Motor suspension force pulsation calculation method considering torque armature magnetic field modulation harmonic waves

Abstract

The invention discloses a motor suspension force pulsation calculation method considering a torque armature magnetic field modulation harmonic wave, and the method comprises the steps: firstly, after an iron core is saturated, air gap magnetic conductance varies, a saturation coefficient is introduced, and a modulation unit is converted from stator slot independent modulation to stator slot and saturation coefficient combined modulation, thereby changing the harmonic wave component of air gap flux density; secondly, on the premise of introducing the saturation coefficient, the influence of a permanent magnetic field, torque armature magnetic field fundamental waves and harmonic waves and suspension armature magnetic field fundamental waves and harmonic waves is completely considered, the effective traveling wave pair of the air gap flux density of the bearingless permanent magnet synchronous motor can be completely determined, and then the traveling wave pair generating suspension force pulsation can be accurately obtained. The number of harmonic pole pairs and the rotating speed after the air gap flux density is changed are determined through Fourier decomposition, the traveling wave pair generating the suspension force pulsation is found according to the condition that the number of the pole pairs differs by a pair of poles and the rotating speed is different to generate the suspension force pulsation, and an existing method for analyzing the suspension force pulsation of the bearingless permanent magnet synchronous motor is effectively supplemented.

Description

Technical Field

[0001] The invention belongs to the technical field of motor body design, and in particular relates to a method for analyzing suspension force pulsation of a bearingless permanent magnet synchronous motor. Background Art

[0002] The bearingless permanent magnet synchronous motor is a new type of motor that combines magnetic levitation technology with a permanent magnet synchronous motor. Compared with traditional permanent magnet motors, it has the characteristics of long service life, no mechanical friction, high efficiency, high power density, etc. It has important application value in high-tech fields such as life sciences, aerospace, centrifuges, and semiconductor industries.

[0003] In order to realize active suspension of the motor, two sets of torque and suspension windings are added to the stator slots of the bearingless permanent magnet synchronous motor. The addition of the suspension winding will not only increase the thermal load of the motor, but also increase the coupling degree of the air gap magnetic field because the torque magnetic field and the suspension magnetic field have the same magnetic flux path, which makes it difficult to decouple the electromagnetic torque and the suspension force, further affecting the reliable operation of the motor. Therefore, in order to achieve high torque and high suspension performance of the bearingless permanent magnet synchronous motor, it is particularly important to accurately mathematically model the suspension force model of the bearingless permanent magnet synchronous motor.

[0004] In recent years, with the emergence of magnetic field modulation motors, a new motor theory corresponding to it, the magnetic field modulation theory, has attracted widespread attention from scholars. At first, the magnetic field modulation theory was only applied to a few special motors such as magnetic gear motors, vernier motors, reverse flux motors, and magnetic field modulation dual-rotor motors. Later, scholars gradually discovered that many magnetic problems in traditional motors can be explained by the principle of magnetic field modulation. As a result, a new motor research theory based on the principle of magnetic field modulation has been developed, providing new ideas for the design and analysis of traditional motors.

[0005] In 2011, Li Jingcan and Liao Yong from Chongqing University published a paper titled "Permanent Magnet Synchronous Motor Model Considering Saturation and Rotor Magnetic Field Harmonics" in the Proceedings of the Chinese Society of Electrical Engineering. They considered the influence of core saturation and rotor magnetic field harmonics and established a dq axis nonlinear model of permanent magnet synchronous motor based on finite element. However, in order to simplify the problem, the model only considered the influence of saturation on d and q axis inductance and fundamental flux of rotor permanent magnet, and ignored the influence of saturation on harmonic flux. Moreover, the nonlinear mathematical model is a variable coefficient differential equation, and the inductance and flux in the equation need to be processed by table lookup, and there are also complex matrix operations. Therefore, the saturation mathematical model analysis method of permanent magnet synchronous motor still has defects and cannot be applied to the theoretical analysis of suspension force pulsation of bearingless permanent magnet synchronous motor.

