Method and equipment for calculating hysteresis loss of axial electromagnetic bearing

Abstract

The invention provides a method and equipment for calculating hysteresis loss of an axial electromagnetic bearing, and belongs to the technical field of hysteresis loss calculation. The method comprises the following steps: establishing an equivalent magnetic circuit model; under the condition of axial vibration of the thrust disc, magnetomotive force is calculated, and total dynamic magnetic flux is determined through an equivalent magnetic circuit model; establishing a quantitative relationship between any two of the maximum magnetic flux density amplitude, the magnetic hysteresis loss and the angle parameter representing the magnetic hysteresis effect; taking magnetomotive force as magnetic field excitation, taking total dynamic magnetic flux as magnetic field response, and constructing complex permeability based on a quantitative relation; updating the equivalent magnetic circuit model by using the complex permeability; solving the maximum magnetic flux density amplitude of each region of the iron core under the dynamic working condition through iterative calculation; calculating the hysteresis loss of each region based on the quantitative relation and the maximum magnetic flux density amplitude of each region; and the total magnetic hysteresis loss is calculated. Based on the method, the invention further provides calculation equipment for the hysteresis loss of the axial electromagnetic bearing. According to the method, the hysteresis loss of the axial electromagnetic bearing under the dynamic operation condition can be accurately calculated.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of hysteresis loss calculation, and particularly relates to a method and device for calculating hysteresis loss of an axial electromagnetic bearing. BACKGROUND

[0002] Electromagnetic bearings have the advantages of non-contact, no friction, no lubrication, high speed, long life, controllability, etc., and are widely used in flywheel energy storage systems, medical devices, turbine machinery and mechanical manufacturing tools. Although mechanical friction loss is eliminated, there is still a certain power loss in actual use, mainly including copper loss of the coil and core loss, which affects the operating characteristics of the electromagnetic bearing. In particular, the hysteresis loss directly affects the temperature rise, efficiency and control accuracy of the system, and is one of the key factors restricting the performance and reliability. The actual core loss of the axial electromagnetic bearing is complex to analyze, and compared with the core loss in the radial electromagnetic bearing which is mainly caused by the rotation of the rotor cutting the magnetic field, the core loss of the axial electromagnetic bearing is mainly caused by the two parts of the control current alternation and the axial vibration of the thrust disc. For the axial electromagnetic bearing, the thrust disc inevitably vibrates when working stably, causing the thrust disc to cut the magnetic field, and at this time the closed-loop control system of the magnetic suspension system passes alternating control current in the stator winding coil to generate electromagnetic force to maintain the rotor at a specific position according to the vibration signal. Since the axial electromagnetic bearing adopts a solid pure iron structure, when the axial sinusoidal vibration of the thrust disc and the control current alternation jointly act on the magnetic field, significant core loss will be generated on the stator and the thrust disc.

[0003] The prior art mainly has the following technical problems in hysteresis loss calculation: 1. The traditional equivalent magnetic circuit modeling of magnetic bearings is mostly based on theoretical working condition assumptions, often considering control current alternation or mechanical structure static characteristics alone, ignoring the dynamic coupling effect of the axial sinusoidal vibration of the thrust disc and the control current alternation, resulting in a large deviation between the model and the actual operating condition; 2. The traditional model fails to realize deep coupling of the edge effect, magnetic leakage, eddy current effect, hysteresis effect and nonlinearity of the core material in the magnetic circuit, so that the traditional equivalent magnetic circuit model cannot accurately reflect the evolution law of the electromagnetic characteristics inside the magnetic bearing, and it is difficult to accurately obtain the maximum magnetic flux density of the axial electromagnetic bearing. The lack of accuracy of the maximum magnetic flux density as a core parameter for hysteresis loss calculation directly leads to reduced reliability of the subsequent hysteresis loss calculation results, further increasing the technical difficulty of accurate hysteresis loss calculation. Therefore, it is urgent to propose a new method that can integrate multiple physical field effects and realize accurate hysteresis loss calculation. SUMMARY

[0004] To solve the above technical problems, the application provides a method and device for calculating hysteresis loss of an axial electromagnetic bearing, which can accurately calculate the hysteresis loss of the axial electromagnetic bearing under dynamic operating conditions.

