magnetic bearing control apparatus according to an embodiment of the present invention.
- the eddy current gap sensors 107A and 107B are arranged in pairs with the rotor shaft 113 in between, and are respectively disposed between the eddy current gap sensor 107A and the rotor shaft 113, and between the eddy current gap sensor 107B and the rotor shaft 113.
- the displacement in the radial direction is detected in the form of voltage.
- the eddy current gap sensors 107A and 107B are the same for the lower radial sensor and the axial sensor, which are explained using the upper radial sensor as an example.
- the detected sensor signals 12A and 12B are input to the eddy current gap detection circuit 40.
- the eddy current gap detection circuit 40 calculates the gap between the rotor shaft 113 and the protective bearing 120 based on the deviation based on the output of the sensor signals 12A and 12B, and outputs the gap signal 42 to the sensor sensitivity adjustment circuit 50 and the calculation circuit 90. It is like this.
- the arithmetic circuit 90 calculates / corrects the sensor sensitivity correction values of the eddy current gap sensors 107A and 107B, and the sensor sensitivity adjustment circuit 50 calculates the sensor sensitivity based on the correction values. It will be corrected so that the sensitivity is appropriate!
- the sensor corrected by the sensor sensitivity adjustment circuit 50 The rotor shaft 113 is adjusted to be positioned at the center of the inner diameter of the protective bearing 120 based on the signal. The center position is designated by the arithmetic circuit 90.
- the signal adjusted by the offset / levitation gain adjustment circuit 60 is subjected to PID compensation by the magnetic levitation compensation circuit 70, and then amplified by the current amplification circuit 80 and supplied to the electromagnets 104X + and 104X-. Yes.
- the sensitivity of the eddy current gap sensors 107A and 107B varies depending on factors such as individual sensor differences, gap detection circuit errors, and cable length changes. For this reason, even if these factors are present, correction is performed so that a displacement abnormality of the rotor shaft 113 can be detected with a constant sensor sensitivity.
- step 100 of FIG. 2 first, the rotor shaft 113 is moved to the right side from the center O of the inner diameter of the protective bearing 120 as shown in FIG. 3, and it is determined whether or not the force is in contact with the right side of the protective bearing 120 in step 102. Refused.
- the position of the rotor shaft 113 is always detected by the eddy current gap sensors 107A and 107B, but the signals of the eddy current gap sensors 107A and 107B do not change even if the excitation current to the electromagnets 104X + and 104X— is changed. It can be seen that they are in contact with each other because they are saturated.
- the contact position is determined by the arithmetic circuit 90 based on the potentials detected by the eddy current gap sensors 107A and 107B, and this data A [V] is stored in the storage circuit 95 in step 104.
- the reference value (R) is, for example, 10 [mV / ⁇ m].
- the sensitivity is adjusted by correcting the change in sensitivity of the eddy current gap sensors 107A and 107B until the reference value (R) is reached, and an anomaly is determined under a certain reference value.
- R reference value
- the sensitivity is adjusted until it corresponds to characteristic a-and then the abnormal level is detected. To do.
- the offset is output from the arithmetic circuit 90 to the levitation gain adjustment circuit 60.
- A1 is the value of the data A [V] whose sensor sensitivity is adjusted in step 114
- B1 is the value of the data B [V] whose sensor sensitivity is adjusted in step 114.
- step 118 Similar control is performed on the Y axis in step 118, and control on the Z axis is performed in step 120.
- the rotor shaft will be adjusted after sensor sensitivity adjustment. Since the center position of 113 is controlled to the center position of the protective bearing 120, the magnetic levitation position control during this time is performed with extremely high accuracy.
- timing for correcting the error of the eddy current gap sensors 107A and 107B can be arbitrarily started manually, or automatically recognized after assembly or when the combination of the pump and the control circuit is different. Let's start with.
