A method and apparatus for calculating hysteresis loss of axial electromagnetic bearings.

Abstract

This invention proposes a method and apparatus for calculating the hysteresis loss of axial electromagnetic bearings, belonging to the field of hysteresis loss calculation technology. The method involves: establishing an equivalent magnetic circuit model; calculating the magnetomotive force under axial vibration of the thrust disk, and then determining the total dynamic magnetic flux through the equivalent magnetic circuit model; establishing a quantitative relationship between the maximum magnetic flux density amplitude, hysteresis loss, and any two angle parameters characterizing the hysteresis effect; constructing a complex permeability based on the quantitative relationship, using the magnetomotive force as the magnetic field excitation and the total dynamic magnetic flux as the magnetic field response; updating the equivalent magnetic circuit model using the complex permeability; calculating the maximum magnetic flux density amplitude of each region of the core under dynamic operating conditions through iterative calculation; calculating the hysteresis loss of each region based on the quantitative relationship and the maximum magnetic flux density amplitude of each region; and finally, calculating the total hysteresis loss. Based on this method, an apparatus for calculating the hysteresis loss of axial electromagnetic bearings is also proposed. This invention can accurately calculate the hysteresis loss of axial electromagnetic bearings under dynamic operating conditions.

Description

Technical Field

[0001] This invention belongs to the field of hysteresis loss calculation technology, and specifically relates to a method and device for calculating hysteresis loss of axial electromagnetic bearings. Background Technology

[0002] Electromagnetic bearings possess advantages such as contactless operation, frictionless operation, lubrication-free operation, high speed, long lifespan, and controllability, making them widely used in flywheel energy storage systems, medical equipment, turbine machinery, and machine manufacturing tools. Although mechanical friction losses are eliminated, certain power losses still exist during actual use, primarily including copper losses in the coils and core losses, affecting the operating characteristics of the electromagnetic bearing. Hysteresis losses, in particular, directly impact the system's temperature rise, efficiency, and control accuracy, and are one of the key factors restricting its performance and reliability. The actual core loss mechanism of axial electromagnetic bearings is complex to analyze. Compared to radial electromagnetic bearings, where core loss mainly originates from the rotor's rotation cutting the magnetic field, axial electromagnetic bearing core loss is primarily caused by both alternating control current and axial vibration of the thrust plate. For axial electromagnetic bearings, the thrust plate inevitably vibrates during stable operation, causing it to cut the magnetic field. At this time, the closed-loop control system of the magnetic levitation system, based on the vibration signal, applies alternating control current to the stator winding coils to generate electromagnetic force, maintaining the rotor in a specific position. Because the axial electromagnetic bearing uses a solid pure iron structure, when the axial sinusoidal vibration of the thrust disk and the alternating control current act together on the magnetic field, significant iron core losses will occur on the stator and the thrust disk.

[0003] Existing technologies for calculating hysteresis loss mainly suffer from the following technical problems: 1. Traditional equivalent magnetic circuit modeling for magnetic bearings is often based on theoretical operating condition assumptions, frequently considering only the alternating control current or the static characteristics of the mechanical structure, neglecting the dynamic coupling effect between the axial sinusoidal vibration of the thrust disk and the alternating control current, leading to significant deviations between the model and actual operating conditions; 2. Traditional models fail to achieve deep coupling of edge effects, leakage flux, eddy current effects, hysteresis effects, and the nonlinearity of the core material in the magnetic circuit. This makes it difficult for traditional equivalent magnetic circuit models to accurately reflect the evolution of electromagnetic characteristics within the magnetic bearing, and to accurately obtain the maximum magnetic flux density of the axial electromagnetic bearing core. Since the maximum magnetic flux density is a core parameter for hysteresis loss calculation, insufficient accuracy directly reduces the reliability of subsequent hysteresis loss calculation results, further exacerbating the technical difficulty of accurate hysteresis loss calculation. Therefore, there is an urgent need to propose a novel method that can integrate multi-physics field effects and achieve accurate hysteresis loss calculation. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a method and apparatus for calculating the hysteresis loss of axial electromagnetic bearings, which can accurately calculate the hysteresis loss of axial electromagnetic bearings under dynamic operating conditions.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for calculating the hysteresis loss of an axial electromagnetic bearing includes the following steps:

[0007] Based on the structural parameters of the axial electromagnetic bearing, an equivalent magnetoresistive model integrating edge effect and eddy current effect is established. On the basis of the equivalent magnetoresistive model, combined with the dynamic air gap magnetoresistive introduced by the axial vibration of the thrust disk and the leakage magnetic effect included by the leakage magnetic coefficient, an equivalent magnetic circuit model of the axial electromagnetic bearing is established. Under the condition of axial sinusoidal vibration of the thrust disk, the magnetomotive force is calculated based on the real-time control current, and the total dynamic magnetic flux is determined by the equivalent magnetic circuit model.

[0008] Based on the static hysteresis characteristics of the core material, a quantitative relationship is established between any two of the three factors: maximum magnetic flux density amplitude, hysteresis loss, and angular parameters characterizing the hysteresis effect.

[0009] Using magnetomotive force as magnetic field excitation and total dynamic magnetic flux as magnetic field response, complex permeability is constructed based on the quantitative relationship; the equivalent magnetic circuit model is updated using complex permeability; and the maximum magnetic flux density amplitude of each region of the core under dynamic conditions is solved synchronously through iterative calculation.

[0010] Based on the quantitative relationship and the maximum magnetic flux density amplitude of each region, the hysteresis loss of each region is calculated; and the hysteresis loss of all regions is combined to obtain the total hysteresis loss of the axial electromagnetic bearing.

[0011] The present invention also proposes a calculation device for axial electromagnetic bearing hysteresis loss, comprising at least one processor and a memory, wherein the memory stores a computer program, characterized in that the computer program, when executed by the at least one processor, implements the method for calculating axial electromagnetic bearing hysteresis loss as described above.

