A motor eccentric unbalance magnetic pull model construction method and compensation control system

Abstract

The application discloses a construction method of a motor eccentric unbalance magnetic pull model and a compensation control system, adopts a six-tooth one-pole motor structure; first, a stator and rotor coordinate system of the six-tooth one-pole motor and a coordinate conversion relationship are established; the rotor eccentricity is regarded as a perturbation, a sub-domain equation and a boundary equation of a permanent magnet and an air gap are established; zero-order and first-order solutions of the air gap sub-domain and radial and tangential magnetic densities when the rotor is eccentric are obtained; according to a slotting modulation ratio, each required parameter of the six-tooth one-pole motor is calculated; the slotting modulation ratio is introduced into the radial and tangential magnetic density calculation when the rotor is eccentric for the first time, and the radial and tangential magnetic densities when the rotor is eccentric considering the slotting influence are reconstructed; according to a Maxwell stress tensor method, accurate values of the unbalance magnetic pull of the sheet motor considering the slotting influence are solved. The application makes up for the deficiency of a traditional unbalance magnetic pull mathematical model applied in the sheet motor, and improves the accuracy of the unbalance magnetic pull mathematical model.

Description

Technical Field

[0001] The present invention relates to the technical field of bearingless motor control, and mainly relates to a method for constructing a motor eccentric unbalanced magnetic pull model based on a slot modulation effect and a compensation control system. Background Art

[0002] Due to its special structure without mechanical bearings, the thin-film motor has very high requirements for whether the rotor can be suspended smoothly and without eccentricity in the center position. The unbalanced magnetic pull of the motor has a great influence on the performance of the motor's radial suspension. Therefore, accurately analyzing the eccentric unbalanced magnetic pull of the thin-film permanent magnet synchronous motor and compensating for it has become a major factor affecting whether the thin-film motor can be suspended with high quality.

[0003] The document "Dorrell DG, Smith A C. Calculation and measurement of unbalanced magnetic pull in cage induction motors with eccentric rotors. IEE Proceedings Electric Power Applications, 1996, 143(3): 193-210." uses a one-dimensional analytical method as the basis. By establishing a rotor magnetomotive force model and combining it with an air gap permeability model, the magnetic field distribution of a permanent magnet motor with eccentricity is obtained in a simple and intuitive manner. However, different rotor eccentricity types, such as static eccentricity and dynamic eccentricity, are not distinguished, and only a qualitative analysis of the unbalanced magnetic pull can be performed. The literature

[12] Dorrell DG, Hsieh MF, Guo YG. Unbalanced Magnet Pull in Large Brushless Rare-Earth Permanent Magnet Motors with Rotor Eccentricity. IEEE Transactions on Magnetics, 2009, 45(10): 4586-4589. derived an unbalanced magnetic pull model to distinguish between dynamic and static eccentricity in permanent magnet motors, improving the model accuracy. However, it focused on analyzing the harmonic characteristics of the unbalanced magnetic pull and ignored the high-precision quantitative analysis of the unbalanced magnetic pull. The analysis in the above articles is based on one-dimensional analysis. The model accuracy is not high enough and is only suitable for qualitative analysis of the unbalanced magnetic pull. When used to analyze the magnitude of the unbalanced magnetic pull, the error is large.

[0004] In addition, the literature "

[15] Zhu ZQ, Howe D, Bolte E, Ackermann B. Instantaneous Magnetic Field Distribution in Brushless Permanent Magnet dc Motors. IEEE Transactions on Magnetics, 1993, 29(1): 124-158." uses the subdomain method as the basis to establish a two-dimensional magnetic field distribution analytical model for permanent magnet motors, realizing the transformation of motor analysis from one-dimensional to two-dimensional. In the literature "Li Y, Lu Q, Zhu ZQ. Unbalanced magnetic force prediction in permanent magnet machines with rotor eccentricity by improved superposition method. Iet Electric Power Applications, 2017, 11(6): 1095-1104.", the subdomain superposition method is used to equate the eccentric magnetic field to the superposition of multiple concentric magnetic fields, but no specific analytical formula is given. Subsequently, domestic and foreign scholars combined the first-order perturbation method with the subdomain method to establish an analytical model of the eccentric magnetic field of surface-mounted permanent magnet motors and plug-in permanent magnet motors, improving the analytical accuracy. For ease of analysis, the above models do not consider the influence of stator slots. When performing quantitative analysis on traditional motors with bearings, which have relatively simple eccentricity, the accuracy is acceptable. However, when used for bearingless thin-film motors with complex and changeable eccentricity, the error caused by the slots is difficult to ignore.