[0005] To achieve the above object, the application adopts the following technical solutions: A method for calculating hysteresis loss of an axial electromagnetic bearing, comprising 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 axial sinusoidal vibration of the thrust disc, a magnetic motive force is calculated based on a real-time control current, and then the total dynamic magnetic flux is determined through the equivalent magnetic circuit model; Based on the static hysteresis characteristics of the core material, a quantitative relationship between any two of the maximum magnetic flux density amplitude, the hysteresis loss and the angle parameter representing the hysteresis effect is established; Taking the magnetic motive force as the magnetic field excitation and the total dynamic magnetic flux as the magnetic field response, a complex magnetic permeability is constructed based on the quantitative relationship; the equivalent magnetic circuit model is updated using the complex magnetic permeability; and the maximum magnetic flux density amplitude of each region of the core under dynamic working conditions 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.

[0006] The application further provides a computing device for hysteresis loss of an axial electromagnetic bearing, comprising at least one processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the at least one processor, the computer program realizes the method for calculating hysteresis loss of an axial electromagnetic bearing.

[0007] The effects provided in the summary are only the effects of the embodiments, not all the effects of the application, and one of the above technical solutions has the following advantages or beneficial effects: 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

[0008] 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. 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; 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; 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; 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; Figure 6 This 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; Figure 7A schematic diagram of a computing device for calculating the hysteresis loss of an axial electromagnetic bearing is provided for Embodiment 2 of the present application. DETAILED DESCRIPTION

[0009] To clearly illustrate the technical features of the present application, the present application will be described in detail below with specific embodiments and in conjunction with the accompanying drawings. The following disclosure provides many different embodiments or examples for implementing the various structures of the present application. In order to simplify the disclosure of the present application, the components and settings of specific examples are described below. In addition, the present application can repeatedly refer to numerals and / or letters in different examples. Such repetition is for the purpose of simplification and clarity, and does not in itself indicate the relationship between the various embodiments and / or settings being discussed. It should be noted that the components illustrated in the drawings are not necessarily drawn to scale. The present application omits the description of well-known components and processing techniques and processes to avoid unnecessarily limiting the present application.

[0010] Embodiment 1 The present application provides a method for calculating the hysteresis loss of an axial electromagnetic bearing, which solves the technical problem of insufficient accuracy of traditional calculation methods due to model simplification and lack of multiple physical effects.

[0011] The main implementation process of the method for calculating the hysteresis loss of an axial electromagnetic bearing provided by Embodiment 1 of the present application is as follows: in the process of modeling the equivalent magnetic circuit model, both the axial sinusoidal vibration of the thrust disc and the alternating control current are considered, the nonlinear iterative solution of the equivalent magnetic circuit model of the magnetic bearing is carried out based on the static magnetization curve fitting formula of the core material and the maximum magnetic flux density and hysteresis angle relationship curve fitting, and factors such as edge effect, leakage, eddy current effect, hysteresis effect and material nonlinearity are deeply coupled in the process, so as to accurately obtain the maximum magnetic flux density of each region of the core, and then, based on the maximum magnetic flux density and the hysteresis loss relationship curve fitting formula, the hysteresis loss of each region of the core in a unit cycle and a unit volume is determined according to the correlation rule of the hysteresis loss and the maximum magnetic flux density amplitude in Bertotti theory; finally, the hysteresis loss of each region of the core of the magnetic bearing is calculated one by one through the hysteresis loss calculation formula, the hysteresis losses of each region are superimposed, and the total hysteresis loss of the axial electromagnetic bearing is obtained when considering the axial sinusoidal vibration of the thrust disc and the alternating control current.

[0012] Figure 1 A flowchart of the method for calculating the hysteresis loss of an axial electromagnetic bearing provided by Embodiment 1 of the present application is shown in the figure. In step S1, the process is started.

[0013] In step S2, the basic structural parameters of the axial electromagnetic bearing are obtained.

