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

Abstract

A method for verifying linear motor design variables and a method for optimizing linear motor design variables are disclosed. The method for verifying linear motor design variables comprises: a first step of deriving a magnetic permeability matrix of the linear motor from linear motor design variables; a second step of deriving a Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor through LU decomposition; a third step of deriving one or more verification physical quantities selected from a group including the force of the linear motor, the magnetic flux linkage passing through each coil of the stator of the linear motor, the back EMF 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 verification conditions are met by comparing the verification physical quantities with a predetermined reference value.

Description

Technology Field

[0001] The present invention relates to a method for verifying linear motor design variables and a method for optimizing linear motor design variables. Background Technology

[0002] Iron-core linear motors were frequently used in industries requiring high acceleration and thrust characteristics to achieve high yields. In such iron-core linear motors, force waves originating from the motor's structural characteristics occur, which necessitated a method to predict electromagnetic properties based on design parameters during the initial design phase.

[0003] Accordingly, there have been many techniques for calculating Maxwell's equations for static magnetometry, which are governing equations in electromagnetic problems and are in the form of systems of partial differential equations, using numerical methods such as the finite element method. In motor analysis using such numerical methods, there was a problem that a lot of time was required for the analysis when performing calculations while changing various design parameters, because the structural shape of the motor had to be divided into a large number of nodes and meshes. Prior art literature

[65535] Korean Published Patent 10-2008-0079133 Korean Published Patent 10-2007-0096276 HM Hasanien, AS Abd-Rabou, and SM Sakr, "Design optimization of transverse flux linear motor for weight reduction and performance improvement using response surface methodology and genetic algorithms," IEEE Trans. Energy Convers., vol. 25, no. 3, p. 598, Sep. 2010. Hasanien, H.M., Abd-Rabou, AS, & Sakr, SM (2010). Design optimization of transverse flux linear motor for weight reduction and performance improvement using response surface methodology and genetic algorithms. IEEE Transactions on Energy Conversion, 25(3), 598. The problem to be solved

[0004] One objective of the present invention is to provide a method for rapidly verifying linear motor design parameters.

[0005] Another objective of the present invention is to provide a method for rapidly optimizing linear motor design parameters.

[0006] Another objective of the present invention is to provide a linear motor manufactured according to linear motor design variables verified and / or optimized through the verification method or optimization method.

[0007] In particular, the present invention aims to provide a new type of analysis technique that improves upon the problems of conventional technology and enables the rapid prediction of electromagnetic characteristics of a prototype motor by providing frequency-based modeling based on a magnetic investment matrix. means of solving the problem

[0008] In one aspect, the present invention provides a method for verifying linear motor design variables, comprising: a first step of deriving a magnetic permeability matrix of the linear motor from the linear motor design variables through the following equation (1); a second step of deriving a Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor through LU decomposition; a third step of deriving one or more verification physical quantities selected from the group including the force of the linear motor, the magnetic flux linkage passing through each coil of the stator of the linear motor, the back EMF 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 verification conditions are met by comparing the verification physical quantities with a predetermined reference value.

[0009] (1)

[0010] Here, x and y are the x and y coordinates of the linear motor, respectively, μ is the magnetic permeability of the material of the linear motor, and m i and n j are respectively (2π / λ x )i and (2π / λ y Defined as )j, and m k and n l are respectively (2π / λ x )k and (2π / λ y Defined as )l, and λ x and λ y ε₀ and γ₀ are the fundamental periods of trigonometric functions for the x and y directions, respectively, and α, β, γ, ξ, ε₀ and ρ are 2-dimensional magnetic permeability matrices.

[0011] In one embodiment, the LU decomposition of the second step can be performed through the following equation (2).

[0012] (2)

[0013] Here, H x , H y and H z and represent the magnetic field strength in the x, y, and z directions, respectively, and B x , B y and B z represents the magnetic flux densities in the x, y, and z directions, respectively, and M and N are respectively the above m i and n j It is a diagonal matrix with as diagonal elements, and T and λ cc are respectively {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 It is the eigenvector matrix and eigenvalue matrix of, and U and λ cs are respectively {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 is the eigenvector matrix and eigenvalue matrix, and L, M, N, and O are the magnetic field constants of the Maxwell matrix to be derived, respectively.

[0014] In one embodiment, the power of the linear motor in the third step can be derived through the following equation (3).