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- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Magnetic Bearings And Hydrostatic Bearings (AREA)
- Non-Positive Displacement Air Blowers (AREA)
Abstract
Description
Claims
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2004-268414 | 2004-09-15 | ||
JP2004268414A JP2006083924A (ja) | 2004-09-15 | 2004-09-15 | 磁気軸受制御装置 |
Publications (1)
Publication Number | Publication Date |
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WO2006030824A1 true WO2006030824A1 (ja) | 2006-03-23 |
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Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
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PCT/JP2005/016930 WO2006030824A1 (ja) | 2004-09-15 | 2005-09-14 | 磁気軸受制御装置 |
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WO (1) | WO2006030824A1 (ja) |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP2644917B1 (en) | 2010-11-24 | 2016-01-13 | Edwards Japan Limited | Magnetic bearing control device, and exhaust pump provided with the device |
CN109723719A (zh) * | 2019-03-04 | 2019-05-07 | 青岛大学 | 一种差动检测式自传感电磁轴承及其实现方法 |
US10359046B2 (en) | 2013-11-29 | 2019-07-23 | Edwards Japan Limited | Magnetic bearing device and vacuum pump |
FR3129722A1 (fr) * | 2021-11-26 | 2023-06-02 | Skf Magnetic Mechatronics | Dispositif d’estimation de la sensibilié d’un capteur, procédé et système associé |
Citations (8)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH05149337A (ja) * | 1991-11-22 | 1993-06-15 | Mitsubishi Heavy Ind Ltd | 磁気軸受装置 |
JPH0665619U (ja) * | 1993-02-22 | 1994-09-16 | セイコー精機株式会社 | 磁気軸受制御回路 |
JP2700904B2 (ja) * | 1988-10-18 | 1998-01-21 | セイコー精機株式会社 | 磁気浮上体の制御装置 |
JPH10299773A (ja) * | 1997-04-28 | 1998-11-10 | Seiko Seiki Co Ltd | 磁気軸受の制御装置 |
JPH11166534A (ja) * | 1997-12-04 | 1999-06-22 | Daikin Ind Ltd | 磁気軸受装置 |
JP2001352114A (ja) * | 2000-06-08 | 2001-12-21 | Ebara Corp | エキシマレーザ装置用磁気軸受装置 |
JP2002081444A (ja) * | 2000-09-05 | 2002-03-22 | Shimadzu Corp | 磁気軸受装置および磁気軸受装置のセンサ感度調整方法 |
JP2003222130A (ja) * | 2002-01-28 | 2003-08-08 | Shimadzu Corp | 磁気軸受装置 |
-
2004
- 2004-09-15 JP JP2004268414A patent/JP2006083924A/ja active Pending
-
2005
- 2005-09-14 WO PCT/JP2005/016930 patent/WO2006030824A1/ja active Application Filing
Patent Citations (8)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2700904B2 (ja) * | 1988-10-18 | 1998-01-21 | セイコー精機株式会社 | 磁気浮上体の制御装置 |
JPH05149337A (ja) * | 1991-11-22 | 1993-06-15 | Mitsubishi Heavy Ind Ltd | 磁気軸受装置 |
JPH0665619U (ja) * | 1993-02-22 | 1994-09-16 | セイコー精機株式会社 | 磁気軸受制御回路 |
JPH10299773A (ja) * | 1997-04-28 | 1998-11-10 | Seiko Seiki Co Ltd | 磁気軸受の制御装置 |
JPH11166534A (ja) * | 1997-12-04 | 1999-06-22 | Daikin Ind Ltd | 磁気軸受装置 |
JP2001352114A (ja) * | 2000-06-08 | 2001-12-21 | Ebara Corp | エキシマレーザ装置用磁気軸受装置 |
JP2002081444A (ja) * | 2000-09-05 | 2002-03-22 | Shimadzu Corp | 磁気軸受装置および磁気軸受装置のセンサ感度調整方法 |
JP2003222130A (ja) * | 2002-01-28 | 2003-08-08 | Shimadzu Corp | 磁気軸受装置 |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP2644917B1 (en) | 2010-11-24 | 2016-01-13 | Edwards Japan Limited | Magnetic bearing control device, and exhaust pump provided with the device |
US10359046B2 (en) | 2013-11-29 | 2019-07-23 | Edwards Japan Limited | Magnetic bearing device and vacuum pump |
CN109723719A (zh) * | 2019-03-04 | 2019-05-07 | 青岛大学 | 一种差动检测式自传感电磁轴承及其实现方法 |
FR3129722A1 (fr) * | 2021-11-26 | 2023-06-02 | Skf Magnetic Mechatronics | Dispositif d’estimation de la sensibilié d’un capteur, procédé et système associé |
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