Method and apparatus for calculating eddy current losses in an axial electromagnetic bearing

Abstract

The application discloses a kind of eddy current loss calculation method and equipment of axial electromagnetic bearing, belong to eddy current loss calculation technical field.The method is divided into multiple units with air gap and corresponding setting magnetic resistance, the current resistance of each magnetic resistance is determined;Based on the principle of differential control, the relationship between the change of upper and lower stator coil current and the displacement of thrust disc when thrust disc axial vibration is determined;According to the series-parallel relationship of each magnetic resistance, the total equivalent magnetic resistance is calculated, and the dynamic magnetic flux is calculated accordingly;According to the dynamic magnetic flux, the eddy current field model of each core unit is established, the surface magnetic field intensity distribution function is derived, and the eddy current density distribution function is calculated;The volume integral of the instantaneous eddy current loss of each core unit is summed up, and the average eddy current loss of axial electromagnetic bearing in a vibration cycle is obtained.The application simultaneously considers the coupling effect of thrust disc axial vibration and control current alternation, realizes the accurate and rapid analytical calculation of core eddy current loss under actual working condition.

Description

Technical Field

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

[0002] Axial electromagnetic bearings achieve contactless levitation support of the rotor through electromagnetic force, offering significant advantages such as frictionless operation, no lubrication required, high speed, and low power consumption, making them promising for applications in high-speed rotating machinery. Currently, industrially used axial electromagnetic bearings typically employ a solid iron core structure rather than a laminated structure. Under external excitation, the thrust disc vibrates axially. The control system adjusts the current in the stator coils in real time based on the vibration signal, thereby altering the electromagnetic force to levitate the thrust disc at its equilibrium position. The axial vibration of the thrust disc and the alternating current of the coils generate an alternating magnetic field in the iron core, leading to core losses, primarily hysteresis losses and eddy current losses, with eddy current losses being dominant. If the thrust disc vibrates at a high frequency and with a large amplitude, excessive eddy currents in the core not only generate significant eddy current losses and heat, leading to increased core temperature, but also reduce the electromagnetic force, affecting the reliability, stability, and dynamic performance of the axial electromagnetic bearing system. Therefore, accurate calculation of core eddy current losses is a crucial foundation for the electromagnetic design, structural parameter optimization, and heat analysis of axial electromagnetic bearings.

[0003] Existing methods for calculating eddy current losses in the core of axial electromagnetic bearings have the following shortcomings: First, existing methods only analyze the eddy current losses in a single operating condition where the thrust disc vibrates axially but the control current remains constant, or the control current alternates but the thrust disc remains stationary. These two situations differ significantly from actual operating conditions and cannot reflect the true variation of eddy current losses in the core when axial vibration of the thrust disc and alternating control current act simultaneously. Second, existing methods lack analytical models that can accurately characterize the variation of the magnetic field strength on the surface of the core element. They typically employ approximate assumptions or simplifications, resulting in insufficient accuracy in eddy current loss calculations. Third, while finite element simulation methods offer high accuracy, they suffer from complex modeling, long calculation cycles, and are not convenient for rapid engineering analysis.

[0004] Therefore, there is an urgent need for an analytical calculation method for eddy current loss of axial electromagnetic bearing core that can simultaneously consider the axial vibration of the thrust disk and the alternating effect of the control current. This method would establish an accurate analytical expression for the surface magnetic field strength function of the core unit, enabling rapid and accurate calculation of eddy current loss and laying the foundation for structural optimization and performance improvement of axial electromagnetic bearings. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a method and apparatus for calculating eddy current losses in axial electromagnetic bearings. By establishing an equivalent magnetic circuit model that simultaneously considers the axial vibration of the thrust disk and the alternation of the control current, as well as an analytical function for the surface magnetic field strength of the core unit, rapid and accurate analytical calculation of eddy current losses in the core of axial electromagnetic bearings is achieved.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention proposes a method for calculating eddy current losses in axial electromagnetic bearings, comprising the following steps: Based on the magnetic flux path distribution of the axial electromagnetic bearing, the core and air gap are divided into multiple units, each unit is equipped with a corresponding magnetic reluctance, and the current resistance value of each magnetic reluctance is determined; the magnetic reluctance includes the main air gap magnetic reluctance, the edge air gap magnetic reluctance, the non-corner region core magnetic reluctance, and the corner region core magnetic reluctance. Based on the differential control principle of axial electromagnetic bearings, the relationship between the current of the upper stator coil and the current of the lower stator coil as the thrust disk displacement is determined when the thrust disk vibrates axially. The total equivalent reluctance is calculated based on the current resistance value of each reluctance and the series-parallel relationship between them; and the dynamic magnetic flux is calculated based on the ratio of the total magnetomotive force to the total equivalent reluctance; the total magnetomotive force is determined by the upper stator coil current and the lower stator coil current. Based on the dynamic magnetic flux, an eddy current field model for each core unit is established, the surface magnetic field intensity distribution function of each core unit is derived, and the eddy current density distribution function of each core unit is calculated based on Maxwell's equations. The instantaneous eddy current loss of each core element is obtained by volume integration. The summation of these losses yields the average eddy current loss of the axial electromagnetic bearing over one vibration cycle.

[0007] Furthermore, based on the magnetic flux path distribution of the axial electromagnetic bearing, the core and air gap are divided into multiple units, specifically: Considering the influence of air gap edge effect, nonlinearity of core material permeability and eddy current effect on magnetic flux distribution and magnetic reluctance characteristics, the core and air gap are divided into main air gap region, air gap edge region, non-corner core region and corner core region.

[0008] Furthermore, the current resistance value of each magnetoresistor is determined as follows: The current resistance of the main air gap reluctance is the sum of the static reluctance of the main air gap reluctance and the change in resistance. The current resistance of the edge air gap reluctance is the static reluctance of the edge air gap reluctance; The current resistance value of the core reluctance in the non-corner region is composed of the static reluctance and dynamic reluctance of the core reluctance in the non-corner region. The current resistance of the iron core reluctance in the corner region is the static reluctance of the iron core reluctance in the corner region.

[0009] Furthermore, the change in resistance of the main air gap reluctance is determined based on the axial vibration displacement of the thrust disk, whereby the axial vibration displacement of the thrust disk is expressed as: ; in, Indicates axial vibration displacement; Indicates the axial amplitude of the thrust disk; Indicates the angular frequency of vibration; Indicates time; The current resistance value of the main air gap reluctance is expressed as: ; in, This indicates the current resistance value of the main air gap reluctance of the stator poles; The static reluctance represents the reluctance of the main air gap between the internal poles of the stator. This represents the change in resistance of the main air gap reluctance of the stator poles; This indicates the current resistance value of the main air gap reluctance of the stator external poles; Static reluctance, representing the main air gap reluctance of the stator external poles; This represents the change in resistance of the main air gap reluctance of the stator's outer magnetic poles.