[0015] (3)

[0016] Here, 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, and B x , B y and B zε₀ and y₀ are the magnetic flux densities in the x, y, and z directions, respectively, and μ₀ is the magnetic permeability in 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 through the following equation (4).

[0018] (4)

[0019] Here, Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, and ▽×A represents the magnetic vector potential rotation value.

[0020] In one embodiment, the back EMF of the linear motor in the third step can be derived through the following equation (5).

[0021] (5)

[0022] Here, V bemf E is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the above linear motor, t is time, and y r is the travel 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 through the following equation (6).

[0024] (6)

[0025] Here, 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.

[0026] In another aspect, the present invention provides a method for optimizing linear motor design variables, comprising: a first step of deriving a magnetic permeability matrix of each linear motor from each design variable of two or more virtual linear motors through the following equation (1); a second step of deriving a Maxwell matrix of each linear motor from the magnetic permeability matrix of each linear motor through LU decomposition; a third step of deriving one or more verification physical quantities selected from a group including the force of each linear motor, the magnetic flux linkage passing through each coil of the stator of each linear motor, the back EMF of each linear motor, and the inductance of each linear motor from the Maxwell matrix of each linear motor; and a fourth step of comparing the verification physical quantities of each linear motor to select a linear motor having a verification physical quantity that is close to the desired design direction.

[0027] (1)

[0028] Here, x and y are the x and y coordinates of the linear motor, respectively, μ is the magnetic permeability of the material of the linear motor, and m i and n j are respectively (2π / λ x )i and (2π / λ y Defined as )j, and m k and n l are respectively (2π / λ x )k and (2π / λ y Defined as )l, and λ x and λ y ε₀ and γ₀ are the fundamental periods of trigonometric functions for the x and y directions, respectively, and α, β, γ, ξ, ε₀ and ρ are 2-dimensional magnetic permeability matrices.

[0029] 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 one or more times for two or more virtual linear motors including the linear motor selected in the fourth step.

[0030] In one embodiment, the LU decomposition of the second step can be performed through the following equation (2).

[0031] (2)

[0032] Here, H x , H y and H z and represent the magnetic field strength in the x, y, and z directions, respectively, and B x , B y and B z represents the magnetic flux densities in the x, y, and z directions, respectively, and M and N are respectively the above m i and n j It is a diagonal matrix with as diagonal elements, and T and λ cc are respectively {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 It is the eigenvector matrix and eigenvalue matrix of, and U and λ cs are respectively {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 is the eigenvector matrix and eigenvalue matrix, and L, M, N, and O are the magnetic field constants of the Maxwell matrix to be derived, respectively.

[0033] In one embodiment, the force of each linear motor in the third step can be derived through the following equation (3).

[0034] (3)

[0035] Here, 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, and B x , B y and B z ε₀ and y₀ are the magnetic flux densities in the x, y, and z directions, respectively, and μ₀ is the magnetic permeability in vacuum.

[0036] 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 through the following equation (4).

[0037] (4)

[0038] Here, Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, and ▽×A represents the magnetic vector potential rotation value.

[0039] In one embodiment, the back EMF of each linear motor in the third step can be derived through the following equation (5).

[0040] (5)

[0041] Here, V bemf E is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the above linear motor, t is time, and y r is the travel distance, and v is the speed of the mover of the linear motor.

[0042] In one embodiment, the inductance of each linear motor in the third step can be derived through the following equation (6).

[0043] (6)

[0044] Here, 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. Effects of the invention

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

[0046] Through the linear motor design variable optimization method according to an embodiment of the present invention, design variables of a linear motor can be optimized quickly and accurately to identify design variables of a linear motor capable of achieving desired performance.

