Linear Motor Variable Verification Using Frequency-Domain Maxwell Matrices
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Solution Overview
Problem
Existing methods for predicting electromagnetic characteristics of iron core linear motors in the early design stage are time-consuming due to the need for numerical calculations and mesh division, which hampers rapid verification and optimization of design variables.
Innovation Solution
A frequency-based modeling approach using a magnetic permeability matrix is introduced, allowing for quick derivation of Maxwell matrices via LU decomposition and subsequent calculation of verification target physical quantities such as force, magnetic flux linkage, counter electromotive force, and inductance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerical calculation method such as finite element method is used to calculate Maxwell equation, then electromagnetic characteristics can be predicted, but analysis time becomes excessively long
Solution Approach 1:
The patent transforms the partial differential equation into an algebraic equation by applying Fourier series expansion, changing the mathematical parameters from continuous spatial derivatives to discrete frequency domain coefficients. This parameter transformation enables rapid calculation while maintaining prediction accuracy, directly resolving the contradiction between accurate electromagnetic characteristic prediction and excessive analysis time
Solution Approach 2:
The patent replaces the traditional finite element method (mechanical mesh division and iterative numerical solving) with a frequency domain analytical method using Fourier series. This substitution eliminates the need for complex mesh generation and iterative calculations, achieving both speed and accuracy in electromagnetic characteristic prediction
2Measurement precision
If structural shape is divided into large number of nodes and elements for mesh, then calculation accuracy is improved, but device complexity and analysis time increase
Solution Approach 1:
The patent extracts the essential electromagnetic field characteristics by representing the magnetic permeability distribution through Fourier series coefficients, rather than maintaining the complete complex mesh structure. This extraction of key frequency domain parameters simplifies the problem while preserving calculation accuracy, eliminating the need for fine mesh division
Solution Approach 2:
The patent changes the representation parameters from spatial mesh coordinates to Fourier frequency coefficients. This parameter transformation converts the complex geometric mesh problem into a simpler algebraic problem in the frequency domain, reducing device complexity while maintaining accuracy
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method enables rapid and accurate verification and optimization of linear motor design variables, significantly reducing analysis time while maintaining high accuracy comparable to commercial finite element analysis programs.
Implementation Method 1
a first step of deriving a magnetic permeability matrix of a linear motor from a linear motor design variable
Implementation Method 2
a second step of deriving a Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor via LU decomposition
Implementation Method 3
a third step of deriving, from the Maxwell matrix of the linear motor, at least one verification target physical quantity selected from a group including a force of the linear motor, a magnetic flux linkage passing through each of coils of a stator of the linear motor, a counter electromotive force of the linear motor, and an inductance of the linear motor
Data Source
AI summary
A linear motor design variable verification method and a linear motor design variable optimization method are disclosed. The linear motor design variable verification method includes a first step of deriving a magnetic permeability matrix of a linear motor from a linear motor design variable; a second step of deriving a Maxwell matrix of the linear motor from the magnetic permeability matrix of the linear motor via LU decomposition; a third step of deriving, from the Maxwell matrix of the linear motor, at least one verification target physical quantity selected from a group including a force of the linear motor, a magnetic flux linkage passing through each of coils of a stator of the linear motor, a counter electromotive force of the linear motor, and an inductance of the linear motor; and a fourth step of comparing the derived verification target physical quantity with a predetermined reference value, and determining whether a target verification condition is satisfied, based on the comparing result.