[0010] Furthermore, based on the differential control principle of the axial electromagnetic bearing, the relationship between the current in the upper stator coil and the current in the lower stator coil as the thrust disk displaces during axial vibration is determined, specifically as follows: ; in, Pass functions to the controller. For power amplifier gain, For displacement sensor gain, The sensor outputs a voltage signal when the thrust disk is in the equilibrium position. This is the coil bias current. Control current for the coil; This is the current in the upper stator coil. This is the current in the lower stator coil.

[0011] Furthermore, the total equivalent magnetoresistance is expressed as: ; in, Indicates the total equivalent magnetic reluctance; This represents the total equivalent magnetic reluctance of the core in the non-corner region; This represents the total static magnetic reluctance in the corner region; This represents the equivalent air gap reluctance after the main air gap reluctance and the edge air gap reluctance of the stator poles are connected in parallel. This represents the equivalent air gap reluctance after the main air gap reluctance and the edge air gap reluctance of the stator outer poles are connected in parallel. The total magnetomotive force is expressed as: ; in, It represents the total magnetomotive force. Indicates the number of coil turns; Indicates the bias current; Indicates control current; Indicates the total magnetic flux; Indicates the total equivalent magnetic reluctance; At this time, the total magnetic flux generated by the combined action of the bias current and the control current under the axial periodic vibration of the thrust disk is: ; in, Indicates static magnetic flux; Indicates dynamic magnetic flux.

[0012] Furthermore, the total equivalent magnetic reluctance of the non-corner region of the core is determined based on the relative permeability of the core unit, and the total magnetic flux is obtained through iterative calculation, specifically as follows: Under static conditions, by combining the fitting equation of the nonlinear magnetization curve of the core material, the static operating point of the axial electromagnetic bearing is determined by updating the relative permeability of each core unit in real time, and the relative permeability of each core unit at the static operating point is obtained. Under dynamic operating conditions, the relative permeability of each core unit at the equilibrium operating point is taken to calculate the total magnetic flux of the axial electromagnetic bearing under dynamic operating conditions.

[0013] Furthermore, based on the dynamic magnetic flux, an eddy current field model is established for each core unit, and the surface magnetic field intensity distribution function of each core unit is derived, specifically: For an iron core unit with magnetic flux flowing radially, the surface magnetic field strength of the iron core unit can be obtained by inverse calculation from the dynamic magnetic flux according to the definition of magnetic flux. Combined with the magnetic field strength distribution function in cylindrical coordinate system, the relationship between the radial magnetic field strength of the iron core unit and the radius can be obtained. For an iron core unit with magnetic flux flowing along the axial direction, the surface magnetic field strength of the iron core unit can be obtained by inverse calculation from the dynamic magnetic flux according to the definition of magnetic flux. Combined with the magnetic field strength distribution function in the cylindrical coordinate system, the relationship between the magnetic field strength along the axial direction and the radius of the iron core unit can be obtained.

[0014] Furthermore, by volume integrating the instantaneous eddy current losses of each core element, the instantaneous eddy current losses of each core element are obtained. Summing these values ​​yields the average eddy current loss of the axial electromagnetic bearing over one vibration cycle, specifically: ; in, This represents the average eddy current loss in the upper stator region during one thrust disk axial vibration cycle. Indicates the angular frequency of vibration; Indicates the index of the core unit number in the non-corner region; Indicates the first Instantaneous eddy current loss of a non-corner region core element; When the axial periodic vibration of the thrust disk and the alternating control current act simultaneously, the total eddy current loss of the axial electromagnetic bearing is: ; in, This represents the total eddy current loss of the axial electromagnetic bearing core.

[0015] Secondly, the present invention also proposes an eddy current loss calculation device for an axial electromagnetic bearing, comprising at least one processor and a memory, wherein the memory stores a computer program, and the computer program, when executed by the at least one processor, implements a method for calculating eddy current loss of an axial electromagnetic bearing.

[0016] The technical solution provided by this invention has the following advantages compared with the prior art: (i) Accurate calculation of eddy current losses under actual working conditions has been achieved. Existing methods for calculating eddy current losses in axial electromagnetic bearing cores only consider a single operating condition of thrust disk axial vibration or alternating control current, failing to reflect the true variation of core eddy current losses when both conditions act simultaneously. This invention establishes an equivalent magnetic circuit model that simultaneously considers the periodic axial vibration of the thrust disk and the alternating control current, deriving analytical expressions for the total equivalent reluctance and dynamic flux under the simultaneous action of these two factors. This achieves accurate calculation of core eddy current losses under actual operating conditions, overcoming the technical deficiency of existing methods where simplified operating conditions lead to significant deviations between calculated and actual results. Furthermore, this invention establishes a dynamic reluctance model for non-corner region core elements, consisting of parallel static and dynamic reluctance, accurately considering the influence of core eddy current effects on the magnetic field. For corner region core elements, considering the sparse flux distribution in the corner region due to the skin effect, static reluctance is used for characterization, making the calculation of total equivalent reluctance more accurate.

[0017] (ii) An accurate analytical expression for the surface magnetic field strength of the iron core unit was established, and computational efficiency was improved. Existing methods lack analytical models that accurately characterize the variation of the magnetic field intensity on the surface of core elements, typically employing approximate assumptions or simplifications, leading to insufficient accuracy in eddy current loss calculations. This invention establishes magnetic field intensity distribution functions based on cylindrical coordinates for core elements with different magnetic flux directions. The surface magnetic field intensity of each core element is derived from the dynamic magnetic flux, achieving an accurate characterization of the variation of the surface magnetic field intensity and fundamentally improving the accuracy of eddy current loss calculations. Furthermore, compared to finite element simulation methods, which suffer from complex modeling, long computation cycles, and inconvenience for rapid engineering analysis, this invention employs an analytical calculation method. It eliminates the need for complex finite element models and extensive mesh generation and iterative calculations, significantly improving computational efficiency and facilitating rapid eddy current loss assessment and structural parameter optimization of electromagnetic bearings in engineering design.

