Low-harmonic bidirectional integrated Lorentz force motor permanent magnet array, modeling method thereof and application of low-harmonic bidirectional integrated Lorentz force motor permanent magnet array to bidirectional Lorentz force motor

Abstract

The invention belongs to the related technical field of permanent magnet array electromagnetic modeling, and discloses a low-harmonic bidirectional integrated Lorentz force motor permanent magnet array, which comprises a vertical permanent magnet unit and a horizontal permanent magnet unit which are vertically aligned with each other, each of the vertical permanent magnet unit and the horizontal permanent magnet unit comprises a first permanent magnet unit and a second permanent magnet unit, and a gap between the first permanent magnet unit and the second permanent magnet unit is an air-gap magnetic field; the first permanent magnet unit comprises a first magnetized permanent magnet which is arranged according to a Halbach arrangement mode and is vertically arranged along the negative direction of the y-axis, a second magnetized permanent magnet which is horizontally arranged rightwards and a third magnetized permanent magnet which is vertically arranged along the positive direction of the y-axis, and the second magnetized unit and the first magnetized unit have the same structure and the same polarization direction; the invention also provides a modeling method of the permanent magnet array and a bidirectional Lorentz force motor. According to the invention, the problems of large electromagnetic force fluctuation and time-consuming calculation are solved for the force control of the bidirectional integrated Lorentz force motor.

Description

Technical Field

[0001] The present invention relates to the technical field related to electromagnetic modeling of permanent magnet arrays, and particularly relates to a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor, a modeling method thereof, and an application thereof to a bidirectional Lorentz force motor. Background Art

[0002] The characteristic dimensions of microfabrication technology have become smaller and smaller, gradually entering the sub-nanometer level from the nanometer level. The requirements for the motion accuracy, speed, acceleration, and motion degrees of freedom of the drive system of manufacturing equipment are also increasing day by day. Ultra-precision positioning platforms are required in more and more occasions. Such ultra-precision positioning platforms provide a load platform that can achieve ultra-precision positioning and precise motion for fields such as lithography technology, numerical control machining, biotechnology, and nano-surface topography measurement. Currently, the typical representative that embodies the highest achievements of nano-level ultra-precision positioning platforms is the lithography machine. Lorentz motors are mainly applied to precision and ultra-precision micro-vibration suppression, such as being applied to high-end lithography machines and scanning transmission electron microscopes to achieve vibration suppression and nano-level precision composite positioning. At the same time, they are widely applied in the field of precision machining (such as precision lathes), the medical field (such as magnetic resonance imagers), etc. Compared with traditional transmission methods, the system structure is simplified. It has advantages such as good linearity, fast response, high sensitivity, simple structure, and small inertia.

[0003] A Lorentz motor is a two-dimensional planar direct drive mechanism driven by a linear Lorentz force, and it is an important technology for ultra-precision positioning platforms. Conventional planar motion mechanisms mostly use a stacked structure of a traditional XY workbench to indirectly achieve planar positioning. For this type of planar motion mechanism composed of two or more directly driven linear motors, the complexity of the drive system is increased, resulting in high costs and large volumes. Moreover, there are a series of problems such as friction, backlash, and deformation in the linear motion conversion structure, making it difficult to be applied in precision vibration damping. The new type of planar motor directly generates planar motion using electromagnetic energy. Since the intermediate conversion device from rotational motion to linear motion and then to planar motion is omitted, the control object and the motor can be made into an integrated structure, simplifying the system structure. It has advantages such as good linearity, fast response, high sensitivity, simple structure, and small inertia. It is suitable for micro-vibration suppression and composite positioning of precision and ultra-precision equipment, and also has broad application prospects in other related fields.

[0004] In the prior art, real-time control mostly uses unidirectional output motors, and there are few motors that can simultaneously consider multi-directional output. For the micro-vibration suppression system of compact and ultra-precision equipment, to achieve multi-degree-of-freedom micro-vibration suppression and composite positioning, motors must be arranged in different directions. However, the more independent motors there are, the more complex the system becomes, and the more difficult it is to achieve composite positioning between the motors. At the same time, there are also technical problems such as short effective stroke, small bandwidth, high heat consumption, small output, poor linearity, and difficult heat dissipation of the motors. Therefore, with the development of motor technology, it is imperative and urgent to research and explore multi-directional integrated Lorentz force motors, as well as Lorentz force motors with large stroke, high bandwidth, low heat consumption, large output, small temperature rise, and high linearity.