[0012] The effects described in the invention are merely those of the embodiments, and not all the effects of the invention. One of the above technical solutions has the following advantages or beneficial effects:

[0013] This invention proposes a method and device for calculating the hysteresis loss of an axial electromagnetic bearing, belonging to the field of hysteresis loss calculation technology. The method includes: establishing an equivalent reluctance model integrating edge effects and eddy current effects based on the structural parameters of the axial electromagnetic bearing; establishing an equivalent magnetic circuit model of the axial electromagnetic bearing based on the equivalent reluctance model, combined with the dynamic air gap reluctance introduced by the axial vibration of the thrust disk, and the leakage magnetic effect included through the leakage magnetic coefficient; calculating the magnetomotive force based on the real-time control current under the condition of axial vibration of the thrust disk, and then determining the total dynamic magnetic flux through the equivalent magnetic circuit model; based on the core material... Based on the static hysteresis characteristics, a quantitative relationship is established between any two of the following three parameters: maximum magnetic flux density amplitude, hysteresis loss, and an angular parameter characterizing the hysteresis effect. Using magnetomotive force as the magnetic field excitation and total dynamic magnetic flux as the magnetic field response, a complex permeability is constructed based on the quantitative relationship. The equivalent magnetic circuit model is updated using the complex permeability. The maximum magnetic flux density amplitude of each region of the core under dynamic operating conditions is solved synchronously through iterative calculation. Based on the quantitative relationship and the maximum magnetic flux density amplitude of each region, the hysteresis loss of each region is calculated. Finally, the hysteresis losses of all regions are synthesized to obtain the total hysteresis loss of the axial electromagnetic bearing. Based on this method for calculating the hysteresis loss of an axial electromagnetic bearing, a calculation device for the hysteresis loss of an axial electromagnetic bearing is also proposed. This invention provides comprehensive and accurate theoretical support for the magnetic circuit analysis and hysteresis loss calculation of axial electromagnetic bearings. By systematically integrating the dynamic operating conditions of magnetic bearings in actual operation with the physical factors affecting their electromagnetic characteristics, it can establish an accurate equivalent magnetic circuit model of magnetic bearings. This breaks through the technical bottleneck of the difficulty in accurately calculating hysteresis loss in traditional magnetic bearing magnetic circuit modeling methods, providing reliable technical support for the system and having great practical application value. Attached Figure Description

[0014] Figure 1 This is a flowchart of a method for calculating the hysteresis loss of an axial electromagnetic bearing, as proposed in Embodiment 1 of the present invention.

[0015] Figure 2 This is a schematic diagram showing the basic structure and dimensions of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention;

[0016] Figure 3 This is a schematic diagram of the axial electromagnetic bearing reluctance partitioning and equivalent magnetic circuit model proposed in Embodiment 1 of the present invention;

[0017] Figure 4 This is a schematic diagram of the magnetic flux distribution in the air gap between the stator and thrust disk of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention;

[0018] Figure 5 This is a schematic diagram of the static hysteresis loop and equivalent ellipse of the axial electromagnetic bearing core material proposed in Embodiment 1 of the present invention;

[0019] Figure 6This is a flowchart of the iterative calculation of the nonlinear magnetic circuit equation of the magnetic bearing core proposed in Embodiment 1 of the present invention;

[0020] Figure 7 This is a schematic diagram of a device for calculating the hysteresis loss of an axial electromagnetic bearing, as proposed in Embodiment 2 of the present invention. Detailed Implementation

[0021] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific embodiments and in conjunction with the accompanying drawings. The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure of the invention, components and arrangements of specific examples are described below. Furthermore, reference numerals and / or letters may be repeated in different examples. This repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed. It should be noted that the components illustrated in the drawings are not necessarily drawn to scale. Descriptions of well-known components, processing techniques, and processes are omitted in this invention to avoid unnecessarily limiting the invention.

[0022] Example 1

[0023] Embodiment 1 of this invention proposes a method for calculating the hysteresis loss of axial electromagnetic bearings, which solves the technical problem of insufficient accuracy of traditional calculation methods due to model simplification and the lack of multiple physical effects.

[0024] The main implementation process of the axial electromagnetic bearing hysteresis loss calculation method proposed in Embodiment 1 of this invention is as follows: During the modeling of the equivalent magnetic circuit model, the two actual operating conditions of axial sinusoidal vibration of the thrust disk and alternating control current are considered simultaneously. Based on the fitting formula of the static magnetization curve of the core material and the fitting curve of the relationship between the maximum magnetic flux density and the hysteresis angle, the equivalent magnetic circuit model of the magnetic bearing is solved nonlinearly. During the process, factors such as edge effect, leakage flux, eddy current effect, hysteresis effect and material nonlinearity are deeply coupled to accurately obtain the maximum magnetic flux density of each region of the core. Then, combined with the correlation law between hysteresis loss and the amplitude of the maximum magnetic flux density in Bertotti theory, the hysteresis loss of each region of the core per unit volume per unit period is determined based on the fitting formula of the relationship between the maximum magnetic flux density and the hysteresis loss. Finally, the hysteresis loss of each region of the magnetic bearing core is calculated one by one through the hysteresis loss calculation formula. The hysteresis losses of each region are superimposed to obtain the total hysteresis loss of the axial electromagnetic bearing when considering both axial sinusoidal vibration of the thrust disk and alternating control current.

[0025] Figure 1 This is a flowchart of a method for calculating the hysteresis loss of an axial electromagnetic bearing, as proposed in Embodiment 1 of the present invention.

[0026] In step S1, the process begins.

[0027] In step S2, the basic structural parameters of the axial electromagnetic bearing are obtained.

[0028] The basic structural parameters in this application include: geometric dimensions, material electromagnetic properties, and operating point and dynamic excitation parameters. Geometric dimensions include stator core dimensions, thrust disk dimensions, air gap parameters, and the number of turns in the stator coils. Material electromagnetic properties include the magnetic properties of the core material and the parameters of the insulating material. Operating point and dynamic excitation parameters include electromagnetic excitation parameters and mechanical dynamic parameters.

