CN115130252B - Design method of radial magnetic bearing and radial magnetic bearing - Google Patents
Design method of radial magnetic bearing and radial magnetic bearing Download PDFInfo
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Abstract
The disclosure provides a design method of a radial magnetic bearing and the radial magnetic bearing. The design method of the radial magnetic bearing comprises the following steps: determining the number of turns of the bias winding and the number of turns of the control winding in the stator winding of the radial magnetic bearing according to the design parameters of the radial magnetic bearing comprises: determining the total number of turns of a stator winding according to a first design parameter of the radial magnetic bearing, determining the number of turns of a bias winding according to a second design parameter of the radial magnetic bearing and a magnetization performance parameter of a stator core of the radial magnetic bearing, and calculating the number of turns of a control winding based on the total number of turns of the stator winding and the number of turns of the bias winding; and on a stator iron core of the radial magnetic bearing, winding is respectively carried out according to the number of turns of the bias winding and the number of turns of the control winding to form the control winding and the bias winding which are mutually independent. The radial magnetic bearing designed based on the design method of the radial magnetic bearing provided by the disclosure not only can realize quick dynamic response, but also can ensure the control precision of the radial magnetic bearing in the use process.
Description
Technical Field
The disclosure relates to the technical field of bearing correlation, and in particular relates to a design method of a radial magnetic bearing and the radial magnetic bearing.
Background
In the related art, industrial electricity accounts for about 70% of the total social electricity consumption, and the motor consumes 75% of the industrial electricity, and the motor becomes the largest power consuming machine. The traditional industrial motor in China is supported by a mechanical bearing and is limited by the friction of the mechanical bearing and the vibration of a rotor, and the motor can only run at a low rotating speed, so that the power density is low and the efficiency is low. In industrial applications such as high-pressure blowers, compressors, vacuum pumps and the like, a multi-stage speed increasing mechanism is required, so that a motor system is huge, high in energy consumption, poor in reliability, and serious in noise pollution and oil pollution.
The high-speed motor supported by the magnetic bearing eliminates friction and wear, and the magnetic bearing does not need lubrication, so that the rotating speed of the high-speed motor can reach tens of thousands of revolutions per minute, and the high-speed motor has the advantages of high power density, small volume, light weight, quick response and the like. The magnetic bearing can be used as a direct drive power source to be connected with high-speed mechanical equipment, can effectively improve the system efficiency, has obvious energy-saving effect, and is an ideal supporting component for the development of high-speed rotary power machinery in the future. Currently, an active magnetic bearing can be divided into a permanent magnet biased magnetic bearing and a pure electromagnetic magnetic bearing according to a generation mode of bias magnetic flux, wherein the permanent magnet provides a bias magnetic field, and the non-contact suspension support of a rotor is realized by positive and negative superposition of the bias magnetic field and a control magnetic field generated by control current. However, the existing permanent magnet biased radial magnetic bearing has magnetic force and magnetic path coupling between the x-axis magnetic path channel and the y-axis magnetic path channel, thereby improving the complexity of a control system, and reducing the control precision of the magnetic bearing compared with a pure electromagnetic reluctance magnetic bearing. The pure electromagnetic magnetic bearing has two controllable magnetic fields, namely two controllable currents (bias current and control current), and in a power-off state, the magnetic pole surface has no magnetic field, so that the stator and the rotor do not generate attraction in the assembling process, and the magnetic suspension product is easier to install. And the pure electromagnetic magnetic bearing can structurally realize the decoupling of the magnetic channel and the magnetic channel of the magnetic bearing, has a simple control system and higher control precision, and is widely applied to high-speed motion occasions such as a magnetic suspension blower, a magnetic suspension motor, a magnetic suspension energy storage flywheel, a magnetic suspension bias momentum wheel, a magnetic suspension control moment gyro and the like.
However, the existing pure electromagnetic magnetic bearings all adopt a single-winding structure, and the number of turns of a control winding is large, so that the inductance of a control loop is large, the dynamic response performance of the magnetic bearing is reduced, and the displacement response speed of a rotor is influenced. When the rotor is interfered by the outside, the position of the rotor can be adjusted for too long time, so that the magnetic suspension high-speed power equipment can be adjusted quickly and stably.
Therefore, it is desirable to provide a magnetic bearing capable of ensuring control accuracy and achieving a rapid dynamic response.
Disclosure of Invention
The following is a summary of the subject matter described in detail in this disclosure. This summary is not intended to limit the scope of the claims.
The present disclosure provides a radial magnetic bearing and a method for designing the same.
According to a first aspect of an embodiment of the present disclosure, there is provided a method of designing a radial magnetic bearing, the method of designing the radial magnetic bearing including:
determining the number of turns of a bias winding and the number of turns of a control winding in a stator winding of the radial magnetic bearing according to the design parameters of the radial magnetic bearing, wherein the determining comprises the following steps: determining a total number of turns of the stator winding according to a first design parameter of the radial magnetic bearing; determining the number of turns of the bias winding according to a second design parameter of the radial magnetic bearing and a magnetization performance parameter of a stator core of the radial magnetic bearing; calculating the number of turns of the control winding based on the total number of turns of the stator winding and the number of turns of the bias winding;
and winding the stator iron core of the radial magnetic bearing according to the number of turns of the bias winding and the number of turns of the control winding to form the control winding and the bias winding which are independent of each other.