[0014] The basic structure parameters in the application include geometric size parameters, material electromagnetic characteristic parameters, and working point and dynamic excitation parameters, etc. The geometric size parameters include stator core size, thrust disc size, air gap parameters, and stator coil turns. The material electromagnetic characteristic parameters include core material magnetic characteristic and insulation material parameters. The working point and dynamic excitation parameters include electromagnetic excitation parameters and mechanical dynamic parameters, etc.

[0015] Figure 2 The basic structure and size schematic diagram of the axial electromagnetic bearing proposed for the embodiment 1 of the application; including a stator, a thrust disc, a rotor, and an air gap, the stator including a stator core and a winding coil, constituting a differential control mode. Figure 2 In the embodiment 1 of the application, representing the shaft diameter, representing the inner diameter of the stator inner magnetic pole, representing the outer diameter of the stator inner magnetic pole, representing the inner diameter of the stator outer magnetic pole, representing the outer diameter of the thrust disc, representing the inner diameter of the stator outer magnetic pole, representing the outer diameter of the stator outer magnetic pole, representing the thickness of the stator yoke, representing the coil slot height, representing the thickness of the stator outer magnetic pole inner side, representing the air gap thickness, representing the thrust disc thickness. The axial electromagnetic bearing size protected by the application is not limited to the specific sizes listed in the embodiment 1, and the person skilled in the art can make reasonable choices according to the actual situation. Figure 2 In the embodiment 1 of the application,

[0016] The scope of protection of the application is not limited to the structure parameters listed in the embodiment 1, and the person skilled in the art can make reasonable choices according to the actual situation.

[0017] In step S3, an equivalent magnetic resistance model is established. Figure 3 The schematic diagram of the magnetic resistance partition and equivalent magnetic circuit model of the axial electromagnetic bearing proposed for the embodiment 1 of the application; according to the magnetic flux path distribution of the axial electromagnetic bearing, the core structure and air gap area can be divided into several units, and due to the axial symmetry characteristics of the geometric shape and magnetic flux distribution of the magnetic bearing, it can be simplified as a two-dimensional analysis model.

[0018] Figure 4 The schematic diagram of the magnetic flux distribution in the stator and thrust disc air gap of the axial electromagnetic bearing proposed for the embodiment 1 of the application; due to the very compact structure of the magnetic bearing and the very small air gap between the stator and the thrust disc, the magnetic pole edge effect between the adjacent is particularly significant. Therefore, the influence of the magnetic pole edge effect needs to be considered when establishing the equivalent magnetic circuit model of the magnetic bearing.

[0019] Therefore, in the equivalent magnetic resistance model in the present application, the average cross-sectional area of the air gap magnetic circuit between the stator and the thrust disc will be larger than the cross-sectional area of the end face of the inner and outer magnetic poles of the stator due to the edge effect. Therefore, the equivalent magnetic area of the air gap of the inner and outer magnetic poles in the main circuit considering the edge effect is: ; (1) is an equivalent magnetic area expansion coefficient of the air gap, which is related to the air gap length between the stator and the thrust disc; is the equivalent magnetic area of the air gap of the inner magnetic pole, is the equivalent magnetic area of the air gap of the outer magnetic pole; is the magnetic area of the air gap of the inner magnetic pole, is the magnetic area of the air gap of the outer magnetic pole.

[0020] According to the equivalent magnetic circuit model of the axial electromagnetic bearing shown in FIG. 1, the magnetic resistances of the regions of the core can be simplified in series and parallel, and when the thrust disc does not vibrate and the control current Figure 2 is 0 A, the core magnetization frequency is zero hertz, at this time, there is no generation of alternating magnetic field, and the total static magnetic resistance expression of the axial electromagnetic bearing is as follows: ; (2) wherein, is the total static magnetic resistance of the core; is the static magnetic resistance of each region of the core.

