CN-116467844-B - Dynamic modeling method for three-orthogonal magnetic resistance translation magnetic bearing

Abstract

The invention discloses a dynamic modeling method of a tri-orthogonal magnetic resistance translational magnetic bearing, which is characterized in that magnetic circuit analysis is carried out based on an equivalent magnetic circuit method, a single-group magnetic pole electromagnetic force model of the tri-orthogonal magnetic bearing is obtained by utilizing a magnetic circuit ohm law, orthogonal model magnetic circuits of the three groups of magnetic poles are constructed according to a mode that right-angle regular triangular pyramid lateral edges are used as references and three groups of magnetic poles are circumferentially and uniformly distributed, a coordinate transformation matrix directional cosine array of an electromagnetic force coordinate system and a position coordinate system is constructed by analyzing geometric characteristics of the tri-orthogonal magnetic bearing, and when a magnetic suspension rotor is subjected to external disturbance, the current flowing through a coil winding of the magnetic bearing is changed according to the displacement variation of the rotor, so that the rotor is controlled. The dynamic modeling method of the three-orthogonal magnetic resistance translation magnetic bearing can realize three-degree-of-freedom translation and preset position suspension of a platform carried by the magnetic bearing, and has wide application prospect in the technical field of novel spacecraft attitude control.

Inventors

• WANG WEIJIE
• Pang Weikun
• Duan Leqiang
• REN YUAN
• WANG LIFEN
• FAN YAHONG
• ZHU HONGYE
• LI LEI
• LI ZONGYU
• CHEN FEIYU

Assignees

• 中国人民解放军战略支援部队航天工程大学

Dates

Publication Date

20260505

Application Date

20230228

Claims (1)