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

[0048] In particular, iron-core linear motors are adopted to implement linear motion capable of generating high thrust in various applications. Generally, during the initial design phase, it is essential to quickly and accurately predict the electromagnetic characteristics of a motor prototype. In this invention, by utilizing the analytical solution of Maxwell's equations for static magnetism through a magnetic permeability matrix, motor analysis is made possible with an accuracy of over 95% compared to commercial finite element analysis programs. Furthermore, since this invention does not require the process of dividing the structure of the motor to be analyzed into nodes and elements, it is possible to significantly reduce the time required for analysis compared to commercial finite element analysis programs. Through the high-speed electromagnetic analysis method of this invention, it is possible to design a motor more quickly while maintaining the accuracy of design methods using finite element analysis programs based on conventional numerical calculation methods. Brief explanation of the drawing

[0049] FIG. 1 is a block diagram showing an electromagnetic analysis model used in a linear motor design parameter verification method according to an embodiment of the present invention. Figure 2 shows a linear motor that verifies design variables through a linear motor design variable verification method according to an embodiment of the present invention. Specific details for implementing the invention

[0050] Hereinafter, embodiments of the present invention will be described in detail with reference to the attached drawings. Since the present invention is susceptible to various modifications and may take various forms, specific embodiments are illustrated in the drawings and described in detail in the text. However, this is not intended to limit the present invention to the specific disclosed forms, and it should be understood that it includes all modifications, equivalents, and substitutions that fall within the spirit and scope of the present invention. Similar reference numerals have been used for similar components in the description of each drawing. In the attached drawings, the dimensions of the structures are shown enlarged compared to the actual dimensions for the clarity of the present invention.

[0051] The terms used in this application are used merely to describe specific embodiments and are not intended to limit the invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, terms such as “comprising” or “having” are intended to specify the presence of the features, numbers, steps, actions, components, or combinations thereof described in the specification, and should be understood as not precluding the existence or addition of one or more other features, numbers, steps, actions, components, 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 figures described in the specification.

[0052] Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as generally understood by those skilled in the art to which the present invention pertains. Terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant technology, and should not be interpreted in an ideal or overly formal sense unless explicitly defined in this application.

[0053] FIG. 1 is a block diagram showing an electromagnetic analysis model used in a linear motor design parameter verification method according to an embodiment of the present invention.

[0054] Figure 2 shows a linear motor that verifies design variables through a linear motor design variable verification method according to an embodiment of the present invention.

[0055] Referring to FIGS. 1 and 2, a linear motor design parameter verification method and an electromagnetic analysis model used therein according to an embodiment of the present invention receive numerical information regarding the motor shape, calculate a magnetic permeability matrix based on said information, construct a Maxwell matrix, and derive a magnetic field in the motor stator therefrom. Electromagnetic data of the motor are calculated based on the calculated magnetic field, and said electromagnetic data includes motor force, magnetic flux linkage, and the resulting back EMF and inductance.

[0056] Referring continuously to FIGS. 1 and 2, a method for verifying linear motor design variables 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 linear motor design variables through the following equation (1); a second step of deriving a Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor through LU decomposition; a third step of deriving one or more verification physical quantities selected from the group including the force of the linear motor, the magnetic flux linkage passing 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 verification conditions are met by comparing the verification physical quantities with a predetermined reference value.

[0057] (1)

[0058] Here, x and y are the x and y coordinates of the linear motor, respectively, μ is the magnetic permeability of the material of the linear motor, and m i and n j are respectively (2π / λ x )i and (2π / λ y Defined as )j, and m k and n l are respectively (2π / λ x )k and (2π / λ y Defined as )l, and λ x and λ y ε₀ and γ₀ are the fundamental periods of trigonometric functions for the x and y directions, respectively, and α, β, γ, ξ, ε₀ and ρ are 2-dimensional magnetic permeability matrices.

[0059] In the context of this specification, magnetic permeability may refer to a physical quantity indicating how much a medium is magnetized with respect to a given magnetic field.

[0060] The first step above is to derive the magnetic permeability matrix of a linear motor. In the context of this specification, the magnetic permeability matrix may mean a matrix having magnetic permeability as a component, and may be composed of Fourier coefficients obtained by performing a 2D Fourier series expansion of basis functions (here, referring to functions formed by the product of trigonometric functions for each x and y direction, such as cos(mx), cos(ny), cos(mx), and sin(ny)) multiplied by the magnetic permeability function μ(x,y).

[0061] The present invention is based at least on the discovery that it is possible to calculate physical quantities as approximations within a significant level by deriving a self-investment matrix without using the finite element method, and then deriving a Maxwell matrix through the steps described below. In the context of this specification, the finite element method may refer to a method for obtaining approximate solutions to partial differential equations, integrals, heat equations, etc.

