Vibration of a rotating flexible ferromagnetic disc subjected to a solenoid electromagnet

Abstract

A rotating flexible ferromagnetic annular disc with initial unstressed transverse runout subjected to a solenoid electromagnet is modelled and investigated. The total transverse deflection of the steady-state response of the rotating disc is analysed, and the condition of undamped resonance induced by the initial transverse runout and the stiffness of the electromagnetic force is evaluated. A quadratic eigenvalue problem is obtained and employed to study natural frequency and dynamic stability of the rotating disc. Analytical results show that the solenoid electromagnet can cause not only dynamic instability but also system resonance of the rotating disc if it has the initial transverse runout; the instability and resonance tend to occur at a lower rotational speed with the increase of the stiffness of the electromagnetic force.

Keywords

rotating flexible disc ferromagnetic plate solenoid electromagnet steady-state response dynamic stability

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References

Young

T. H.

Lin

C. Y.

Stability of a spinning disk under a stationary oscillating unit. J. Sound Vib., 2006, 298(1–2), 307–318.

Ouyang

H. J.

Mottershead

J. E.

Unstable travelling waves in the friction-induced vibration of discs. J. Sound Vib., 2001, 248(4), 768–779.

Ouyang

H. J.

Stationary and non-stationary vibration of atomising discs. J. Sound Vib., 2007, 308(3–5), 699–708.

Q. S.

C. W. S.

Huang

K. L.

Dynamic stability and bifurcation of an alternating load and magnetic field excited magnetoelastic beam. J. Sound Vib., 1995, 181(5), 873–891.

G. Y.

The analysis of dynamic instability and vibration motions of a pinned beam with transverse magnetic fields and thermal loads. J. Sound Vib., 2005, 284(1–2), 343–360.

Tian

J. F.

Hutton

S. G.

Traveling-wave modal identification based on forced or self-excited resonance for rotating discs. J. Vib. Control, 2001, 7(1), 3–18.

Pei

Y.-C.

Tan

Q.-C.

Stability of rotating flexible disk under AC electromagnet. Eng. Mech., 2009, 26(10), 217–220.

Michalek

A. J.

Marzocca

Moosbrugger

Hasanyan

Effects of an in-plane axisymmetric magnetic field on the vibration of a thin conductive spinning disk. J. Appl. Phys., 2005, 97(10), 10R509–10R509.

Benson

R. C.

Cole

K. A.

Transverse ‘runout’ of a nonflat spinning disk. Tribol. Trans., 1991, 34(4), 545–552.

10.

Jia

H. S.

Analysis of transverse runout in rotating flexible disks by using Galerkin’s method. Int. J. Mech. Sci., 2000, 42(2), 237–248.

11.

Chen

J.-S.

Lin

C.-C.

Axisymmetrical snapping of a spinning nonflat disk. Trans. ASME, J. Appl. Mech., 2005, 72(6), 879–886.

12.

Chen

J.-S.

Chang

Y.-Y.

On the unsymmetrical deformation and reverse snapping of a spinning non-flat disk. Int. J. Non-Linear Mech., 2007, 42(8), 1000–1009.

13.

Pei

Y.-C.

F.-J.

The transverse runout of a rotating flexible disc under stationary sliders. Proc. IMechE, Part C: J. Mechanical Engineering Science, 2009, 223(6), 1319–1326.

14.

Pei

Y.-C.

Tan

Q.-C.

Parametric instability of flexible disk rotating at periodically varying angular speed. Meccanica, 2009, 44(6), 711–720.

15.

D’Angelo

Mote

D. Natural frequencies of a thin disk, clamped by thick collars with friction at the contacting. J. Sound Vib., 1993, 168(1), 1–14.

16.

Hamidzadeh

H. R.

Non-linear free transverse vibration of thin rotating discs. Proc. IMechE, Part K: J. Multi-body Dynamics, 2007, 221(3), 467–473.