[0029] Figure 2 This is a schematic diagram of the basic structure and dimensions of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention; it consists of a stator, a thrust disk, a rotor, and an air gap. The stator includes a stator core and winding coils, forming a differential control mode. Figure 2 middle Represents shaft diameter, Represents the inner diameter of the stator's inner magnetic poles, Represents the outer diameter of the stator inner magnetic poles, Represents the inner diameter of the outer magnetic pole of the stator. Represents the outer diameter of the thrust disk, Represents the inner diameter of the outer side of the stator's outer magnetic poles, Represents the outer diameter of the outer pole of the stator. Represents the thickness of the stator yoke, Represents the height of the coil slot, Represents the thickness of the inner side of the stator outer magnetic poles, Represents air gap thickness, This represents the thickness of the thrust disk. The dimensions of the axial electromagnetic bearing protected by this invention are not limited to... Figure 2 The specific dimensions listed herein can be selected by those skilled in the art based on the actual situation.

[0030] The scope of protection of this invention is not limited to the structural parameters listed in Example 1, and those skilled in the art can make reasonable selections based on the actual situation.

[0031] In step S3, an equivalent magnetoresistive model is established. Figure 3 This is a schematic diagram of the magnetic reluctance partitioning and equivalent magnetic circuit model of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. According to the magnetic flux path distribution of the axial electromagnetic bearing, its core structure and air gap region can be divided into several units. Since the geometry and magnetic flux distribution of the magnetic bearing have axisymmetric characteristics, it can be simplified into a two-dimensional analysis model.

[0032] Figure 4This is a schematic diagram of the magnetic flux distribution in the air gap between the stator and thrust disk of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. Because the magnetic bearing has a very compact structure and the air gap between the stator and thrust disk is very small, the edge effect between adjacent magnetic poles is particularly significant. Therefore, the influence of the edge effect needs to be considered when establishing the equivalent magnetic circuit model of the magnetic bearing.

[0033] Therefore, when establishing the equivalent reluctance model in this application, due to the edge effect, the average cross-sectional area of ​​the air gap magnetic circuit between the stator and the thrust disk will be greater than the cross-sectional area of ​​the inner and outer magnetic pole faces of the stator. Therefore, considering the edge effect, the equivalent magnetic permeable area of ​​the air gap between the inner and outer magnetic poles of the main circuit is:

[0034] (1)

[0035] It is the expansion factor of the equivalent magnetic conductive area of ​​the air gap, which is related to the length of the air gap between the stator and the thrust disk; This represents the equivalent magnetic permeability area of ​​the air gap between the inner magnetic poles. The equivalent magnetic permeable area of ​​the air gap of the outer magnetic pole; The magnetic permeable area of ​​the air gap between the inner magnetic poles. It represents the magnetically conductive area of ​​the air gap between the outer magnetic poles.

[0036] according to Figure 2 The equivalent magnetic circuit model of the axial electromagnetic bearing shown can simplify the magnetic reluctance of each region of the iron core by connecting them in series and parallel. This is possible when the thrust disk does not vibrate and the control current... When the current is 0A, the core magnetization frequency is zero Hertz, and no alternating magnetic field is generated. The expression for the total static reluctance of the axial electromagnetic bearing is as follows:

[0037] (2)

[0038] in, The total static magnetic reluctance of the iron core; The static magnetic reluctance of each region of the iron core.

[0039] By introducing a dynamic equivalent magnetoresistive meter and the influence of eddy current effect on the magnetic flux of the axial electromagnetic bearing, the magnetoresistive force in each region of the bearing is decomposed into two components: a static magnetoresistive force and a frequency-dependent dynamic magnetoresistive force. Based on the direction of magnetic flux flow inside the iron core, the expression for the equivalent magnetoresistive force in each region of the bearing, considering the eddy current effect, can be derived as follows:

[0040] (3)

[0041] in, Equivalent magnetic reluctance; The dynamic reluctance coefficient, , Alternating frequency;

[0042] Combining the expression for total static reluctance and the equivalent reluctance of each region of the magnetic bearing, the total effective reluctance of the axial electromagnetic bearing considering eddy current effects under an alternating magnetic field can be obtained. .

[0043] The corrected magnetoresistance of each region is synthesized according to the series and parallel relationship of the magnetic flux path to establish an equivalent magnetoresistance model that integrates edge effect and eddy current effect.

[0044] In step S4, based on the equivalent magnetic reluctance model, the dynamic air gap magnetic reluctance introduced by the axial vibration of the thrust disk and the leakage magnetic effect included by the leakage magnetic coefficient are further combined to complete the construction of the equivalent magnetic circuit model; thus, the equivalent magnetic circuit model integrates the consideration of edge effect, leakage magnetic effect and eddy current effect.

[0045] The static magnetization curve of the core material was introduced to account for material nonlinearity, and the following was introduced: Changing hysteresis angle In order to take into account the hysteresis effect.

[0046] The process of obtaining the equivalent magnetic circuit model includes:

[0047] Total effective reluctance of the equivalent reluctance model , and the number of coil turns Bias current and control current Jointly determined magnetomotive force These are interconnected and constitute the basic equations of a magnetic circuit;

[0048] Under the axial sinusoidal vibration condition of the thrust disk, the time-varying magnetic reluctance generated by the air gap change due to vibration will be... Introducing the total effective magnetic reluctance;

[0049] By introducing the leakage coefficient To correct the air gap main magnetic flux This allows us to obtain the total dynamic flux used to calculate the losses. Ultimately, an equivalent magnetic circuit model is formed that can characterize the complete electromagnetic properties of the axial electromagnetic bearing under dynamic working conditions.

[0050] In step S5, under the condition of axial vibration of the thrust disk, the magnetomotive force is calculated based on the real-time control current, and the total dynamic magnetic flux is determined through the equivalent magnetic circuit model.

[0051] When constructing the equivalent magnetic circuit model, the air gap vibration displacement is sinusoidally varying when the thrust disk vibrates axially:

[0052] (4)

[0053] in, This refers to the real-time air gap of the thrust disc; To balance the air gap; This represents the axial vibration amplitude. Angular velocity; , The vibration frequency is the same as the alternating frequency of the control current.

