Linear motor design variable verification method and linear motor design variable optimization method

Abstract

The invention discloses a linear motor design variable verification method and a linear motor design variable optimization method. The linear motor design variable verification method comprises the following steps: 1, deriving a magnetic conductivity matrix of a linear motor from a linear motor design variable; a second step of deriving a Maxwell matrix of the linear motor through LU decomposition from the permeability matrix of the linear motor; a third step of deriving, from a Maxwell matrix of the linear motor, a verification physical quantity of at least one selected from the group consisting of a force of the linear motor, a flux linkage passing through each coil of a stator of the linear motor, a back electromotive force of the linear motor, and an inductance of the linear motor; and a fourth step of determining whether a verification condition is satisfied by comparing the verification physical quantity with a predetermined reference value.

Description

Technical Field

[0001] The invention relates to a linear motor design variable verification method and a linear motor design variable optimization method. Background Art

[0002] Industries that require high acceleration and high thrust characteristics to achieve high production volumes often use iron core linear motors. In such iron core linear motors, force waves are generated due to the structural characteristics of the motor, which requires a method to predict the electromagnetic characteristics based on the design variables of the motor in the early design stage.

[0003] Therefore, there are many technologies that use numerical calculation methods such as the finite element method to calculate the static Maxwell equations in the form of simultaneous partial differential equations, which are the governing equations in electromagnetic problems. In motor analysis using such numerical calculation methods, the structural shape of the motor must be divided into a large number of nodes and units (mesh), so there is a problem that the analysis requires a lot of time when performing calculations while changing various design variables. Summary of the invention

[0004] An object of the present invention is to provide a method for quickly verifying design variables of a linear motor.

[0005] Another object of the present invention is to provide a method for optimizing design variables of a fast linear motor.

[0006] Another object of the present invention is to provide a linear motor manufactured by using the linear motor design variables verified and / or optimized by the above-mentioned verification method or optimization method.

[0007] Specifically, the object of the present invention is to provide a novel analysis technology which improves the problems of the prior art by providing an autoencoder to provide frequency-based modeling and quickly perform work on the electromagnetic characteristics of a motor at the prototype stage.

[0008] On the one hand, the present invention provides a method for verifying design variables of a linear motor, comprising: a first step, deriving the magnetic permeability matrix of the linear motor from the design variables of the linear motor by using the following formula (1); a second step, deriving the Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor by using LU decomposition; a third step, deriving at least one verification physical quantity selected from the group consisting of the force of the linear motor, the magnetic flux through each coil of the stator of the linear motor, the back electromotive force of the linear motor, and the inductance of the linear motor from the Maxwell matrix of the linear motor; and a fourth step, determining whether the verification condition is met by comparing the verification physical quantity with a predetermined reference value.

[0009]

[0010] Wherein, x and y are the x-coordinate and y-coordinate of the linear motor, μ is the magnetic permeability of the linear motor material, and m i and n j They are defined as (2π / λ x )i and (2π / λ y )j,m k and n l They are defined as (2π / λ x )k and (2π / λ y )l,λ x and y are the fundamental periods of the trigonometric functions in the x-direction and the y-direction respectively. α, β, γ, ξ, ε and ρ are the two-dimensional magnetic permeability matrix.

[0011] In one embodiment, the LU decomposition in the second step can be performed by the following formula (2).

[0012]

[0013] Among them, H x , H y and H z Refers to the magnetic field strength in the x, y and z directions respectively, B x , B y , B z The magnetic flux density in the x-direction, y-direction, and z-direction, respectively, and M and N are the diagonal components with the m i and n j The diagonal matrix of cc They are {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of U and λ cs They are {β -1 (Mρ -1 M+Nγ - 1 N)} 1 / 2are the eigenvector matrix and eigenvalue matrix of , L, M, N and O are the magnetic field constants of the Maxwell matrix to be derived.