[0006] The document "An analytical method for cogging torque of permanent magnet motor considering core saturation (application number 202411209146.7)" has taken into account 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. If the suspension force pulsation is calculated according to this idea, the calculation will be inaccurate because the torque armature magnetic field modulation harmonics are not considered. Summary of the invention

[0007] In order to solve the problems mentioned in the above background technology, the purpose of the present invention is to provide a method for calculating the motor suspension force pulsation taking into account the torque armature magnetic field modulation harmonics. Under the premise of introducing the saturation coefficient, the influence of the permanent magnet magnetic field, the torque armature magnetic field fundamental wave and harmonics, and the suspension armature magnetic field fundamental wave and harmonics are fully considered. The effective traveling wave pairs of the air gap magnetic flux of the bearingless permanent magnet synchronous motor can be fully determined, and then the traveling wave pairs that generate the suspension force pulsation can be accurately obtained.

[0008] The purpose of the present invention can be achieved through the following technical solutions:

[0009] A method for calculating the pulsation of motor suspension force considering the torque armature magnetic field modulation harmonics is divided into six main steps: parallel magnetization of permanent magnets, introduction of saturation coefficient to obtain variable air gap magnetic permeability, determination of permanent magnet magnetic field, torque armature magnetic field fundamental wave and harmonics, suspension armature magnetic field fundamental wave and harmonics as sources of harmonic pairs, obtaining the changed air gap magnetic density, Fourier decomposition of the air gap magnetic density, and obtaining the harmonic pairs that generate suspension force pulsation.

[0010] 1. The permanent magnets are magnetized in parallel, and the magnetomotive force is perfectly sinusoidal. 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 after Fourier decomposition of air gap permeability without considering core saturation:

[0013]

[0014] Considering the variation of air gap permeability after core saturation, the saturation coefficient after Fourier decomposition is introduced:

[0015]

[0016] The final air gap permeability is the original permeability multiplied by the saturation coefficient:

[0017]

[0018] 3. Determine that the permanent magnetic field, the fundamental wave and harmonics of the torque armature magnetic field, and the fundamental wave and harmonics of the suspension armature magnetic field all interact with the above-mentioned final air gap permeability, thereby obtaining a complete harmonic pair that forms the suspension force pulsation; 4. No-load air gap magnetic density B PM Equal to the permanent magnet magnetomotive force F PM The product of the air gap permeability P is:

[0019]

[0020] Armature reaction air gap sub-dense B S Equal to the armature winding magnetomotive force F S The product of the air gap permeability P is:

[0021]

[0022] 5. Perform Fourier decomposition on the no-load air gap magnetic flux density:

[0023]

[0024] Perform Fourier decomposition on the armature reaction air gap flux density:

[0025]

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

[0027] 6. Through Fourier decomposition of the no-load air gap magnetic flux, the harmonic pole pairs and rotation speed of the no-load air gap magnetic flux are obtained, which are pole pairs|p r ±jN s |, rotation speed Pole pair number|(2n+1)p r ±jN s |, rotation speed Pole pairs|(2n-1)p r ±jN s |, rotation speed Six different harmonics. By Fourier decomposition of the armature reaction magnetic field air gap flux density, different armature reaction magnetic field air gap flux density harmonic pole pairs and rotation speeds are obtained, which are pole pairs | k ± j N s |, rotation speed Pole pairs|m±jN s|, rotation speed Pole pairs|2np r +k±jN s |, rotation speed Pole pairs|2np r -k±jN s |, rotation speed Pole pairs|2np r +m±jN s |, rotation speed Pole pairs|2np r -m±jN s |, rotation speed 12 different harmonics. According to the difference of one pole pair in the number of poles, different speeds will produce the condition of suspension force pulsation. Find the harmonic order that produces suspension force pulsation that meets this condition, and use finite element software to obtain the amplitude and phase of these harmonics according to the specific motor parameters. Substitute the amplitude and phase of these harmonics into the suspension force pulsation expression to calculate the value of suspension force pulsation.