[0005] The main application of existing Lorentz motors is voice coil motors. However, the application of voice coil motors is limited because their magnetic field distribution is not uniform. To prevent non-uniform magnetic field distribution from causing non-linear output, the operating stroke of voice coil motors is generally selected in the part with relatively uniform magnetic field distribution, resulting in a small operating stroke of voice coil motors and fluctuations between the expected Lorentz force and the actual Lorentz force. This greatly limits the application of voice coil motors and has become a problem in this field. Summary of the Invention

[0006] In view of the above defects or improvement requirements of the prior art, the present invention provides a modeling method for a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor, thereby solving the problems of complex coupling between the bidirectional outputs of unidirectional motors, small available stroke of existing Lorentz motors, large electromagnetic force fluctuations, and long calculation time.

[0007] To achieve the above object, according to one aspect of the present invention, there is provided a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor, including a vertical permanent magnet unit and a horizontal permanent magnet unit, which are placed perpendicular to each other and aligned; both the vertical permanent magnet unit and the horizontal permanent magnet unit include a first permanent magnet unit and a second permanent magnet unit. The first permanent magnet unit is the upper magnet of the motor, and the second permanent magnet unit is embedded in the lower magnet of the motor. The gap between the first permanent magnet unit and the second permanent magnet unit is the air gap magnetic field; the first permanent magnet unit includes a first magnetized permanent magnet arranged in the Halbech arrangement and vertically arranged along the negative y-axis direction, a second magnetized permanent magnet arranged horizontally to the right, and a third magnetized permanent magnet arranged vertically along the positive y-axis direction. The second permanent magnet unit includes a fourth magnetized permanent magnet arranged in the Halbech arrangement and vertically arranged along the positive y-axis direction, a fifth magnetized permanent magnet arranged horizontally to the left, and a sixth magnetized permanent magnet arranged vertically along the negative y-axis direction. The second magnetization unit has the same structure and polarization direction as the first magnetization unit.

[0008] To achieve the above object, according to one aspect of the present invention, there is provided a modeling method for a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor, including the following steps:

[0009] S1: Determine the sizes of the permanent magnets and the air gap in the vertical permanent magnet unit according to the desired coil output, stroke, and volume limitations.

[0010] S2: Extend the permanent magnets obtained in step S1 along the x-axis to the entire domain, and obtain the periodic distribution model of the magnetic field through the magnetic field distribution factor. After performing Fourier series expansion and combination, obtain the expression of the harmonic periodic distribution model of the magnetization intensity vector inside the permanent magnet array.

[0011] The Take the partial derivatives at the magnetic field boundaries of the air gap above and below the permanent magnet and the permanent magnet magnetic field to obtain the expressions of the magnetic induction intensity B1 and B3 in the air gap magnetic field, and then obtain the expression of the magnetic induction intensity B at a certain point in the air gap.

[0012] S3: For the magnetic induction intensity B obtained in step S2, calculate the geometric mean of the total harmonic distortion rates of each point of B in the air gap to obtain B. THD If B THD < 90%, the high-order harmonic distortion of the air gap magnetic field is too high, and the sizes of the permanent magnet and the air gap are redesigned.

[0013] S4: Repeat the above steps until B THD > 90%. At this time, the high-order harmonic distortion of the air gap magnetic field is low, and the accuracy of the magnetic induction intensity B calculated according to this set of permanent magnet and air gap size parameters is high, so as to calculate the force on the coil in the air gap.

[0014] Preferably, the specific steps of step S2 are as follows:

[0015] Extend the first magnetized permanent magnet, the second magnetized permanent magnet, the third magnetized permanent magnet, the fourth magnetized permanent magnet, the fifth magnetized permanent magnet, and the sixth magnetized permanent magnet in the vertical permanent magnet unit of step S1 along the x-axis to the entire domain, and superimpose the magnetic field components of their magnetic field intensities projected along the x-axis to obtain the magnetic field distribution factor λ. x And superimpose the magnetic field components of their magnetic field intensities projected along the y-axis to obtain the magnetic field distribution factor λ. y Combine the magnetic field distribution factor λ x with the magnetic field distribution factor λ y to obtain the periodic distribution model of the magnetic field.

[0016] Perform Fourier series expansion on the magnetic field distribution factor λ x and the magnetic field distribution factor λ y respectively, convert them into harmonic representation forms λ x and λ y and combine them to obtain the expression of the harmonic periodic distribution model of the magnetization intensity vector inside the permanent magnet array.