[0021] By introducing a dynamic equivalent magnetic resistance to consider the influence of eddy current effect on the magnetic flux of the axial electromagnetic bearing, the magnetic resistances of the regions of the magnetic bearing are divided into two components, one part is the static magnetic resistance, and the other part is the dynamic magnetic resistance related to the frequency. According to the flow direction of the magnetic flux in the core, the equivalent magnetic resistance expression of each region of the magnetic bearing considering the eddy current effect is derived as follows: ; (3) wherein, is the equivalent magnetic resistance; is the dynamic magnetic resistance coefficient, , is the alternating frequency; Combined with the total static magnetic resistance expression and the equivalent magnetic resistance of each region of the magnetic bearing, the total effective magnetic resistance of the axial electromagnetic bearing under the action of the alternating magnetic field considering the eddy current effect is obtained as follows: .

[0022] The modified magnetic resistances of the regions are synthesized according to the series and parallel relationship of the magnetic flux path, and the equivalent magnetic resistance model integrated with the edge effect and the eddy current effect is established.

[0023] ​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.

[0024] 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.

[0025] The process of obtaining the equivalent magnetic circuit model includes: 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; 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; 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.

[0026] 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. When constructing the equivalent magnetic circuit model, the air gap vibration displacement is sinusoidally varying when the thrust disk vibrates axially: (4) 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. 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: (5) ; ; in, The air gap reluctance of the inner magnetic pole end surface of the main loop when the air gap changes sinusoidally due to the vibration of the thrust disc The air gap reluctance of the outer magnetic pole end surface of the main loop when the air gap changes sinusoidally due to the vibration of the thrust disc The air gap reluctance of the inner magnetic pole considering the eddy current effect under the balance air gap The air gap reluctance of the outer magnetic pole considering the eddy current effect under the balance air gap The amplitude of the sinusoidal change part of the air gap reluctance of the inner magnetic pole The amplitude of the sinusoidal change part of the air gap reluctance of the outer magnetic pole The vacuum permeability When the axial sinusoidal vibration of the thrust disc and the alternating control current act simultaneously, the magnetic reluctance generated by the sinusoidal change of the air gap should be considered. The total effective magnetic reluctance of the axial electromagnetic bearing considering the eddy current effect is: ; (6) Wherein, The total effective magnetic reluctance of the axial electromagnetic bearing considering the sinusoidal change of the air gap The amplitude of the sinusoidal change part of the total air gap reluctance of the inner and outer magnetic poles ; Wherein, The equivalent cross-sectional area at the air gap is calculated by And In parallel.

[0027] Considering that the sinusoidal vibration of the thrust disc and the alternating control current exist simultaneously, the mathematical model for calculating the magnetic potential of the magnetic bearing is derived based on the equivalent magnetic circuit model shown in Figure 3 , and the dynamic magnetic flux calculation equation is given; When the thrust disc vibrates axially, the axial electromagnetic bearing closed-loop control system will pass alternating control current into the stator winding coil according to the collected vibration feedback signal to suppress the vibration of the thrust disc. At this time, the magnetic bearing will form the main magnetic flux in the air gap region, which is jointly generated by the bias current And the control current : ; (7) Wherein, The bias magnetic flux generated by the bias current when the thrust disc vibrates sinusoidally The control magnetic flux generated by the bias current when the thrust disc vibrates sinusoidally

[0028] 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.: (8) 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.

[0029] Combining formula (7) and formula (8), we can obtain the total magnetic flux of the axial electromagnetic bearing considering leakage flux. The expression is: (9) 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; 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: (10) in, It is a magnetomotive force; This represents the total current flowing through the coil; ; 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.

[0030] 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: (11) in, This refers to the number of turns of the iron core coil; Because the amplitude of the sinusoidal vibration 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. The bias magnetic flux generated by the bias current when the thrust disc is in sinusoidal vibration can be expanded by Taylor series is decomposed into two parts. The static bias magnetic flux is decomposed into two parts. The static bias magnetic flux and the dynamic bias magnetic flux containing eddy current , specifically: ; (12) As can be seen from formula (12), when the thrust disc cuts the magnetic lines of force, the sinusoidal magnetic flux will generate eddy current, and the effective magnetic resistance on the magnetic flux path includes not only the static magnetic resistance, but also the equivalent dynamic magnetic resistance formed by the eddy current.