[0054] The formula for calculating the air gap reluctance of the inner and outer magnetic end faces of the main circuit when the air gap changes sinusoidally due to thrust disk vibration is as follows:

[0055] (5)

[0056] ; ;

[0057] in, The air gap reluctance of the inner magnetic end face of the main circuit when the air gap changes sinusoidally due to the vibration of the thrust disk; The air gap reluctance of the outer magnetic end face of the main circuit when the air gap changes sinusoidally due to the vibration of the thrust disk; To balance the eddy current effect under the air gap, the internal magnetic pole air gap magnetoresistance is designed; To balance the eddy current effect under the air gap, the external magnetic pole air gap magnetoresistance is considered; This represents the amplitude of the sinusoidal variation of the reluctance in the air gap between the inner magnetic poles. This represents the amplitude of the sinusoidal variation of the reluctance in the air gap of the outer magnetic pole; The vacuum permeability;

[0058] When the axial sinusoidal vibration of the thrust disk and the alternating control current act simultaneously, the magnetic reluctance generated by the sinusoidal change in the air gap should be considered. The total effective magnetic reluctance of the axial electromagnetic bearing, taking into account the eddy current effect, is:

[0059] (6)

[0060] in, The total effective magnetic reluctance of the axial electromagnetic bearing is calculated considering the sinusoidal variation of the air gap. This represents the amplitude of the sinusoidal variation of the total magnetic reluctance in the air gap between the inner and outer magnetic poles. ;

[0061] in, The equivalent cross-sectional area at the air gap is given by... and It was obtained through parallel calculation.

[0062] Considering the simultaneous existence of sinusoidal vibration of the thrust disk and alternating control current, based on Figure 3 The equivalent magnetic circuit model shown is used to derive the mathematical model for calculating the magnetomotive force of the magnetic bearing, and the equation for calculating the dynamic magnetic flux is given.

[0063] When the thrust disk vibrates sinusoidally in the axial direction, the axial electromagnetic bearing closed-loop control system applies an alternating control current to the stator winding coils based on the collected vibration feedback signal to suppress the thrust disk vibration. At this time, the magnetic bearing will generate a bias current in the air gap region. and control current The main magnetic flux generated by the combined action :

[0064] (7)

[0065] in, The bias flux generated by the bias current during the sinusoidal vibration of the thrust disk; The control flux generated by the bias current during the sinusoidal vibration of the thrust disk.

[0066] In axial electromagnetic bearings, magnetic flux leakage in the actual magnetic circuit is almost unavoidable, and the leakage flux distribution is quite complex. To simplify the study, this invention assumes that the leakage flux and the main magnetic flux change with time in the same way, i.e., with the same amplitude, only differing in magnitude. Therefore, the ratio of the leakage flux to the main air gap flux can be defined as the flux leakage coefficient, i.e.:

[0067] (8)

[0068] in, The flux leakage coefficient; Leakage flux refers to the magnetic flux that does not pass through the air gap between the inner and outer magnetic end faces of the main circuit.

[0069] Combining formula (7) and formula (8), we can obtain the total magnetic flux of the axial electromagnetic bearing considering leakage flux. The expression is:

[0070] (9)

[0071] in, The total magnetic flux of the axial electromagnetic bearing is considered in relation to leakage flux; The bias current generated in the air gap region of the magnetic bearing and control current The main magnetic flux generated by the combined effect;

[0072] From the law of magnetic flux and Figure 3 The equivalent magnetic circuit model of the magnetic bearing shown can be used to derive the magnetomotive force of the axial electromagnetic bearing:

[0073] (10)

[0074] in, It is a magnetomotive force; This represents the total current flowing through the coil; ;

[0075] Based on the principle of magnetic field superposition in electromagnetic field theory, in order to clearly distinguish the magnetic flux excitation mechanisms of the bias current and the control current, this invention will calculate the magnetic flux components generated by the bias current and the control current respectively.

[0076] According to formulas (7), (9) and (10), when the eddy current effect of the iron core caused by the vibration of the thrust disk is not considered, that is, the equivalent dynamic magnetic reluctance term of the iron core is ignored, the axial electromagnetic bearing bias flux generated by the bias current excitation can be obtained. The expression is:

[0077] (11)

[0078] in, This refers to the number of turns of the iron core coil;

[0079] Because the sinusoidal vibration amplitude of the thrust disk is very small compared to the air gap length at the equilibrium position, the sinusoidally varying air gap magnetic reluctance... It is also much smaller than the total static magnetic reluctance of the magnetic bearing. Formula (11) can be expanded using Taylor series to obtain the bias flux generated by the bias current during the sinusoidal vibration of the thrust disk. It is divided into two parts. Decomposed into static bias flux and dynamic bias flux containing eddy currents Specifically:

[0080] (12)

[0081] As can be seen from formula (12), when the thrust disk vibrates and cuts the magnetic field lines, the sinusoidally changing magnetic flux will generate eddy currents. The effective magnetic resistance on the magnetic flux path includes not only static magnetic resistance, but also the equivalent dynamic magnetic resistance formed by the eddy currents.

[0082] Similarly, according to formulas (7), (9) and (10), the dynamic magnetic flux generated by the control current can be obtained. The expression is:

[0083] (13)

[0084] When the thrust disk vibrates sinusoidally in the axial direction, static and dynamic magnetic fluxes will be generated in the core of the electromagnetic bearing. The static magnetic flux generates a DC magnetic field, which will not cut the magnetic field and generate eddy current effect; while the dynamic magnetic flux generates an alternating magnetic field that magnetizes the core, causing core loss in the magnetic bearing.

[0085] Combining formulas (12) and (13), the total dynamic magnetic flux of the axial electromagnetic bearing during sinusoidal vibration of the thrust disk can be obtained as follows:

[0086] ;(14)

[0087] In step S6, the equivalent magnetic circuit model is updated using the complex permeability; the maximum magnetic flux density amplitude of each region of the core under dynamic conditions is simultaneously solved through iterative calculation. .