According to some embodiments of the disclosure, the first design parameter comprises: the maximum current density of the stator winding, the winding height of the stator winding, the winding cavity width of the stator winding and the stator slot filling factor of the winding cavity of the stator winding.
According to some embodiments of the present disclosure, determining a total number of turns of the stator windings according to a first design parameter of the radial magnetic bearing comprises:
establishing a stator winding turn number model based on the maximum current density of the stator winding, the winding height of the stator winding, the winding cavity width of the stator winding and the stator slot filling rate of the winding cavity of the stator winding;
determining the total turn range of the stator winding according to the stator winding turn model;
and selecting the optimal total turns of the stator winding from the range of the total turns of the stator winding according to a preset rule as the total turns of the stator winding.
According to some embodiments of the disclosure, the stator winding turn number model comprises:
wherein the content of the first and second substances,N b the number of turns of the bias winding;N c the number of turns of the control winding;λthe stator slot filling rate of a winding cavity of the stator winding is set;S w is the winding cavity area of the stator winding;I max the maximum current allowed to be introduced into the conducting wire of the stator winding;J max is the maximum current density of the stator winding.
According to some embodiments of the disclosure, the second design parameter comprises: an air gap length of a magnetic bearing equilibrium position of the radial magnetic bearing; the stator core magnetization performance parameters of the radial magnetic bearing comprise: the soft magnetic material of the stator core has a saturated magnetic density.
According to some embodiments of the present disclosure, determining the number of turns of the bias winding according to a second design parameter of the radial magnetic bearing and a stator core magnetization performance parameter of the radial magnetic bearing comprises:
establishing a bias winding turn number model based on the air gap length of the magnetic bearing balance position of the radial magnetic bearing and the saturation magnetic density of the soft magnetic material of the stator iron core;
and calculating the number of turns of the bias winding according to the model of the number of turns of the bias winding.
According to some embodiments of the disclosure, the bias winding turn number model comprises:
wherein the content of the first and second substances,N b the number of turns of the bias winding;B s a saturation magnetic density for the soft magnetic material of the stator core;gbalancing the magnetic bearingThe air gap length of the location;μ 0 is a vacuum magnetic conductivity;I max the maximum current allowed to pass through the wires of the stator winding.
According to some embodiments of the present disclosure, calculating the number of turns of the control winding based on the total number of turns of the stator winding and the number of turns of the bias winding comprises:
calculating the number of turns of the control winding according to a preset relational expression, wherein the preset relational expression isN c =N General assembly -N b ；
Wherein the content of the first and second substances,N general assembly Is the total number of turns of the stator winding;N b is the number of turns of the bias winding;N c is the number of turns of the control winding.
According to a second aspect of an embodiment of the present disclosure, there is provided a radial magnetic bearing employing the design method of the radial magnetic bearing provided by the first aspect of the present disclosure; the radial magnetic bearing includes:
a rotor sleeve;
a stator assembly comprising: the stator iron cores are circumferentially distributed around the outer circumferential surface of the rotor sleeve;
a stator winding comprising: the control winding is arranged on the stator core and is positioned on one side of the stator core, which is far away from the rotor sleeve; the offset winding is arranged on the stator core and is positioned on one side, close to the rotor sleeve, of the stator core.
Has the advantages that: the design method of the radial magnetic bearing is provided by optimizing the radial magnetic bearing, the number of turns of a bias winding and the number of turns of a control winding in a stator winding of the radial magnetic bearing are determined firstly, and then the control winding and the bias winding are wound on a stator core of the radial magnetic bearing respectively and are independent from each other according to the number of turns of the bias winding and the number of turns of the control winding. The radial magnetic bearing designed based on the design method of the radial magnetic bearing provided by the disclosure not only improves the dynamic response performance of the magnetic bearing, but also can ensure the control precision of the radial magnetic bearing in the use process.
Other aspects will be apparent upon reading and understanding the attached figures and detailed description.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the disclosure and together with the description, serve to explain the principles of the embodiments of the disclosure. In the drawings, like reference numerals are used to indicate like elements. The drawings in the following description are directed to some, but not all embodiments of the disclosure. For a person skilled in the art, other figures can be derived from these figures without inventive effort.
FIG. 1 is a flow chart illustrating a method of designing a radial magnetic bearing in accordance with an exemplary embodiment;
FIG. 2 is a flow chart illustrating the determination of the total number of turns of the stator windings according to an exemplary embodiment;
FIG. 3 is a flowchart illustrating the determination of the total number of turns of the bias winding in accordance with one exemplary embodiment;
FIG. 4 is a cross-sectional view of a radial magnetic bearing shown in accordance with an exemplary embodiment.
