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Research Papers: Applications

Generalized Three-Dimensional Mathematical Models for Force and Stiffness in Axially, Radially, and Perpendicularly Magnetized Passive Magnetic Bearings With “n” Number of Ring Pairs

[+] Author and Article Information
Siddappa I. Bekinal

Bearings Laboratory,
Department of Mechanical Engineering,
KLS Gogte Institute of Technology,
Belagavi 590008, Karnataka, India
e-mail: sibekinal@git.edu

Soumendu Jana

Bearings and Rotor Dynamics Laboratory,
Propulsion Division,
National Aerospace Laboratories,
Bengaluru 560017, Karnataka, India
e-mail: sjana@nal.res.in

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received August 15, 2015; final manuscript received January 7, 2016; published online May 6, 2016. Assoc. Editor: Daejong Kim.

J. Tribol 138(3), 031105 (May 06, 2016) (9 pages) Paper No: TRIB-15-1298; doi: 10.1115/1.4032668 History: Received August 15, 2015; Revised January 07, 2016

This work deals with generalized three-dimensional (3D) mathematical model to estimate the force and stiffness in axially, radially, and perpendicularly polarized passive magnetic bearings with “n” number of permanent magnet (PM) ring pairs. Coulombian model and vector approach are used to derive generalized equations for force and stiffness. Bearing characteristics (in three possible standard configurations) of permanent magnet bearings (PMBs) are evaluated using matlab codes. Further, results of the model are validated with finite element analysis (FEA) results for five ring pairs. Developed matlab codes are further utilized to determine only the axial force and axial stiffness in three stacked PMB configurations by varying the number of rings. Finally, the correlation between the bearing characteristics (PMB with only one and multiple ring pairs) is proposed and discussed in detail. The proposed mathematical model might be useful for the selection of suitable configuration of PMB as well as its optimization for geometrical parameters for high-speed applications.

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References

Figures

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Fig. 1

PMB configurations with (a) n axially polarized ring pairs, (b) n radially polarized ring pairs, and (c) n perpendicularly polarized ring pairs

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Fig. 2

The pth ring pair of PMB with axially polarized ring pairs with elements on polarized surfaces

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Fig. 3

The pth ring pair of PMB with radially polarized ring pairs with elements on polarized surfaces

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Fig. 4

The pth ring pair of PMB with perpendicularly polarized ring pairs with elements on polarized surfaces

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Fig. 5

Comparison of results of an axial force by 3D mathematical model and 3D FEA for five ring pairs: (a) configuration I, (b) configuration II, (c) configuration III, and (d) maximum axial force generated in configuration II in ansys

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Fig. 6

The axial force generated by the outer rings on the inner rings for different axial positions of the rotor in the configuration I: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

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Fig. 7

The axial stiffness of configuration I for different axial positions of the rotor: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

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Fig. 8

The axial force generated by the outer rings on the inner rings for different axial positions of the rotor in configuration II: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

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Fig. 9

The axial stiffness of configuration II for different axial positions of the rotor: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

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Fig. 10

The axial force generated by the outer rings on the inner rings for different axial positions of the rotor in configuration III: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

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Fig. 11

The axial stiffness of configuration III for different axial positions of the rotor: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

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