[0017] Take Derive partial derivatives at the air gaps above and below the permanent magnet and at the boundary of the permanent magnet magnetic field to obtain the expressions B1 and B3 for the magnetic induction intensity in the air gap magnetic field;

[0018] Define the center of the coil between the first permanent magnet unit and the second permanent magnet unit as O C , O C The permanent magnet unit on one side of the O point along the y-axis direction is the first permanent magnet unit, and the magnetic induction intensity it generates is B t ; O C The permanent magnet unit on the side opposite to the y-axis direction of the O point is the second permanent magnet unit, and the magnetic induction intensity it generates is B b ;

[0019] O1 is centrosymmetric about O C in the xoy plane to obtain O2, from which the relationship between B t B b and B1, B3 can be obtained. According to B t B b combine to obtain the expression for the magnetic induction intensity B at a certain point in the air gap.

[0020] Preferably, the periodic distribution model of the magnetic field in step S2 The expression is:

[0021]

[0022] where μ0 is the vacuum magnetic permeability, and B r is the remanent magnetization intensity of the vertical permanent magnet unit.

[0023] Preferably, the vertical permanent magnet unit extended in the x direction in step S2 is expanded by Fourier series to obtain the series expansion form of the magnetization intensity Its expression is:

[0024]

[0025] where n is the harmonic order in the positive x-axis direction of the coordinate system O1, W m is the width of the vertically magnetized permanent magnet, y t -y b is the height of the vertically magnetized permanent magnet, L m is the length of the vertically magnetized permanent magnet; τ m -W m is the width of the horizontally magnetized permanent magnet, y t -y b is the height of the horizontally magnetized permanent magnet, L m is the length of the horizontally magnetized permanent magnet.

[0026] Preferably, in step S2, by introducing the magnetic scalar potential and differentiating the magnetic field at the boundary, the expressions of the components of the magnetic field in the air gap below the permanent magnet are obtained:

[0027]

[0028] Among them, μ r is the relative magnetic permeability, and λ, C2, C5, and C0 are intermediate variables.

[0029] The calculation formulas for the intermediate variables λ, C2, C5, and C0 are as follows:

[0030] λ = nω

[0031]

[0032]

[0033] Among them, y t , y b are the coordinates of the projections of the upper and lower surfaces of the first permanent magnet array on the y-axis.

[0034] Preferably, the specific method for obtaining the expression of the magnetic induction intensity B at a certain point in the air gap in step S2 is as follows:

[0035] Define a point Q(x, y, z) in space. The magnetic field generated by the first permanent magnet unit at point Q is B t , and the magnetic field generated by the second permanent magnet unit at point Q is B b ; Define the center of the coil between the first permanent magnet unit and the second permanent magnet unit as O C , and O1 is centrosymmetric about O C in the xoy plane to obtain O2. The expression of B b is obtained in O2, and thus the relationship between B t B b and B1B3 can be obtained. According to B t B b the expression of the magnetic induction intensity B at a certain point in the air gap is obtained by combination:

[0036] B t = B3(x, y)

[0037] B b = B3(τ m -x, -airgap - y)

[0038]

[0039] Among them, airgap is the air gap thickness.

[0040] Preferably, the total harmonic distortion rate B in step S2THD The expression is:

[0041]

[0042] where B n is the magnetic induction intensity at different harmonic orders.

[0043] To achieve the above object, according to one aspect of the present invention, a low-harmonic bidirectional integrated Lorentz force motor is provided. By using the above permanent magnet array modeling method and parametrically designing different magnet sizes, it is convenient for optimized design, ensuring stable electromagnetic force while reducing fluctuations.

[0044] Generally speaking, compared with the prior art through the above technical solutions conceived by the present invention, the following beneficial effects are obtained:

[0045] 1. The low-harmonic bidirectional integrated Lorentz force motor provided by the present invention includes a vertical permanent magnet unit and a horizontal permanent magnet unit. By using a bidirectional integrated Lorentz motor, the system structure is simplified compared with the traditional transmission method; it has the advantages of good linearity, fast response, high sensitivity, simple structure, and small inertia.

[0046] 2. The first permanent magnet unit of the vertical permanent magnet unit of the bidirectional integrated Lorentz force motor described in the present invention includes two vertically magnetized permanent magnets and horizontally magnetized permanent magnets. According to the Halbech arrangement, the two horizontally magnetized permanent magnets are distributed on both sides of the vertically magnetized permanent magnets. The magnetized permanent magnets are cuboids. By using the iterative design method, the total harmonic distortion rate can be reduced without reducing the air-gap magnetic induction intensity, effectively reducing the electromagnetic force fluctuation in the actual control of the motor.

