A method for calculating motor levitation force pulsation considering torque armature magnetic field modulation harmonics

Abstract

This invention discloses a method for calculating the levitation force pulsation of a motor considering the harmonic modulation of the torque armature magnetic field. First, considering the variation in air gap permeability after core saturation, a saturation coefficient is introduced. The modulation unit changes from individual stator slot modulation to a combination of stator slot and saturation coefficient modulation, thereby altering the harmonic components of the air gap magnetic flux density. Second, under the premise of introducing the saturation coefficient, the influence of the permanent magnet magnetic field, the fundamental and harmonic waves of the torque armature magnetic field, and the fundamental and harmonic waves of the levitation armature magnetic field are fully considered. This allows for the complete determination of the effective traveling wave pairs of the air gap magnetic flux density in a bearingless permanent magnet synchronous motor, thus accurately obtaining the traveling wave pairs that generate levitation force pulsation. Fourier decomposition is used to determine the number of harmonic pole pairs and rotational speed after the change in air gap magnetic flux density. Based on the condition that a difference of one pole pair in the number of pole pairs results in different rotational speeds and thus generates levitation force pulsation, the traveling wave pairs that generate levitation force pulsation are found, effectively supplementing existing methods for analyzing the levitation force pulsation of bearingless permanent magnet synchronous motors.

Description

Technical Field

[0001] This invention belongs to the field of motor body design technology, and in particular relates to a method for analyzing the levitation force pulsation of a bearingless permanent magnet synchronous motor. Background Technology

[0002] Bearingless permanent magnet synchronous motors are a new type of motor that combines magnetic levitation technology with permanent magnet synchronous motors. Compared with traditional permanent magnet motors, they have the characteristics of long service life, no mechanical friction, high efficiency, and high power density. They have important application value in high-tech fields such as life sciences, aerospace, centrifuges, and semiconductor industry.

[0003] To achieve active levitation in a bearingless permanent magnet synchronous motor, two sets of windings—one for torque and one for levitation—are simultaneously added to the stator slots. However, the addition of the levitation windings not only increases the motor's thermal load but also, because the torque and levitation magnetic fields share the same flux path, increases the coupling degree of the air gap magnetic field. This makes decoupling control between the electromagnetic torque and levitation force difficult, further affecting the motor's reliable operation. Therefore, accurate mathematical modeling of the levitation force model of a bearingless permanent magnet synchronous motor is crucial for achieving high torque and high levitation performance.

[0004] In recent years, with the rapid rise of field-modulated motors, a corresponding new motor theory—field modulation theory—has attracted widespread attention from scholars. Initially, field modulation theory was only applied to a few special types of motors, such as magnetic gear motors, vernier motors, reverse flux motors, and field-modulated dual-rotor motors. Later, scholars gradually discovered that many magnetic problems in traditional motors could be explained by the principle of field modulation. This led to the development of a new motor research theory based on the principle of field modulation, providing new ideas for the design and analysis of traditional motors.

[0005] In 2011, Li Jingcan and Liao Yong of Chongqing University published a paper entitled "Model of Permanent Magnet Synchronous Motor Considering Saturation and Rotor Magnetic Field Harmonics" in the Proceedings of the Chinese Society for Electrical Engineering. This paper considered the effects of core saturation and rotor magnetic field harmonics, establishing a dq-axis nonlinear model of a permanent magnet synchronous motor based on the finite element method. However, to simplify the problem, the model only considered the effects of saturation on the d- and q-axis inductances and the fundamental flux linkage of the rotor permanent magnet, neglecting the effect of saturation on harmonic flux linkages. Furthermore, the nonlinear mathematical model consists of variable-coefficient differential equations, requiring table lookups for inductance and flux linkage, and involving complex matrix operations. Therefore, the analytical method for saturation mathematical models of permanent magnet synchronous motors still has shortcomings and cannot be applied to the theoretical analysis of levitation force pulsation in bearingless permanent magnet synchronous motors.

[0006] The document "An Analytical Method for Cogging Torque of a Permanent Magnet Motor Considering Core Saturation (Application No. 202411209146.7)" has already considered the saturation modulation effect caused by the permanent magnet magnetic field in the process of calculating the motor positioning torque, thus improving the analytical accuracy of the cogging torque. However, if this approach is followed to calculate the levitation force pulsation, the calculation will be inaccurate because the torque armature magnetic field modulation harmonics are not considered. Summary of the Invention

[0007] To address the problems mentioned in the background section, the present invention aims to provide a method for calculating motor levitation force pulsation considering torque armature magnetic field modulation harmonics. By introducing a saturation coefficient, the method fully considers the influence of the permanent magnet magnetic field, the fundamental and harmonic waves of the torque armature magnetic field, and the fundamental and harmonic waves of the levitation armature magnetic field. This method can completely determine the effective traveling wave pairs of the air gap magnetic flux density of a bearingless permanent magnet synchronous motor, thereby accurately obtaining the traveling wave pairs that generate levitation force pulsation.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] A method for calculating motor levitation force pulsation considering torque armature magnetic field modulation harmonics consists of six main steps: parallel magnetization of permanent magnets, introduction of saturation coefficients to obtain variable air gap permeability, determination of the fundamental and harmonic waves of permanent magnet magnetic field, torque armature magnetic field, and levitation armature magnetic field as the sources of harmonic pairs, obtaining the modified air gap magnetic flux density, and Fourier decomposition of air gap magnetic flux density to obtain the harmonic pairs that generate levitation force pulsation.