[0014] In one embodiment, the force of the linear motor in the third step can be derived by the following formula (3).

[0015]

[0016] Among them, F x 、F y and F z are the forces in the x-, y- and z-directions of the linear motor, T is the Maxwell stress tensor, B x , B y and B z are the magnetic flux densities in the x, y and z directions respectively, and μ0 is the magnetic permeability in a vacuum.

[0017] In one embodiment, the magnetic flux linkage passing through each coil of the stator of the linear motor in the third step can be derived by the following formula (4).

[0018]

[0019] Where Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, Refers to the magnetic vector potential rotation value.

[0020] In one embodiment, the back electromotive force of the linear motor in the third step can be derived by the following formula (5).

[0021]

[0022] Among them, V bemf is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the linear motor, t is the time, y is the r is the moving distance, and v is the speed of the mover of the linear motor.

[0023] In one embodiment, the inductance of the linear motor in the third step can be derived by the following formula (6).

[0024] L=φI, wherein L is the inductance of the stator of the linear motor, and I is the magnitude of the current applied to the stator of the linear motor.

[0025] On the other hand, the present invention provides a method for optimizing design variables of a linear motor, comprising: a first step, deriving the magnetic permeability matrix of each linear motor from each design variable of more than two virtual linear motors by the following formula (1); a second step, deriving the Maxwell matrix of each linear motor from the magnetic permeability matrix of each linear motor by LU decomposition; a third step, deriving at least one verified physical quantity selected from the group consisting of the force of each linear motor, the magnetic flux through each coil of the stator of each linear motor, the back electromotive force of each linear motor, and the inductance of each linear motor from the Maxwell matrix of each linear motor; and a fourth step, comparing the verified physical quantities of each linear motor and selecting a linear motor whose verified physical quantity is close to the desired design direction.

[0026]

[0027] Wherein, x and y are the x-coordinate and y-coordinate of the linear motor, μ is the magnetic permeability of the linear motor material, and m i and n j They are defined as (2π / λ x )i and (2π / λ y )j,m k and n l They are defined as (2π / λ x )k and (2π / λ y )l,λ x and y are the fundamental periods of the trigonometric functions in the x-direction and the y-direction respectively. α, β, γ, ξ, ε and ρ are the two-dimensional magnetic permeability matrix.

[0028] In one embodiment, the linear motor design variable optimization method according to the embodiment of the present invention may include repeating the first step to the fourth step multiple times for more than two virtual linear motors including the linear motor selected in the fourth step.

[0029] In one embodiment, the LU decomposition in the second step can be performed by the following formula (2).

[0030]

[0031] Among them, H x , H y and H z Refers to the magnetic field strength in the x, y and z directions respectively, B x , B y , Bz The magnetic flux density in the x-direction, y-direction, and z-direction, respectively, and M and N are the diagonal components with the m i and n j The diagonal matrix of cc They are {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of U and λ cs They are {β -1 (Mρ -1 M+Nγ - 1 N)} 1 / 2 are the eigenvector matrix and eigenvalue matrix of , L, M, N and O are the magnetic field constants of the Maxwell matrix to be derived.

[0032] In one embodiment, the force of each linear motor in the third step can be derived by the following formula (3).

[0033]

[0034] Among them, F x 、F y and F z are the forces in the x-, y- and z-directions of the linear motor, T is the Maxwell stress tensor, B x , B y and B z are the magnetic flux densities in the x, y and z directions respectively, and μ0 is the magnetic permeability in a vacuum.

[0035] In one embodiment, the magnetic flux linkage passing through each coil of the stator of each linear motor in the third step can be derived by the following formula (4).

[0036]

[0037] Where Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, Refers to the magnetic vector potential rotation value.

[0038] In one embodiment, the back electromotive force of each linear motor in the third step can be derived by the following formula (5).

[0039]

[0040] Among them, V bemf is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the linear motor, t is the time, y is the r is the moving distance, and v is the speed of the mover of the linear motor.

