A novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine

In this study, a stochastic differential equation capable of describing (using the motion function) the automatic manufacturing process of a lithium battery with a sleeve shell is introduced. The boundary-condition modeling method for this type of motion is an ordinary differential equation. The non...

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Autor principal:	Xian-Ming Liu
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2022
Materias:	Non-linear differential equations Assembly process of lithium batteries Mathematical model of a manufacturing process Improved application of the Euler algorithm Error calculation and analysis Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/d95aa178309242dfb6a0f3834cc9a73c
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spelling	oai:doaj.org-article:d95aa178309242dfb6a0f3834cc9a73c2021-12-02T04:59:42ZA novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine1110-016810.1016/j.aej.2021.07.034https://doaj.org/article/d95aa178309242dfb6a0f3834cc9a73c2022-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S1110016821005032https://doaj.org/toc/1110-0168In this study, a stochastic differential equation capable of describing (using the motion function) the automatic manufacturing process of a lithium battery with a sleeve shell is introduced. The boundary-condition modeling method for this type of motion is an ordinary differential equation. The nonlinear equation is found using a dynamic method. The equations of the motions for the assembly process are derived by reducing the order of terms and separating the variables. Both the derivatives and integrals of the motion functions are derived and applied to describe the assembly process for a lithium battery. By using a characteristic constitutive assembly model, a new method to calculate the nonlinear terms is proposed. The main advantage of this method is that it can simplify the problem, which is done by finding the algebraic error in the region space of the motion function. The reliability and the applicability of the method were confirmed using a real-life example. Finally, by solving and improving the Euler model, the fourth-order Kutta method and Taylor series are applied to verify the correctness of the algorithm, and the convergence order of the function and the optimization of the assembly model are discussed. Through a one-dimensional search of the convergence domain, a method is found to make the analytical solution approximate the exact solution and reduce the calculation cost. This method in dynamics and mathematical engineering.Xian-Ming LiuElsevierarticleNon-linear differential equationsAssembly process of lithium batteriesMathematical model of a manufacturing processImproved application of the Euler algorithmError calculation and analysisEngineering (General). Civil engineering (General)TA1-2040ENAlexandria Engineering Journal, Vol 61, Iss 3, Pp 1892-1910 (2022)
institution	DOAJ
collection	DOAJ
language	EN
topic	Non-linear differential equations Assembly process of lithium batteries Mathematical model of a manufacturing process Improved application of the Euler algorithm Error calculation and analysis Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Non-linear differential equations Assembly process of lithium batteries Mathematical model of a manufacturing process Improved application of the Euler algorithm Error calculation and analysis Engineering (General). Civil engineering (General) TA1-2040 Xian-Ming Liu A novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine
description	In this study, a stochastic differential equation capable of describing (using the motion function) the automatic manufacturing process of a lithium battery with a sleeve shell is introduced. The boundary-condition modeling method for this type of motion is an ordinary differential equation. The nonlinear equation is found using a dynamic method. The equations of the motions for the assembly process are derived by reducing the order of terms and separating the variables. Both the derivatives and integrals of the motion functions are derived and applied to describe the assembly process for a lithium battery. By using a characteristic constitutive assembly model, a new method to calculate the nonlinear terms is proposed. The main advantage of this method is that it can simplify the problem, which is done by finding the algebraic error in the region space of the motion function. The reliability and the applicability of the method were confirmed using a real-life example. Finally, by solving and improving the Euler model, the fourth-order Kutta method and Taylor series are applied to verify the correctness of the algorithm, and the convergence order of the function and the optimization of the assembly model are discussed. Through a one-dimensional search of the convergence domain, a method is found to make the analytical solution approximate the exact solution and reduce the calculation cost. This method in dynamics and mathematical engineering.
format	article
author	Xian-Ming Liu
author_facet	Xian-Ming Liu
author_sort	Xian-Ming Liu
title	A novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine
title_short	A novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine
title_full	A novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine
title_fullStr	A novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine
title_full_unstemmed	A novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine
title_sort	novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine
publisher	Elsevier
publishDate	2022
url	https://doaj.org/article/d95aa178309242dfb6a0f3834cc9a73c
work_keys_str_mv	AT xianmingliu anovelalgorithmtosolvethenonlineardifferentialequationofthemotionfunctionofalithiumbatteryassemblymachine AT xianmingliu novelalgorithmtosolvethenonlineardifferentialequationofthemotionfunctionofalithiumbatteryassemblymachine
_version_	1718400920102895616

A novel algorithm to solve the nonlinear differential equation of the motion function of a lithium-battery assembly machine

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