[0010] 1. The permanent magnet is magnetized in parallel, and the magnetomotive force is a perfect sine wave. There is no need to perform Fourier decomposition on the magnetomotive force, and the magnetomotive force only has the fundamental wave.

[0011] Mathematical model of magnetomotive force: F(θ,t)=Acosp r (ω r t-θ)

[0012] 2. Mathematical model of air gap permeability after Fourier decomposition without considering core saturation:

[0013]

[0014] Considering the variation in air gap permeability after core saturation, we introduce the saturation coefficient obtained from Fourier decomposition:

[0015]

[0016] The final air gap permeability is the product of the original permeability and the saturation coefficient:

[0017]

[0018] 3. Determine that the fundamental and harmonic waves of the permanent magnet magnetic field, the torque armature magnetic field, and the levitation armature magnetic field all interact with the final air gap magnetic permeability mentioned above, thereby obtaining a complete harmonic pair that forms the levitation force pulsation; 4. Unloaded air gap magnetic flux density B PM Equal to the magnetomotive force F of the permanent magnet PM Product with air gap permeability P:

[0019]

[0020] Armature reaction air gap sub-density B S Equal to the armature winding magnetomotive force F S Product with air gap permeability P:

[0021]

[0022] 5. Fourier decomposition of the unloaded air gap magnetic flux density:

[0023]

[0024] Fourier decomposition of the air gap magnetic flux density of the armature reaction:

[0025]

[0026] Where A is the magnetomotive force amplitude, P j N is the magnetic permeability amplitude. s Where a is the number of stator slots, a0 is the saturation coefficient constant, and P r ω is the number of rotor pole pairs. r Let θ be the rotor mechanical angular frequency, θ be the magnetomotive force phase angle, and α be the angular frequency. n is the amplitude of each saturation coefficient harmonic, n is the order of the saturation coefficient harmonic, t is time, and m and k represent integers from 0 to positive infinity.

[0027] 6. By performing Fourier decomposition of the unloaded air gap magnetic flux density, the pole pair number and rotational speed of different unloaded air gap magnetic flux density harmonics are obtained, which are respectively the pole pair number |p r ±jN s | Rotation speed Extreme logarithm | (2n+1)p r ±jN s | Rotation speed Extreme logarithm |(2n-1)p r ±jN s | Rotation speed Six different harmonics. Through Fourier decomposition of the air-gap magnetic flux density of the armature reaction magnetic field, the pole pair number and rotational velocity of the different armature reaction magnetic field air-gap magnetic flux density harmonics were obtained, respectively, as the pole pair number |k±jN. s | Rotation speed Polar number |m±jN s| Rotation speed Extreme logarithm | 2np r +k±jN s | Rotation speed Extreme logarithm | 2np r -k±jN s | Rotation speed Extreme logarithm | 2np r +m±jN s | Rotation speed Extreme logarithm | 2np r -m±jN s | Rotation speed Twelve different harmonics. Based on the condition that a difference of one pole pair in the number of pole pairs will produce levitation force pulsation at different speeds, the harmonic orders that produce levitation force pulsation that meet this condition are identified. The amplitude and phase of these harmonics are obtained using finite element software based on the specific motor parameters. By substituting the amplitude and phase of these harmonics into the levitation force pulsation expression, the numerical value of the levitation force pulsation can be calculated.

[0028] The beneficial effects that can be achieved by adopting the above technical solutions conceived in this invention are as follows:

[0029] Considering core saturation, this invention, based on the introduction of a saturation coefficient, takes into account the interaction of the fundamental and harmonic waves of the permanent magnet magnetic field, the torque armature magnetic field, and the levitation armature magnetic field with the final air gap permeability, thus obtaining a complete effective traveling wave pair of the air gap magnetic flux density in a bearingless permanent magnet synchronous motor. Traditional theories do not consider core saturation or the harmonics before and after armature reaction magnetic field modulation, missing some harmonic pairs that generate levitation force pulsations. However, considering core saturation significantly increases the levitation force pulsations generated by the bearingless permanent magnet synchronous motor. Core saturation has a significant impact on the levitation force pulsations of the bearingless permanent magnet synchronous motor. Therefore, this invention considers core saturation, introduces a saturation coefficient, derives a modified air gap permeability formula, and considers the fundamental and harmonic waves of the permanent magnet magnetic field, the torque armature magnetic field, and the levitation armature magnetic field, obtaining a complete set of harmonics that generate levitation force pulsations. Theoretically, this supplements and improves the existing magnetic field modulation theory analysis of the causes of levitation force pulsations in bearingless permanent magnet synchronous motors; in practical engineering applications, it can provide accurate feedback information for levitation force pulsation feedforward control. Attached Figure Description

