Non dimensional analysis of axially polarized passive magnetic bearings
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Non dimensional analysis of axially polarized passive magnetic bearings Mintu Karmakar1 · Susenjit Sarkar1 Received: 9 October 2019 / Accepted: 22 April 2020 © Springer Nature Switzerland AG 2020
Abstract Ranges of investigation on passive magnetic bearing exist where radial and axial forces and variations of a few coefficients of radial and axial stiffnesses are shown for a particular set of chosen parameters and dimensions. The paper presents a non-dimensional approach for the same with additional parameters like all coefficients of stiffnesses and natural frequency. The model is considered for static analysis of axially polarised ring shaped magnets for both stator and rotor part in three degrees of freedom with three linear translations in 3D Cartesian coordinate system. The significance of this non-dimensional method is more generalised to the designer where boundary parameters like maximum force on the rotor of passive magnetic bearing, natural frequency, etc. can be easily estimated by simple conversion without doing separate numerical simulation for different parameters every time. The analysis of additional parameters like non-dimensional natural frequency can be the input for non-dimensional dynamic analysis. This paper also provides a way for maximization of radial force with the optimized solution of physical dimensions of passive magnetic bearing as inner radius of stator and outer radius of rotor magnet while keeping others as input parameters. The proposed model is validated with data available for radial and axial forces as well as for radial and axial stiffnesses that found in existing literature for similar kind of problem. Keywords Non-dimensional · Passive magnetic bearing · Radial force maximization · Natural frequency · Axially polarised Abbreviations Fsr Magnetic force between ( stator and rotor (N) ) H or Tm 𝜇0 Absolute permeability 4𝜋 × 10−7 AN2 or m A
𝜋 3.1415926535 (Non-dimensional) qs Magnetic pole strength of stator magnet (Wb or Am) qr Magnetic pole strength of rotor magnet (Wb or Am) rsr Distance between stator and rotor magnetic pole (m) 𝜎s Stator magnetic surface charge density (T) 𝜎r Rotor magnetic surface charge density (T) Ss Stator magnetic pole surface area per pole ( m2) Sr Rotor magnetic pole surface area per pole ( m2)
Br1 Residual magnetism of rotor magnetic material (T) Br2 Residual magnetism of stator magnetic material (T) r1 Radial distance of rotor small elemental area d Sr from rotor axis (m) r2 Radial distance of stator small elemental area d Ss from stator axis (m) α Angular displacement of stator small elemental area d Ss about stator axis measured from x axis (radian) β Angular displacement of rotor small elemental area d Sr about rotor axis measured from x axis (radian)
* Mintu Karmakar, [email protected]; Susenjit Sarkar, [email protected] | 1Department of Mechanical Engineering, Jadavpur University, Kolkata, West Bengal 700032, India. SN Applied Sciences
(2020) 2:987
| https://doi.org/10.1007/s42452-020-2809-x
Vol.:(01234
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