[0018] (iii) The high calculation accuracy verifies the accuracy and effectiveness of the method. This invention uses the eddy current loss obtained from finite element simulation as the standard value for accuracy evaluation. The eddy current loss calculated by the proposed method at different vibration frequencies is basically consistent with the finite element simulation results. The maximum relative error and the overall average relative error are both kept at a low level, which verifies the accuracy and effectiveness of the proposed analytical calculation method for eddy current loss of axial electromagnetic bearings. It provides a reliable calculation tool and theoretical basis for the electromagnetic design, structural parameter optimization and heat analysis of axial electromagnetic bearings, and has important engineering application value for improving the reliability, stability and dynamic performance of axial electromagnetic bearing systems. Attached Figure Description

[0019] Figure 1 This is a flowchart of a method for calculating eddy current losses in an axial electromagnetic bearing, as proposed in Embodiment 1 of the present invention. Figure 2 This is a schematic diagram of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention; Figure 3 This refers to the equivalent magnetic reluctance division region of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention; Figure 4 This is a basic control block diagram of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention; Figure 5 The equivalent magnetic circuit model of the axial electromagnetic bearing proposed in Embodiment 1 of this invention ( Figure 5 (a) in the figure represents the original equivalent magnetic circuit model; Figure 5 (b) is the equivalent magnetic circuit model after appropriate series and parallel simplification. Figure 6 This is an iterative flowchart of the equivalent magnetic circuit model of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention; Figure 7The relative permeability of each core unit when the thrust disk is at its equilibrium operating point, as proposed in Embodiment 1 of the present invention; Figure 8 The curve showing the dynamic magnetic flux of the axial electromagnetic bearing as a function of frequency when the amplitude is 0.02 mm, as proposed in Embodiment 1 of the present invention; Figure 9 This is a schematic diagram of the magnetic flux direction within the solid iron core unit of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. Figure 9 In the diagram, (a) represents the case where the magnetic flux flows radially; Figure 9 (b) shows the case where the magnetic flux flows along the axial direction. Figure 10 The curve showing the variation of eddy current loss of the axial electromagnetic bearing core with frequency when the amplitude is 0.02 mm, as proposed in Embodiment 1 of the present invention ( Figure 10 (a) in the figure is a comparison chart of the calculation results; Figure 10 (b) is a comparison chart of relative errors. Figure 11 This is a schematic diagram of an eddy current loss calculation device for an axial electromagnetic bearing proposed in Embodiment 2 of the present invention. Detailed Implementation

[0020] 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.

[0021] Example 1 Embodiment 1 of this invention proposes a method for calculating eddy current loss of axial electromagnetic bearings. This method addresses the technical problems of existing methods for calculating eddy current loss of axial electromagnetic bearing cores, which only consider a single working condition of thrust disk axial vibration or alternating control current. These methods cannot accurately reflect the actual eddy current loss variation when both conditions act simultaneously, and lack an analytical model that can accurately characterize the variation of magnetic field strength on the surface of the core unit, resulting in insufficient calculation accuracy and low calculation efficiency.

[0022] Figure 1 This is a flowchart of a method for calculating eddy current losses in an axial electromagnetic bearing, as proposed in Embodiment 1 of the present invention. In step S1, according to the magnetic flux path distribution of the axial electromagnetic bearing, the core and air gap are divided into multiple units, each unit is equipped with a corresponding magnetic reluctance, and the current resistance value of each magnetic reluctance is determined; the magnetic reluctance includes the main air gap magnetic reluctance, the edge air gap magnetic reluctance, the non-corner region core magnetic reluctance, and the corner region core magnetic reluctance. Figure 2 This is a schematic diagram of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. Figure 2 In China, axial electromagnetic bearings are mainly composed of stator core, thrust bearing (TMB), coil and other components. An axial air gap is provided between the stator core and the thrust bearing. The thrust bearing is fixedly connected to the rotor shaft. During operation, the thrust bearing rotates with the rotor and may experience axial vibration.

[0023] Table 1: Basic structural parameters and meanings of axial electromagnetic bearings.

[0024]

[0025] Combination Figure 2 The axial electromagnetic bearing structure shown, based on the magnetic flux path distribution, and to comprehensively consider the influence of air gap edge effects, nonlinearity of core material permeability, and eddy current effects on magnetic flux distribution and reluctance characteristics, divides the core and air gap into 14 units, resulting in the equivalent reluctance division region as shown below. Figure 3 As shown. Figure 3 The figure shows the equivalent magnetic reluctance region of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. The figure illustrates the magnetic reluctance of each unit in the form of a two-dimensional axisymmetric cross-section. and It is the main air gap magnetic reluctance, corresponding to the magnetic reluctance of the main air gap region between the thrust disk and the stator core. , , and The air gap edge reluctance is used to account for the effect of magnetic pole edge effect on the magnetic flux path expansion. , and The magnetic reluctance of the iron core is in the radial direction of the magnetic flux; , and The core reluctance is in the axial direction of the magnetic flux. , and This refers to the stator corner reluctance. Considering the inherent symmetry of the axial electromagnetic bearing, Figure 3 Only the corresponding reluctance on the upper stator side is shown in the figure; the reluctance on the lower stator side can be derived similarly.

[0026] Determine the current resistance value of each reluctance, specifically as follows: The current resistance of the main air gap reluctance is the sum of the static reluctance of the main air gap reluctance and the change in resistance. The current resistance of the edge air gap reluctance is the static reluctance of the edge air gap reluctance; The current resistance value of the core reluctance in the non-corner region is composed of the static reluctance and dynamic reluctance of the core reluctance in the non-corner region. The current resistance of the iron core reluctance in the corner region is the static reluctance of the iron core reluctance in the corner region.

[0027] The axial vibration displacement of the thrust disk is expressed as: (1) in, Indicates axial vibration displacement; Indicates the axial amplitude of the thrust disk; Indicates the angular frequency of vibration; Indicates time; Based on the above vibration displacement expression and the electromagnetic definition of magnetic reluctance, the expressions for the main air gap reluctance of the inner and outer poles of the stator when the air gap changes due to the axial periodic vibration of the thrust disk can be obtained, specifically: (2) in, This indicates the current resistance value of the main air gap reluctance of the stator poles; The static reluctance represents the reluctance of the main air gap between the internal poles of the stator. This represents the change in resistance of the main air gap reluctance of the stator poles; This indicates the current resistance value of the main air gap reluctance of the stator external poles; Static reluctance, representing the main air gap reluctance of the stator external poles; This represents the change in resistance of the main air gap reluctance of the stator's outer magnetic poles.

[0028] For edge air gap magnetoresistance , , and Its resistance value is taken as static reluctance.