[0028] By adopting the above technical solution conceived by the present invention, the beneficial effects that can be achieved are as follows:

[0029] Considering the core saturation, on the basis of introducing the saturation coefficient, the interaction between the permanent magnetic field, the fundamental wave and harmonics of the torque armature magnetic field, and the fundamental wave and harmonics of the suspension armature magnetic field and the final air gap permeability is considered, and the effective traveling wave pair of the air gap magnetic density of the bearingless permanent magnet synchronous motor is completely obtained. The traditional theory does not consider the core saturation and the harmonics before and after the armature reaction magnetic field modulation, and misses some harmonic pairs that produce suspension force pulsation. After considering the core saturation, the suspension force pulsation generated by the bearingless permanent magnet synchronous motor is significantly increased. The core saturation will have an important impact on the suspension force pulsation of the bearingless permanent magnet synchronous motor. Therefore, the present invention considers the core saturation, introduces the saturation coefficient, and introduces the variant air gap permeability formula, considering the permanent magnetic field, the fundamental wave and harmonics of the torque armature magnetic field, and the fundamental wave and harmonics of the suspension armature magnetic field, and obtains the complete harmonics that produce the suspension force pulsation. In theory, it is a supplement and improvement to the existing magnetic field modulation theory to analyze the cause of the suspension force pulsation of the bearingless permanent magnet synchronous motor; in practical engineering applications, it can provide accurate feedback information for the suspension force pulsation feedforward control. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0032] Figure 3The present invention considers the saturation of the core and establishes a mathematical model for the saturation coefficient;

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

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

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

[0036] Figure 7 The present invention is a flow chart of the method. DETAILED DESCRIPTION

[0037] This embodiment provides a method for calculating the pulsation of the motor suspension force considering the torque armature magnetic field modulation harmonics, which is divided into five main steps: parallel magnetization of permanent magnets, introduction of saturation coefficient to obtain variable air gap permeance, obtaining the changed air gap flux density, Fourier decomposition of the air gap flux density, and obtaining the harmonics that generate the cogging torque. Figure 4 The figure shows a fractional-slot permanent magnet motor with 6 stator teeth and 1 pair of poles.

[0038] 1. The permanent magnets are magnetized in parallel, and the magnetomotive force is perfectly sinusoidal, such as Figure 1 As shown, there is no need to perform Fourier decomposition on the magnetomotive force. The magnetomotive force only has the fundamental wave, and the permanent magnet has one pair of poles. The mathematical model of the magnetomotive force is:

[0039] F(θ,t)=Acosp r (ω r t-θ)

[0040] 2. Ignoring the air gap permeability of the core saturation, Figure 2 As shown, N s is 6. The mathematical model after Fourier decomposition:

[0041]

[0042] Considering that after the core is saturated, the air gap permeability changes, the 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 original permeability multiplied by the saturation coefficient:

[0045]

[0046] 3. Determine that the permanent magnetic field, the fundamental wave and harmonics of the torque armature magnetic field, and the fundamental wave and harmonics of the suspension armature magnetic field all interact with the above-mentioned final air gap permeability, so as to obtain a complete harmonic pair that forms the suspension 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. Perform Fourier decomposition on the no-load air gap magnetic flux density:

[0050]

[0051] Perform Fourier decomposition on the armature reaction air gap flux density:

[0052]

[0053] 6. Through Fourier decomposition of the no-load air gap magnetic flux, we can obtain the number of harmonic pole pairs and rotation speed of the no-load air gap magnetic flux. s =6, p r = 1 and substitute it into the equation, the harmonics are the pole pair number |1±j6|, the rotation speed Pole pair number |(2n+1)±j6|, rotation speed Pole pair number|(2n-1)±j6j, rotation speed Six different harmonics. By Fourier decomposition of the armature reaction magnetic field air gap magnetic flux density, different armature reaction magnetic field air gap magnetic flux density harmonic pole pairs and rotation speeds are obtained, which are pole pairs |k±j6|, rotation speed Pole pairs |m±j6|, rotation speed Pole pair number |2n+k±j6|, rotation speed Pole pair number |2n-k±j6|, rotation speed Pole pair number |2n+m±j6|, rotation speed Pole pair number |2n-m±j6|, rotation speed 12 different harmonics.

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

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

[0056]

[0057] Table 2 Harmonics generated by permanent magnet magnetic field modulated only by saturation coefficient

[0058] Harmonic order Speed 1 (1 is adjusted to 1 by the saturation factor 2) <![CDATA[ω r ]]> 3 (1 is adjusted to 3 by the saturation factor 2) <![CDATA[ω r ]]> 5 (1 is adjusted to 5 by the saturation factor 4) <![CDATA[ω r ]]> 7 (1 is adjusted to 7 by the saturation factor 6) <![CDATA[ω r ]]>

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

[0060]

[0061]

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

[0063]

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

[0065]

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

[0067]

[0068]

[0069] Table 7 Harmonics generated when the magnetic field of the suspended winding is modulated only by the stator slots

[0070]

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

[0072]

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

[0074]

[0075]

[0076] According to the conditions of suspension force pulsation caused by one pair of pole pairs and different rotation speed, the harmonic pairs that cause suspension force pulsation can be obtained in the table. The cause of suspension force pulsation after considering the saturation of the stator core is found, and the complete suspension force pulsation is calculated by combining the data of the harmonic magnetic field amplitude of the finite element, such as Figure 5 shown.