[0047] 3. The present invention provides a low-harmonic modeling method for a bidirectional integrated Lorentz force motor. Based on the Fourier series method, it is equivalent to vector superposition of two magnetic fields that are centrosymmetric about the midpoint of the air gap to obtain an exponential expression. The expression obtained by this modeling method can ensure the calculation accuracy and reduce the calculation complexity in the case of low harmonics, which is of great benefit in real-time control. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a schematic diagram of the vertical permanent magnet array and its coil in the coordinate system O1;

[0049] Figure 2 is a top view of the magnetic induction intensity of the first permanent magnet unit of the vertical permanent magnet array in the coordinate system O1;

[0050] Figure 3 is a top view of the magnetic induction intensity of the first permanent magnet unit of the vertical permanent magnet array after x-direction expansion in the coordinate system O1;

[0051] Figure 4 It is a schematic diagram of the x - direction magnetic field distribution factor of the first permanent - magnet unit of the vertical permanent - magnet array in the coordinate system O1;

[0052] Figure 5 It is a schematic diagram of the y - direction magnetic field distribution factor of the first permanent - magnet unit of the vertical permanent - magnet array in the coordinate system O1;

[0053] Figure 6 It is a schematic diagram of the air - gap definition of the first permanent - magnet unit of the vertical permanent - magnet array in the y - direction;

[0054] Figure 7 It is a flowchart of a design method for a low - harmonic bidirectional integrated Lorentz motor;

[0055] Figure 8 It is a comparison of the magnetic induction intensity in finite - element simulation and that in MATLAB mathematical modeling.

[0056] Figure 9 It is an axonometric view of the vertical permanent - magnet array and its coil

[0057] Figure 10 It is a schematic diagram of the voice - coil motor frame yoke and the magnetic steel embedded in the upper yoke

[0058] Figure 11 It is a top - view of the vertical permanent - magnet array and the horizontal permanent - magnet array embedded in the upper magnetic steel

[0059] In all the drawings, the same reference numerals are used to represent the same elements or structures, where:

[0060] 1 - Coil in the air - gap of the vertical permanent - magnet array, 2 - First permanent - magnet unit of the vertical permanent - magnet array, 3 - Second permanent - magnet unit of the vertical permanent - magnet array;

[0061] 4 - Vertically downward magnetized permanent - magnet of the first permanent - magnet unit of the vertical permanent - magnet array, 5 - Horizontally right - magnetized permanent - magnet of the first permanent - magnet unit of the vertical permanent - magnet array, 6 - Vertically downward magnetized permanent - magnet of the first permanent - magnet unit of the vertical permanent - magnet array;

[0062] 7 - Vertically downward magnetized permanent - magnet of the second permanent - magnet unit of the vertical permanent - magnet array, 8 - Horizontally right - magnetized permanent - magnet of the second permanent - magnet unit of the vertical permanent - magnet array, 9 - Vertically downward magnetized permanent - magnet of the second permanent - magnet unit of the vertical permanent - magnet array;

[0063] 10 - Horizontally left - magnetized permanent - magnet with x - direction extension of the first permanent - magnet unit of the vertical permanent - magnet array;

[0064] 11 - Upper air - gap of the first permanent - magnet unit of the vertical permanent - magnet array; 12 - Lower air - gap of the first permanent - magnet unit of the vertical permanent - magnet array;

[0065] 13 - Horizontal permanent - magnet array; 14 - Upper magnetic steel; 15 - Lower magnetic steel. Detailed implementation manners

[0066] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0067] The present invention provides a low-harmonic bidirectional Lorentz motor and designs a fast modeling method for the magnetic induction intensity in the air-gap magnetic field, thereby solving the problems of complex coupling between the bidirectional outputs of the unidirectional motor, small available stroke of the existing Lorentz motor, large electromagnetic force fluctuation, and long calculation time.

[0068] An embodiment of the present invention provides a low-harmonic bidirectional integrated Lorentz force motor permanent magnet array, which includes a vertical permanent magnet unit and a horizontal permanent magnet unit, and the two are placed perpendicular to each other and aligned; both the vertical permanent magnet unit and the horizontal permanent magnet unit include a first permanent magnet unit 2 and a second permanent magnet unit 3. The first permanent magnet unit 2 is the upper magnet of the motor, and the second permanent magnet unit 3 is embedded in the lower magnet of the motor. The gap between the first permanent magnet unit 2 and the second permanent magnet unit 3 is the air-gap magnetic field; the first permanent magnet unit 2 includes a first magnetized permanent magnet 4 arranged in the Halbech arrangement and vertically arranged along the negative y-axis direction, a second magnetized permanent magnet 5 arranged horizontally to the right, and a third magnetized permanent magnet 6 vertically arranged along the positive y-axis direction. The second permanent magnet unit 3 includes a fourth magnetized permanent magnet 7 arranged in the Halbech arrangement and vertically arranged along the positive y-axis direction, a fifth magnetized permanent magnet 8 arranged horizontally to the left, and a sixth magnetized permanent magnet 9 vertically arranged along the negative y-axis direction. The second magnetization unit has the same structure and polarization direction as the first magnetization unit.