[0005] In the paper "Yu Jikun, Li Liyi, Zhang Jiangpeng, Cao Jiwei. Analytical calculation of air gap ratio permeance of stator slotted permanent magnet synchronous motor. Transactions of China Electrotechnical Society, 2016, 31(S1):45-52", the analysis and research of slot modulation effect only focused on the influence of slot on positioning torque, the influence of slot on modulation torque and the influence of slot on air gap permeability ratio, without involving the influence of slot on unbalanced magnetic field force and accurate modeling. Summary of the Invention

[0006] Purpose of the invention: In response to the problems existing in the above-mentioned background technology, the present invention provides an accurate mathematical model of unbalanced magnetic pull taking into account the influence of stator slots, analyzes the generation mechanism of unbalanced magnetic pull during eccentricity from the perspective of magnetic field modulation, and reconstructs the eccentric unbalanced magnetic pull of the motor taking into account the influence of slots. Compared with the traditional unbalanced magnetic pull mathematical model, this model has higher accuracy and is more suitable for compensating for the unbalanced magnetic pull of thin-film motors.

[0007] Technical solution: To achieve the above purpose, the technical solution adopted by the present invention is:

[0008] A model for the eccentric unbalanced magnetic pull of a motor based on the slot modulation effect employs a six-tooth, one-pole motor structure. The motor comprises six L-shaped stators. Each L-shaped stator consists of an axial stator yoke and radial stator teeth, surrounding a thin-film rotor. The radial stator teeth are flush with the rotor. Each axial stator yoke is wound with a suspension winding and a torque winding. The torque winding has one pair of poles, while the suspension winding has two pairs of poles, achieving both suspension and rotation control. The bottom of the L-shaped stator is connected to the core through a magnetic ring. A pair of permanent magnets is attached to the outside of the thin-film rotor. Based on this motor structure, a mathematical model for the unbalanced magnetic pull that takes into account the slot effect is constructed.

[0009] Specifically, first establish θ-O with the stator center as the coordinate origin s -r stator coordinate system, establish α-O with the rotor center as the coordinate origin r -β rotor coordinate system, such as Figure 1 As shown, where e is the eccentricity of the suspended rotor, is the eccentric angle of the motor rotor. The rotor rotates counterclockwise at the speed ω. p is any point on the rotor. θ is the angle between p and the horizontal coordinate of the stator coordinate system. ψ is the angle between p and the horizontal coordinate of the rotor coordinate system. From the geometric relationship, we can see that the transformation relationship between the two coordinate systems is shown in formula (1):

[0010]

[0011] According to the subdomain method, the subdomain equations of the permanent magnet and the air gap can be expressed in the form of formula (2):

[0012]

[0013] Where A Z1 With A Z2 are the vector magnetic potentials of the permanent magnet and the air gap subdomain, μ0 is the vacuum permeability, and its value is 4π*10 -7 H / m, M represents the magnetization intensity of the permanent magnet, in the rotor coordinate system

[0014]

[0015] According to the coordinate transformation formula (1), in the stator coordinate

[0016]

[0017] In the rotor coordinate system, α and β represent the radial and tangential unit vectors respectively, M α and M βRepresent the radial and tangential components of the permanent magnet magnetization intensity respectively. In the stator coordinate system, r and θ represent the radial and tangential unit vectors respectively. r and M θ Denote the radial and tangential components of the permanent magnet’s magnetization intensity, B R is the remanence of the permanent magnet.