[0029] The higher the axial vibration frequency of the thrust disk, the higher the alternating frequency of the control current. Under the skin effect, the magnetic flux distribution at the corner region of the stator core is sparser. Therefore, the change of magnetic reluctance in this region with the vibration of the thrust disk is ignored, and only the static magnetic reluctance of the core is considered. , and For the equivalent magnetic reluctance of the core unit in the non-corner region, the influence of the dynamic magnetoresistive meter and the core eddy current effect on the magnetic field is introduced, and the core magnetic reluctance model is established as follows:

[0030] in, For the first One core unit ( The equivalent magnetic reluctance of ) This refers to the static reluctance of the unit. This refers to the dynamic magnetoresistive force of the unit.

[0031] Dynamic magnetoresistive Related to the axial vibration displacement of the thrust disk: The axial vibration of the thrust disk causes a periodic change in the air gap length, resulting in the generation of an alternating magnetic field within the core unit. This, in turn, causes a dynamic change in the magnetic reluctance of the core unit due to the eddy current effect. Therefore, the dynamic magnetic reluctance... It is a function of the axial vibration displacement of the thrust disk, and it changes with the axial vibration displacement of the thrust disk.

[0032] In step S2, based on the differential control principle of the axial electromagnetic bearing, the relationship between the current of the upper stator coil and the current of the lower stator coil as the thrust disk displacement is determined when the thrust disk vibrates axially. Figure 4 This is a basic control block diagram of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. Figure 4 As shown, the axial electromagnetic bearing is a closed-loop control system operating in differential mode. The axial displacement of the thrust disc is detected by a displacement sensor, converted into a voltage signal by the sensor and detection circuit, and then compared with a reference voltage to obtain a deviation signal. This deviation signal is then sequentially passed through the controller transfer function. and power amplifier gain Generate control current This ultimately drives the stator coils to generate the corresponding electromagnetic force.

[0033] The relationship between the stator coil current and the thrust disk displacement can be expressed as: (3) in, Pass functions to the controller. For power amplifier gain, For displacement sensor gain, The sensor outputs a voltage signal when the thrust disk is in the equilibrium position. This is the coil bias current. Control current for the coil; This is the current in the upper stator coil. This is the current in the lower stator coil.

[0034] When the thrust plate vibrates axially, the controller adjusts the control current in real time. The direction and amplitude of the current in the upper and lower coils are adjusted to cause differential changes in the current, thereby generating a restoring force opposite to the direction of offset, thus achieving stable levitation.

[0035] In step S3, the total equivalent magnetic reluctance is calculated based on the current resistance value of each reluctance and the series-parallel relationship between each reluctance; and the dynamic magnetic flux is calculated based on the ratio of the total magnetomotive force to the total equivalent magnetic reluctance; the total magnetomotive force is determined by the upper stator coil current and the lower stator coil current. Figure 5 This is the equivalent magnetic circuit model of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. Figure 5 (a) in the figure is the original equivalent magnetic circuit model, which fully shows the series and parallel connection relationship of each reluctance on the upper stator side and the lower stator side; Figure 5 (b) in the diagram is the equivalent magnetic circuit model after appropriate series and parallel simplification. According to... Figure 5 The series-parallel relationship shown further simplifies the magnetic circuit model, and the expression for the total equivalent magnetic reluctance of the axial electromagnetic bearing when the axial periodic vibration of the thrust disk and the alternating control current act simultaneously can be obtained as follows: (4) in, Indicates the total equivalent magnetic reluctance; The total equivalent magnetic reluctance of the iron core in the non-corner region is the total equivalent magnetic reluctance of the iron core in the non-corner region obtained by connecting the magnetic reluctances of iron core units 2, 4, 5, 6, 7, and 8 in series, taking into account eddy current effects and skin effect. This represents the total static magnetic reluctance in the corner region, i.e., magnetic reluctance. , and The total static magnetic reluctance of the stator corner region obtained by series connection; This represents the equivalent air gap reluctance after the main air gap reluctance and the edge air gap reluctance of the stator poles are connected in parallel. The equivalent air gap reluctance is represented by the parallel connection of the main air gap reluctance and the edge air gap reluctance of the stator outer poles; respectively: (5) Based on the expression for total equivalent magnetic reluctance, when the thrust disk does not experience axial vibration and the control current... When the magnetization frequency is 0, the core magnetization frequency is zero. At this time, there is no alternating magnetic field. Ignoring the periodic changes in the air gap and the influence of eddy currents on the core, the total static reluctance expression for the axial electromagnetic bearing can be obtained as follows: (6) in, The total static magnetic reluctance of the non-corner iron core obtained by series connection; and The equivalent static air gap reluctance, obtained by connecting the main air gap reluctance of the inner and outer magnetic poles of the stator in parallel with the air gap edge reluctance, are expressed as follows: (7) According to electromagnetic field theory, the total magnetomotive force of the axial electromagnetic bearing is: (8) in, It represents the total magnetomotive force. Indicates the number of coil turns; Indicates the bias current; Indicates control current; Indicates the total magnetic flux; Indicates the total equivalent magnetic reluctance; At this time, the total magnetic flux generated by the combined action of the bias current and the control current under the axial periodic vibration of the thrust disk is: (9) in, Indicates the total magnetic flux; This represents the static magnetic flux generated by the bias current when the thrust disk is in the center position, used to maintain the static levitation operating point; This represents the dynamic magnetic flux generated by the combined action of bias current and control current during the axial periodic vibration of the thrust disk. It induces eddy currents in the iron core, leading to core losses. Static magnetic flux... and dynamic magnetic flux The expression is: (10) in, and The meanings are the same; Indicates the number of coil turns; Indicates the coil bias current; This represents the dynamic flux component generated by the bias current. This represents the dynamic magnetic flux component generated by the control current; This represents the total static reluctance in the stator corner region, determined by the reluctance. , and Obtained by connecting in series; Based on the theoretical derivation of the equivalent magnetic circuit model of the axial electromagnetic bearing under the simultaneous action of axial periodic vibration of the thrust disk and alternating control current, and combined with the fitting equation of the nonlinear magnetization curve of the core material, Figure 6 This is an iterative flowchart of the equivalent magnetic circuit model of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. Figure 6 As shown, the iterative calculation process is divided into two stages: Stage 1 is the static operating point nonlinear iteration stage, and Stage 2 is the dynamic operating condition calculation stage.

[0036] Phase 1: Static operating point nonlinear iteration Stage 1 is used to determine the static operating point of the axial electromagnetic bearing under static conditions, and to obtain the relative permeability of each core element at the static operating point. This stage specifically includes the following steps: First, the static operating parameters and the initial relative permeability of each core unit are given. The static operating parameters include the coil bias current, the axial air gap length at the equilibrium position, etc.; the initial relative permeability of each core unit can be set according to the fitting equation of the nonlinear magnetization curve of the core material.