[0062] The second step above is a step of deriving a Maxwell matrix from the derived magnetic inclination matrix, and the third step above is a step of calculating a physical quantity to be verified from the derived Maxwell matrix. The physical quantity to be verified is not limited to those that can be derived from the Maxwell matrix and includes magnetic flux linkage passing through each coil of the stator of the linear motor, back electromotive force of the linear motor, inductance of the linear motor, and physical quantities derived therefrom.

[0063] The above-mentioned fourth step is a step of determining whether the calculated physical quantity has reached a target value, that is, whether a verification condition has been achieved by comparing it with a predetermined reference value. In the context of this specification, achieving a verification condition for a physical quantity means confirming whether an advantageous effect has been achieved by being greater than or smaller than a predetermined reference value, from the perspective obvious to a person skilled in the art or from the perspective intended by the practitioner.

[0064] In the core portion of an iron-core motor, the magnetic permeability μ depends on the motor coordinates s Or it can be μ0.

[0065] In one embodiment, the LU decomposition of the second step can be performed through the following equation (2).

[0066] (2)

[0067] Here, H x , H y and H z and represent the magnetic field strength in the x, y, and z directions, respectively, and B x , B y and B z represents the magnetic flux densities in the x, y, and z directions, respectively, and M and N are respectively the above m i and n j It is a diagonal matrix with as diagonal elements, and T and λ cc are respectively {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 It is the eigenvector matrix and eigenvalue matrix of, and U and λ cs are respectively {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 is the eigenvector matrix and eigenvalue matrix, and L, M, N, and O are the magnetic field constants of the Maxwell matrix to be derived, respectively.

[0068] In one embodiment, the power of the linear motor in the third step can be derived through the following equation (3).

[0069] (3)

[0070] Here, 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, and B x , B y and B z ε₀ and y₀ are the magnetic flux densities in the x, y, and z directions, respectively, and μ₀ is the magnetic permeability in vacuum. Since most of the force in an electromagnetic motor is generated in the air gap between the stator (coil part) and the mover (magnet part), the [0 0-1]^T, which corresponds to the normal vector of the air gap, is multiplied by the Maxwell stress tensor to obtain the angular components F of the force generated in the motor air gap. x , F y and F z Calculate.

[0071] 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 through the following equation (4).

[0072] (4)

[0073] Here, Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, and ▽×A represents the magnetic vector potential rotation value.

[0074] In one embodiment, the back EMF of the linear motor in the third step can be derived through the following equation (5).

[0075] (5)

[0076] Here, V bemf E is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the above linear motor, t is time, and y rε is the distance traveled, and v is the speed of the mover of the linear motor. According to Faraday's law, the back EMF is equal to the negative value of the time rate of change of the magnetic flux passing through the coil. Applying the chain rule, the time rate of change of the magnetic flux (d Φ / dt) is the rate of change of magnetic flux with respect to the distance traveled (d Φ / dy r ) and the rate of change of distance with respect to time (dy r It can be expressed as a product of / dt. Since the rate of change of distance with respect to time is equal to the velocity v of the mover (magnetic part), the back EMF V generated in the coil bemf ..., the rate of change of the distance traveled by the magnetic flux passing through the coil (d Φ / dy r It can be expressed as the product of ) and the mover's velocity (v).

[0077] In one embodiment, the inductance of the linear motor in the third step can be derived through the following equation (6).

[0078] (6)

[0079] Here, 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.

[0080] Meanwhile, a linear motor design variable optimization method according to an embodiment of the present invention may include: a first step of deriving a magnetic permeability matrix of each linear motor from each design variable of two or more virtual linear motors through the following equation (1); a second step of deriving a Maxwell matrix of each linear motor from the magnetic permeability matrix of each linear motor through LU decomposition; a third step of deriving one or more verification physical quantities selected from a group including the force of each linear motor, the magnetic flux linkage passing through each coil of the stator of each linear motor, the back EMF of each linear motor, and the inductance of each linear motor from the Maxwell matrix of each linear motor; and a fourth step of comparing the verification physical quantities of each linear motor to select a linear motor having a verification physical quantity that is close to the desired design direction.

[0081] (1)

[0082] Here, x and y are the x and y coordinates of the linear motor, respectively, μ is the magnetic permeability of the material of the linear motor, and m i and n j are respectively (2π / λ x )i and (2π / λ y Defined as )j, and m k and n l are respectively (2π / λ x )k and (2π / λ y Defined as )l, and λ x and λ y ε₀ and γ₀ are the fundamental periods of trigonometric functions for the x and y directions, respectively, and α, β, γ, ξ, ε₀ and ρ are 2-dimensional magnetic permeability matrices.