[0041] In one embodiment, the inductance of each linear motor in the third step can be derived by the following formula (6).

[0042] L=φI

[0043] Wherein, L is the inductance of the stator of the linear motor, and I is the magnitude of the current applied to the stator of the linear motor.

[0044] Effects of the Invention

[0045] By using the linear motor design variable verification method according to the embodiment of the present invention, the design variables of the linear motor can be verified quickly and accurately to derive operability and the possibility of achieving desired performance.

[0046] By using the linear motor design variable optimization method according to the embodiment of the present invention, the design variables of the linear motor can be optimized quickly and accurately to explore the design variables of the linear motor that can achieve the desired performance.

[0047] The linear motor according to the embodiment of the present invention can be designed to have desired performance through the above-mentioned verification method and / or optimization method.

[0048] In particular, iron core linear motors are used to achieve linear motion that produces high thrust in various applications. Generally, it is crucial to quickly and accurately predict the electromagnetic characteristics of a motor prototype in the early design stage. In the present invention, an analytical solution of the static Maxwell equations through a magnetic permeability matrix is ​​utilized, thereby having an accuracy of more than 95% for commercial finite element analysis programs and enabling motor analysis. In addition, since the present invention does not require a process of dividing the motor structure to be analyzed into nodes and elements, the time required for analysis can be significantly reduced compared to commercial finite element analysis programs. Through the high-speed electromagnetic analysis method of the present invention, there is an effect of more quickly involving the motor while maintaining the accuracy of the design method using a finite element analysis program based on an existing numerical calculation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a block diagram showing an electromagnetic analysis model used in a linear motor design variable verification method according to an embodiment of the present invention.

[0050] Figure 2 is a diagram of a linear motor whose design variables are verified by the linear motor design variable verification method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] Below, embodiments of the present invention are described in detail with reference to the accompanying drawings. The present invention can be subjected to various modifications and can have various forms, so specific embodiments are illustrated in the drawings and described in detail in this specification. However, it should be understood that this does not limit the present invention to a specific disclosure method, but includes all modifications, equivalent technical solutions and alternative solutions included in the concept and technical scope of the present invention. When describing the drawings, similar components are marked with similar reference numerals. In the drawings, in order to clarify the present invention, the size of the structure is enlarged than the actual size.

[0052] The terms used in this application are only used to illustrate specific embodiments and are not intended to limit the present invention. Unless the context clearly indicates a different meaning, expressions in the singular include expressions in the plural. In this application, terms such as "including" or "having" are used to specify the presence of features, numbers, steps, actions, constituent elements, or combinations thereof recorded in the specification, and shall not be understood as excluding in advance the presence or additional possibilities of one or more other features or numbers, steps, actions, constituent elements, or combinations thereof. In the context of this specification, terms such as "about" may mean about ±1%, about ±2%, about ±3%, about ±4%, about ±5%, about ±6%, about ±7%, about ±8%, about ±9%, or about ±10% of the numerical value recorded in the specification.

[0053] Unless otherwise defined, all terms used in this application, including technical and scientific terms, have the same meaning as commonly understood by those skilled in the art to which the invention belongs. Terms defined in commonly used dictionaries should be interpreted as having the same meaning as that in the context of the relevant art, and, unless explicitly defined in this application, should not be interpreted in an idealized or overly formalized sense.

[0054] Figure 1 is a block diagram showing an electromagnetic analysis model used in a linear motor design variable verification method according to an embodiment of the present invention.

[0055] Figure 2 3 is a view of a linear motor whose design variables are verified by a linear motor design variable verification method according to an embodiment of the present invention.

[0056] Reference Figure 1 and Figure 2According to the linear motor design variable verification method and the electromagnetic analysis model used in the embodiment of the present invention, numerical information about the motor shape is received, a magnetic permeability matrix is ​​calculated based on the information, and a Maxwell matrix is ​​constructed and the magnetic field of the motor stator is derived therefrom. Electromagnetic data of the motor are calculated based on the calculated magnetic field, and the electromagnetic data include motor force and flux linkage, back electromotive force and inductance generated thereby, etc.