[0037] Next, the average magnetic flux density of the core unit is calculated. Based on the given initial relative permeability and static operating parameters, combined with the geometric dimensions and magnetic flux path of each core unit, the average magnetic flux density of each core unit is calculated.

[0038] Then, the average magnetic flux density of the other core units is determined according to the law of continuity of magnetic flux. According to Kirchhoff's laws of magnetic circuits, the magnetic flux is continuous in each branch of the magnetic circuit, and the average magnetic induction intensity of the remaining core units can be determined accordingly.

[0039] Next, by The relative permeability of the core elements is calculated based on the fitting equation of the nonlinear magnetization curve of the core material, derived from the average magnetic induction intensity of each core element. Inversely calculate the corresponding magnetic field strength And then from The relative permeability of each core unit was calculated.

[0040] Subsequently, the equivalent reluctance of the core is calculated by substituting it into the equivalent reluctance model. The updated relative permeability is then substituted into the equivalent reluctance model of each core element to calculate the equivalent reluctance of each core element.

[0041] Then, the total magnetic flux is obtained by equivalent magnetic circuit calculation. Based on the series and parallel relationship of the reluctance of each core unit, combined with the air gap reluctance and the edge air gap reluctance, the total equivalent reluctance is calculated, and the total magnetic flux is obtained from the ratio of the total magnetomotive force to the total equivalent reluctance.

[0042] Finally, the judgment Is this condition met? Compare the magnetic flux density calculated in this iteration with the result of the previous iteration. If the absolute value of the difference between the two is less than the preset convergence threshold... If the iteration converges, it is determined that the iteration has converged; otherwise, return to the "Calculate the average magnetic flux density of the core unit" step and recalculate the iteration with the updated relative permeability.

[0043] Once the iteration converges, output the relative permeability of each core element at the static operating point. As input for the dynamic working condition calculation in Phase 2.

[0044] Phase 2 involves taking the static operating point value to calculate the total magnetic flux of the axial electromagnetic bearing under dynamic operating conditions. This specifically includes the following steps: First, input dynamic operating parameters are given. These parameters include the axial vibration amplitude of the thrust disk, vibration frequency, and control current.

[0045] Secondly, the relative permeability of each core unit at the static operating point Calculate the equivalent reluctance of each core element. Using the relative permeability of each core element obtained after the convergence of the first iteration as input, substitute it into the equivalent reluctance model to calculate the equivalent reluctance of each core element under dynamic operating conditions.

[0046] Then, a dynamic equivalent reluctance model and an equivalent magnetic circuit model are established. Based on the relationship between the dynamic reluctance of each core unit and the air gap reluctance and the axial vibration of the thrust disk, an equivalent magnetic circuit model under dynamic operating conditions is established.

[0047] Finally, the magnetic field and electromagnetic force of the thrust disk under dynamic operating conditions are solved. Based on the dynamic equivalent magnetic circuit model, the total magnetic flux of the axial electromagnetic bearing under dynamic operating conditions is calculated, and thus the magnetic field distribution and electromagnetic force of the thrust disk under dynamic operating conditions are obtained, concluding the process.

[0048] Through iterative calculations in the two stages described above, this invention can accurately determine the relative permeability and equivalent reluctance of each core unit under static operating point and dynamic operating condition, taking into account the nonlinear magnetization characteristics and eddy current effect of the core material. This provides accurate input for subsequent analytical calculations of eddy current losses of each core unit.

[0049] Figure 7 The relative permeability of each core unit when the thrust disk is at its equilibrium operating point, as proposed in Embodiment 1 of the present invention. Figure 7 The diagram shows the relative permeability values ​​of each core element at the equilibrium operating point. These relative permeabilities are obtained after convergence of the nonlinear iterative calculation at the static operating point in stage 1. Figure 7 As can be seen, due to the differences in magnetic flux path, geometric dimensions, and magnetic field strength among the core units of the axial electromagnetic bearing, the relative permeability of each core unit at the equilibrium operating point varies significantly. Specifically, the relative permeability of core unit 2 (thrust disk) is 607.293, that of core unit 4 is 2416.591, that of core unit 5 is 2658.387, that of core unit 6 is 2805.316, that of core unit 7 is 2473.213, and that of core unit 8 is 2449.926. Among them, core unit 6 has the highest relative permeability, and core unit 2 has the lowest relative permeability. The relative permeability of each core unit generally falls between 607 and 2805. Figure 7 The relative permeability of each core unit shown is used as input for the dynamic operating condition calculation in stage 2, and is used to calculate the equivalent magnetic reluctance of each core unit under dynamic operating conditions.

[0050] Figure 8 This is the curve showing the dynamic magnetic flux variation of the axial electromagnetic bearing with frequency when the amplitude is 0.02 mm, as proposed in Embodiment 1 of the present invention. Figure 8The trend of dynamic magnetic flux as the vibration frequency increases is given. Figure 8 It is evident that, with the axial vibration amplitude of the thrust disk remaining constant at 0.02 mm, as the axial vibration frequency of the thrust disk increases, the alternating frequency of the control current also increases, enhancing the eddy current effect in the core. The dynamic magnetic flux amplitude exhibits a nonlinear trend with increasing vibration frequency. This dynamic magnetic flux is the core variable for subsequently establishing the eddy current field model for each core unit, deriving the magnetic field intensity distribution function on the surface of each core unit, and calculating the eddy current loss of each core unit.

[0051] In step S4, based on the dynamic magnetic flux, an eddy current field model for each core unit is established, the surface magnetic field intensity distribution function of each core unit is derived, and the eddy current density distribution function of each core unit is calculated based on Maxwell's equations. Figure 9 This is a schematic diagram of the magnetic flux direction within the solid iron core unit of the axial electromagnetic bearing proposed in Embodiment 1 of the present invention. Figure 9 (a) in the figure represents the case where the magnetic flux flows radially, corresponding to core unit 2 (thrust disk), unit 5, and unit 7; Figure 9 (b) in the figure represents the case where the magnetic flux flows along the axial direction, corresponding to core unit 4, unit 6 and unit 8.

[0052] (1) Core Unit 2 Core unit 2 is the thrust disk portion of the axial electromagnetic bearing. Magnetic flux flows radially, and the eddy current paths are located within the cross-section perpendicular to the radially flowing main magnetic flux, forming a closed loop. Figure 9 As shown in (a) of the diagram. To quantitatively describe its electromagnetic process, the complex vector form of Maxwell's equations is introduced: (11) in, Represents the magnetic field strength vector; Represents the eddy current density vector; Represents the magnetic flux density vector; Represents the electric field intensity vector; Indicates the electrical conductivity of the core material; Indicates the magnetic permeability of the core material; Combining the above equation, the magnetic field strength distribution function of the iron core element 2 in cylindrical coordinates can be obtained as follows: (12) in, Indicates the radial position of core element 2 axial position The magnetic field strength at that location; This represents the propagation constant of core element 2; Indicates the axial thickness of the thrust disk; This represents the surface magnetic field strength of core unit 2.