[0088] Based on the law of magnetic flux, the expression for the magnetic flux density of the air gap between the inner and outer magnetic poles can be derived from formulas (1) and (14):

[0089] (15)

[0090] in, The magnetic flux density of the air gap between the inner magnetic poles; It is the magnetic flux density of the air gap of the outer magnetic pole.

[0091] exist Figure 3 In this calculation, since the cross-sectional areas of the radially flowing magnetic flux in regions 2, 5, and 7 of the magnetic bearing core are not continuous, to simplify the calculation, the central cross-sectional area of ​​the magnetic flux in each radially flowing region is taken as the average cross-sectional area of ​​that region. Based on the law of conservation of magnetic flux, when the magnetic flux is constant, the maximum magnetic flux density of the magnetic bearing core is inversely proportional to the cross-sectional area of ​​the region through which the magnetic flux flows. Therefore, a quantitative relationship between the maximum magnetic flux density in the air gap of the magnetic bearing and the maximum magnetic flux density in each region of the core can be derived:

[0092] (16)

[0093] in, The average magnetic flux density in the thrust disk region; The magnetic flux density of the axial section of the stator inner poles; The magnetic flux density of the radial section of the stator inner poles; The magnetic flux density of the stator yoke region; The magnetic flux density of the radial section of the stator's outer poles; The magnetic flux density of the axial section of the stator's outer magnetic poles; This represents the average cross-sectional area of ​​the thrust disk region; This is the average cross-sectional area of ​​the axial segment of the inner magnetic poles of the stator. This represents the average cross-sectional area of ​​the radial segment of the inner magnetic poles of the stator. The average cross-sectional area of ​​the stator yoke region; This represents the average cross-sectional area of ​​the radial segment of the stator's outer magnetic poles. This represents the average cross-sectional area of ​​the axial segment of the stator's outer magnetic poles.

[0094] Obtaining the maximum magnetic flux density based on the static hysteresis loop of the iron core material With hysteresis loss The first relationship curve;

[0095] Based on the principle of equivalent ellipse, establish hysteresis loss With hysteresis angle The relationship is used to obtain the maximum magnetic flux density. With hysteresis angle The second relationship curve.

[0096] Bertotti's theory defines the total loss in magnetic materials as three components: hysteresis, eddy current, and additional loss. However, in actual axial magnetic bearings, these loss components cannot be directly measured because eddy current loss and additional loss are both caused by the eddy current effect in the core. Furthermore, the eddy current effect is closely related to material thickness; magnetic bearings using large blocks of solid pure iron produce significant eddy current effects, and the core structure differs from the toroidal structure of traditional motors and transformers. Eddy current loss and additional loss are also related to material thickness and structural shape. Existing traditional measurement methods such as the Epstein square ring and toroidal winding methods cannot meet the core loss measurement requirements of magnetic bearings under actual operating conditions. Directly analyzing power loss through the current flowing through the magnetic bearing coil windings makes it difficult to accurately separate hysteresis loss from the overall core. Therefore, this invention utilizes the equivalent ellipse principle and, based on Bertotti's loss separation theory, defines the static hysteresis loop of the core material to establish a hysteresis loss... With hysteresis angle The relationship is to take into account the hysteresis effect of the core material.

[0097] Based on Bertotti's iron loss separation theory, the total core loss is... Separation into hysteresis loss Eddy current loss and abnormal losses ;Right now (17)

[0098] According to Bertotti's loss separation theory, the area of ​​the hysteresis loop increases with frequency because frequency leads to eddy current losses and additional losses. Therefore, as long as the maximum AC magnetic flux density amplitude is the same under different sinusoidal excitations, the hysteresis loss per unit volume per unit period is also the same, which is the static hysteresis loop area, related to the alternating magnetic flux density amplitude.

[0099] Based on the static hysteresis loop of the iron core material, the hysteresis loss per unit volume per unit period is obtained by calculating the area of ​​the hysteresis loop. ;

[0100] (18)

[0101] in, For the hysteresis loss parameter in Bertotti's loss separation theory; To describe the magnetic field strength of a static hysteresis loop;

[0102] Based on Bertotti's loss separation theory, the hysteresis loss per unit volume per unit period is converted into hysteresis loss power per unit time. ;

[0103] (19)

[0104] in, This is the sum of the volumes of the thrust disk and the stator core in the magnetic bearing; It is an alternating frequency.

[0105] To account for the hysteresis effect in electromagnetic bearings during the modeling process, this invention utilizes... Figure 5 The diagram shows the static hysteresis loop and equivalent ellipse of the magnetic bearing core material. Figure 5 middle Represents the major semi-axis; This represents the minor semi-axis. Based on the principle of equivalent ellipse, the area of ​​the equivalent ellipse is... Since the area enclosed by the actual static hysteresis loop of the core material is consistent, formula (19) can be transformed into the relationship between hysteresis loss and hysteresis angle:

[0106] (20)

[0107] in, This is the sum of the volumes of the thrust disk and the stator core in the magnetic bearing; Maximum magnetic field strength; hysteresis angle This is used to account for the hysteresis effect of the core material of magnetic bearings.

[0108] Combination Figure 4 By fitting the static hysteresis loop area of ​​the core material with formula (20), the maximum magnetic flux density of the electromagnetic bearing core material can be obtained. With hysteresis angle Relationship curve and maximum magnetic flux density With hysteresis loss power The relationship curves were then fitted using the least squares method to establish the maximum magnetic flux density. With hysteresis angle Relationship curve and maximum magnetic flux density With hysteresis loss power The fitting formula for the relationship curve.

[0109] Introducing the iterative method of nonlinear magnetic circuit equations and maximum magnetic flux density With hysteresis angle Relationship curve calculation of magnetic bearings under different conditions with maximum magnetic flux density Changing hysteresis angle and complex permeability To account for the nonlinearity and hysteresis effect of the core material, an accurate equivalent magnetic circuit model of the magnetic bearing is established, and the maximum magnetic flux density in each region of the core considering the hysteresis effect is analytically determined.