[0018] Under the vector magnetic potential, the radial and tangential components of the magnetic flux density B and magnetic field intensity H can be expressed as

[0019]

[0020] Among them, μ r Represents relative magnetic permeability, H r and H θ are the radial and components of the magnetic field intensity H respectively.

[0021] According to the perturbation method, the rotor eccentricity is regarded as a perturbation, and the boundary equation of the interface between the permanent magnet and the rotor subdomain is obtained using formula (1):

[0022]

[0023] In the stator coordinate system, the normal vector equation of the boundary can be expressed as:

[0024]

[0025] Among them, e r and e θ are the radial and tangential unit components of the eccentricity e, respectively.

[0026] A pair of annular permanent magnets is used as the motor rotor. The interface under the eccentric state satisfies the following equation:

[0027]

[0028] Performing vector operations on equation (8) yields the following equation:

[0029]

[0030] According to the perturbation method, Equation (2) is substituted into Equation (9), and when r = R m Expanding at , we can get the zero-order equation (10) and the boundary condition (11)

[0031]

[0032]

[0033] According to the boundary conditions, separation of variables method and model symmetry, the zero-order and first-order solutions of the air gap subdomain are

[0034]

[0035] According to the perturbation theory, the radial and tangential magnetic flux densities when the rotor is eccentric are:

[0036]

[0037] In summary, combined with equations (12) and (13), we can obtain the air gap flux density after a pair of pole annular permanent magnet rotor is eccentric:

[0038]

[0039] Assume that the air gap magnetic flux density before and after the motor is slotted is B slotloss and B slot , are all plural forms, and their expressions are

[0040]

[0041] Among them, B rslotloss and B θslotloss They are the radial and tangential magnetic flux density before slotting, B rslot and B θslot are the radial and tangential flux densities after slotting, respectively. The slot modulation ratio ξ(r,θ) is defined to describe the effect of stator slotting at any position on the air gap flux density, denoted as ξ, and its expression is:

[0042]

[0043] The specific expression of the slot modulation ratio is shown in formula (38):

[0044]

[0045] Where R1 is the inner diameter of the stator, R2 is the outer diameter of the rotor, α1 is the stator slot width, α2 is the stator slot width, cn(z|k 2 )、dn(z|k 2 )、sn(z|k 2 )、K(k1 2 ) are three Jacobi elliptic functions and the first kind complete elliptic integral respectively. The values ​​of z, k and w can be confirmed by equations (18) and (19):

[0046]

[0047] Where Z(z|k 2 ) is the Jacobi Zeta function.

[0048] According to the definition of slot modulation ratio, the eccentric air gap magnetic flux density considering the slot effect is:

[0049]

[0050] Furthermore, according to formula (20), the eccentric unbalanced magnetic pull considering the slotting effect can be obtained as

[0051]

[0052] The present invention also provides a motor displacement compensation control system, which adds the unbalanced magnetic pull model formula (6) in claim 1 to the displacement compensation control system. The specific process is as follows: a feedback displacement is detected by a displacement detection device, a given displacement is subtracted from the feedback displacement, and the displacement difference is input into a PI regulator to obtain a controllable suspension force; the detected displacement is substituted into formula (6) to obtain an unbalanced magnetic pull; the controllable suspension force is added to the unbalanced magnetic pull, and the resultant is divided by the suspension force coefficient to obtain a suspension current, and a three-phase inverter is used to realize a closed loop of the suspension current.

[0053] The precise mathematical model of unbalanced magnetic pull that takes into account the influence of stator slotting provided by the present invention has the following beneficial effects compared with existing models:

[0054] (1) By taking into account the influence of stator slotting, the accuracy of the unbalanced magnetic pull mathematical model is improved.

[0055] (2) When compensating for the unbalanced magnetic pull of the thin-film motor, the compensation effect is better than the traditional unbalanced magnetic pull mathematical model that ignores the influence of slotting.

[0056] (3) Since the unbalanced magnetic pull of the thin-film motor is accurately compensated, the control difficulty of the thin-film motor is reduced and the control cost is reduced.