In the figure: 1. a stator core; 2. a control winding; 3. a bias winding; 4. a stator lock nut; 5. rotor lamination; 6. a rotor sleeve; 7. a rotor lock nut; 8. a stator sleeve.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present disclosure more clear, the technical solutions in the embodiments of the present disclosure will be described clearly and completely with reference to the drawings in the embodiments of the present disclosure, and it is obvious that the described embodiments are some embodiments of the present disclosure, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments disclosed herein without making any creative effort, shall fall within the protection scope of the present disclosure. It should be noted that, in the present disclosure, the embodiments and the features of the embodiments may be arbitrarily combined with each other without conflict.
In the related art, the dynamic response speed of the pure electromagnetic bearing is low. The invention provides a design method of a radial magnetic bearing capable of realizing high-frequency dynamic quick response, which optimizes a control winding and a bias winding in the radial magnetic bearing: firstly, the number of turns of a bias winding and the number of turns of a control winding in a stator winding of the radial magnetic bearing are determined according to the design parameters of the radial magnetic bearing, and then the control winding and the bias winding are wound on a stator iron core of the radial magnetic bearing respectively according to the number of turns of the bias winding and the number of turns of the control winding, so that the control winding and the bias winding which are mutually independent are formed, the inductance in a loop formed by the control winding can be reduced, and the response performance of the radial magnetic bearing is improved. The radial magnetic bearing designed based on the design method not only can realize quick dynamic response, but also can ensure the control precision of the radial magnetic bearing in the use process.
The present disclosure is described below with reference to the accompanying drawings and specific embodiments.
An exemplary embodiment of the present disclosure provides a method for designing a radial magnetic bearing, as shown in fig. 1, and fig. 1 is a flowchart illustrating a method for designing a radial magnetic bearing according to an exemplary embodiment. The design method comprises the following steps:
step S101, determining the number of turns of a bias winding and the number of turns of a control winding in a stator winding of the radial magnetic bearing according to design parameters of the radial magnetic bearing;
and S102, winding the stator iron core of the radial magnetic bearing according to the number of turns of the bias winding and the number of turns of the control winding to form the control winding and the bias winding which are independent of each other.
Considering that the number of turns of winding coils in a stator winding can influence the dynamic response speed of the radial magnetic bearing, particularly, the existing radial magnetic bearing adopts a single-winding arrangement mode, so that the number of turns of a control winding is more, further the inductance of a control loop is larger, and the influence on the response speed of the magnetic bearing is larger. In order to improve the dynamic response speed of the radial magnetic bearing, the design method of the radial magnetic bearing in the exemplary embodiment adopts a mode of separately arranging the control winding and the bias winding, and comprehensively determines the number of turns of the suitable bias winding and the number of turns of the control winding based on the design parameters of the radial magnetic bearing, thereby reducing the number of turns of the control winding on the whole and improving the dynamic response speed of the radial magnetic bearing.
In order to determine the factors influencing the dynamic behavior of the radial magnetic bearing, in the exemplary embodiment, the analysis is carried out by establishing a voltage-current model of the radial magnetic bearing, wherein a control loop is provided on each stator core of the radial magnetic bearing, which control loop comprises a control winding pair of two control windings wired in series, from which it follows that the total number of turns of the control loop isn=2N c ，N c Is the number of turns of one control winding. By controlling the total flux linkage of the winding
（ΦFor each channel flux of the magnetic bearing, n is the total number of turns of the control loop) and the relationship between the induced voltage at the control winding ends and the total flux linkage of the control winding
(e is the voltage induced at the control winding end,
a differential unit for controlling the total flux linkage of the winding), calculating the terminal voltage of the obtained control windingu c ，
In the formulau c In order to control the terminal voltage of the winding,rin order to control the resistance of the winding pairs,
in order to control the differentiating unit of the total flux linkage of the windings,I c to control the current of the winding.
For each channel of magnetic bearingTong (Chinese character of 'tong')ΦTaking the derivative, we can get:
a two-dimensional coordinate system is established on a plane of a radial tangent plane of the radial magnetic bearing, wherein,N b is the number of turns of the bias winding;N c to control the number of turns of the winding;I b is the current of the bias winding;I c to control the current of the winding;Φ x+ is composed ofxMagnetic flux generated by the main magnetic circuit in the positive direction of the axis;Φ y+ is composed ofyMagnetic flux generated by the main magnetic circuit in the positive direction of the axis;Φ x- is composed ofxMagnetic flux generated by the main magnetic circuit in the negative direction of the shaft;Φ y- is composed ofyMagnetic flux generated by the main magnetic circuit in the negative direction of the shaft;R x+ is composed ofxThe total magnetic resistance of the main magnetic circuit in the positive direction of the axis;R x- is composed ofxThe total magnetic resistance of the main magnetic circuit in the axial negative direction;R y+ is composed ofyThe total magnetic resistance of the main magnetic circuit in the positive direction of the axis;R y- is composed ofyThe total magnetic resistance of the main magnetic circuit in the negative axis direction.