[0110] In step S7, the established equivalent magnetic circuit model calculates the equivalent magnetic permeable area of ​​the air gap to account for the magnetic pole edge effect, introduces the leakage magnetic flux coefficient to account for leakage magnetic flux, introduces the dynamic equivalent magnetic reluctance to account for the eddy current effect, introduces the static magnetization curve of the core material to consider the material nonlinearity, and introduces the variable... Changing hysteresis angle In order to take into account the hysteresis effect.

[0111] In step S8, based on the nonlinear characteristics of the static magnetization curve, in order to more accurately calculate the maximum magnetic flux density and hysteresis loss of the electromagnetic bearing, this invention fits the static magnetization curve of the core material using an exponential equation, and then considers the nonlinear factors of the core material in the equivalent magnetic circuit model.

[0112] The static permeability of the material calculated from the static magnetization curve As a real part, it can only reflect... and The amplitude relationship was not considered, and energy loss was not taken into account. Furthermore, when the axial sinusoidal vibration of the thrust disk and the alternating control current simultaneously create an alternating magnetic field, the magnetic bearing will experience core losses, and the permeability will no longer be solely the static permeability. And becomes complex permeability ;

[0113] in, is the real part of the complex permeability; This represents the imaginary part of the complex permeability, corresponding to the energy loss of the core material.

[0114] In step S9, the relationship between hysteresis loss and hysteresis angle is established based on the principle of equivalent ellipse.

[0115] In step S10, based on the maximum magnetic flux density and hysteresis angle The relationship is combined.

[0116] Formula (3) has already given the dynamic equivalent magnetic reluctance of the axial electromagnetic bearing to account for the eddy current effect. In order to further consider the hysteresis effect and material nonlinearity of the magnetic bearing core, this invention further proposes... Figure 6 The iterative method for calculating the equivalent magnetic circuit model of the axial electromagnetic bearing using the nonlinear magnetic circuit equation of the shown magnetic bearing core is as follows:

[0117] First, an initial value for the magnetic field strength of a region of the iron core is given. The initial maximum magnetic flux density in the region was calculated using the formula for fitting the static magnetization curve of the core material.

[0118] Secondly, based on the magnetic flux density relation (16), the maximum magnetic flux density distribution in other regions of the iron core is derived, and then... Calculate the static permeability of each region of the iron core. .

[0119] Furthermore, through the maximum magnetic flux density of the core material With hysteresis angle The relationship curve fitting formula is used to establish the complex permeability of each region of the axial electromagnetic bearing core, considering the hysteresis effect. Calculation formula:

[0120] ;(twenty one)

[0121] In the formula, The static permeability is obtained from the static magnetization curve.

[0122] Then, based on the definition of reluctance calculation, the complex permeability obtained by iterative calculation can be... By substituting the nonlinear magnetic circuit equation back into formula (6) to calculate the total effective magnetic reluctance of the magnetic bearing, an equivalent magnetic reluctance model considering the hysteresis effect can be obtained.

[0123] Finally, an error criterion is introduced. The equivalent magnetic circuit of the magnetic bearing is solved iteratively. When the iteration converges, the complex permeability of the material in each region of the iron core and the maximum magnetic flux density in the magnetic circuit can be obtained. The equivalent magnetic circuit model of the axial electromagnetic bearing that takes into account factors such as edge effect, leakage flux, eddy current effect, hysteresis effect and material nonlinearity can be accurately established.

[0124] The maximum magnetic flux density of each region of the iron core obtained in step S11 iteration With respect to the maximum magnetic flux density and hysteresis loss of the core material The relationship curve determines the hysteresis loss per unit volume per unit period in each region of the core. This is achieved by calculating the volume of each region of the core. And the hysteresis loss of each region of the magnetic bearing can be solved by using the hysteresis loss calculation formula (19). Finally, the hysteresis loss of each region is superimposed and expressed in a 2x form to account for the positive and negative magnetic poles, so as to obtain the total hysteresis loss of the axial electromagnetic bearing when considering both the axial sinusoidal vibration of the thrust disk and the alternation of the control current:

[0125] ;(twenty two)

[0126] In the formula, This represents the total hysteresis loss of the magnetic bearing. For Iron Heart Hysteresis loss in the region.

[0127] In step S12, the process ends.

[0128] The present invention, in Embodiment 1, proposes a method for calculating hysteresis loss in axial electromagnetic bearings. By introducing the air gap equivalent magnetic field area expansion coefficient, dynamic equivalent magnetic reluctance, leakage magnetic coefficient, and complex permeability, it innovatively integrates five key physical effects—edge effect, eddy current effect, leakage magnetic effect, material nonlinearity, and hysteresis effect—into a unified equivalent magnetic circuit model. This breaks through the technical limitations of traditional models where effects are independent or partially ignored, achieving a precise characterization of the complex electromagnetic environment of axial electromagnetic bearings. In particular, through the principles of complex permeability and equivalent ellipticity, it successfully decouples the difficult-to-separate hysteresis loss from the total iron loss, enabling accurate calculation of pure hysteresis loss.

[0129] Example 2

[0130] The present invention also proposes a device, Figure 7 This is a schematic diagram of a device for calculating the hysteresis loss of an axial electromagnetic bearing, as proposed in Embodiment 2 of the present invention.

[0131] At the hardware level, the electronic device 700 includes a processor 710, and optionally, an internal bus 720, a network interface 730, and memory. The memory may include main memory 740, such as high-speed random-access memory (RAM), or it may also include non-volatile memory, such as at least one disk drive. Of course, the electronic device may also include other hardware required for other business operations.

[0132] The processor 710, network interface 730, and memory can be interconnected via an internal bus 720. This internal bus 720 can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be categorized as an address bus, data bus, control bus, etc. For ease of illustration, only a single bidirectional arrow is used in this diagram, but this does not imply that there is only one bus or one type of bus. The memory is used to store programs. Specifically, the program can include program code, which includes computer operation instructions. The memory can include main memory 740 and non-volatile memory 750, and provides instructions and data to the processor 710.