1. 1. A dynamic modeling method of a tri-orthogonal magnetic resistance translation magnetic bearing is characterized in that magnetic circuit analysis is carried out based on an equivalent magnetic circuit method, a single-group magnetic pole electromagnetic force model of the tri-orthogonal magnetic bearing is obtained by utilizing a magnetic circuit ohm law, orthogonal model magnetic circuit construction of the three groups of magnetic poles is carried out on the magnetic bearing in a mode of uniformly distributing the circumferences of the three groups of magnetic poles by taking right-angle regular triangular pyramid side edges as a reference, a coordinate transformation matrix directional cosine array of an electromagnetic force coordinate system and a position coordinate system is constructed by analyzing geometric characteristics of the tri-orthogonal magnetic bearing, when a magnetic levitation rotor is subjected to external disturbance, the size of current flowing through a coil winding of the magnetic bearing is changed according to the displacement variation of the rotor, and the control of the rotor is realized, and the dynamic modeling method specifically comprises the following steps: (1) Three-orthogonal magnetic bearing single-group magnetic pole electromagnetic force modeling based on equivalent magnetic circuit method The three orthogonal magnetic resistance translational magnetic bearing is composed of three groups of identical magnetic poles, wherein the magnetic circuit of a single group of magnetic poles mainly comprises an inner iron core, an outer iron core, a radial inner magnetic pole, an outer magnetic pole, a rotor and an air gap between the rotor and the radial inner magnetic pole and the radial outer magnetic pole, the magnetic flux loops formed by the inner magnetic pole and the outer magnetic pole are all formed by the N poles of a coil winding, the magnetic flux loops pass through the air gap between the iron core and the rotor and the air gap between the rotor and the S pole, and return to the S pole to form a closed loop: Wherein the method comprises the steps of 、 、 、 Respectively represents the air gap magnetic resistance between the inner magnetic pole and the outer magnetic pole and the rotor, 、 Respectively representing the total magnetic resistance of the magnetic circuits of the two channels of the single-group magnetic pole; The single air gap reluctance is expressed as: Where delta is the length of the air gap between the mover and the pole face, Is the magnetic permeability in the vacuum state, Representing the area of each magnetic pole; the magnetic flux of two channels of a single magnetic pole group can be obtained by the following steps: In the middle of For the current in the coil when the mover is in the equilibrium position, Represents control current, N represents the number of turns of the coil; force applied by the mover in two channels of single-group magnetic pole 、 Expressed as: Substituting the formula (1), the formula (2) and the formula (3) into the above formula can obtain electromagnetic attraction force born by the rotor in the two channels with single magnetic poles: as can be obtained from the above, when the mover is at the preset equilibrium position, the electromagnetic force is: From the above, it can be seen that the electromagnetic force applied to the mover is proportional to the square of the current flowing in the coil winding; When the mover is at the balance position, the displacement detected by the position sensor is S, and when the displacement detected by the offset balance position is S, the mover receives electromagnetic attraction forces at two ends of a single magnetic pole, namely: the total electromagnetic resultant force of the single group of magnetic poles born by the rotor is as follows: Carrying out Taylor expansion on the above formula and discarding high-order terms to obtain an electromagnetic attraction formula after linearization of a single degree of freedom of the rotor: In the formula, Called current stiffness , Referred to as displacement stiffness ; (2) Three-orthogonal magnetic bearing magnetic pole configuration creation based on right-angle regular triangular pyramid The three groups of magnetic poles of the three-orthogonal magnetic resistance translation magnetic bearing are uniformly distributed along the circumference in the same radial plane, namely, the included angle between every two adjacent magnetic poles is 120 degrees, the three groups of magnetic poles adopt an oblique mounting mode at the same time, the axes of the magnetic poles of each group are defined as the direction of electromagnetic force of the magnetic poles, the axes of the magnetic poles of the three groups form a right-angle regular triangular pyramid in space, namely, the side face of the right-angle regular triangular pyramid is an isosceles right-angle triangle, the bottom face of the right-angle regular triangular pyramid is the radial plane where the magnetic poles are located, and the right-angle regular triangular pyramid is obtained according to an equal volume method and the property of the equilateral triangle: Volume is calculated by taking the side surface as a reference: Volume is calculated on the condition of the bottom surface equilateral triangle: According to It is easy to know that: The geometric characteristics of the right-angle regular triangular pyramid can be obtained by: from the formulas (13) and (14): Wherein l is the length of the side edge of the triangular pyramid, h is the height from the radial plane to the apex of the triangular pyramid, Is the included angle between the side edges of the triangular pyramid and the radial plane; The electromagnetic force generated by the three groups of magnetic poles a, b and c can be decomposed into two orthogonal components in the radial plane 、 And a component passing through the apex of the triangular pyramid and perpendicular to the radial plane The formula can be derived from: The electromagnetic resultant force generated by each group of magnetic poles passes through the sphere center and is mutually perpendicular, and the radial two-degree-of-freedom translation and the axial one-degree-of-freedom translation of the control rotor can be realized by changing the magnitude of current flowing through the coil winding; (3) Construction of cosine array in electromagnetic force direction of three-orthogonal magnetic bearing With the apex of the triangular pyramid as the origin Establishing an electromagnetic force coordinate system, wherein three coordinate axes point to the bottom surface direction of the triangular pyramid along three side edges alpha, beta and gamma of the triangular pyramid, and the coordinate system meets the Cartesian right-hand rule; With the base of the triangular pyramid, i.e. the centre of the radial plane Establishing a position coordinate system for an origin, wherein the x-axis is the projection of the alpha-axis on a radial plane, and the z-axis is along the radial plane The y-axis is located in a radial plane, satisfying the right hand rule; Solving an electromagnetic force coordinate system Coordinate system of position The conversion matrix P between the two is that the position coordinate system is firstly Rotated about the y-axis Obtaining the transition system Which is provided with Shaft and electromagnetic force coordinate system Is overlapped with the alpha axis of the (C) Winding machine Rotation of the shaft Then, the position coordinate system is easily known to rotate to the electromagnetic force coordinate system; Based on the analysis, the elementary conversion matrices in the first rotation and the second rotation can be obtained respectively as follows: the transitivity according to the directional cosine array is as follows: Is easy to obtain according to the space geometrical relationship of the regular triangular pyramid ; (4) Three-orthogonal magnetic bearing three-degree-of-freedom translational decoupling magnetic resistance modeling Combining electromagnetic attraction force corresponding to displacement offset 、 、 Electromagnetic attraction provided by the conversion matrix P and the magnetic drag magnetic bearing 、 、 The three degrees of freedom translational dynamics model of the rotor is obtained by means of association; according to Newton's second law: According to the coordinate transformation, the electromagnetic attraction force F corresponding to the displacement offset is provided by the conversion matrix P and the magnetic resistance magnetic bearing The link is as follows: Substitution into And Is obtained by solving the values of (1): Substitution into Simplifying and obtaining: According to an electromagnetic suction formula after the single-degree-of-freedom linearization of the mover, the method can be as follows: And combining a single degree of freedom dynamic equation of the mover obtained by Newton's second law: linearizing electromagnetic attraction force in three directions of a position coordinate system x, y and z to obtain a three-degree-of-freedom translational dynamics model of the rotor: In the formula, 、 、 Is the displacement actually measured by the displacement sensor; 、 、 is three groups of magnetic resistance magnetic bearings for controlling current.