[0053] According to the definition of magnetic flux, the relationship between dynamic magnetic flux and the surface magnetic field strength of the core element 2 flowing radially can be expressed as: (13) in, Indicates the radial position of core element 2 axial position Magnetic flux density at the location; Indicates the permeability of free space; This represents the relative permeability of core unit 2 (thrust disk).

[0054] Therefore, the surface magnetic field strength of the core element 2 flowing radially can be derived from equation (13) as follows: (14) Substituting equation (12) into the total current law equation in equation (11), we can obtain the eddy current density distribution function of core element 2 as follows: (15) The instantaneous eddy current loss of the core element of an axial electromagnetic bearing is defined as the product of the eddy current density vector and its conjugate component, or the volume of the square of the magnitude of the eddy current density vector. , can be represented as: (16) Substituting equations (14) and (15) into equation (16) and performing algebraic operations and function integration, we can obtain the analytical expression for the instantaneous eddy current loss of core element 2: (17) in, The electrical conductivity of the material in core unit 2 (i.e., the thrust disk); This indicates the skin depth of core unit 2.

[0055] (2) Core Unit 4 The eddy currents in core unit 4 appear in a closed loop distribution within the cross-section perpendicular to the main magnetic flux flowing along the axial direction, such as... Figure 9 As shown in (b) of the diagram.

[0056] Combining equation (11), the magnetic field intensity distribution function of the iron core element 4 in cylindrical coordinates can be obtained as follows: (18) In the formula, Let be the propagation constant of core element 4. ; For the skin depth of core unit 4, The electrical conductivity of the stator core material; is the relative permeability of core element 4; The surface magnetic field strength flowing along the axial direction in core unit 4; Indicates the permeability of free space; This represents the inner radius of the inner section of the stator's outer magnetic pole, i.e., the radial inner boundary of core unit 4; Indicates the outer radius of the thrust disk; This represents a first-order modified Bessel function of the 0th order; This represents the first-order modified Bessel function of the first kind; This represents the second kind of 0th order modified Bessel function; This represents a first-order modified Bessel function of the second kind; According to the definition of magnetic flux, the relationship between dynamic magnetic flux and the surface magnetic field strength flowing along the axial direction in core element 4 can be expressed as: (19) Therefore, the surface magnetic field strength of the iron core unit 4 can be derived from equation (19) as follows: (20) Substituting equation (18) into the total current law equation in equation (11), we can obtain the eddy current density distribution function of core element 4 as follows: ;(twenty one) Substituting equations (20) and (21) into equation (16) and performing algebraic operations and function integration, we can obtain the analytical expression for the instantaneous eddy current loss of core element 4: ;(twenty two) (3) Core Unit 5 The dynamic magnetic flux flows radially in both core element 5 and core element 2. Due to the skin effect, the magnetic field strength attenuates in the same axial direction. Therefore, the analytical expression for the instantaneous eddy current loss of core element 5 has the same form as that of core element 2, and can be expressed as: ;(twenty three) In the formula, Let be the propagation constant of core element 5. ; The skin depth of core unit 5; The relative permeability of core unit 5; Indicates the outer radius of the thrust disk; This indicates the outer radius of the stator's outer magnetic poles.

[0057] (4) Core Unit 6 The dynamic magnetic flux flows axially in both core element 6 and core element 4. Due to the skin effect, the magnetic field strength attenuates in the same axial direction. Therefore, the analytical expression for the instantaneous eddy current loss of core element 6 has the same form as that of core element 4, and can be expressed as: :(twenty four) In the formula, Let be the propagation constant of core element 6. ; The skin depth of core unit 6; The relative permeability of core unit 6; This indicates the outer radius of the stator's outer magnetic poles.

[0058] (5) Core Unit 7 The dynamic magnetic flux flows radially in both core element 7 and core element 2. Due to the skin effect, the magnetic field strength attenuates in the same axial direction. Therefore, the analytical expression for the instantaneous eddy current loss of core element 7 has the same form as that of core element 2, and can be expressed as: (25) In the formula, Let be the propagation constant of core element 7. ; The skin depth of core unit 7; is the relative permeability of core unit 7.

[0059] (6) Core Unit 8 Dynamic magnetic flux flows axially in core unit 8 and core units 4 and 6, and the magnetic field strength attenuates radially under the same pattern due to the skin effect. However, since core unit 8 is a cylindrical structure, when... When it approaches 0, The meaning is the propagation constant. With radial radius Results It will tend towards infinity. Therefore, the magnetic field intensity distribution function of core element 8 can be approximated as: (26) In the formula, Let be the propagation constant of core element 8. ; This represents the surface magnetic field strength flowing along the axial direction in core unit 8; According to the definition of magnetic flux, the relationship between dynamic magnetic flux and the surface magnetic field strength flowing along the axial direction in core element 8 can be expressed as: (27) Therefore, the surface magnetic field strength of the iron core unit 8 can be derived from equation (27) as follows: (28) Substituting equation (26) into the total current law equation in equation (11), we can obtain the eddy current density distribution function of the core element 8 as follows: (29) Substituting equations (28) and (29) into equation (16) and performing algebraic operations and function integration, we can obtain the analytical expression for the instantaneous eddy current loss of core element 8: (30) In step S5, the instantaneous eddy current loss of each core unit is integrated by volume to obtain the instantaneous eddy current loss of each core unit. After summing, the average eddy current loss of the axial electromagnetic bearing in one vibration cycle is obtained.

[0060] Combining equations (16), (21), (22), (23), (24), and (29), the average eddy current loss in the stator region of the axial electromagnetic bearing during one thrust disk axial vibration cycle can be obtained as follows: (31) in, This represents the average eddy current loss in the upper stator region during one thrust disk axial vibration cycle. , , , , and These represent the instantaneous eddy current losses of core elements 2, 4, 5, 6, 7, and 8, respectively.

[0061] Based on the differential principle and the symmetry of the axial electromagnetic bearing itself, it can be seen that the average eddy current loss in the lower stator region during one thrust disk axial vibration cycle is consistent with equation (31). Therefore, the eddy current loss of the axial electromagnetic bearing core when the thrust disk axial periodic vibration and the control current alternation act simultaneously can be obtained as: (32) in, This represents the total eddy current loss of the axial electromagnetic bearing core.