Substituting equation (2) into equation (1) yields:
wherein, the first and the second end of the pipe are connected with each other,
-controlling a current derivative matrix;L-an inductance matrix of the control winding;R m -a matrix of the number of turns of the control winding coupled with the state of the rotor movement;r-a resistor matrix of control windings;I c -a current matrix of the control winding;U c -a voltage matrix across the control winding;E-a motion state matrix of the rotor;
rewriting the above equation (3) into a state space is described as:
in the formula
、L、R m 、r、I c 、U c AndEare respectively:
wherein the content of the first and second substances,I cx+ is composed ofxThe control current of the magnetic bearing in the axial direction is large or small;I cy+ is composed ofyThe control current of the magnetic bearing in the axial direction is large or small;I cx- is composed ofxThe control current of the magnetic bearing in the axial negative direction is large or small;I cy- is composed ofyThe control current of the magnetic bearing in the axial negative direction is large or small;N c to control the number of turns of the winding;N b is the number of bias winding turns;I b is the current of the bias winding;μ 0 in order to achieve the magnetic permeability in vacuum,μ 0 =4π×10 -7 H/m；g x+ is composed ofxThe size of the air gap of the magnetic bearing in the axial direction;g y+ is composed ofyThe size of the air gap of the magnetic bearing in the axial direction;g x- is composed ofxThe size of the air gap of the magnetic bearing in the axial negative direction;g y- are respectively asyThe size of the air gap of the magnetic bearing in the negative direction of the shaft;R x+ is composed ofxThe total magnetic resistance of the main magnetic circuit in the positive direction of the axis;R x- is composed ofxThe total magnetic resistance of the main magnetic circuit in the axial negative direction;R y+ is composed ofyThe total magnetic resistance of the main magnetic circuit in the positive direction of the axis;R y- is composed ofyThe total magnetic resistance of the main magnetic circuit in the axial negative direction;r cx+ is composed ofxA control winding resistance of the magnetic bearing in the axial direction;r cy+ is composed ofyA control winding resistance of the magnetic bearing in the axial direction;r cx- is composed ofxA control winding resistance of the magnetic bearing in the axial negative direction;r cy- is composed ofyA control winding resistance of the magnetic bearing in the axial negative direction;u cx+ is composed ofxVoltage across the control winding of the magnetic bearing in the axial direction;u cy+ is composed ofyVoltage across the control winding of the magnetic bearing in the axial direction;u cx- is composed ofxVoltage across the control winding of the magnetic bearing in the negative direction of the shaft;u cy- is composed ofyThe voltage across the control winding of the magnetic bearing in the negative direction of the shaft.
By performing a modification according to the above equation (4), a voltage-current model can be obtained:
it can be seen from the voltage-current model that the current variation at both ends of the radial magnetic bearing winding is respectively related to the voltage at both ends of the winding, the winding inductance and the rotor motion state, wherein the voltage at both ends of the winding and the rotor motion state can be optimized by a control algorithm, and the winding inductance can only be optimized by the magnetic bearing structural design. When the control winding and the bias winding are arranged together, if the current change in the bias winding also affects the inductance of the control winding, and when the number of turns of the control winding is not designed reasonably, the inductance in a control loop corresponding to the control winding may be larger. Therefore, the design method of the radial magnetic bearing in the embodiment optimizes the number of turns of the control winding coil for the radial magnetic bearing, and separately sets the control winding and the bias winding, thereby reducing the inductance of a control loop, improving the response speed of the control current in the control winding of the radial magnetic bearing, and further improving the dynamic performance of the radial magnetic bearing.
In the present exemplary embodiment, the determination process of the number of turns of the bias winding and the number of turns of the control winding in step S101 is also exemplarily explained. As shown in fig. 1, determining the number of turns of the bias winding and the number of turns of the control winding in the stator winding of the radial magnetic bearing according to the design parameters of the radial magnetic bearing includes: determining the total number of turns of the stator winding according to a first design parameter of the radial magnetic bearing; determining the number of turns of the bias winding according to a second design parameter of the radial magnetic bearing and a magnetization performance parameter of a stator core of the radial magnetic bearing; the number of turns of the control winding is calculated based on the total number of turns of the stator winding and the number of turns of the bias winding.
In some exemplary embodiments, the first design parameter includes a maximum current density of the stator winding, a winding height of the stator winding, a winding cavity width of the stator winding, a stator slot filling ratio of the winding cavity of the stator winding, and the like, wherein the maximum current density may be determined according to a design specification of the corresponding stator winding, i.e., a maximum value of current densities required in compliance with the corresponding national standard. Considering that the total number of turns of the stator winding is related to the corresponding design parameters of the stator winding current density, the winding height, the winding cavity width, the stator slot filling factor of the winding cavity of the stator winding, etc., the design method of the radial magnetic bearing in the present exemplary embodiment provides the following ways: the number of turns of the bias winding is determined by combining the first design parameter, then the number of turns of the bias winding is determined by combining the second design parameter and the magnetization performance parameter of the stator core of the radial magnetic bearing, and finally the number of turns of the control winding is calculated according to the number of turns of the bias winding and the number of turns of the stator winding, so that the number of turns of the control winding and the number of turns of the bias winding which meet the design requirements are finally obtained.