[0133] The processor 710 reads the corresponding computer program from the non-volatile memory 750 into the main memory 740 and then runs it, forming a device for locating the target user at the logical level. The processor 710 executes the program stored in the memory and specifically performs the following:

[0134] Based on the structural parameters of the axial electromagnetic bearing, an equivalent reluctance model integrating edge effect and eddy current effect is established; on the basis of the equivalent reluctance model, combined with the dynamic air gap reluctance introduced by the axial vibration of the thrust disk and the leakage magnetic effect included by the leakage magnetic coefficient, an equivalent magnetic circuit model of the axial electromagnetic bearing is established.

[0135] Under the condition of axial vibration of the thrust disk, the magnetomotive force is calculated based on the real-time control current, and the total dynamic magnetic flux is determined through the equivalent magnetic circuit model.

[0136] Based on the static hysteresis characteristics of the core material, a quantitative relationship is established between any two of the three factors: maximum magnetic flux density amplitude, hysteresis loss, and angular parameters characterizing the hysteresis effect.

[0137] Using magnetomotive force as magnetic field excitation and total dynamic magnetic flux as magnetic field response, complex permeability is constructed based on the quantitative relationship; the equivalent magnetic circuit model is updated using complex permeability; and the maximum magnetic flux density amplitude of each region of the core under dynamic conditions is solved synchronously through iterative calculation.

[0138] Based on the quantitative relationship and the maximum magnetic flux density amplitude of each region, the hysteresis loss of each region is calculated; and the hysteresis loss of all regions is combined to obtain the total hysteresis loss of the axial electromagnetic bearing.

[0139] Figure 1It can be applied to processor 710, or implemented by processor 710. The processor may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by the integrated logic circuit in the processor or by instructions in the form of software. The processor mentioned above can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software module can reside in a mature storage medium in the field, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0140] Of course, in addition to software implementation, the electronic device of this application does not exclude other implementation methods, such as logic devices or a combination of hardware and software, etc. In other words, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0141] The description of the relevant parts of the axial electromagnetic bearing hysteresis loss calculation device provided in Embodiment 2 of this application can be found in the detailed description of the corresponding parts of the axial electromagnetic bearing hysteresis loss calculation method provided in Embodiment 1 of this application, and will not be repeated here.

[0142] The device for calculating hysteresis loss of axial electromagnetic bearings proposed in Embodiment 2 of this invention innovatively integrates five key physical effects—edge effect, eddy current effect, leakage magnetic effect, material nonlinearity, and hysteresis effect—into a unified equivalent magnetic circuit model by introducing the air gap equivalent magnetic permeability expansion coefficient, dynamic equivalent magnetic reluctance, leakage magnetic coefficient, and complex permeability. This breaks through the technical limitations of traditional models where effects are independent or partially ignored, achieving a complete characterization of the complex electromagnetic environment of axial electromagnetic bearings. In particular, through the principles of complex permeability and equivalent ellipticity, the difficult-to-separate hysteresis loss is successfully decoupled from the total iron loss, enabling accurate calculation of pure hysteresis loss.

[0143] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that the elements inherent in a process, method, article, or apparatus that includes a list of elements are included. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. Additionally, portions of the technical solutions provided in the embodiments of this application that are consistent with the implementation principles of corresponding technical solutions in the prior art have not been described in detail to avoid excessive elaboration.

[0144] While specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art can make other modifications or variations based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method of calculating hysteresis losses of an axial electromagnetic bearing, characterized in that, The method comprises the following steps: Based on the structural parameters of the axial electromagnetic bearing, an equivalent magnetic resistance model integrating edge effect and eddy current effect is established; on the basis of the equivalent magnetic resistance model, a dynamic air gap magnetic resistance introduced by axial vibration of the thrust disc and a leakage magnetic effect through a leakage coefficient are combined to establish an equivalent magnetic circuit model of the axial electromagnetic bearing; Under the condition of axial vibration of the thrust disc, a magnetic motive force is calculated based on a real-time control current, and then total dynamic magnetic flux is determined through the equivalent magnetic circuit model; Based on the static magnetic hysteresis characteristics of the core material, a quantitative relationship between any two of the maximum magnetic flux density amplitude, the hysteresis loss and an angle parameter representing the hysteresis effect is established; With the magnetic motive force as the magnetic field excitation and the total dynamic magnetic flux as the magnetic field response, a complex magnetic permeability reflecting the material nonlinearity and the hysteresis effect is constructed based on the quantitative relationship; The equivalent magnetic circuit model is updated by using the complex magnetic permeability; and the maximum magnetic flux density amplitude of each region of the core under the dynamic working condition is synchronously solved through iterative calculation; Based on the quantitative relationship and the maximum magnetic flux density amplitude of each region, the hysteresis loss of each region is calculated; and the hysteresis losses of all regions are synthesized to obtain the total hysteresis loss of the axial electromagnetic bearing.

2. The method of claim 1, wherein, Based on the structural parameters of the axial electromagnetic bearing, an equivalent magnetic resistance model integrating edge effect and eddy current effect is established; specifically: According to the magnetic flux path, the magnetic bearing core and the air gap region are divided into multiple logical units, and each unit is assigned a static magnetic resistance; Reference air gap equivalent permeance area expansion coefficient , according to the formula The air gap permeance area of the inner and outer magnetic poles is corrected; wherein, The inner magnetic pole air gap equivalent permeance area, The outer magnetic pole air gap equivalent permeance area; The inner magnetic pole air gap permeance area, The outer magnetic pole air gap permeance area; By introducing dynamic equivalent reluctance, according to the formula The magnetic bearing region reluctance is corrected; wherein, The equivalent reluctance is; The dynamic reluctance coefficient is, , The alternating frequency is; The core region static magnetic reluctance is, The magnetic reluctance division region serial number is; The corrected magnetic resistance of each region is synthesized according to the series-parallel connection relationship of the magnetic flux path to establish an equivalent magnetic resistance model integrating edge effect and eddy current effect.