[0031] Similarly, according to formula (7), formula (9) and formula (10), the expression of the dynamic magnetic flux generated by the control current is: ; (13) When the thrust disc is in sinusoidal vibration, static magnetic flux and dynamic magnetic flux will be generated in the electromagnetic bearing core. The static magnetic flux generates a direct current magnetic field and does not cut the magnetic field to generate eddy current effect; while the dynamic magnetic flux generates an alternating magnetic field of the magnetized core, which causes the core loss of the magnetic bearing.

[0032] Combining formula (12) and formula (13), the total dynamic magnetic flux of the axial electromagnetic bearing when the thrust disc is in sinusoidal vibration can be obtained as: ; (14).

[0033] In step S6, 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 dynamic working condition is solved synchronously by iterative calculation .

[0034] Based on the magnetic flux law, the expression of the inner and outer pole air gap flux density can be derived from formula (1) and formula (14): ; (15) wherein, is the inner pole air gap flux density; is the outer pole air gap flux density.

[0035] In Figure 3In the middle, because the cross-sectional area of the magnetic flux in the radial flow area 2, 5 and 7 in the magnetic bearing core is not continuous, for the sake of simplifying the operation, the cross-sectional area of the magnetic flux in the center of each radial flow area is taken as the average cross-sectional area in the area. Based on the law of conservation of magnetic flux, when the magnetic flux is constant, the maximum magnetic flux density of the magnetic bearing gap is inversely proportional to the cross-sectional area of the area through which the magnetic flux flows, and the quantitative relationship between the maximum magnetic flux density of the magnetic bearing gap and the maximum magnetic flux density of each area of the core can be derived: (16) wherein, is the average magnetic density in the thrust disc area; is the axial segment magnetic density of the stator inner magnetic pole; is the radial segment magnetic density of the stator inner magnetic pole; is the magnetic yoke area magnetic density of the stator; is the radial segment magnetic density of the stator outer magnetic pole; is the axial segment magnetic density of the stator outer magnetic pole; is the average cross-sectional area in the thrust disc area; is the average cross-sectional area of the axial segment of the stator inner magnetic pole; is the average cross-sectional area of the radial segment of the stator inner magnetic pole; is the average cross-sectional area of the magnetic yoke area of the stator; is the average cross-sectional area of the radial segment of the stator outer magnetic pole; is the average cross-sectional area of the axial segment of the stator outer magnetic pole.

[0036] Based on the static hysteresis loop of the core material, the first relationship curve of the maximum magnetic flux density and the hysteresis loss is obtained; Based on the equivalent ellipse principle, the relationship between the hysteresis loss and the hysteresis angle is established, and the second relationship curve of the maximum magnetic flux density and the hysteresis angle is obtained.

[0037] Bertotti theory defines the total loss in magnetic materials as three components, namely hysteresis, eddy current and additional loss. However, in the actual axial magnetic bearing, each loss term cannot be directly measured because the eddy current loss and the additional loss are caused by the core eddy current effect. In addition, the eddy current effect is closely related to the thickness of the material, and the magnetic bearing uses a large block of solid pure iron, which will produce significant eddy current effect, and the core structure is different from the ring structure of the traditional motor and transformer; while the eddy current loss and the additional loss are related to the thickness of the material and the structure shape, the existing Epstein square and ring winding method and other traditional measurement methods cannot meet the core loss measurement demand of the magnetic bearing in the actual operation condition; and it is also difficult to accurately separate the hysteresis loss from the whole core by analyzing the power loss through the current of the magnetic bearing coil winding. Therefore, the application uses the equivalent ellipse principle, and establishes the hysteresis loss and the relationship between the hysteresis angle and the hysteresis loss considering the hysteresis effect of the core material.

[0038] Based on the Bertotti iron loss separation theory, the total loss of the core is separated into hysteresis loss , eddy current loss and abnormal loss ; that is ; (17) According to the Bertotti loss separation theory, with the increase of the frequency, the area of the hysteresis loop will increase, because the frequency will cause the generation of eddy current loss and additional loss. Therefore, as long as the alternating current maximum magnetic flux density amplitude generated under different sinusoidal excitations is the same, the hysteresis loss per unit volume per unit period is also the same, that is, the area of the static hysteresis loop, which is related to the alternating magnetic flux density amplitude.

