Analytical vibration of middle rotor of coaxial magnetic gear with complicated structure due to holes and screws

• Autores: Yaser Heidari, Mohammad Arefi, Seyed Ahmadreza Afsari Kashani, Mohsen Irani Rahaghi
• Localización: Mechanics based design of structures and machines, ISSN 1539-7734, Vol. 52, Nº. 3, 2024, págs. 1252-1277
• Idioma: inglés
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• Resumen

  • Coaxial magnetic gear is a cutting-edge technology introduced a few years ago. Its middle rotor is a rotating steel cylindrical shell with a variable array of holes that are filled by brass screws, hence it is such a complicated structure due to these holes. At first glance, it seems impossible to apply shear deformation theories to this unusual geometry, but for the first time, this article has introduced a novel mathematical methodology that creatively makes this possible. Consequently, an analytical formulation is presented for free vibration of this complicated structure, with no need to finite element software. The final aim is to extract natural frequencies and critical speeds in terms of different parameters. The formulation begins with the first-order shear deformation theory as the displacement field and continues with the Hamilton approach to gain governing equations of motion. Additionally, the effect of an external radial magnetic field is modeled by Maxwell’s relation. In the end, the Galerkin scheme is followed for discretization of the governing equations. This scheme is compared to an older article to guarantee its accuracy. Subsequently, the natural frequencies are estimated in terms of physical parameters of the rotor such as angle and number of holes, hole-thickness to total-thickness ratio, magnetic field and some other parameters. The mode shapes are also depicted for better interoperation of rotor’s behavior. The findings show that unlike geometric parameters (e.g., angle and number of holes), the radial magnetic field does not significantly affect the natural frequency.