[0069] The first magnetized permanent magnet 4, the second magnetized permanent magnet 5, the third magnetized permanent magnet 6, the fourth magnetized permanent magnet 7, the fifth magnetized permanent magnet 8, and the sixth magnetized permanent magnet 9 are all square columns, that is, the vertically magnetized permanent magnets (the first magnetized permanent magnet 4, the third magnetized permanent magnet 6, the fourth magnetized permanent magnet 7, and the sixth magnetized permanent magnet 9) are rectangular parallelepipeds, with a length of L m , a width of W m , the upper surface is z = y t , the lower surface is z = y b ; the horizontally magnetized permanent magnets (the second magnetized permanent magnet 5 and the sixth magnetized permanent magnet 8) are also rectangular parallelepipeds, with a length of L m , a width of τ - W m , the upper surface is z = y t , the lower surface is z = y b .

[0070] Since the horizontal permanent magnet unit and the vertical permanent magnet unit are exactly the same and are placed perpendicular to each other, the influencing factors of the magnetic field intensity in the air gap of the vertical permanent magnet unit are vertical and horizontal. However, the horizontal permanent magnet unit and the vertical permanent magnet unit are far apart and decoupled from each other, so the horizontal influence is very small and can be ignored. Therefore, the following research focuses on the vertical permanent magnet unit.

[0071] According to another aspect of the embodiments of the present invention, a method for modeling a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor is provided, which mainly uses the Fourier series method to accurately and quickly model the air gap magnetic field of the above permanent magnet array.

[0072] As Figure 7 shown, the modeling method includes the following steps:

[0073] S1: According to the desired coil output force, stroke, and volume limit, determine the size of the permanent magnet and the air gap size in the vertical permanent magnet unit;

[0074] Since the vertical permanent magnet unit and the horizontal permanent magnet unit are far apart and the magnetic fields are decoupled from each other, the MIMO (multiple input multiple output) problem can be transformed into a SISO (single input single output) problem for research on the vertical permanent magnet unit. A single vertical permanent magnet unit is formed by arranging the first permanent magnet unit 2 and the second permanent magnet unit 3 in alignment along the vertical direction of the motor. The internal arrangements of the first permanent magnet unit 2 and the second permanent magnet unit 3 are the same, so the magnetic field arrangements around these two permanent magnet units are the same, and the magnetic field intensity at a certain point in the air gap between them can be obtained by adding the magnetic field intensity vectors of the two permanent magnet units at this point; therefore, further research is carried out on a single permanent magnet unit, such as the first permanent magnet unit of the vertical permanent magnet unit, for harmonic modeling, and then using symmetry, the second permanent magnet unit of the vertical permanent magnet unit is calculated, and the air gap magnetic field expression of a vertical permanent magnet unit is obtained by superposition.

[0075] S2: Extend the permanent magnet obtained in step S1 along the x-axis to the entire domain. As Figure 3 described, the horizontally left-magnetized permanent magnet 10 extended in the x-direction of the first permanent magnet unit of the vertical permanent magnet array is a "virtual" left-magnetized permanent magnet extended from the first permanent magnet unit 2 of the vertical permanent magnet unit for calculation needs and does not actually exist.

[0076] Obtain the periodic distribution model of the magnetic field through the magnetic field distribution factor After performing Fourier series expansion and combination, obtain the expression of the harmonic periodic distribution model of the magnetization intensity vector inside the permanent magnet array

[0077] The Taking the partial derivatives at the magnetic field boundaries of the air gaps above and below the permanent magnet, the expressions of the magnetic induction intensity B1 and B3 in the air gap magnetic field are obtained, and then the expression of the magnetic induction intensity B at a certain point in the air gap is obtained;

[0078] The specific steps of step S2 are as follows:

[0079] Extend the first magnetized permanent magnet 4, the second magnetized permanent magnet 5, the third magnetized permanent magnet 6, the fourth magnetized permanent magnet 7, the fifth magnetized permanent magnet 8, and the sixth magnetized permanent magnet 9 in the vertical permanent magnet unit in step S1 along the x-axis direction to the whole domain, and superimpose the magnetic field components of their magnetic field intensities projected along the x-axis to obtain the magnetic field distribution factor λ x and superimpose the magnetic field components of their magnetic field intensities projected along the y-axis to obtain the magnetic field distribution factor λ y , the magnetic field distribution factor λ x and the magnetic field distribution factor λ y are combined to obtain the periodic distribution model of the magnetic field