[0083] The description of the linear motor design variable optimization method according to the embodiment of the present invention applies identically or similarly to the description of the linear motor design variable verification method according to the embodiment of the present invention regarding terms or configurations identical or similar to those described above. In particular, the description of the linear motor design variable optimization method according to the embodiment of the present invention differs from the description of the linear motor design variable verification method according to the embodiment of the present invention only in that the same analysis model is applied to multiple linear motors rather than a single linear motor in the first to third steps, and in that, in the fourth step, a design variable closer to the design direction among the multiple linear motors is selected rather than a single linear motor design variable being compared with a reference value; otherwise, the description is substantially similar. Therefore, it should be understood that parts omitted in the description of the linear motor design variable optimization method according to the embodiment of the present invention are intended to avoid repetition.

[0084] The above fourth step is a step of selecting a linear motor among a plurality of linear motor candidates in a direction where the desired design variable is advantageous or in which a physical quantity that can be derived from the design variable is advantageous. 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 one or more times for two or more virtual linear motors including the linear motor selected in the fourth step.

[0085] In one embodiment, the LU decomposition of the second step can be performed through the following equation (2).

[0086] (2)

[0087] Here, H x , H y and H z and represent the magnetic field strength in the x, y, and z directions, respectively, and Bx , B y and B z represents the magnetic flux densities in the x, y, and z directions, respectively, and M and N are respectively the above m i and n j It is a diagonal matrix with as diagonal elements, and T and λ cc are respectively {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 It is the eigenvector matrix and eigenvalue matrix of, and U and λ cs are respectively {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 is the eigenvector matrix and eigenvalue matrix, and L, M, N, and O are the magnetic field constants of the Maxwell matrix to be derived, respectively.

[0088] In one embodiment, the force of each linear motor in the third step can be derived through the following equation (3).

[0089] (3)

[0090] Here, 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, and B x , B y and B z ε₀ and y₀ are the magnetic flux densities in the x, y, and z directions, respectively, and μ₀ is the magnetic permeability in vacuum.

[0091] 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 through the following equation (4).

[0092] (4)

[0093] Here, Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, and ▽×A represents the magnetic vector potential rotation value.

[0094] In one embodiment, the back EMF of each linear motor in the third step can be derived through the following equation (5).

[0095] (5)

[0096] Here, V bemf E is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the above linear motor, t is time, and y r is the travel distance, and v is the speed of the mover of the linear motor.

[0097] In one embodiment, the inductance of each linear motor in the third step can be derived through the following equation (6).

[0098] (6)

[0099] Here, 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.

[0100] Although the present invention has been described above with reference to preferred embodiments, those skilled in the art will understand that various modifications and changes can be made to the invention without departing from the spirit and scope of the invention as set forth in the following claims.