[0057] (4) After accurately compensating for the unbalanced magnetic pull of the thin-film motor, the motor's suspension performance is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram of the stator and rotor coordinate system provided by the present invention;

[0059] Figure 2 This is an axial cross-sectional view of a six-tooth, one-pole, bearingless permanent magnet thin-film motor provided by the present invention;

[0060] Figure 3 is a fitting diagram of the unbalanced magnetic pull x-axis component in the simulation and the calculated value of the unbalanced magnetic pull x-axis component with the slot effect neglected and the slot effect considered provided by the present invention;

[0061] Figure 4 is a fitting diagram of the y-axis component of the unbalanced magnetic pull in the simulation and the calculated value of the y-axis component of the unbalanced magnetic pull with the slot effect neglected and the slot effect considered provided by the present invention;

[0062] Figure 5 is a fitting diagram of the unbalanced magnetic pull in the simulation and the calculated value of the unbalanced magnetic pull with the slotting effect neglected and the slotting effect considered provided by the present invention;

[0063] Figure 6 It is an unbalanced magnetic pull compensation system;

[0064] Figure 7 is the uncompensated displacement waveform;

[0065] Figure 8 It is a displacement waveform based on existing model compensation;

[0066] Figure 9 It is a displacement waveform based on the compensation of the model of the present invention. DETAILED DESCRIPTION

[0067] The present invention will be further described below with reference to the accompanying drawings. It should be understood that the embodiments described herein are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are also within the scope of protection of the present invention.

[0068] The present invention adopts Figure 2 The bearingless permanent magnet thin-film motor shown in the figure uses a six-teeth-per-pole motor structure and includes six L-shaped stators 2. Each L-shaped stator 2 consists of an axial stator yoke and radial stator teeth, surrounding a thin-film rotor. The radial stator teeth are flush with the rotor. Each axial stator yoke is wound with a suspension winding 4 and a torque winding 5. The torque winding has one pair of poles, and the suspension winding has two pairs of poles, achieving both suspension and rotation control. The bottom of the L-shaped stators is connected by an iron core magnetic ring 3. A pair of permanent magnets is attached to the outside of the thin-film rotor 1.

[0069] Specifically, first establish θ-O with the stator center as the coordinate origin s -r stator coordinate system, establish α-O with the rotor center as the coordinate origin r -β rotor coordinate system, such as Figure 1 As shown, where e is the eccentricity of the suspended rotor, is the eccentric angle of the motor rotor. The rotor rotates counterclockwise at the speed ω. p is any point on the rotor. θ is the angle between p and the horizontal coordinate of the stator coordinate system. ψ is the angle between p and the horizontal coordinate of the rotor coordinate system. From the geometric relationship, we can see that the transformation relationship between the two coordinate systems is shown in formula (1):

[0070]

[0071] According to the subdomain method, the subdomain equations of the permanent magnet and the air gap can be expressed in the form of formula (2):

[0072]

[0073] Where A Z1 With A Z2 are the vector magnetic potentials of the permanent magnet and the air gap subdomain, μ0 is the vacuum permeability, and its value is 4π*10 -7 H / m, M represents the magnetization intensity of the permanent magnet, in the rotor coordinate system

[0074]

[0075] According to the coordinate transformation formula (1), in the stator coordinate

[0076]

[0077] In the rotor coordinate system, α and β represent the radial and tangential unit vectors respectively, M α and M β Represent the radial and tangential components of the permanent magnet magnetization intensity respectively. In the stator coordinate system, r and θ represent the radial and tangential unit vectors respectively. r and M θ Denote the radial and tangential components of the permanent magnet’s magnetization intensity, B R is the remanence of the permanent magnet.

[0078] Under the vector magnetic potential, the radial and tangential components of the magnetic flux density B and magnetic field intensity H can be expressed as

[0079]

[0080] Among them, μ r Represents relative magnetic permeability, H r and H θ are the radial and components of the magnetic field intensity H respectively.

[0081] According to the perturbation method, the rotor eccentricity is regarded as a perturbation, and the boundary equation of the interface between the permanent magnet and the rotor subdomain is obtained using formula (1):

[0082]

[0083] In the stator coordinate system, the normal vector equation of the boundary can be expressed as:

[0084]

[0085] Among them, e r and e θ are the radial and tangential unit components of the eccentricity e, respectively.