[0039] Based on the static hysteresis loop of the core material, the hysteresis loss per unit volume per unit period is obtained by calculating the area of the hysteresis loop. ; (18) wherein is the hysteresis loss parameter in the Bertotti loss separation theory; is the magnetic field strength describing the static hysteresis loop; Based on the Bertotti loss separation theory, the hysteresis loss per unit volume per unit period is converted into the hysteresis loss power per unit time . ; (19) wherein is the sum of the volume of the thrust disc and the stator core in the magnetic bearing; for alternating frequency.

[0040] In order to consider the magnetic hysteresis effect in the modeling process of the electromagnetic bearing, the present application utilizes Figure 5 the static magnetic hysteresis loop of the magnetic bearing core material and the equivalent ellipse diagram as shown in the figure, Figure 5 in the formula (19) represents the long semi-axis; represents the short semi-axis. The equivalent ellipse area is made consistent with the actual static magnetic hysteresis loop area of the core material based on the equivalent ellipse principle, so that the formula (19) can be transformed into the magnetic hysteresis loss and magnetic hysteresis angle relationship formula: ; (20) 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; the magnetic hysteresis angle is used to consider the magnetic hysteresis effect of the magnetic bearing core material.

[0041] In combination with Figure 4 and the formula (20), the static magnetic hysteresis loop area of the core material is fitted, so that the maximum magnetic flux density of the electromagnetic bearing core material and the magnetic hysteresis angle relationship curve and the maximum magnetic flux density and the magnetic hysteresis loss power relationship curve can be obtained; through least square fitting, the fitting relationship formula of the maximum magnetic flux density and the magnetic hysteresis angle relationship curve and the maximum magnetic flux density and the magnetic hysteresis loss power relationship curve is established.

[0042] The nonlinear magnetic circuit equation iteration method and the maximum magnetic flux density and the magnetic hysteresis angle relationship curve are introduced to calculate the magnetic hysteresis angle and the complex permeability of the magnetic bearing at different to consider the nonlinearity and the magnetic hysteresis effect of the core material, to establish an accurate equivalent magnetic circuit model of the magnetic bearing, and to analyze the maximum magnetic flux density of each region of the core considering the magnetic hysteresis effect.

[0043] In step S7, the equivalent magnetic circuit model established calculates the air gap equivalent magnetic area to take into account the magnetic pole edge effect, introduces the leakage magnetic coefficient to take into account the leakage magnetic flux, introduces the dynamic equivalent magnetic resistance to take into account the eddy current effect, introduces the static magnetization curve of the core material to consider the material nonlinearity, and introduces the magnetic hysteresis angle to take into account the magnetic hysteresis effect. for alternating frequency.

[0040] In order to consider the magnetic hysteresis effect in the modeling process of the electromagnetic bearing, the present application utilizes Figure 5 the static magnetic hysteresis loop of the magnetic bearing core material and the equivalent ellipse diagram as shown in the figure, Figure 5 in the formula (19) represents the long semi-axis; represents the short semi-axis. The equivalent ellipse area is made consistent with the actual static magnetic hysteresis loop area of the core material based on the equivalent ellipse principle, so that the formula (19) can be transformed into the magnetic hysteresis loss and magnetic hysteresis angle relationship formula: ; (20) 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; the magnetic hysteresis angle is used to consider the magnetic hysteresis effect of the magnetic bearing core material.

[0041] In combination with Figure 4 and the formula (20), the static magnetic hysteresis loop area of the core material is fitted, so that the maximum magnetic flux density of the electromagnetic bearing core material and the magnetic hysteresis angle relationship curve and the maximum magnetic flux density and the magnetic hysteresis loss power relationship curve can be obtained; through least square fitting, the fitting relationship formula of the maximum magnetic flux density and the magnetic hysteresis angle relationship curve and the maximum magnetic flux density and the magnetic hysteresis loss power relationship curve is established.