[0057] Continue to refer Figure 1 and Figure 2 , a method for verifying design variables of a linear motor according to an embodiment of the present invention may include: a first step of deriving a magnetic permeability matrix of the linear motor from the design variables of the linear motor by using the following formula (1); a second step of deriving a Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor by using LU decomposition; a third step of deriving at least one verification physical quantity selected from the group consisting of the force of the linear motor, the flux linkage through each coil of the stator of the linear motor, the back electromotive force of the linear motor, and the inductance of the linear motor from the Maxwell matrix of the linear motor; and a fourth step of determining whether a verification condition is met by comparing the verification physical quantity with a predetermined reference value.

[0058]

[0059] Wherein, x and y are the x-coordinate and y-coordinate of the linear motor, μ is the magnetic permeability of the linear motor material, and m i and n j They are defined as (2π / λ x )i and (2π / λ y )j,m k and n l They are defined as (2π / λ x )k and (2π / λ y )l,λ x and y are the fundamental periods of the trigonometric functions in the x-direction and the y-direction respectively. α, β, γ, ξ, ε and ρ are the two-dimensional magnetic permeability matrix.

[0060] In the context of this specification, magnetic permeability may refer to a physical quantity indicating the degree of magnetization of a certain medium to a given magnetic field.

[0061] The first step is to derive the magnetic permeability matrix of the linear motor. In the context of this specification, the magnetic permeability matrix may refer to a matrix having magnetic permeability as a component, and the basis function (here, the function consisting of the product of the trigonometric functions of the x and y directions such as cos(mx), cos(ny), cos(mx), sin(ny) etc.) of the magnetic permeability function μ(x, y) is formed by the Fourier coefficients during the 2D Fourier series expansion.

[0062] The present invention is based at least on the fact that, after deriving the magnetic permeability matrix, the Maxwell matrix can be derived by the steps described below, and the physical quantity can be calculated as an approximation within a significant level without using the finite element method. In the context of this specification, the finite element method can refer to a method for finding approximate solutions to partial differential equations, integrals, heat equations, etc.

[0063] The second step is a step of deriving a Maxwell matrix from the derived magnetic permeability matrix, and the third step is a step of calculating a physical quantity of the object to be verified from the derived Maxwell matrix. The physical quantity of the object to be verified can be derived from the Maxwell matrix, including the flux linkage of each coil of the stator of the linear motor, the back electromotive force of the linear motor, the inductance of the linear motor, and the physical quantity derived therefrom.

[0064] The fourth step is to determine whether the calculated physical quantity reaches the target value, that is, whether the verification condition is met, by comparing with a predetermined reference value. In the context of this specification, meeting the verification condition of the physical quantity means confirming whether the beneficial effect is achieved by being greater than or less than the predetermined reference value from an obvious perspective for a person skilled in the art or from an expected perspective for a person skilled in the art.

[0065] In the iron core part of the iron core motor, the magnetic permeability can be μs or μ0 depending on the coordinates of the motor.

[0066] In one embodiment, the LU decomposition in the second step can be performed by the following formula (2).

[0067]

[0068] Among them, H x , H y and H z Refers to the magnetic field strength in the x, y and z directions respectively, B x , B y , B zThe magnetic flux density in the x-direction, y-direction, and z-direction, respectively, and M and N are the diagonal components with the m i and n j The diagonal matrix of cc They are {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of U and λ cs They are {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 are the eigenvector matrix and eigenvalue matrix of , L, M, N and O are the magnetic field constants of the Maxwell matrix to be derived.

[0069] In one embodiment, the force of the linear motor in the third step can be derived by the following formula (3).