It is to be understood that the determination of the number of turns of the control winding and the number of turns of the bias winding in the stator winding is described in this exemplary embodiment only in an exemplary manner. When the number of turns of the bias winding and the total number of turns of the stator winding are determined, the number of turns of the bias winding can be determined by combining the second design parameter and the magnetization performance parameter of the stator core, then the total number of turns of the stator winding is determined, and finally the number of turns of the control winding is calculated by combining the total number of turns of the stator winding and the number of turns of the bias winding.
Wherein, as shown in fig. 2, fig. 2 is a flow chart illustrating determining the total number of turns of the stator windings according to an exemplary embodiment. Determining a total number of turns of the stator windings based on a first design parameter of the radial magnetic bearing, comprising:
step S201, establishing a stator winding turn number model based on the maximum current density of the stator winding, the winding height of the stator winding, the winding cavity width of the stator winding and the stator slot filling rate of the winding cavity of the stator winding;
step S202, determining the total turn range of the stator winding according to the stator winding turn model;
and S203, selecting the optimal total turns of the stator winding from the range of the total turns of the stator winding as the total turns of the stator winding according to a preset rule.
Considering that the number of turns of the stator winding is determined by combining constraint factors such as the maximum current density of the stator winding, the winding height of the stator winding, the winding cavity width of the stator winding, and the stator slot filling factor of the winding cavity of the stator winding in the exemplary embodiment, the total number of turns range of the stator winding can be determined based on the stator winding number model, and the optimal total number of turns can be selected from the total number of turns range by combining corresponding preset rules. In the present embodiment, a stator winding turn number model is exemplarily shown, which includes:
wherein, the first and the second end of the pipe are connected with each other,N b is the number of turns of the bias winding;N c to control the number of turns of the winding;λthe stator slot filling factor of the winding cavity of the stator winding;S w the winding cavity area of the stator winding and the winding cavity area of the stator windingS w = winding height of stator windingh w Width of winding cavity of x stator windingb w ；I max The maximum current allowed to be introduced into the stator winding lead;J max is the maximum current density of the stator winding, wherein the maximum current density can be determined according to the design specification of the corresponding stator winding, namely, the maximum value of the current density required in the corresponding national standard is met.
Since the product of the area of the cross section of the wire and the current density is equal to the product of the number of winding turns and the current, and considering the load factor of the winding cavity, it is possible to obtain:
in the formula:N b is the number of turns of the bias winding;N c to control the number of turns of the winding;I max the maximum current allowed to be introduced into the stator winding lead;J max is the maximum current density of the stator winding;S N is the area of the cross section of the wire;S w is the winding cavity area of the stator winding, wherein the winding cavity area of the stator windingS w = winding height of stator windingh w Width of winding cavity of x stator windingb w 。
Based on the above formula (5), it can be known that the number of turns of the stator winding can be determined, and considering that the winding coil needs to have enough heat dissipation space, the full factor of the stator slot of the winding cavity of the stator winding should not be too large, therefore, in the design method of the radial magnetic bearing, the above equation is correspondingly deformed, and finally the above stator winding turn model is obtained, that is:
and (3) forming the total turn range of the stator winding according to the value calculated by the stator winding turn model, and selecting the optimal total turn within the total turn range by combining with a corresponding preset rule. Illustratively, N may be chosen b +N c Maximum positive integer satisfying the above conditionAnd taking the numerical value as the optimal total number of turns.
In the present exemplary embodiment, after the corresponding first design parameter is obtained, the total number of turns of the stator winding is determined. Thus, if other specifications of the radial magnetic bearing are desired, the total number of turns of the stator winding can be combined, such as: when the specification parameters such as the area of the stator magnetic pole, the air gap flux of the magnetic pole at the balance position and the like are determined, a magnetic bearing structure mathematical model with the size of the magnetic bearing and the magnetization of the stator core as constraint conditions is established based on the size of the bearing structure and the magnetization of the stator core. Wherein the stator pole area can be determined by formula derivation:
in the formula:Ais the stator pole area;F max the maximum bearing capacity can be determined according to the gyro moment generated by the rotor torque of the radial magnetic bearing and the gravity of the rotor assembly,B s saturation magnetic density for soft magnetic material of the stator core;μ 0 in order to achieve a magnetic permeability in a vacuum,μ 0 =4π×10 -7 H/m；cosαis less thanαCosine of (a), whereinαIs half of the included angle between the adjacent 2 upper and lower magnetic poles, as shown in fig. 4.
In the formula:Φ 0 is the pole gap flux at the equilibrium position;Ais the stator pole area;B s saturation magnetic density for soft magnetic material of the stator core;N b is the number of turns of the bias winding;N c to control the number of turns of the winding;I max =J max A w the maximum current allowed to be introduced into the winding lead;J max andA w the maximum current density and the cross-sectional area of the winding coil are respectively;J max generally 2 to 4A/mm 2 ；RIs the pole air gap reluctance at the magnetic bearing equilibrium location of the radial magnetic bearing.