[0080] Perform Fourier series expansions on the magnetic field distribution factor λ x and the magnetic field distribution factor λ y respectively, and convert them into harmonic representation forms λ x and λ y , and combine them to obtain the expression of the harmonic periodic distribution model of the magnetization intensity vector inside the permanent magnet array

[0081] Taking the partial derivatives at the magnetic field boundaries of the air gaps above and below the permanent magnet, the expressions of the magnetic induction intensity B1 and B3 in the air gap magnetic field are obtained;

[0082] Define the center of the coil between the first permanent magnet unit 2 and the second permanent magnet unit 3 as O C , O C The permanent magnet unit on one side of the O t point along the y-axis direction is the first permanent magnet unit 2, and the magnetic induction intensity generated by it is B C ; The permanent magnet unit on the opposite side of the O b point along the y-axis direction is the second permanent magnet unit 3, and the magnetic induction intensity generated by it is B

[0083] O1 is centrosymmetric about O C in the xoy plane to obtain O2, and thus the relationship between B t B b and B1 B3 can be obtained. According to B t B b the expression of the magnetic induction intensity B at a certain point in the air gap is obtained by combination.

[0084] According to the magnetization direction of the first permanent magnet array of the vertical permanent magnet unit, the magnetization direction factor of the first permanent magnet array can be obtained. For example, Figure 4 , Figure 5 As shown, the expression of the periodic distribution model M of the magnetic field in step S2 is:

[0085]

[0086] where μ0 is the magnetic permeability of vacuum, and B r is the remanent magnetization intensity of the vertical permanent magnet unit.

[0087] Perform Fourier series expansion on the vertical permanent magnet unit extended in the x direction to obtain the series expansion form of the magnetization intensity Its expression is:

[0088]

[0089] where n is the harmonic order in the positive x-axis direction of the coordinate system O1, W m is the width of the vertically magnetized permanent magnet, y t -y b is the height of the vertically magnetized permanent magnet, and L m is the length of the vertically magnetized permanent magnet; τ m -W m is the width of the horizontally magnetized permanent magnet, y t -y b is the height of the horizontally magnetized permanent magnet, and L m is the length of the horizontally magnetized permanent magnet.

[0090] In the present invention, the length L of the permanent magnet m should completely envelop the length of the coil. Otherwise, it completely violates the shape design requirements. Therefore, the length of the permanent magnet does not affect the calculation of the magnetic field strength, and in this example, the length of the permanent magnet can be regarded as infinite.

[0091] According to the arrangement of the permanent magnet array, the space can be divided into three parts as shown in Figure 6 : the upper air gap, the permanent magnet, and the lower air gap. In step S2, by introducing the magnetic scalar potential and taking the derivative of the magnetic field at the boundary, the expressions of the components of the magnetic field in the air gap below the permanent magnet are obtained:

[0092]

[0093] where μ0 is the magnetic permeability of vacuum, μ r is the relative magnetic permeability, and λ, C2, C5, and C0 are intermediate variables.

[0094] The calculation formulas for the intermediate variables λ, C2, C5, and C0 are respectively:

[0095] λ = nω

[0096]

[0097] Among them, y t and y b are the coordinates of the projections of the upper and lower surfaces of the first permanent magnet array 2 on the y-axis.

[0098] According to the expressions of each component of the magnetic field in the air gap above and below the permanent magnet obtained above, the specific method for obtaining the expression of the magnetic induction intensity B at a certain point in the air gap in step S2 is as follows:

[0099] Define a point Q(x, y, z) in space. The magnetic field generated by the first permanent magnet unit 2 at point Q is B t , and the magnetic field generated by the second permanent magnet unit 3 at point Q is B b ; Define the center of the coil between the first permanent magnet unit 2 and the second permanent magnet unit 3 as O C , O1 is centrosymmetric about O C in the xoy plane to obtain O2. Obtain the expression of B b in O2. According to B t B b combine to obtain the expression of the magnetic induction intensity B at a certain point in the air gap:

[0100] B t = B3(x, y)

[0101] B b = B3(τ m -x, -airgap - y)

[0102]

[0103] Among them, airgap is the air gap thickness.

[0104] The above is the magnetic field intensity of the vertical permanent magnet unit. The solution of the magnetic field intensity of the horizontal permanent magnet unit is the same.