[0070]

[0071] Among them, F x 、F y and F z are the forces in the x-, y- and z-directions of the linear motor, T is the Maxwell stress tensor, B x , B y and B z are the magnetic flux densities in the x, y, and z directions, respectively, and μ0 is the magnetic permeability in a vacuum. Since most of the force in an electromagnetic motor occurs in the air gap between the stator (coil part) and the mover (magnet part), the force components F generated in the air gap of the motor are calculated by multiplying the normal vector [0 0-1]^T corresponding to the air gap by the Maxwell strain tensor. x 、F y and F z .

[0072] In one embodiment, the magnetic flux linkage passing through each coil of the stator of the linear motor in the third step can be derived by the following formula (4).

[0073]

[0074] Where Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, Refers to the magnetic vector potential rotation value.

[0075] In one embodiment, the back electromotive force of the linear motor in the third step can be derived by the following formula (5).

[0076]

[0077] Among them, V bemf is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the linear motor, t is the time, y is the r is the moving distance, and v is the speed of the actuator of the linear motor. According to Faraday's law, the back electromotive force is equal to the negative value of the time rate of change of the magnetic flux passing through the coil. If the chain rule is applied, the time rate of change of the magnetic flux (d Φ / dt) can be expressed as the rate of change of magnetic flux with respect to moving distance (d Φ / dy r ) and the rate of change of moving distance over time (dy r / dt). Since the rate of change of the moving distance over time is the same as the speed v of the mover (magnet part), the back electromotive force V generated in the coil bemf The rate of change of the magnetic flux through the coil with respect to the moving distance (d Φ / dy r ) and the velocity of the mover (v).

[0078] In one embodiment, the inductance of the linear motor in the third step can be derived by the following formula (6).

[0079] L=φI

[0080] Wherein, L is the inductance of the stator of the linear motor, and I is the magnitude of the current applied to the stator of the linear motor.

[0081] On the other hand, the linear motor design variable optimization method according to an embodiment of the present invention may include: a first step, deriving the magnetic permeability matrix of each linear motor from each design variable of more than two virtual linear motors through the following formula (1); a second step, deriving the Maxwell matrix of each linear motor from the magnetic permeability matrix of each linear motor through LU decomposition; a third step, deriving at least one verification physical quantity selected from the group consisting of the force of each linear motor, the magnetic flux through each coil of the stator of each linear motor, the back electromotive force of each linear motor, and the inductance of each linear motor from the Maxwell matrix of each linear motor; and a fourth step, comparing the verification physical quantities of each linear motor and selecting a linear motor whose verification physical quantity is close to the desired design direction.

[0082]

[0083] Wherein, x and y are the x-coordinate and y-coordinate of the linear motor, μ is the magnetic permeability of the linear motor material, and m i and n j They are defined as (2π / λ x )i and (2π / λ y )j,m k and n l They are defined as (2π / λ x )k and (2π / λ y )l,λ x and y are the fundamental periods of the trigonometric functions in the x-direction and the y-direction respectively. α, β, γ, ξ, ε and ρ are the two-dimensional magnetic permeability matrix.

[0084] In the above description of the method for verifying the design variables of a linear motor according to an embodiment of the present invention, the same or similar terms or structures are applicable in the same or similar manner to the description of the method for optimizing the design variables of a linear motor according to an embodiment of the present invention. Specifically, the description of the method for optimizing the design variables of a linear motor according to an embodiment of the present invention is different from the description of the method for verifying the design variables of a linear motor according to an embodiment of the present invention in that, for multiple linear motors instead of a single linear motor, the same analytical model is applied in the first to third steps, and in the fourth step, instead of comparing the design variables of a single linear motor with a reference value, a design variable that is closer to the design direction is selected from multiple linear motors, but is substantially the same. Therefore, it should be understood that the omitted parts in the description of the method for optimizing the design variables of a linear motor according to an embodiment of the present invention are to avoid repeated descriptions.