[0086] A pair of annular permanent magnets is used as the motor rotor. The interface under the eccentric state satisfies the following equation:

[0087]

[0088] Performing vector operations on equation (8) yields the following equation:

[0089]

[0090] According to the perturbation method, Equation (2) is substituted into Equation (9), and when r = R m Expanding at , we can get the zero-order equation (10) and the boundary condition (11)

[0091]

[0092] According to the boundary conditions, separation of variables method and model symmetry, the zero-order and first-order solutions of the air gap subdomain are

[0093]

[0094] According to the perturbation theory, the radial and tangential magnetic flux densities when the rotor is eccentric are:

[0095]

[0096] In summary, combined with equations (12) and (13), we can obtain the air gap flux density after a pair of pole annular permanent magnet rotor is eccentric:

[0097]

[0098] Assume that the air gap magnetic flux density before and after the motor is slotted is B slotloss and B slot , are all plural forms, and their expressions are

[0099]

[0100] Among them, B rslotloss and B θslotloss They are the radial and tangential magnetic flux density before slotting, B rslot and B θslot are the radial and tangential flux densities after slotting, respectively. The slot modulation ratio ξ(r,θ) is defined to describe the effect of stator slotting at any position on the air gap flux density, denoted as ξ, and its expression is:

[0101]

[0102] The specific expression of the slot modulation ratio is shown in formula (17):

[0103]

[0104] Where R1 is the inner diameter of the stator, R2 is the outer diameter of the rotor, α1 is the stator slot width, α2 is the stator slot width, cn(z|k 2 )、dn(z|k 2 )、sn(z|k 2 )、K(k1 2 ) are three Jacobi elliptic functions and the first kind complete elliptic integral respectively. The values ​​of z, k and w can be confirmed by equations (18) and (19):

[0105]

[0106]

[0107] Where Z(z|k 2 ) is the Jacobi Zeta function.

[0108] According to the definition of slot modulation ratio, the eccentric air gap magnetic flux density considering the slot effect is:

[0109]

[0110] Furthermore, according to formula (20), the eccentric unbalanced magnetic pull considering the slotting effect can be obtained as

[0111]

[0112] To verify whether the derivation is correct, the unbalanced magnetic pulls in the x, y and resultant directions of the thin-film motor are simulated in the MAXWELL simulation, and are fitted with the theoretically derived values ​​to verify whether the theoretical derivation is correct.

[0113] Figure 3 is a fitting diagram of the unbalanced magnetic pull x-axis component in the simulation and the calculated value of the unbalanced magnetic pull x-axis component with the slotting effect neglected and the slotting effect considered provided by the present invention, Figure 4 is a fitting diagram of the unbalanced magnetic pull force y-axis component in the simulation and the calculated value of the unbalanced magnetic pull force y-axis component with the slotting effect neglected and the slotting effect considered provided by the present invention, Figure 5 This is a fitting diagram of the unbalanced magnetic pull in the simulation and the calculated value of the unbalanced magnetic pull with the slot effect ignored and the slot effect considered provided by the present invention. From the comparison of several figures, it can be seen that the accurate mathematical model of the unbalanced magnetic pull with the stator slot effect considered provided by the present invention is

[0114] (1) The simulated values ​​of the x-axis and y-axis components of the unbalanced magnetic pull are basically consistent with the theoretically derived values, verifying the correctness of the constructed model.

[0115] (2) The theoretical value of the unbalanced magnetic pull when the slotting effect is ignored is the largest, which is about 5.2% larger than the simulation value.

[0116] (3) The theoretical value of the unbalanced magnetic pull considering the effect of slotting is closest to the simulation value, which is about 0.5% larger than the simulation value.

[0117] (4) The eccentric unbalanced magnetic pull of the slotted thin-film motor is not a constant value. The theoretical value of the unbalanced magnetic pull when the slot effect is ignored is a constant value, while the theoretical value of the unbalanced magnetic pull when the slot effect is taken into account reflects this point, and the trend is basically consistent with the simulation value.