[0105] S3: According to the method above, the magnetic field intensity at any point in the air gap can be obtained. For the magnetic induction intensity B obtained in step S2, find the geometric mean of the total harmonic distortion rates of each point of B in the air gap to obtain B THD . If B THD < 90%, then the high-order harmonic distortion of the air gap magnetic field is too high, and the accuracy of the magnetic induction intensity B calculated by the size parameters of this group of permanent magnets and air gaps is not good enough, and a new group of permanent magnet and air gap size parameters need to be redesigned.

[0106] S4: Repeat the above steps until B THD> 90%, at this time the higher-order harmonic distortion of the air-gap magnetic field is low, and the accuracy of the magnetic induction intensity B calculated according to the set of permanent magnet and air-gap size parameters is high. The force on the coil in the air gap can be calculated quickly and accurately, which is beneficial to real-time control.

[0107] Among them, the total harmonic distortion rate B THD The expression of is:

[0108]

[0109] Among them, B n is the magnetic induction intensity at different harmonic orders.

[0110] In the above examples, the width, thickness, installation gap, and magnetization intensity of the permanent magnet can all be adjusted, and can be parametrically represented to provide guidance for subsequent optimization.

[0111] At the same time, the present invention designs a low-harmonic bidirectional integrated Lorentz force motor, in which the horizontal motor and the vertical motor are decoupled and arranged in the same motor, aiming to reduce the complex installation and mutual coupling between multiple distributed motors. This design innovatively uses Fourier analysis technology to simulate the air-gap magnetic field of the magnet. The specific method is to perform superposition analysis on the first and second permanent magnet arrays aligned in the y direction, so as to efficiently calculate the magnetic field distribution of the entire magnetic array. By using the above permanent magnet array modeling method, different magnet sizes are parametrically designed, which is convenient for optimization design, ensures stable electromagnetic force while reducing fluctuations. This method accelerates the calculation process and is very suitable for real-time control systems that require fast response.

[0112] Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor, characterized in that, It includes a vertical permanent magnet unit and a horizontal permanent magnet unit, which are placed vertically aligned with each other; both the vertical permanent magnet unit and the horizontal permanent magnet unit include a first permanent magnet unit (2) and a second permanent magnet unit (3), and the gap between the first permanent magnet unit (2) and the second permanent magnet unit (3) is the air-gap magnetic field; The first permanent magnet unit (2) includes a first magnetized permanent magnet (4) arranged in the Halbech arrangement and vertically arranged in the negative y-axis direction, a second magnetized permanent magnet (5) arranged horizontally to the right, and a third magnetized permanent magnet (6) arranged vertically in the positive y-axis direction, The second permanent magnet unit (3) includes a fourth magnetized permanent magnet (7) arranged in the Halbech arrangement and vertically arranged in the positive y-axis direction, a fifth magnetized permanent magnet (8) arranged horizontally to the left, and a sixth magnetized permanent magnet (9) arranged vertically in the negative y-axis direction. The second magnetized unit (3) has the same structure and the same polarization direction as the first magnetized unit (2).

2. The modeling method of the permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor according to claim 1, characterized in that It includes the following steps: S1: According to the desired coil output force, stroke, and volume limitation, determine the size of the permanent magnet and the air-gap size in the vertical permanent magnet unit; S2: Extend the permanent magnet obtained in step S1 along the x-axis direction to the entire domain, and obtain the periodic distribution model of the magnetic field through the magnetic field distribution factor. After performing Fourier series expansion and combination, obtain the expression of the harmonic periodic distribution model of the magnetization intensity vector inside the permanent magnet array. Will Derive partial derivatives at the magnetic field boundaries of the air gaps above and below the permanent magnet with respect to the permanent magnet, obtain the expressions of the magnetic induction intensity B1 and B3 in the air gap magnetic field, and further obtain the expression of the magnetic induction intensity B at a certain point in the air gap; S3: For the magnetic induction intensity B obtained in step S2, calculate the geometric mean of the total harmonic distortion rate of each point of B in the air gap to obtain B THD , if B THD < 90%, the high-order harmonic distortion of the air-gap magnetic field is too high, and the permanent magnet and the air-gap size parameters are redesigned; S4: Repeat the above steps until B THD > 90%, at this time the higher harmonic distortion of the air-gap magnetic field is low, and the accuracy of the magnetic induction intensity B calculated according to the set of permanent magnet and air-gap size parameters is high, so as to calculate the force on the coil in the air gap.