[0042] The nonlinear magnetic circuit equation iteration method and the maximum magnetic flux density and the magnetic hysteresis angle relationship curve are introduced to calculate the magnetic hysteresis angle and the complex permeability of the magnetic bearing at different to consider the nonlinearity and the magnetic hysteresis effect of the core material, to establish an accurate equivalent magnetic circuit model of the magnetic bearing, and to analyze the maximum magnetic flux density of each region of the core considering the magnetic hysteresis effect.

[0043] In step S7, the equivalent magnetic circuit model established calculates the air gap equivalent magnetic area to take into account the magnetic pole edge effect, introduces the leakage magnetic coefficient to take into account the leakage magnetic flux, introduces the dynamic equivalent magnetic resistance to take into account the eddy current effect, introduces the static magnetization curve of the core material to consider the material nonlinearity, and introduces the magnetic hysteresis angle to take into account the magnetic hysteresis effect.

[0044] 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.

[0045] 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 ; 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.

[0046] In step S9, the relationship between hysteresis loss and hysteresis angle is established based on the principle of equivalent ellipse.

[0047] In step S10, based on the maximum magnetic flux density and hysteresis angle The relationship is combined.

[0048] 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: 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.

[0049] 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. .

[0050] 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: ;(twenty one) In the formula, is the static permeability, which is obtained from the static magnetization curve.

[0051] Then, based on the definition of magnetic resistance calculation, the complex permeability obtained by iterative calculation The total effective magnetic resistance of the magnetic bearing is calculated by re-substituting the nonlinear magnetic circuit equation into formula (6), and the equivalent magnetic resistance model considering the magnetic hysteresis effect is obtained.

[0052] Finally, the error criterion is introduced to iteratively solve the equivalent magnetic circuit of the magnetic bearing; when the iteration converges, the complex permeability of the material in each region of the core and the maximum magnetic flux density in the magnetic circuit are obtained, and the equivalent magnetic circuit model of the axial electromagnetic bearing considering the edge effect, leakage, eddy current effect, magnetic hysteresis effect and material nonlinearity is accurately established.

[0053] In step S11, the maximum magnetic flux density of each region of the core obtained by iteration and the maximum magnetic flux density hysteresis loss of the core material determine the hysteresis loss per unit volume per unit period of each region of the core, and the volume of each region of the core is calculated , and the hysteresis loss of each region of the magnetic bearing is solved by using the hysteresis loss calculation formula (19), and finally the hysteresis loss of each region is superimposed and represented in the form of 2 times to take into account the positive and negative magnetic poles, and the total hysteresis loss of the axial electromagnetic bearing considering the axial sinusoidal vibration of the thrust disc and the alternating control current is obtained: ; (22) In the formula, is the total hysteresis loss of the magnetic bearing, is the hysteresis loss of the core region.

[0054] In step S12, the process ends.

[0055] The calculation method of the hysteresis loss of the axial electromagnetic bearing proposed in embodiment 1 of the application introduces the air gap equivalent permeable area expansion coefficient, the dynamic equivalent magnetic resistance, the leakage coefficient and the complex permeability, and innovatively integrates the five key physical effects of edge effect, eddy current effect, leakage effect, material nonlinearity and hysteresis effect in a unified equivalent magnetic circuit model. The technical limitations of the traditional model that each effect is independent or partially ignored are broken, and the complex electromagnetic environment of the axial electromagnetic bearing is accurately described. Especially by using the complex permeability and the equivalent ellipse principle, the difficult-to-separate hysteresis loss is successfully decoupled from the total iron loss, and the pure hysteresis loss is accurately calculated.

[0056] Embodiment 2 The application also proposes a device, Figure 7A schematic diagram of a computing device for calculating hysteresis loss of an axial electromagnetic bearing is provided for embodiment 2 of the present application.