3. The method of claim 2, wherein, When the thrust disc is axially sinusoidally vibrated, the sinusoidal variation air gap displacement is: ； wherein, is the real-time air gap of the thrust disc; is the balance air gap; is the axial vibration amplitude; is the angular velocity; When the thrust disc is axially sinusoidally vibrated, the sinusoidal variation air gap displacement is: ； ； ； wherein, is the inner pole end face air gap reluctance of the main circuit when the air gap varies sinusoidally due to the thrust disc vibration; is the outer pole end face air gap reluctance of the main circuit when the air gap varies sinusoidally due to the thrust disc vibration; is the inner pole air gap reluctance considering the eddy current effect under the balance air gap; is the outer pole air gap reluctance considering the eddy current effect under the balance air gap; is the amplitude of the sinusoidal variation part of the inner pole air gap reluctance; is the amplitude of the sinusoidal variation part of the outer pole air gap reluctance; is the vacuum permeability; When the thrust disc is axially sinusoidally vibrated and the control current is alternated, the total effective magnetic resistance of the axial electromagnetic bearing considering the eddy current effect is: ； wherein, is the total effective magnetic resistance of the axial electromagnetic bearing considering the sinusoidal variation of the air gap; is the amplitude of the sinusoidal variation of the total magnetic resistance of the air gap between the inner and outer magnetic poles; is the equivalent cross-sectional area at the air gap.

4. The method of claim 3, wherein, When the equivalent magnetic circuit model is constructed, the leakage magnetic effect is taken into account through the leakage coefficient, specifically: The magnetic bearing forms a main magnetic flux in the air gap region resulting from the bias current and the control current acting together ; ； wherein is bias flux; is control flux; Introducing the leakage coefficient calculating the total magnetic flux taking into account the leakage effect: ； ； wherein, total magnetic flux of the axial electromagnetic bearing taking into account the leakage magnetic flux; leakage magnetic flux The magnetic motive force of the axial electromagnetic bearing is calculated: ； wherein is the magnetomotive force; is the total current through the coil; ; Bias current Excitation generated axial electromagnetic bearing bias flux Is: ； Control current Generated dynamic magnetic flux Is: ； wherein, is the bias magnetic flux generated by the bias current when the thrust disc is sinusoidally oscillating; is the control magnetic flux generated by the control current when the thrust disc is sinusoidally oscillating; is the number of turns of the core coil; To decompose into a static bias magnetic flux and a dynamic bias magnetic flux containing eddy currents , in particular: ； The total dynamic magnetic flux under the combined action of axial vibration of the thrust disc and alternating control current is: 。 5. The method of claim 4, wherein, The method further comprises the following steps before establishing the quantitative relationship: Based on Bertotti's iron loss separation theory, the total core loss is... Separation into hysteresis loss Eddy current loss and abnormal losses ;Right now ; Based on the static hysteresis loop of the core material, the hysteresis loss per unit volume per cycle is obtained by calculating the area of the hysteresis loop ; ； wherein, is the magnetic hysteresis loss parameter in the Bertotti loss separation theory; is the magnetic field strength describing the static hysteresis loop; Converting hysteresis loss per unit volume per unit cycle into hysteresis loss power per unit time ; wherein, is the sum of the volumes of the thrust disc and the stator core in the magnetic bearing; is the alternating frequency.

6. The method of claim 5, wherein, Based on the static magnetic hysteresis characteristics of the core material, a quantitative relationship between any two of the maximum magnetic flux density amplitude, the hysteresis loss and an angle parameter representing the hysteresis effect is established; specifically: Based on the static hysteresis loop of the core material, the maximum magnetic flux density is obtained and the first relationship curve of the hysteresis loss ​ Based on the equivalent ellipse principle, a relationship between the magnetic hysteresis loss and the hysteresis angle is established, and a second relationship curve between the maximum magnetic flux density and the hysteresis angle is obtained; wherein the relationship between the magnetic hysteresis loss and the hysteresis angle is: ； wherein, is the sum of the volume of the thrust disc and the stator core in the magnetic bearing; is the maximum magnetic field strength; is the maximum magnetic flux density.

7. The method of claim 6, wherein, With the magnetic motive force as the magnetic field excitation and the total dynamic magnetic flux as the magnetic field response; based on the quantitative relationship, a complex magnetic permeability reflecting the material nonlinearity and the hysteresis effect is constructed; specifically: With the magnetomotive force F as the magnetic field excitation, the total dynamic magnetic flux As the magnetic field response; Based on the maximum magnetic flux density With the quantitative relationship of the magnetic hysteresis angle Reflecting the material nonlinear and hysteresis effect of complex permeability, specifically: ; wherein is the complex permeability; is the static permeability.

8. The method of claim 7, wherein, The method also includes, in the course of the iteration, calculating a total dynamic magnetic flux With the equivalent magnetic area, the air-gap flux density is calculated, and then the quantitative relationship between the maximum air-gap flux density of the magnetic bearing and the maximum flux density of each region of the core is derived. The calculation formula of the air gap magnetic flux density is: ； wherein, is the inner pole air gap flux density; is the outer pole air gap flux density; The quantitative relationship formula is: ； wherein, is the average magnetic flux density in the thrust disc area; is the stator inner pole axial segment magnetic flux density; is the stator inner pole radial segment magnetic flux density; is the stator yoke area magnetic flux density; is the stator outer pole radial segment magnetic flux density; is the stator outer pole axial segment magnetic flux density; is the average cross-sectional area in the thrust disc area; is the stator inner pole axial segment average cross-sectional area; is the stator inner pole radial segment average cross-sectional area; is the stator yoke area average cross-sectional area; is the stator outer pole radial segment average cross-sectional area; is the stator outer pole axial segment average cross-sectional area.

9. The method of claim 8, wherein, The total hysteresis loss is: ； wherein is the total hysteresis loss of the magnetic bearing; is the hysteresis loss of the core region.

10. A device for calculating hysteresis losses of an axial electromagnetic bearing, comprising at least one processor and a memory, the memory storing a computer program, characterized in that, The computer program is executed by the at least one processor to realize the method for calculating the hysteresis loss of the axial electromagnetic bearing according to any one of claims 1 to 9.

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