[0030] Figure 1 A mathematical model of magnetomotive force established for parallel magnetization of the permanent magnet in this invention;

[0031] Figure 2 The mathematical model established for the air gap permeability of this invention does not consider core saturation;

[0032] Figure 3The mathematical model for the saturation coefficient is established to account for core saturation in this invention.

[0033] Figure 4 The 6-slot, 1-pole permanent magnet synchronous motor topology used as an example in this invention;

[0034] Figure 5 The levitation force waveform of a bearingless permanent magnet synchronous motor with 6 slots and 1 pole pair, considering armature magnetic field modulation harmonics.

[0035] Figure 6 The levitation force waveform of a bearingless permanent magnet synchronous motor with 6 slots and 1 pole pair, without considering armature magnetic field modulation harmonics.

[0036] Figure 7 This is a flowchart of the method of the present invention. Detailed Implementation

[0037] This embodiment provides a method for calculating the pulsation of motor levitation force considering the harmonic modulation of the armature magnetic field. It consists of five main steps: parallel magnetization of the permanent magnet, introducing a saturation coefficient to obtain the variable air gap permeability, obtaining the altered air gap magnetic flux density, Fourier decomposition of the air gap magnetic flux density, and obtaining the harmonics that generate cogging torque. The motor is as follows: Figure 4 The image shows a fractional-slot permanent magnet motor with 6 stator teeth and 1 pair of poles.

[0038] 1. The permanent magnet is magnetized in parallel, and the magnetomotive force is a perfect sine wave, such as... Figure 1 As shown, Fourier decomposition of the magnetomotive force is not required; the magnetomotive force only has a fundamental wave, and the permanent magnet has one pole pair. The mathematical model of the magnetomotive force is:

[0039] F(θ,t)=Acosp r (ω r t-θ)

[0040] 2. Air gap permeability without considering core saturation, such as Figure 2 As shown, N s The value is 6. The mathematical model after Fourier decomposition:

[0041]

[0042] Considering the variation in air gap permeability after core saturation, a saturation coefficient is introduced, such as... Figure 3 As shown. The saturation coefficient after Fourier decomposition is:

[0043]

[0044] The final air gap permeability is the product of the original permeability and the saturation coefficient:

[0045]

[0046] 3. Determine that the fundamental and harmonic waves of the permanent magnet magnetic field, the torque armature magnetic field, and the levitation armature magnetic field all interact with the final air gap magnetic permeability mentioned above, thereby obtaining a complete harmonic pair that forms the levitation force pulsation;

[0047] 4. The air gap magnetic flux density B is equal to the product of the permanent magnet magnetomotive force F and the air gap magnetic permeability P:

[0048]

[0049] 5. Fourier decomposition of the unloaded air gap magnetic flux density:

[0050]

[0051] Fourier decomposition of the air gap magnetic flux density of the armature reaction:

[0052]

[0053] 6. By performing Fourier decomposition of the unloaded air gap magnetic flux density, the pole pair number and rotation speed of different unloaded air gap magnetic flux density harmonics are obtained, and N is then... s =6, p r Substituting 1 into the equation, we obtain the harmonics as the pole pair number |1±j6| and the rotational speed. Number of pole pairs |(2n+1)±j6|, rotational speed Number of pole pairs |(2n-1)±j6j, rotational speed Six different harmonics. Through Fourier decomposition of the air-gap magnetic flux density of the armature reaction magnetic field, the pole pair number and rotational velocity of the different harmonics of the air-gap magnetic flux density of the armature reaction magnetic field were obtained, namely, the pole pair number |k±j6|, and the rotational velocity... Number of pole pairs |m±j6|, rotational speed Number of pole pairs |2n+k±j6|, rotational speed Number of pole pairs |2n-k±j6|, rotational speed Number of pole pairs |2n+m±j6|, rotational speed Number of pole pairs |2n-m±j6|, rotational speed 12 different harmonics.

[0054] The obtained harmonics are shown in Tables 1, 2, and 3 below.

[0055] Table 1 Harmonics generated when the magnetic field of the permanent magnet is modulated only by the stator slot.