[0085] The fourth step is a step of selecting a favorable linear motor with a desired physical quantity from a plurality of candidate linear motors, wherein the physical quantity can derive the physical quantity of the desired design variable from a favorable direction or design variable. The fourth step is to select a linear motor with favorable desired design variables or favorable physical quantities that can be derived from the design variables from a plurality of candidate linear motors. In one embodiment, the linear motor design variable optimization method according to an embodiment of the present invention may include repeating the first step to the fourth step multiple times for more than two virtual linear motors including the linear motor selected in the fourth step.

[0086] In one embodiment, the LU decomposition in the second step can be performed by the following formula (2).

[0087]

[0088] Among them, H x , H y and H z Refers to the magnetic field strength in the x, y and z directions respectively, B x , B y , B z The magnetic flux density in the x-direction, y-direction, and z-direction, respectively, and M and N are the diagonal components with the m i and n j The diagonal matrix of cc They are {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of U and λ cs They are {β -1 (Mρ -1 M+Nγ - 1 N)} 1 / 2 are the eigenvector matrix and eigenvalue matrix of , and L, M, N and O are the magnetic field constants of the Maxwell matrix to be derived.

[0089] In one embodiment, the force of each linear motor in the third step can be derived by the following formula (3).

[0090]

[0091] Among them, F x 、F y and Fz are the forces in the x-, y- and z-directions of the linear motor, T is the Maxwell stress tensor, B x , B y and B z are the magnetic flux densities in the x, y and z directions respectively, and μ0 is the magnetic permeability in a vacuum.

[0092] In one embodiment, the magnetic flux linkage passing through each coil of the stator of each linear motor in the third step can be derived by the following formula (4).

[0093]

[0094] Where Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, Refers to the magnetic vector potential rotation value.

[0095] In one embodiment, the back electromotive force of each linear motor in the third step can be derived by the following formula (5).

[0096]

[0097] Among them, V bemf is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the linear motor, t is the time, y is the r is the moving distance, and v is the speed of the mover of the linear motor.

[0098] In one embodiment, the inductance of each linear motor in the third step can be derived by the following formula (6).

[0099] L=φI

[0100] Wherein, L is the inductance of the stator of the linear motor, and I is the magnitude of the current applied to the stator of the linear motor.

[0101] Although the present invention has been described above with reference to preferred embodiments, it should be understood that a person skilled in the art may make various modifications and changes to the present invention within the spirit and scope of the invention as described in the claims.

Claims

1. A linear motor design variable verification method, wherein: include: The first step is to derive the magnetic permeability matrix of the linear motor from the linear motor design variables by the following formula (1); The second step is to derive the Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor by LU decomposition; The third step is to derive at least one verification physical quantity selected from the group consisting of the force of the linear motor, the flux linkage through each coil of the stator of the linear motor, the back electromotive force of the linear motor, and the inductance of the linear motor from the Maxwell matrix of the linear motor; as well as The fourth step is to determine whether the verification condition is met by comparing the verification physical quantity with a predetermined reference value: in, x and y are the x-coordinate and y-coordinate of the linear motor respectively, μ is the magnetic permeability of the linear motor material, m i and n j They are defined as (2π / λ x )i and (2π / λ y )j, m k and n l They are defined as (2π / λ x )k and (2π / λ y )l, λ x and y are the basic periods of trigonometric functions in the x and y directions, α, β, γ, ξ, ε and ρ are two-dimensional magnetic permeability matrices.

2. The linear motor design variable verification method according to claim 1, wherein: The LU decomposition in the second step is performed by the following formula (2): in, H x , H y and H z Refers to the magnetic field strength in the x, y and z directions respectively, B x , B y , B z They refer to the magnetic flux density in the x, y and z directions respectively. M and N are diagonal components having the m i and n j The diagonal matrix of T and λ cc They are {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of U and λ cs They are {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of L, M, N and O are the magnetic field constants of the Maxwell matrix to be derived.

