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Identification of force coefficients in inter-shaft squeeze film dampers utilizing complex vector description and computational fluid dynamics

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Abstract

Squeeze film dampers (SFDs) have been widely used in high-speed turbomachinery to provide external damping to the system to improve stability. An inter-shaft damper (ISD) is a SFD-like device inserted between two shafts of a double spool aircraft engine to provide damping to both internal and external rotors. Compared to SFDs, analysis of ISDs is not well established because of added complexity of the mechanism. A new approach to model ISDs is reported in this paper, which converts an ISD model to a dynamically equivalent SFD model. A systematic analysis method for SFDs subjected to whirling motions of a non-circular orbit is established first because the whirling orbit of the equivalent SFD is always non-circular with two major frequency components. The analysis method utilizes complex vector descriptions of the motion and force, and frequency-domain analysis with double-sided frequency spectrums. The proposed approach is validated by comparing computational fluid dynamics (CFD) analysis results and damping coefficients obtained from the original ISD model and its equivalent SFD model. One significant advantage of the new approach is that all design rules and insights developed for SFDs can be directly applied to ISDs. In addition, the analysis method established in this work enables accurate calculation of damping coefficients of SFDs subjected to non-circular whirling motions, essentially all SFDs in in real operations including SFDs in test rigs.

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Abbreviations

SFD:

Squeeze film damper

ISD :

Inter-shaft damper

CFD :

Computational fluid dynamics

ω :

Whirl frequency of the shaft center, rad/s

p :

Pressure, Pa

µ :

Viscosity, kg/m-s

r b :

Radius of the bearing, mm

r h :

Radius of the stator, mm

C :

Clearance of a SFD; (rh − 0), mm

Re :

Reynolds number

ρ :

Density, kg/m3

r k :

k-th component of whirl path, m

r k :

k-th component of whirl velocity, m/s

F k :

Force vector corresponding to the k-th component, N

F r :

Radial force, N

F t :

Tangential force, N

θ F, k :

Phase angle of Fk, deg

θ ṙ, k :

Phase angle of ṙk, deg

c :

Damping coefficient, N-s/m

Δt :

Time step, s

T :

Length of time, s

Δf :

Frequency resolution, Hz

f max :

Maximum frequency, Hz

r eq :

Equivalent whirl orbit, m

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, Ohio, USA

    Gil Jun Lee & Jay Kim

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  1. Gil Jun Lee
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  2. Jay Kim
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Corresponding author

Correspondence to Jay Kim.

Additional information

Recommended by Associate Editor Sungsoo Na

Gil Jun Lee is a Visiting Assistant Professor of Mechanical Engineering at the University of Cincinnati (UC). He received his B.S. (2011) and M.S. (2013) degrees from Sogang University in Republic of Korea, and Ph.D. (2017) from UC in United States, all in Mechanical Engineering. His research area includes structural dynamics and vibration, nonlinear dynamics, acoustics, NVH engineering, squeak and rattle noises, and rotordynamics.

Jay Kim is a Professor and Head of the Mechanical and Materials Engineering Department at the University of Cincinnati (UC). He received his B.S., M.S. and Ph.D. degrees in Mechanical Engineering from the Seoul National University (1977), KAIST (1979) and Purdue University (1988). His research interests are in broad areas of applied mechanics such as vibration of shells and plates, automotive NVH, rotordynamcis, which have been funded by both federal agencies and industry. He is an Associate Editor of Noise Control Engineering Journal and a fellow of ASME.

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Lee, G.J., Kim, J. Identification of force coefficients in inter-shaft squeeze film dampers utilizing complex vector description and computational fluid dynamics. J Mech Sci Technol 33, 4615–4625 (2019). https://doi.org/10.1007/s12206-019-0904-y

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  • DOI: https://doi.org/10.1007/s12206-019-0904-y

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