Description

Dynamic modeling method for three-orthogonal magnetic resistance translation magnetic bearing Technical Field The invention relates to the technical field of magnetic suspension bearing dynamics modeling, in particular to a three-orthogonal magnetic resistance translational magnetic bearing dynamics modeling method. Background The common magnetic resistance magnetic bearing is a combination of single axial direction and double radial directions, the combination mode has the advantages that the translation of three degrees of freedom is mutually independent, less coupling is needed to control conveniently, but the combination mode also has certain defects, the axial direction and the radial direction magnetic bearing can occupy more space, and the structure is relatively fixed and can not adapt to different task demands. If a highly integrated multi-degree-of-freedom combined system is adopted, the degree of coupling among the degrees of freedom of the system is higher, and the control is difficult or even uncontrollable. The dynamic modeling method of the three-orthogonal magnetic resistance translation magnetic bearing can realize three-degree-of-freedom translation and preset position suspension of a platform carried by the magnetic bearing, and has important significance for further simplifying control and improving response speed and precision. Disclosure of Invention The invention aims to provide a dynamic modeling method for a three-orthogonal magnetic resistance translation magnetic bearing, which can accurately establish a dynamic model of the three-orthogonal magnetic resistance translation magnetic bearing so as to solve the problems of three-degree-of-freedom translation and suspension of a rotor of the three-orthogonal magnetic bearing and provide theoretical support for simplifying the control of the magnetic bearing and improving the control precision. The invention provides a technical scheme for realizing the purpose, which comprises the following steps of carrying out magnetic circuit analysis based on an equivalent magnetic circuit method, obtaining a single-group magnetic pole electromagnetic force model of a three-orthogonal magnetic bearing by utilizing a magnetic circuit ohm law, carrying out orthogonal model magnetic circuit construction of the three-group magnetic poles on the magnetic bearing by taking right-angle regular triangular pyramid side edges as references in a mode of uniformly distributing the three-group magnetic pole circumferences, and constructing a coordinate transformation matrix direction cosine array of an electromagnetic force coordinate system and a position coordinate system by analyzing the geometric characteristics of the three-orthogonal magnetic bearing, wherein when a magnetic levitation rotor is subjected to external disturbance, the magnitude of current flowing through a coil winding of the magnetic bearing is changed according to the displacement variation of the rotor, so as to realize the control of the rotor, and the dynamic modeling of the method comprises the following specific steps: (1) Three-orthogonal magnetic bearing single-group magnetic pole electromagnetic force modeling based on equivalent magnetic circuit method The three orthogonal magnetic resistance translational magnetic bearing is composed of three groups of identical magnetic poles, wherein the magnetic circuit of a single group of magnetic poles mainly comprises an inner iron core, an outer iron core, a radial inner magnetic pole, an outer magnetic pole, a rotor and an air gap between the rotor and the radial inner magnetic pole and the radial outer magnetic pole, the magnetic flux loops formed by the inner magnetic pole and the outer magnetic pole are all formed by the N poles of a coil winding, the magnetic flux loops pass through the air gap between the iron core and the rotor and the air gap between the rotor and the S pole, and return to the S pole to form a closed loop: Wherein R 11、R12、R21、R22 represents the air gap magnetic resistance between the inner magnetic pole, the outer magnetic pole and the mover, and R 1、R2 represents the total magnetic resistance of the magnetic circuit of the two channels of the single-group magnetic pole; The single air gap reluctance is expressed as: R=δ/(μ0Ai) (2) Wherein delta is the length of an air gap between the rotor and the magnetic pole face, mu 0 is the magnetic permeability in vacuum, and A i represents the area of each magnetic pole; the magnetic flux of two channels of a single magnetic pole group can be obtained by the following steps: Wherein I 0 is the current in the coil when the rotor is at the balance position, I s is the control current, and N is the number of turns of the coil; The force F 1、F2 to which the mover is subjected in the two channels of the single set of poles can be expressed as: Substituting the formula (1), the formula (2) and the formula (3) into the above formula can obtain electromagnetic attraction force