Claims

Claim 1 A method for verifying linear motor design variables performed by at least one processor, comprising: a first step of deriving a magnetic permeability matrix of the linear motor from the linear motor design variables through the following equation (1); a second step of deriving a Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor through LU decomposition; a third step of deriving one or more verification physical quantities selected from a group including the force of the linear motor, the magnetic flux linkage passing through each coil of the stator of the linear motor, the back EMF 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 verification conditions are met by comparing the verification physical quantities with a predetermined reference value; wherein the LU decomposition of the second step is performed through the following equation (2). (1) (2) Here, x and y are the x and y coordinates of the linear motor, respectively, μ is the magnetic permeability of the material of the linear motor, and m i and n j are respectively (2π / λ x )i and (2π / λ y Defined as )j, and m k and n l are respectively (2π / λ x )k and (2π / λ y Defined as )l, and λ x and λ y and are the fundamental periods of trigonometric functions with respect to the x and y directions, respectively, and α, β, γ, ξ, ε, and ρ are 2-dimensional magnetic permeability matrices, and H x , H y and H z represents the magnetic field strength in the x, y, and z directions, respectively, and B x , B y and B z represents the magnetic flux density in the x, y, and z directions, respectively, and M and N are respectively the above m i and n j It is a diagonal matrix with as diagonal elements, and T and λ cc are respectively {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 The eigenvector matrix and eigenvalue matrix of, and U and λ cs are respectively {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 is the eigenvector matrix and eigenvalue matrix, and L, M, N, and O are the magnetic field constants of the Maxwell matrix to be derived, respectively. Claim 2 delete Claim 3 A method for verifying linear motor design variables, wherein in the first step, the power of the linear motor is derived through the following equation (3): (3) Here, 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, and B x , B y and B z ε₀ and y₀ are the magnetic flux densities in the x, y, and z directions, respectively, and μ₀ is the magnetic permeability in vacuum. Claim 4 A method for verifying linear motor design parameters according to claim 1, wherein the magnetic flux linkage passing through each coil of the stator of the linear motor in the third step is derived through the following equation (4): (4) Here, Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, and ▽×A represents the magnetic vector potential rotation value. Claim 5 A method for verifying linear motor design variables, wherein in the first step, the back EMF of the linear motor is derived through the following equation (5): (5) Here, V bemf ε is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the above linear motor, t is time, and y r is the travel distance, and v is the speed of the mover of the linear motor. Claim 6 A method for verifying linear motor design variables, wherein in the first step, the inductance of the linear motor is derived through the following equation (6): (6) Here, 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. Claim 7 A method for optimizing linear motor design variables performed by at least one processor, comprising: a first step of deriving a magnetic permeability matrix of each linear motor from each design variable of two or more virtual linear motors through the following equation (1); a second step of deriving a Maxwell matrix of each linear motor from the magnetic permeability matrix of each linear motor through LU decomposition; and a third step of deriving one or more verification physical quantities selected from a group including the force of each linear motor, the magnetic flux linkage passing through each coil of the stator of each linear motor, the back EMF of each linear motor, and the inductance of each linear motor from the Maxwell matrix of each linear motor. A linear motor design variable optimization method comprising: a fourth step of selecting a linear motor having a verification physical quantity close to the desired design direction by comparing the verification physical quantity of each of the above linear motors; and for two or more virtual linear motors including the linear motor selected in the fourth step, repeating the first step and the fourth step one or more times, wherein the LU decomposition of the second step is performed through the following equation (2): (1) (2) Here, x and y are the x and y coordinates of the linear motor, respectively, μ is the magnetic permeability of the material of the linear motor, and m i and n j are respectively (2π / λ x )i and (2π / λ y Defined as )j, and m k and n l are respectively (2π / λ x )k and (2π / λ y Defined as )l, and λ x and λ y and are the fundamental periods for the x and y directions, respectively, and α, β, γ, ξ, ε, and ρ are 2-dimensional magnetic permeability matrices, and H x , H y and H z represents the magnetic field strength in the x, y, and z directions, respectively, and B x , B y and B z represents the magnetic flux density in the x, y, and z directions, respectively, and M and N are respectively the above m i and n j It is a diagonal matrix with diagonal elements, and T and λcc are respectively {α -1 (Mε -1 M+Nξ -1 N)} 1 / 2 are the eigenvector matrix and eigenvalue matrix of , and U and λcs are {β -1 (Mρ -1 M+Nγ -1 N)} 1 / 2 is the eigenvector matrix and eigenvalue matrix, and L, M, N, and O are the magnetic field constants of the Maxwell matrix to be derived, respectively. Claim 8 delete Claim 9 A linear motor design variable optimization method according to claim 7, wherein the force of each linear motor in the third step is derived through the following equation (3): (3) Here, 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, and B x , B y and B z ε₀ and y₀ are the magnetic flux densities in the x, y, and z directions, respectively, and μ₀ is the magnetic permeability in vacuum. Claim 10 A linear motor design parameter 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 through the following equation (4): (4) Here, Φ is the magnetic flux passing through each coil, B is the magnetic flux density, A is the magnetic vector potential, and ▽×A represents the magnetic vector potential rotation value. Claim 11 A linear motor design variable optimization method according to claim 7, wherein the back EMF of each linear motor in the third step is derived through the following equation (5): (5) Here, V bemf ε is the back-EMF generated in the stator due to the relative motion between the stator and the mover of the above linear motor, t is time, and y r is the travel distance, and v is the speed of the mover of the linear motor. Claim 12 A linear motor design variable optimization method according to claim 7, wherein the inductance of each linear motor in the third step is derived through the following equation (6): (6) Here, 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.

Images