[0062] The scope of protection of Embodiment 1 of the present invention is not limited to the number of core units listed in Embodiment 1, and those skilled in the art can make reasonable adjustments according to the actual situation.

[0063] Figure 10 The curve showing the change of eddy current loss of the axial electromagnetic bearing core with frequency when the amplitude is 0.02 mm, as proposed in Embodiment 1 of the present invention. Figure 10 (a) in the figure is a comparison chart of the calculation results. Figure 10(b) in the figure shows a comparison of relative errors. To verify the accuracy of the method proposed in this invention, the eddy current loss obtained from finite element simulation is used as the standard value to evaluate the accuracy of the three methods in analytically calculating the eddy current loss. Method 1 (the model of this invention) ignores the eddy current effect in the stator corner region. , , Method 1 (conventional model) considers static reluctance and calculates core eddy current loss using the method proposed in this invention; Method 2 introduces dynamic reluctance into all core units to account for the influence of eddy current effects, and calculates eddy current loss using the method proposed in this invention; Method 3 assumes that the surface magnetic field strength of each core unit is equal, and calculates eddy current loss using the method proposed in this invention. The magnetic field strength on the core surface is approximated, and the eddy current loss of the core is calculated.

[0064] Depend on Figure 10 It is evident that the eddy current loss in the iron core exhibits a nonlinear increasing trend with increasing vibration frequency, and the relative error deviations between different methods and finite element simulation results are significant. Specifically, Method 1 (the model of this invention) yields calculation results that are basically consistent with the standard finite element values, with a maximum relative error of 6.1% and an overall average relative error of 3.7%, demonstrating the highest calculation accuracy. Method 2 (the traditional model) yields calculation results significantly lower than the standard values, with a maximum relative error of 35.7% and an overall average relative error of 29.0%, indicating poor calculation accuracy. Method 3 also generally yields calculation results lower than the standard values, with a maximum relative error of 33.1% and an overall average relative error of 22.1%. Therefore, the eddy current loss calculated by this invention at different vibration frequencies maintains low and relatively stable calculation errors compared to the finite element simulation results, verifying the accuracy and effectiveness of the proposed analytical calculation method for eddy current loss in axial electromagnetic bearings.

[0065] In Embodiment 1 of this invention, the iron core and air gap of the axial electromagnetic bearing are divided into multiple units and corresponding magnetic reluctances are set. The relationship between the current changes of the upper and lower stator coils during the axial vibration of the thrust disk is determined by combining the differential control principle. The total equivalent magnetic reluctance and dynamic magnetic flux, which simultaneously reflect the alternating effects of the axial vibration of the thrust disk and the control current, are calculated. Then, an eddy current field model is established for each iron core unit, and the surface magnetic field intensity distribution function and eddy current density distribution function are derived. Finally, the average eddy current loss of the axial electromagnetic bearing in one vibration cycle is obtained by volume integration and summation, thus completing the analytical calculation of the eddy current loss of the axial electromagnetic bearing iron core under actual operating conditions.

[0066] Example 2 Based on the eddy current loss calculation method for axial electromagnetic bearings proposed in Embodiment 1 of this invention, Embodiment 2 of this invention proposes an eddy current loss calculation device for axial electromagnetic bearings. Figure 11 This is a schematic diagram of an eddy current loss calculation device for an axial electromagnetic bearing proposed in Embodiment 2 of the present invention.

[0067] At the hardware level, the electronic device 100 includes a processor 110, and optionally, an internal bus 120, a network interface 130, and memory. The memory may include main memory, 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 its functions.

[0068] The processor 110, network interface 130, and memory can be interconnected via an internal bus 120. This internal bus 120 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 140 and non-volatile memory 150, and provides instructions and data to the processor 110.

[0069] Processor 110 reads the corresponding computer program from non-volatile memory 150 into memory 140 and runs it, forming a method for calculating eddy current losses of the axial electromagnetic bearing at the logical level. Processor 110 executes the program stored in memory and specifically performs the following: In step S1, according to the magnetic flux path distribution of the axial electromagnetic bearing, the core and air gap are divided into multiple units, each unit is equipped with a corresponding magnetic reluctance, and the current resistance value of each magnetic reluctance is determined; the magnetic reluctance includes the main air gap magnetic reluctance, the edge air gap magnetic reluctance, the non-corner region core magnetic reluctance, and the corner region core magnetic reluctance. In step S2, based on the differential control principle of the axial electromagnetic bearing, the relationship between the current of the upper stator coil and the current of the lower stator coil as the thrust disk displacement is determined when the thrust disk vibrates axially. In step S3, the total equivalent magnetic reluctance is calculated based on the current resistance value of each reluctance and the series-parallel relationship between each reluctance; and the dynamic magnetic flux is calculated based on the ratio of the total magnetomotive force to the total equivalent magnetic reluctance; the total magnetomotive force is determined by the upper stator coil current and the lower stator coil current. In step S4, based on the dynamic magnetic flux, an eddy current field model for each core unit is established, the surface magnetic field intensity distribution function of each core unit is derived, and the eddy current density distribution function of each core unit is calculated based on Maxwell's equations. In step S5, the instantaneous eddy current loss of each core unit is integrated by volume to obtain the instantaneous eddy current loss of each core unit. After summing, the average eddy current loss of the axial electromagnetic bearing in one vibration cycle is obtained.

[0070] Figure 1 It can be applied to processor 110, or implemented by processor 110. 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.

[0071] 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.

[0072] The description of the relevant part of the eddy current loss calculation device for an axial electromagnetic bearing provided in Embodiment 2 of this application can be found in the detailed description of the corresponding part of the eddy current loss calculation method for an axial electromagnetic bearing provided in Embodiment 1 of this application, and will not be repeated here.

[0073] 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.

[0074] 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 for calculating eddy current losses in an axial electromagnetic bearing, characterized in that, Includes the following steps: Based on the magnetic flux path distribution of the axial electromagnetic bearing, the core and air gap are divided into multiple units, each unit is equipped with a corresponding magnetic reluctance, and the current resistance value of each magnetic reluctance is determined; the magnetic reluctance includes the main air gap magnetic reluctance, the edge air gap magnetic reluctance, the non-corner region core magnetic reluctance, and the corner region core magnetic reluctance. Based on the differential control principle of axial electromagnetic bearings, the relationship between the current of the upper stator coil and the current of the lower stator coil as the thrust disk displacement is determined when the thrust disk vibrates axially. The total equivalent reluctance is calculated based on the current resistance value of each reluctance and the series-parallel relationship between them; and the dynamic magnetic flux is calculated based on the ratio of the total magnetomotive force to the total equivalent reluctance; the total magnetomotive force is determined by the upper stator coil current and the lower stator coil current. Based on the dynamic magnetic flux, an eddy current field model for each core unit is established, the surface magnetic field intensity distribution function of each core unit is derived, and the eddy current density distribution function of each core unit is calculated based on Maxwell's equations. The instantaneous eddy current loss of each core element is obtained by volume integration. The summation of these losses yields the average eddy current loss of the axial electromagnetic bearing over one vibration cycle.