[0056]

[0057] Table 2 Harmonics generated by the magnetic field of permanent magnets being modulated only by the saturation coefficient

[0058] Harmonic order rotational speed 1 (1 is adjusted to 1 by the saturation coefficient 2) <![CDATA[ω r ]]> 3 (1 is adjusted to 3 by the saturation coefficient 2) <![CDATA[ω r ]]> 5 (1 is adjusted to 5 by a saturation coefficient of 4) <![CDATA[ω r ]]> 7 (1 is adjusted to 7 by the saturation coefficient of 6) <![CDATA[ω r ]]>

[0059] Table 3 Harmonics generated by the simultaneous modulation of the permanent magnet magnetic field by the stator slot and saturation coefficient.

[0060]

[0061]

[0062] Table 4 Harmonics generated when the magnetic field of the torque winding is modulated only by the stator slots

[0063]

[0064] Table 5 Harmonics generated when the magnetic field of the torque winding is modulated only by the saturation coefficient

[0065]

[0066] Table 6 Harmonics generated by the simultaneous modulation of the torque winding magnetic field by the stator slots and saturation coefficient

[0067]

[0068]

[0069] Table 7 Harmonics generated by the magnetic field of the levitation winding being modulated only by the stator slot.

[0070]

[0071] Table 8 Harmonics generated by the magnetic field of the levitation winding being modulated only by the saturation coefficient

[0072]

[0073] Table 9 Harmonics generated by the simultaneous modulation of the magnetic field of the levitation winding by the stator slot and saturation coefficient

[0074]

[0075]

[0076] Based on the condition that a difference of one pole pair in the number of pole pairs results in different rotational speeds and thus levitation force pulsations, the harmonic pairs that generate levitation force pulsations can be obtained from the table. By identifying the cause of levitation force pulsations after stator core saturation, and combining this with the finite element method data on the amplitude of each harmonic magnetic field, the complete levitation force pulsation can be calculated. Figure 5 As shown.

[0077] The calculation method in the document "An Analytical Method for Cogging Torque of a Permanent Magnet Motor Considering Core Saturation (Application No. 202411209146.7)" does not consider armature magnetic field modulation harmonics, that is, it ignores the harmonic pairs in Tables 4 to 9, resulting in inaccurate levitation force pulsation waveforms, such as... Figure 6 As shown.

Claims

1. A method for calculating motor levitation force pulsation considering torque armature magnetic field modulation harmonics, characterized in that, Includes the following steps: Considering the saturation of the iron core, the air gap permeability and the magnetomotive force F of the permanent magnet PM Multiplying yields the unloaded air gap magnetic flux density B. PM ; Considering the air gap permeability and armature winding magnetomotive force F of the core saturation S Multiplying yields the armature reaction air gap magnetic flux density B. S ; For the unloaded air gap magnetic flux density B PM Fourier decomposition was performed to obtain the number of pole pairs and rotational speed of different unloaded air gap magnetic flux density harmonics, which are respectively the number of pole pairs. Rotation speed Extreme logarithm Rotation speed Extreme logarithm Rotation speed There are a total of six different harmonics; among them, The number of rotor pole pairs, The number of stator slots Where n is the rotor mechanical angular frequency, and n is the saturation coefficient harmonic order; For armature reaction air gap magnetic flux density B S Fourier decomposition was performed to obtain the pole pair number and rotational velocity of the air gap magnetic flux density harmonics of different armature reaction magnetic fields, which are respectively the pole pair number. Rotation speed Extreme logarithm Rotation speed Extreme logarithm Rotation speed Extreme logarithm Rotation speed Extreme logarithm Rotation speed Extreme logarithm Rotation speed There are a total of 12 different harmonics; where m and k represent integers from 0 to positive infinity. Based on the condition that a difference of one pole pair in the number of pole pairs will produce levitation force pulsation due to different rotational speeds, we find the harmonic order that produces levitation force pulsation that meets this condition. Based on the motor parameters, we use finite element software to obtain the amplitude and phase of the harmonics. We then substitute the amplitude and phase of the harmonics into the levitation force pulsation expression to calculate the value of the levitation force pulsation.

2. The method for calculating motor levitation force pulsation considering torque armature magnetic field modulation harmonics according to claim 1, characterized in that, For the unloaded air gap magnetic flux density B PM Fourier decomposition yields: ； Where A is the magnetomotive force amplitude. The magnitude of magnetic permeability. For the saturation coefficient constant term, The phase angle of the magnetomotive force. t represents the amplitude of each saturation coefficient harmonic, and t is time.

3. The method for calculating motor levitation force pulsation considering torque armature magnetic field modulation harmonics according to claim 1, characterized in that, Fourier decomposition of the armature reaction air gap magnetic flux density yields: ； in, The magnitude of magnetic permeability. For the saturation coefficient constant term, The phase angle of the magnetomotive force. t represents the amplitude of each saturation coefficient harmonic, and t is time.

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