Coupling parametric instability and resonance of a rotating flexible disk with unstressed initial runout under several parametrical excitations

Abstract

With an improved Hill’s method, which is suitable for harmonic balance processing and coupling of nodal circles and nodal diameters, a dynamics research of a rotating flexible disk is carried out by considering unstressed initial runout and several parametrical excitations. The partial differential equation of disk system is obtained by Galerkin’s method considering three different types of excitations, namely slider loading, speed fluctuation and electromagnetic attraction. The individual and coupling effects of parametrical excitations on system’s instability and resonance are studied via numerical simulation. The instability results are shown by different colors based on RGB color space, and the disk’s steady-state amplitudes under different parameter settings are calculated with different nodal circles and nodal diameters. The calculation results show that these excitations affect the disk system’s stability and resonance in their own way. Meanwhile, this method is universal for the flexible disk’s steady-state vibration problems in practical engineering analysis.

Keywords

Parametric instability resonance rotating disk parametrical excitation coupling effect harmonic balance method

Get full access to this article

View all access options for this article.

References

Hansen

MH.

Effect of high-frequency excitation on natural frequencies of spinning discs. J Sound Vib 2000; 234: 577–589.

Pei

Y-C

Tan

Q-C.

Parametric instability of flexible disk rotating at periodically varying angular speed. Meccanica 2009; 44: 711–720.

Zhang

Yang

Transverse nonlinear vibrations of a circular spinning disk with a varying rotating speed. Sci China Phys Mech Astron 2010; 53: 1536–1553.

Ryzhik

Friction-induced vibrations of squeal type due to transverse contraction in a flexible disk. J Sound Vib 2009; 326: 623–632.

Ryzhik

Suppression of friction-induced bending vibrations in a flexible disk sliding in contact with a rigid surface. J Vib Acoust 2014; 136.

Kang

Moving mode shape function approach for spinning disk and asymmetric disc brake squeal. J Sound Vib 2018; 424: 48–63.

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: 1319–1326.

Pei

Y-C

Chatwin

Vibration of a rotating flexible ferromagnetic disc subjected to a solenoid electromagnet. Proc IMechE, Part K: J Multi-body Dynamics 2011; 225: 195–203.

Kang

Raman

Vibrations and stability of a flexible disk rotating in a gas-filled enclosure—part 1: theoretical study. J Sound Vib 2006; 296: 651–675.

10.

Kang

Raman

Vibrations and stability of a flexible disk rotating in a gas-filled enclosure—part 2: experimental study. J Sound Vib 2006; 296: 676–689.

11.

Jia

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

12.

Chen

J-S

Lin

C-C.

Axisymmetrical snapping of a spinning nonflat disk. J Appl Mech 2005; 72: 879–886.

13.

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: 1000–1009.

14.

Pei

Y-C

F-J

Transverse runout in flexible disk rotating at periodically varying angular speed. Meccanica 2011; 46: 303–311.

15.

Pei

Y-C

Wang

J-H

Yang

Dynamics comparison of rotating flexible annular disk under different edge boundary conditions. Int J Mech Sci 2018; 137: 121–132.

16.

Yang

S-W

Zhang

Hao

Y-X

, et al. Nonlinear vibrations of FGM truncated conical shell under aerodynamics and in-plane force along meridian near internal resonances. Thin-Walled Struct 2019; 142: 369–391.

17.

Yang

S-W

Zhang

Mao

J-J.

Nonlinear vibrations of carbon fiber reinforced polymer laminated cylindrical shell under non-normal boundary conditions with 1:2 internal resonance. Eur J Mech - A/Solids 2019; 74: 317–336.

18.

Bai

Zhang

, et al. Application of probabilistic and nonprobabilistic hybrid reliability analysis based on dynamic substructural extremum response surface decoupling method for a blisk of the aeroengine. Int J Aerosp Eng 2017; 2017: 1–11.

19.

Niu

Zhang

Guo

X-Y.

Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets. Eur J Mech - A/Solids 2019; 77: 103798.

20.

Zhang

Y-F

Niu

Zhang

Nonlinear vibrations and internal resonance of pretwisted rotating cantilever rectangular plate with varying cross-section and aerodynamic force. Eng Struct 2020; 225: 111259.

21.

Zhang

Niu

Behdinan

Vibration characteristics of rotating pretwisted composite tapered blade with graphene coating layers. Aerosp Sci Technol 2020; 98: 105644.

22.

Bai

Zhang

, et al. Application of extremum response surface method-based improved substructure component modal synthesis in mistuned turbine bladed disk. J Sound Vib 2020; 472: 115210.

23.

Tisseur

Meerbergen

The quadratic eigenvalue problem. SIAM Rev 2001; 43: 235–286.

24.

Takahashi

An approach to investigate the instability of the multiple-degree-of-freedom parametric dynamic systems. J Sound Vib 1981; 78: 519–529.

25.

Dorf

Bishop

RH.

Modern control systems. 13th ed. Boston, MA: Pearson, 2016.