3. The linear motor design variable verification method according to claim 1, wherein: The force of the linear motor in the third step is derived by the following formula (3): in, F x 、F y and F z are the forces in the x-, y- and z-directions of the linear motor, respectively, T is the Maxwell stress tensor, B x , B y and B z are the magnetic flux densities in the x, y and z directions respectively, μ0 is the magnetic permeability of vacuum.

4. The linear motor design variable verification method according to claim 1, wherein: The magnetic flux linkage through each coil of the stator of the linear motor in the third step is derived by the following formula (4): in, Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, Refers to the magnetic vector potential rotation value.

5. The linear motor design variable verification method according to claim 1, wherein: The back electromotive force of the linear motor in the third step is derived by the following formula (5): in, V bemf is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the linear motor, t is the time, y r is the moving distance, v is the speed of the mover of the linear motor.

6. The linear motor design variable verification method according to claim 1, wherein: The inductance of the linear motor in the third step is derived by the following formula (6): L=φI in, L is the inductance of the stator of the linear motor, I is the magnitude of the current applied to the stator of the linear motor.

7. A linear motor design variable optimization method, wherein: include: The first step is to derive the magnetic permeability matrix of each linear motor from each design variable of more than two virtual linear motors by the following formula (1); The second step is to derive the Maxwell matrix of each linear motor from the magnetic permeability matrix of each linear motor by LU decomposition; The third step is to derive at least one verification physical quantity selected from the group consisting of the force of each linear motor, the flux linkage through each coil of the stator of each linear motor, the back electromotive force of each linear motor, and the inductance of each linear motor from the Maxwell matrix of each linear motor; as well as The fourth step is to compare the verified physical quantities of the linear motors and select the linear motor whose verified physical quantity is close to the expected design direction. The method comprises repeating the first step to the fourth step a plurality of times for two or more virtual linear motors including the linear motor selected in the fourth step: in, x and y are the x-coordinate and y-coordinate of the linear motor respectively, μ is the magnetic permeability of the linear motor material, m i and n j They are defined as (2π / λ x )i and (2π / λ y )j, m k and n l They are defined as (2π / λ x )k and (2π / λ y )l, λ x and y are the basic periods in the x-direction and the y-direction respectively, α, β, γ, ξ, ε and ρ are two-dimensional magnetic permeability matrices.

8. The linear motor design variable optimization method according to claim 7, wherein: The LU decomposition in the second step is performed by the following formula (2): in, H x , H y and H z Refers to the magnetic field strength in the x, y and z directions respectively, B x , B y , B z They refer to the magnetic flux density in the x, y and z directions respectively. M and N are diagonal components having the m i and n j The diagonal matrix of T and λ cc They are {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of U and λ cs They are {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of L, M, N and O are the magnetic field constants of the Maxwell matrix to be derived.

9. The linear motor design variable optimization method according to claim 7, wherein: The force of each linear motor in the third step is derived by the following formula (3): in, F x 、F y and F z are the forces in the x-, y- and z-directions of the linear motor, respectively, T is the Maxwell stress tensor, B x , B y and B z are the magnetic flux densities in the x, y and z directions respectively, μ0 is the magnetic permeability of vacuum.

10. The linear motor design variable optimization method according to claim 7, wherein: The magnetic flux linkage passing through each coil of the stator of each linear motor in the third step is derived by the following formula (4): in, Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, Refers to the magnetic vector potential rotation value.

11. The linear motor design variable optimization method according to claim 7, wherein: The back electromotive force of each linear motor in the third step is derived by the following formula (5): in, V bemf is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the linear motor, t is the time, y r is the moving distance, v is the speed of the mover of the linear motor.

12. The linear motor design variable optimization method according to claim 7, wherein: The inductance of each linear motor in the third step is derived by the following formula (6): L=φI in, L is the inductance of the stator of the linear motor, I is the magnitude of the current applied to the stator of the linear motor.

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