In some exemplary embodiments, the second design parameter comprises an air gap length of a magnetic bearing equilibrium position of the radial magnetic bearing; the stator core magnetization performance parameters of the radial magnetic bearing include the saturation magnetic density of the soft magnetic material of the stator core. In the present exemplary embodiment, the number of turns of the bias winding is determined by combining the air gap length of the magnetic bearing equilibrium position of the radial magnetic bearing and the soft magnetic material saturation magnetic density of the stator core, whereby an appropriate number of turns of the bias winding can be determined.
In some exemplary embodiments, based on the manner in which the number of turns of the bias winding may be determined by combining the air gap length of the magnetic bearing equilibrium position of the radial magnetic bearing with the soft magnetic material saturation magnetic density of the stator core in the above exemplary embodiments, in the present exemplary embodiment, as shown in fig. 3, fig. 3 is a flowchart illustrating the determination of the number of turns of the bias winding according to an exemplary embodiment, the determining of the number of turns of the bias winding according to the second design parameter of the radial magnetic bearing and the stator core magnetization performance parameter of the radial magnetic bearing includes:
s301, establishing a bias winding turn number model based on the air gap length of the magnetic bearing balance position of the radial magnetic bearing and the saturation magnetic density of the soft magnetic material of the stator core;
and step S302, calculating the number of turns of the bias winding according to the model of the number of turns of the bias winding.
In the present exemplary embodiment, in determining the number of turns of the bias winding in conjunction with the air gap length of the magnetic bearing equilibrium position of the radial magnetic bearing and the soft magnetic material saturation magnetic density of the stator core, there is exemplarily provided a bias winding turn number model including:
wherein, the first and the second end of the pipe are connected with each other,N b is the number of turns of the bias winding;B s is soft of stator coreSaturation magnetic density of magnetic material;gthe air gap length for the equilibrium position of the magnetic bearing;μ 0 in order to achieve a magnetic permeability in a vacuum,μ 0 =4π×10 -7 H/m；I max the maximum current allowed to pass through the stator winding wires.
In the present exemplary embodiment, in order to ensure a large adjustment margin of the electromagnetic levitation force of the radial magnetic bearing when the magnetic bearing bias winding is designed, the radial magnetic bearing should be designed to avoid the magnetic saturation phenomenon of the magnetic material. Combining the characteristics of a magnetic material, according to the ampere loop theorem, the magnetic field intensity of a bearing magnetic circuit is as follows:
whereinBThe magnetic field intensity of the bearing magnetic circuit;N b is the number of turns of the bias winding;N c to control the number of turns of the winding;l ej length of magnetic path of magnetic conductive material;I b to control winding coil current;I c to control winding coil current;μ 0 in order to achieve the magnetic permeability in vacuum,μ 0 =4π×10 -7 H/m；μ r is the relative permeability of the magnetic pole material;gthe air gap length for the equilibrium position of the magnetic bearing. Since the magnetic pole material of the stator core is made of the high-permeability material 1J50 in the present exemplary embodiment, the relative permeability is excellent, and the magnetic resistance is negligible. Thus, the above equation can be simplified to:
in the formula, B is the magnetic field intensity of the bearing magnetic circuit;N b is the number of turns of the bias winding;N c to control the number of turns of the winding; I b to control winding coil current;I c to control winding coil current;μ 0 is trueThe magnetic permeability of the hollow magnetic material is improved,μ 0 =4π×10 -7 H/m；gthe air gap length for the equilibrium position of the magnetic bearing.
According to the pre-magnetization curve in the 1J50B-H curve of the strong magnetic material and the formula, the change rule of the magnetic field intensity of the magnetic material along with the current of the point winding without the air gap and after the air gap is added can be obtained. And from this, the saturation current without air gapI fe Lower, saturation current after addition of air gapI g Far greater than saturation current without air gapI fe . Selecting bias operating point according to magnetic circuit magnetization curve, and setting saturation magnetic density asB s To avoid saturation of the magnetic pole material, the operating point is generally set to be half of the saturation flux density of the magnetic pole material, i.e. the operating point is set to be half of the saturation flux density of the magnetic pole materialB s At the point/2. For a high dynamic response radial pure electromagnetic bearing, a bias winding is separated from a control winding, and the bias current is the maximum allowable current of a winding coil. Therefore, in order to make the electromagnetic force of the magnetic bearing have better linearity, the number of turns of the bias winding is directly setN b Adjusting the working point, and obtaining a model of the number of turns of the bias winding as follows:
in the formula:N b is the number of turns of the bias winding;B s saturation magnetic density for soft magnetic material of the stator core;μ 0 in order to achieve a magnetic permeability in a vacuum,μ 0 =4π×10 -7 H/m；I max the maximum current allowed to be introduced into the stator winding lead;gthe air gap length for the equilibrium position of the magnetic bearing.
In some exemplary embodiments, calculating the number of turns of the control winding based on the total number of turns of the stator winding and the number of turns of the bias winding includes:
calculating the number of turns of the control winding according to a preset relationN c =N General assembly -N b ；
Wherein the content of the first and second substances,N general assembly The total number of turns of the stator winding;N b is the number of turns of the bias winding;N c to control the number of turns of the winding.