[0057] At the hardware level, the electronic device 700 includes a processor 710, optionally, an internal bus 720, a network interface 730, and a memory. The memory can include a memory 740, such as a high-speed random-access memory (RAM), and can also include a non-volatile memory, such as at least one disk memory. Of course, the electronic device can also include other hardware required by the business. The processor 710, the network interface 730, and the memory can be connected to each other through the internal bus 720, which 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 divided into an address bus, a data bus, a control bus, etc. For ease of representation, only one bidirectional arrow is shown in the figure, but it does not mean that there is only one bus or only 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 the memory 740 and the non-volatile memory 750, and provide instructions and data to the processor 710. The processor 710 reads the corresponding computer program from the non-volatile memory 750 into the memory 740 and then runs, forming a device for positioning target users at the logical level. The processor 710 executes the program stored in the memory, and is specifically used to execute: Based on the structural parameters of the axial electromagnetic bearing, an equivalent magnetic resistance model integrating edge effect and eddy current effect is established; based on the equivalent magnetic resistance model, a dynamic air gap magnetic resistance introduced by axial vibration of the thrust disc is combined, and a leakage magnetic effect is taken into account through a leakage coefficient, to establish an equivalent magnetic circuit model of the axial electromagnetic bearing; Under the condition of axial vibration of the thrust disc, the magnetic motive force is calculated based on the real-time control current, and then the total dynamic magnetic flux is determined through the equivalent magnetic circuit model; Based on the static hysteresis characteristics of the core material, a quantitative relationship between any two of the maximum magnetic flux density amplitude, the hysteresis loss, and the angle parameter representing the hysteresis effect is established; The magnetic motive force is taken as the magnetic field excitation, the total dynamic magnetic flux is taken as the magnetic field response, the complex magnetic permeability 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 iron core under the dynamic working condition is synchronously solved by 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 total hysteresis loss of the axial electromagnetic bearing is obtained by synthesizing the hysteresis losses of all regions.

[0058] Figure 1 The processor can be an integrated circuit chip having a signal processing capability. In the implementation process, the steps of the above method can be completed by the integrated logic circuit or the instruction of the software form in the processor. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; and 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, discrete hardware components. The disclosed methods, steps and logic block diagrams in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as a hardware code processor for execution, or a combination of hardware and software modules in the code processor for execution. The software module can be located in a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium in the storage is read by the processor, and the hardware thereof is combined to complete the steps of the above method.

[0059] Of course, in addition to the software implementation, the electronic device of the present application does not exclude other implementation manners, such as logic devices or a combination of software and hardware, etc. That is, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0060] The description of the related part of the calculation device of the hysteresis loss of the axial electromagnetic bearing provided in the embodiment 2 of the present application can refer to the detailed description of the corresponding part of the calculation method of the hysteresis loss of the axial electromagnetic bearing provided in the embodiment 1 of the present application, which will not be repeated here.

[0061] The calculation device for hysteresis loss of the axial electromagnetic bearing provided in Embodiment 2 of the present application introduces an air gap equivalent permeance area expansion coefficient, a dynamic equivalent magnetic resistance, a leakage magnetic coefficient and a complex magnetic permeability, innovatively systematically integrates five key physical effects, i.e., an edge effect, an eddy current effect, a leakage effect, material nonlinearity and a hysteresis effect, in a unified equivalent magnetic circuit model. The technical limitations of traditional models in which the effects are independent or partially ignored are broken, and a complete description of a complex electromagnetic environment of the axial electromagnetic bearing is realized. In particular, the hysteresis loss which is difficult to separate from the total iron loss is successfully decoupled from the total iron loss by the complex magnetic permeability and the equivalent ellipse principle, and the precise calculation of the pure hysteresis loss is realized.

[0062] It should be noted that the relational terms herein such as first and second and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any such actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. Other embodiments of the present application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. For example, the above-described embodiments of the present application can be modified or combined in various ways. It is therefore intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the application being indicated by the following claims.

[0063] The above describes the specific embodiments of the present application in combination with the drawings, but is not a limitation on the protection scope of the present application. For those skilled in the art, other different forms of modifications or changes can be made on the basis of the above description. Here, it is not necessary or possible to exhaust all the embodiments. Various modifications or changes made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the protection scope of the present application.

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; 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 of the air gap 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 of the air gap 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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