2. The method for calculating eddy current losses in an axial electromagnetic bearing according to claim 1, characterized in that, Based on the magnetic flux path distribution of the axial electromagnetic bearing, the core and air gap are divided into multiple units, specifically: Considering the influence of air gap edge effect, nonlinearity of core material permeability and eddy current effect on magnetic flux distribution and magnetic reluctance characteristics, the core and air gap are divided into main air gap region, air gap edge region, non-corner core region and corner core region.

3. The method for calculating eddy current losses in an axial electromagnetic bearing according to claim 1, characterized in that, Determine the current resistance value of each reluctance, specifically as follows: The current resistance of the main air gap reluctance is the sum of the static reluctance of the main air gap reluctance and the change in resistance. The current resistance of the edge air gap reluctance is the static reluctance of the edge air gap reluctance; The current resistance value of the core reluctance in the non-corner region is composed of the static reluctance and dynamic reluctance of the core reluctance in the non-corner region. The current resistance of the iron core reluctance in the corner region is the static reluctance of the iron core reluctance in the corner region.

4. The method for calculating eddy current losses in an axial electromagnetic bearing according to claim 1, characterized in that, The change in resistance of the main air gap reluctance is determined based on the axial vibration displacement of the thrust disk, whereby the axial vibration displacement of the thrust disk is expressed as: ； in, Indicates axial vibration displacement; Indicates the axial amplitude of the thrust disk; Indicates the angular frequency of vibration; Indicates time; The current resistance value of the main air gap reluctance is expressed as: ； in, This indicates the current resistance value of the main air gap reluctance of the stator poles; The static reluctance represents the reluctance of the main air gap between the internal poles of the stator. This represents the change in resistance of the main air gap reluctance of the stator poles; This indicates the current resistance value of the main air gap reluctance of the stator external poles; Static reluctance, representing the main air gap reluctance of the stator external poles; This represents the change in resistance of the main air gap reluctance of the stator's outer magnetic poles.

5. The method for calculating eddy current losses in an axial electromagnetic bearing according to claim 1, characterized in that, Based on the differential control principle of axial electromagnetic bearings, the relationship between the current in the upper stator coil and the current in the lower stator coil as the thrust disk displaces during axial vibration is determined, specifically: ； in, Pass functions to the controller. For power amplifier gain, For displacement sensor gain, The sensor outputs a voltage signal when the thrust disk is in the equilibrium position. This is the coil bias current. Control current for the coil; This is the current in the upper stator coil. This is the current in the lower stator coil.

6. The method for calculating eddy current losses in an axial electromagnetic bearing according to claim 1, characterized in that, The total equivalent magnetic reluctance is expressed as: ； in, Indicates the total equivalent magnetic reluctance; This represents the total equivalent magnetic reluctance of the core in the non-corner region; This represents the total static magnetic reluctance in the corner region; This represents the equivalent air gap reluctance after the main air gap reluctance and the edge air gap reluctance of the stator poles are connected in parallel. This represents the equivalent air gap reluctance after the main air gap reluctance and the edge air gap reluctance of the stator outer poles are connected in parallel. The total magnetomotive force is expressed as: ; in, It represents the total magnetomotive force. Indicates the number of coil turns; Indicates the bias current; Indicates control current; Indicates the total magnetic flux; Indicates the total equivalent magnetic reluctance; At this time, the total magnetic flux generated by the combined action of the bias current and the control current under the axial periodic vibration of the thrust disk is: ； in, Indicates static magnetic flux; Indicates dynamic magnetic flux.

7. The method for calculating eddy current losses in an axial electromagnetic bearing according to claim 6, characterized in that, The total equivalent magnetic reluctance of the non-corner region of the iron core in the total equivalent magnetic reluctance is determined based on the relative permeability of the iron core unit. The total magnetic flux is obtained through iterative calculation, specifically as follows: Under static conditions, by combining the fitting equation of the nonlinear magnetization curve of the core material, the static operating point of the axial electromagnetic bearing is determined by updating the relative permeability of each core unit in real time, and the relative permeability of each core unit at the static operating point is obtained. Under dynamic operating conditions, the relative permeability of each core unit at the equilibrium operating point is taken to calculate the total magnetic flux of the axial electromagnetic bearing under dynamic operating conditions.

8. The method for calculating eddy current losses in an axial electromagnetic bearing according to claim 1, characterized in that, Based on the dynamic magnetic flux, an eddy current field model is established for each core unit, and the surface magnetic field intensity distribution function of each core unit is derived, specifically: For an iron core unit with magnetic flux flowing radially, the surface magnetic field strength of the iron core unit can be obtained by inverse calculation from the dynamic magnetic flux according to the definition of magnetic flux. Combined with the magnetic field strength distribution function in cylindrical coordinate system, the relationship between the radial magnetic field strength of the iron core unit and the radius can be obtained. For an iron core unit with magnetic flux flowing along the axial direction, the surface magnetic field strength of the iron core unit can be obtained by inverse calculation from the dynamic magnetic flux according to the definition of magnetic flux. Combined with the magnetic field strength distribution function in the cylindrical coordinate system, the relationship between the magnetic field strength along the axial direction and the radius of the iron core unit can be obtained.

9. The method for calculating eddy current losses in an axial electromagnetic bearing according to claim 1, characterized in that, By integrating the instantaneous eddy current losses of each core element by volume, the instantaneous eddy current losses of each core element are obtained. Summing these sums yields the average eddy current loss of the axial electromagnetic bearing over one vibration cycle, specifically: ； in, This represents the average eddy current loss in the upper stator region during one thrust disk axial vibration cycle. Indicates the angular frequency of vibration; Indicates the index of the core unit number in the non-corner region; Indicates the first Instantaneous eddy current loss of a non-corner region core element; When the axial periodic vibration of the thrust disk and the alternating control current act simultaneously, the total eddy current loss of the axial electromagnetic bearing is: ； in, This represents the total eddy current loss of the axial electromagnetic bearing core.

10. A device for calculating eddy current losses in an axial electromagnetic bearing, comprising at least one processor and a memory, wherein the memory stores a computer program, characterized in that, When the computer program is executed by the at least one processor, it implements a method for calculating eddy current losses of an axial electromagnetic bearing as described in any one of claims 1 to 9.

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