In some exemplary embodiments, after the corresponding radial magnetic bearing is designed in the above exemplary embodiments, the corresponding differential electromagnetic force can be determined, and then the displacement stiffness and the current stiffness can be calculated.
In the exemplary embodiment, taking an x-axis channel as an example, a magnetic suspension bearing stress model is established according to newton's second law, and the differential electromagnetic force thereof can be expressed as follows:
in the formula:f x+ is composed ofxMagnetic force generated in the axial direction;f x- is composed ofxMagnetic force generated in the axial direction;αis half of the included angle between the adjacent 2 upper and lower magnetic poles, as shown in fig. 4;Φ x+ is composed ofxMagnetic flux generated by the main magnetic circuit in the positive direction of the axis;Φ x- is composed ofxMagnetic flux generated by the main magnetic circuit in the negative direction of the shaft;μ 0 in order to achieve the magnetic permeability in vacuum,μ 0 =4π×10 -7 H/m；Ais the stator pole area. Therefore, the differential electromagnetic force can be simplified as follows:
in the formula:K r is the magnetic bearing coefficient;K r =2cosα/μ 0 A；μ 0 in order to achieve the magnetic permeability in vacuum,μ 0 =4π×10 -7 H/m；μ r is the relative magnetic permeability of the magnetic pole material;N b is the number of turns of the bias winding;I b is the current of the bias winding;N c to controlThe number of winding turns;I c to control the current of the winding;Ais the stator pole area;gthe air gap length for the equilibrium position of the magnetic bearing;δis the displacement of the rotor from the equilibrium position. Balance position return electromagnetic forcefAfter linearization, it can be expressed as:
in the formula:I c to control the current of the winding;δa displacement that is a deviation of the rotor from the equilibrium position;K δ andK I the displacement stiffness and the current stiffness of the magnetic bearing are respectively, wherein the displacement stiffness and the current stiffness can be expressed as:
in the formula (I), the compound is shown in the specification,μ 0 in order to achieve a magnetic permeability in a vacuum,μ 0 =4π×10 -7 H/m；μ r is the relative magnetic permeability of the magnetic pole material;N b is the number of turns of the bias winding;I b is the current of the bias winding;N c to control the number of winding turns;I c to control the current of the winding;Ais the stator pole area;gthe air gap length for the equilibrium position of the magnetic bearing;δis the displacement of the rotor from the equilibrium position.
Exemplary embodiments of the present disclosure provide a radial magnetic bearing designed according to a design method provided by exemplary embodiments of the present disclosure. As shown in fig. 4, fig. 4 is a schematic structural view of a radial magnetic bearing shown in accordance with an exemplary embodiment. The radial magnetic bearing includes:
a rotor sleeve 6;
a stator assembly, comprising: the stator iron core 1 is circumferentially distributed around the outer circumferential surface of the rotor sleeve 6;
a stator winding comprising: the control winding 2 is arranged on the stator core 1, and the control winding 2 is positioned on one side of the stator core 1, which is far away from the rotor sleeve 6; and the offset winding 3 is arranged on the stator core 1, and the offset winding 3 is positioned on one side of the stator core 1 close to the rotor sleeve 6.
In some exemplary embodiments, the radial magnetic bearing further comprises: a stator lock nut 4; a rotor lamination 5; a rotor lock nut 7; a stator sleeve 8. The stator lock nut 4 is also arranged around the circumferential distribution of the stator sleeve 6 along with the stator core 1, wherein the stator lock nut 4 can be matched with the stator sleeve 8 to limit the stator core 1. The rotor lamination 5 is arranged on the outer peripheral wall of the rotor sleeve 6 and is limited by the rotor lock nut 7, a preset distance is reserved between the rotor lamination 5 and the stator core 1 on the outer side to form an air gap of the radial magnetic bearing, and the length of the air gap at the balance position of the magnetic bearing of the radial magnetic bearing is g.
In the present disclosure, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such article or apparatus. Without further limitation, an element defined by the phrases "comprising 8230; \8230;" 8230; "does not exclude the presence of additional like elements in an article or device comprising the element.
While preferred embodiments of the present disclosure have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all alterations and modifications as fall within the scope of the disclosure.
It will be apparent to those skilled in the art that various changes and modifications may be made to the present disclosure without departing from the spirit and scope of the disclosure. Thus, it is intended that the present disclosure also cover the modifications and variations of this disclosure provided they come within the scope of the appended claims and their equivalents.
