Formulation of a non-dimensional criterion for stable dynamical response in coaxial magnetic gears

IF 1.4 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Journal of Engineering Mathematics Pub Date : 2024-02-08 DOI:10.1007/s10665-023-10325-z
Panteleimon Tzouganakis, Vasilios Gakos, Christos Kalligeros, Christos Papalexis, Antonios Tsolakis, Vasilios Spitas
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Abstract

Coaxial magnetic gears have been investigated thoroughly in recent years. However, magnetic gears are prone to slippage that could be caused by overloading or acceleration of the drive. In the present work, the dynamical system of equations in coaxial magnetic gears was investigated in order to calculate the maximum operational characteristic of the drive. A non-dimensional condition was derived analytically that can determine the dynamical behaviour and whether the system will converge or diverge without the requirement of a numerical solution of the dynamical equation of the drive. A case study was performed where different values of acceleration and applied torque were considered. The convergence of the system was initially examined with the developed non-dimensional condition and then the equation was solved numerically in order to verify the prediction. The developed condition correctly predicted the behaviour of the drive in all cases. Finally, with the developed model the operational characteristics of a coaxial magnetic gear that yield a required transmission error can be calculated analytically. Therefore, with the developed model the maximum operational characteristics in coaxial magnetic gears can be determined analytically with a non-dimensional criterion without implementing iterative methods that would significantly increase the computational cost.

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制定同轴磁齿轮稳定动态响应的非尺寸准则
近年来,人们对同轴磁齿轮进行了深入研究。然而,磁力齿轮很容易因超载或驱动加速而打滑。本研究对同轴磁力齿轮的动力学方程组进行了研究,以计算驱动装置的最大运行特性。通过分析推导出了一个非维度条件,该条件可以确定动力学行为以及系统是收敛还是发散,而无需对驱动器的动力学方程进行数值求解。在进行案例研究时,考虑了不同的加速度和应用扭矩值。系统的收敛性首先通过开发的非尺寸条件进行检验,然后对方程进行数值求解,以验证预测结果。所开发的条件在所有情况下都能正确预测驱动器的行为。最后,利用所开发的模型,可以分析计算出产生所需传动误差的同轴磁力齿轮的运行特性。因此,利用所开发的模型,同轴磁力齿轮的最大运行特性可以通过非尺寸准则进行分析确定,而无需采用会显著增加计算成本的迭代方法。
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来源期刊
Journal of Engineering Mathematics
Journal of Engineering Mathematics 工程技术-工程:综合
CiteScore
2.10
自引率
7.70%
发文量
44
审稿时长
6 months
期刊介绍: The aim of this journal is to promote the application of mathematics to problems from engineering and the applied sciences. It also aims to emphasize the intrinsic unity, through mathematics, of the fundamental problems of applied and engineering science. The scope of the journal includes the following: • Mathematics: Ordinary and partial differential equations, Integral equations, Asymptotics, Variational and functional−analytic methods, Numerical analysis, Computational methods. • Applied Fields: Continuum mechanics, Stability theory, Wave propagation, Diffusion, Heat and mass transfer, Free−boundary problems; Fluid mechanics: Aero− and hydrodynamics, Boundary layers, Shock waves, Fluid machinery, Fluid−structure interactions, Convection, Combustion, Acoustics, Multi−phase flows, Transition and turbulence, Creeping flow, Rheology, Porous−media flows, Ocean engineering, Atmospheric engineering, Non-Newtonian flows, Ship hydrodynamics; Solid mechanics: Elasticity, Classical mechanics, Nonlinear mechanics, Vibrations, Plates and shells, Fracture mechanics; Biomedical engineering, Geophysical engineering, Reaction−diffusion problems; and related areas. The Journal also publishes occasional invited ''Perspectives'' articles by distinguished researchers reviewing and bringing their authoritative overview to recent developments in topics of current interest in their area of expertise. Authors wishing to suggest topics for such articles should contact the Editors-in-Chief directly. Prospective authors are encouraged to consult recent issues of the journal in order to judge whether or not their manuscript is consistent with the style and content of published papers.
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