[0118] In summary, compared with the existing unbalanced magnetic force model that ignores the effect of slotting, the unbalanced magnetic force model proposed in this paper, which takes the effect of slotting into account, reduces the error from 5.2% to about 0.5%, greatly improving the model accuracy and making it more suitable for thin-film motors with extremely high requirements for suspension accuracy.

[0119] Figure 6 To compensate for the control system, a displacement detection device detects the feedback displacement. The given displacement is subtracted from the feedback displacement, and the displacement difference is input into the PI regulator to obtain the controllable suspension force. The detected displacement is substituted into Equation (21) to obtain the unbalanced magnetic pull. The controllable suspension force is added to the unbalanced magnetic pull and divided by the suspension force coefficient to obtain the suspension current. A three-phase inverter is used to implement a closed loop for this suspension current.

[0120] Figure 7 When the unbalanced magnetic pull is not compensated, the displacement converges relatively slowly and the amplitude of the displacement fluctuation is relatively large, which seriously affects the suspension performance of the motor.

[0121] Figure 8 After adding unbalanced magnetic pull compensation to the existing model, the displacement convergence is accelerated and the amplitude of displacement fluctuation is significantly reduced compared to without compensation. However, the fluctuation still exists and its impact on the motor suspension performance is still not negligible.

[0122] Figure 9 After the unbalanced magnetic pull compensation is added to the model in this paper, the displacement converges faster and the displacement fluctuation is almost completely eliminated. Under ideal conditions, the impact of the unbalanced magnetic pull on the motor suspension performance can be ignored.

[0123] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for constructing an eccentric unbalanced magnetic pull model of a motor, wherein the motor adopts a six-tooth-one-pole structure, including six L-shaped stators, each L-shaped stator including an axial stator yoke and radial stator teeth, surrounding a thin-sheet rotor, with the radial stator teeth flush with the rotor, and each axial stator yoke is wound with a suspension winding and a torque winding, respectively, the torque winding is a pair of poles, and the suspension winding is two pairs of poles, achieving suspension control and rotation control at the same time; the bottom of the L-shaped stator is connected by an iron core magnetic ring; the outer side of the thin-sheet rotor is affixed with a pair of permanent magnets; characterized in that The construction method comprises the following steps: Step 1: Take the stator center O s Establish θ-O as the coordinate origin s -r stator coordinate system, r and θ represent radial and tangential unit vectors respectively, with the rotor center O r Establish α-O for the coordinate origin r -β rotor coordinate system, α and β represent radial and tangential unit vectors respectively; the coordinate transformation formula of the two coordinate systems is Where e is the eccentricity of the suspended rotor, is the eccentricity angle of the motor rotor. The rotor rotates counterclockwise at the speed ω. p is any point on the rotor. θ is the angle between p and the horizontal coordinate of the stator coordinate system. ψ is the angle between p and the horizontal coordinate of the rotor coordinate system. Step 2: Define the slot modulation ratio ξ(r,θ) to describe the effect of stator slots at any position on the air gap flux density, denoted as ξ, and its expression is B slotloss and B slot are the air gap flux density before and after the motor is slotted, both in plural form; According to B slotloss and B slot The expression of formula (1) is modified as follows: Where R1 is the inner diameter of the stator, R2 is the outer diameter of the rotor, α1 is the stator slot width, α2 is the stator slot width, cn(z|k 2 )、dn(z|k 2 )、sn(z|k 2 )、K(k1 2 ) are three Jacobi elliptic functions and the first kind of complete elliptic integral respectively; the values ​​of z, k and w are confirmed by equations (3) and (4) Where Z(z|k 2 ) is the Jacobi Zeta function; Step 3: When the stator is not slotted, the air gap flux density of a pair of pole-circular permanent magnet rotors after eccentricity is obtained according to the subdomain method and the first-order perturbation method. Where r is the air gap radius, B r and B θ are the radial and tangential components of the air gap flux density, e, ω, μ r are the rotor eccentricity distance, rotor speed, rotor eccentricity angle and relative magnetic permeability of permanent magnet respectively, Rs, Rm and Rr are the stator inner diameter, rotor outer diameter and rotor inner diameter respectively; According to the definition of slot modulation ratio, the radial component and tangential component of the eccentric air gap flux density considering the slot effect are: According to formula (6), the eccentric unbalanced magnetic pull model considering the slotting effect is:

2. The method for constructing a motor eccentric unbalanced magnetic pull model according to claim 1, characterized in that: The calculation steps of the air gap flux density before and after the motor is slotted include: Based on the stator and rotor coordinate system, the subdomain method and the first-order perturbation method are used to treat the rotor eccentricity as a perturbation, and the subdomain equations and boundary equations of the permanent magnet and the air gap are established. According to the perturbation theory, the zero-order and first-order solutions of the air gap subdomain are obtained, and the radial and tangential magnetic flux densities when the rotor is eccentric are further obtained.

3. The method for constructing a motor eccentric unbalanced magnetic pull model according to claim 2, characterized in that: Based on the stator and rotor coordinate systems, the subdomain method and the first-order perturbation method are used to treat the rotor eccentricity as a perturbation, and the subdomain equations and boundary equations of the permanent magnet and air gap are established, including: According to the subdomain method, the subdomain equations of the permanent magnet and the air gap are expressed in the form of formula (8): Where A Z1 With A Z2 They are the vector magnetic potentials of the permanent magnet and the air gap subdomain, μ0 is the vacuum permeability, M represents the magnetization intensity of the permanent magnet, and in the rotor coordinate system According to the coordinate transformation formula, under the stator coordinate In the rotor coordinate system, M α and M β They represent the radial and tangential components of the permanent magnet’s magnetization intensity, respectively. In the stator coordinate system, M r and M θ Denote the radial and tangential components of the permanent magnet’s magnetization intensity, B R is the remanence of the permanent magnet; Under the vector magnetic potential, the radial and tangential components of the magnetic flux density B and magnetic field intensity H are expressed as Among them, μ r Represents relative magnetic permeability, H r and H θ are the radial and components of the magnetic field intensity H respectively; According to the perturbation method, the rotor eccentricity is regarded as a perturbation, and the coordinate transformation formula is used to obtain the boundary equation of the interface between the permanent magnet and the rotor subdomain: In the stator coordinate system, the normal vector equation of the boundary is expressed as: Among them, e r and e θ are the radial and tangential unit components of the eccentricity e, respectively.

4. The method for constructing a motor eccentric unbalanced magnetic pull model according to claim 3, characterized in that: According to the perturbation theory, the zero-order and first-order solutions of the air gap subdomain are obtained, and the radial and tangential magnetic flux densities when the rotor is eccentric are further obtained, including: Taking a pair of annular permanent magnets as the motor rotor, the interface in the eccentric state satisfies the following equation: Performing vector operations on equation (14) yields the following equation: According to the perturbation method, Equation (13) is substituted into Equation (15), and when r = R m Expanding at , we get the zero-order equation (16) and the boundary condition (17) According to the boundary conditions, separation of variables method and model symmetry, the zero-order and first-order solutions of the air gap subdomain are According to the perturbation theory, the radial and tangential magnetic flux densities when the rotor is eccentric are: Combining equations (18) and (19), the air gap flux density after a pair of pole annular permanent magnet rotor is eccentric is obtained as follows:

5. A motor displacement compensation control system, characterized in that: The unbalanced magnetic pull model formula (6) in claim 1 is added to the displacement compensation control system. The specific process is as follows: the feedback displacement is detected by a displacement detection device, the given displacement is subtracted from the feedback displacement, and the displacement difference is input into a PI regulator to obtain a controllable suspension force; the detected displacement is substituted into formula (6) to obtain an unbalanced magnetic pull; the controllable suspension force is added to the unbalanced magnetic pull, and the resultant is divided by the suspension force coefficient to obtain a suspension current, and a three-phase inverter is used to realize a closed loop of the suspension current.

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