Claims (5)
1. A method of designing a radial magnetic bearing, comprising:
determining the number of turns of a bias winding and the number of turns of a control winding in a stator winding of the radial magnetic bearing according to the design parameters of the radial magnetic bearing, wherein the method comprises the following steps: determining the total number of turns of the stator winding according to first design parameters of the radial magnetic bearing, wherein the first design parameters comprise the maximum current density of the stator winding, the winding height of the stator winding, the winding cavity width of the stator winding and the stator slot filling rate of the winding cavity of the stator winding; determining the number of turns of the bias winding according to a second design parameter of the radial magnetic bearing and a magnetization performance parameter of a stator core of the radial magnetic bearing, wherein the second design parameter comprises: the air gap length of the magnetic bearing balance position of the radial magnetic bearing, and the stator core magnetization performance parameters of the radial magnetic bearing comprise: the soft magnetic material saturation magnetic density of the stator core; calculating the number of turns of the control winding based on the total number of turns of the stator winding and the number of turns of the bias winding; wherein determining the total number of turns of the stator windings in accordance with a first design parameter of the radial magnetic bearing comprises: establishing a stator winding turn number model based on the maximum current density of the stator winding, the winding height of the stator winding, the winding cavity width of the stator winding and the stator slot filling rate of the winding cavity of the stator winding; determining the total turn range of the stator winding according to the stator winding turn model; selecting the optimal total number of turns of the stator winding from the range of the total number of turns of the stator winding according to a preset rule to serve as the total number of turns of the stator winding; the stator winding turn number model comprises:
wherein, the first and the second end of the pipe are connected with each other,N b is the number of turns of the bias winding;N c the number of turns of the control winding;λthe stator slot filling factor of a winding cavity of the stator winding is set;S w the area of the winding cavity of the stator winding and the area of the winding cavity of the stator windingS w = winding height of stator windingh w Width of winding cavity of x stator windingb w ；I max The maximum current allowed to be introduced into the conducting wires of the stator winding;J max is the maximum current density of the stator winding;
and respectively winding the stator iron core of the radial magnetic bearing according to the number of turns of the bias winding and the number of turns of the control winding to form the control winding and the bias winding which are mutually independent.
2. The method of designing a radial magnetic bearing of claim 1, wherein determining the number of turns of the bias winding based on a second design parameter of the radial magnetic bearing and a stator core magnetization performance parameter of the radial magnetic bearing comprises:
establishing a bias winding turn number model based on the air gap length of the magnetic bearing balance position of the radial magnetic bearing and the saturation magnetic density of the soft magnetic material of the stator core;
and calculating the number of turns of the bias winding according to the model of the number of turns of the bias winding.
3. The method of designing a radial magnetic bearing of claim 2 wherein the bias winding turn number model comprises:
wherein the content of the first and second substances,N b the number of turns of the bias winding;B s a saturation magnetic density for the soft magnetic material of the stator core;gan air gap length that is a balance position of the magnetic bearing;μ 0 vacuum magnetic conductivity;I max the maximum current allowed to pass through the wires of the stator winding.
4. The method of designing a radial magnetic bearing of claim 1, wherein calculating the number of turns of the control winding based on the total number of turns of the stator winding and the number of turns of the bias winding comprises:
calculating the number of turns of the control winding according to a preset relational expression, wherein the preset relational expression isN c =N General (1) -N b ；
Wherein the content of the first and second substances,N general (1) Is the total number of turns of the stator winding;N b the number of turns of the bias winding;N c the number of turns of the control winding.
5. A radial magnetic bearing, characterized in that it employs the design method of the radial magnetic bearing according to any one of claims 1 to 4; the radial magnetic bearing includes:
a rotor sleeve;
a stator assembly, comprising: the stator iron cores are circumferentially distributed around the outer peripheral surface of the rotor sleeve;
a stator winding comprising: the control winding is arranged on the stator core and is positioned on one side of the stator core, which is far away from the rotor sleeve; the offset winding is arranged on the stator core and is positioned on one side, close to the rotor sleeve, of the stator core.
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| CN111832127A (en) * | 2020-06-22 | 2020-10-27 | 北京控制工程研究所 | Lorentz force radial magnetic bearing design method |
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| JP2003021140A (en) * | 2001-07-06 | 2003-01-24 | Sankyo Seiki Mfg Co Ltd | Control type radial magnetic bearing |
| TWI601363B (en) * | 2015-02-04 | 2017-10-01 | 林高合 | Electric machinery with 8-pole stator and the winding structure of the stator |
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| CN101311571A (en) * | 2007-11-19 | 2008-11-26 | 南京航空航天大学 | Constant-current source bias magnetic suspension bearing |
| CN105114457A (en) * | 2015-08-24 | 2015-12-02 | 南京邮电大学 | Axial-radial electrically-excited magnetic bearing |
| CN106981940A (en) * | 2017-04-11 | 2017-07-25 | 南京邮电大学 | Magnetic suspension switched reluctance motor biases the number of turn design method of winding and armature winding |
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Denomination of invention: A Design Method for Radial Magnetic Bearings, Radial Magnetic Bearings Effective date of registration: 20230628 Granted publication date: 20221213 Pledgee: Bank of Communications Ltd. Weifang branch Pledgor: SHANDONG TIANRUI HEAVY INDUSTRY Co.,Ltd. Registration number: Y2023370000098 |
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Denomination of invention: A design method for radial magnetic bearings and radial magnetic bearings Granted publication date: 20221213 Pledgee: Bank of Communications Ltd. Weifang branch Pledgor: SHANDONG TIANRUI HEAVY INDUSTRY Co.,Ltd. Registration number: Y2024370000015 |