[0077] However, the calculation method of the document "An analytical method for the cogging torque of a permanent magnet motor considering core saturation (application number 202411209146.7)" does not consider the armature magnetic field modulation harmonics, that is, it ignores the harmonic pairs in Tables 4 to 9, and obtains an inaccurate suspension force pulsation waveform, such as Figure 6 shown.

Claims

1. A method for calculating the pulsation of motor suspension force considering the harmonics of torque armature magnetic field modulation, characterized in that: The steps include: The air gap permeability considering the core saturation and the permanent magnet magnetomotive force F PM Multiply to get the no-load air gap magnetic flux B PM ; The air gap permeability considering the core saturation and the armature winding magnetomotive force F S Get the armature reaction air gap density B S ; The no-load air gap magnetic flux density B PM Perform Fourier decomposition to obtain different no-load air gap magnetic flux harmonic pole pairs and rotation speeds; Air gap for armature reaction is sub-dense B S Perform Fourier decomposition to obtain the harmonic pole pairs and rotation speed of different armature reaction magnetic fields; According to the condition that the suspension force pulsation will occur when the pole pair number differs by one pair and the rotation speed is different, the harmonic order that produces the suspension force pulsation that meets this condition is found, and the amplitude and phase of these harmonics are obtained using finite element software according to the specific motor parameters. The amplitude and phase of these harmonics are substituted into the suspension force pulsation expression to calculate the value of the suspension force pulsation.

2. The method for calculating the motor suspension force pulsation considering the torque armature magnetic field modulation harmonic according to claim 1 is characterized in that: The no-load air gap magnetic flux density B PM Perform Fourier decomposition to obtain: Where A is the magnetomotive force amplitude, P j is the permeability amplitude, N s is the number of stator slots, a0 is the saturation coefficient constant, P r is the number of rotor pole pairs, ω r is the rotor mechanical angular frequency, θ is the magnetomotive force phase angle, a n is the amplitude of each saturation coefficient harmonic, n is the number of saturation coefficient harmonic, and t is time.

3. The method for calculating the motor suspension force pulsation considering the torque armature magnetic field modulation harmonics according to claim 1 is characterized in that: The armature reaction air gap flux density is decomposed by Fourier to obtain: Where A is the magnetomotive force amplitude, P j is the permeability amplitude, N s is the number of stator slots, a0 is the saturation coefficient constant, P r is the number of rotor pole pairs, ω r is the rotor mechanical angular frequency, θ is the magnetomotive force phase angle, a n is the amplitude of each saturation coefficient harmonic, n is the saturation coefficient harmonic number, t is time, and m and k represent integers from 0 to positive infinity.

4. The method for calculating the motor suspension force pulsation considering the torque armature magnetic field modulation harmonics according to claim 2 is characterized in that: By Fourier decomposition of the no-load air gap magnetic flux, the pole pairs and rotation speeds of different no-load air gap magnetic flux harmonics are obtained, which are pole pairs|p r ±jN s |, rotation speed Pole pair number|(2n+1)p r ±jN s |, rotation speed Pole pairs|(2n-1)p r ±jN s |, rotation speed Six different harmonics in total.

5. The method for calculating the motor suspension force pulsation considering the torque armature magnetic field modulation harmonics according to claim 3 is characterized in that: By Fourier decomposition of the armature reaction magnetic field air gap flux density, the pole pairs and rotation speed of different armature reaction magnetic field air gap flux density harmonics are obtained, which are pole pairs |k±jN s |, rotation speed Pole pairs|m±jN s |, rotation speed Pole pairs | 2np r +k±jN s |, rotation speed Pole pairs|2np r -k±jN s |, rotation speed Pole pairs|2np r +m±jN s |, rotation speed Pole pairs|2np r -m±jN s |, rotation speed 16 different harmonics in total.

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