3. The permanent magnet array modeling method of a low-harmonic bidirectional integrated Lorentz force motor according to claim 2, wherein The specific steps of step S2 are: Extend the first magnetized permanent magnet (4), the second magnetized permanent magnet (5), the third magnetized permanent magnet (6), the fourth magnetized permanent magnet (7), the fifth magnetized permanent magnet (8), and the sixth magnetized permanent magnet (9) in the vertical permanent magnet unit of step S1 to the entire domain, and superimpose the magnetic field components of the magnetic field intensity projected along the x-axis to obtain the magnetic field distribution factor λ x and superimpose the magnetic field components of the magnetic field intensity projected along the y-axis to obtain the magnetic field distribution factor λ y , the magnetic field distribution factor λ x Combine with the magnetic field distribution factor λ y to obtain the periodic distribution model of the magnetic field The magnetic field distribution factor λ x and the magnetic field distribution factor λ y are respectively expanded by Fourier series and converted into the harmonic representation forms λ x and λ y , and the harmonic periodic distribution model expression of the magnetization intensity vector inside the permanent magnet array is obtained by combination Take The partial derivatives are taken at the air gaps above and below the permanent magnet and at the boundary of the permanent magnet magnetic field to obtain the expressions B1 and B3 for the magnetic induction intensity in the air gap magnetic field; Define the center of the coil between the first permanent magnet unit (2) and the second permanent magnet unit (3) as O C ,O C The permanent magnet unit on one side of the O point along the y-axis direction is the first permanent magnet unit (2), and the magnetic induction intensity generated by it is B t ;O C The permanent magnet unit on the side of the O point along the opposite direction of the y-axis is the second permanent magnet unit (3), and the magnetic induction intensity generated by it is B b ; O1 with respect to O C O2 is obtained by central symmetry about the xoy plane center, from which B can be obtained t B b The relationship with B1B3. According to B t B b Combined to obtain the expression of the magnetic induction intensity B at a certain point in the air gap 4. A method for modeling a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor according to claim 3, characterized in that, Periodic distribution model of the magnetic field in step S2 The expression is: where μ0 is the magnetic permeability of vacuum, and B r is the remanent magnetization of the vertical permanent magnetic unit.

5. A modeling method for a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor according to claim 4, characterized in that, In step S2, the vertical permanent magnet unit extended in the x direction is expanded by Fourier series to obtain the series expansion form of the magnetization intensity Its expression is: where n is the harmonic order in the positive x-axis direction of the coordinate system O1, W m is the width of the vertically magnetized permanent magnet, y t -y b is the height of the vertically magnetized permanent magnet, L m is the length of the vertically magnetized permanent magnet; τ m -W m is the width of the horizontally magnetized permanent magnet, y t -y b is the height of the horizontally magnetized permanent magnet, L m is the length of the horizontally magnetized permanent magnet.

6. A permanent magnet array modeling method for a low - harmonic bidirectional integrated Lorentz force motor according to claim 3, characterized in that, In step S2, by introducing the magnetic scalar potential and taking the partial derivative of the magnetic field at the boundary, the expressions of the magnetic induction intensity B1 and B3 in the air-gap magnetic field are obtained; where μ r is the relative permeability, and λ, C2, C5, and C0 are intermediate variables.

7. A modeling method for a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor as described in claim 6, characterized in that The calculation formulas of the intermediate variables λ, C2, C5, and C0 are respectively: λ = nω where y t and y b are the coordinates of the projections of the upper and lower surfaces of the first permanent magnet array (2) on the y-axis.

8. A permanent magnet array modeling method for a low-harmonic bidirectional integrated Lorentz force motor as claimed in claim 7, wherein The specific method for obtaining the expression of the magnetic induction intensity B at a certain point in the air-gap in step S2 is: Define a point Q(x, y, z) in space. The magnetic field generated by the first permanent magnet unit (2) at point Q is B t , and the magnetic field generated by the second permanent magnet unit (3) at point Q is B b ; Define the center of the coil between the first permanent magnet unit (2) and the second permanent magnet unit (3) as O C , O1 is centrosymmetric about O C in the xoy plane to obtain O2, and obtain the B b expression in O2. From this, B t B b and the relationship between B1B3 can be obtained. According to B t B b combined to obtain the expression of the magnetic induction intensity B at a certain point in the air gap: B t = B3(x, y) B b = B3(τ m -x, -airgap-y) where airgap is the air-gap thickness.

9. A modeling method for a permanent magnet array of a low-harmonic bidirectional integrated Lorentz force motor according to any one of claims 2-8, characterized in that Total harmonic distortion rate B in step S2 THD The expression is as follows: Among them, B n is the magnetic induction intensity at different harmonic orders.

10. A low-harmonic bidirectional integrated Lorentz force motor, characterized in that, Adopt the permanent magnet array modeling method described in claim 9. By parametrically designing different magnet sizes, it is convenient for optimization design, ensuring stable electromagnetic force while reducing fluctuations.

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