Abstract
The enhanced rotational compliance function (eRCF) is a useful concept for estimation of static torsional compliance/stiffness of a structure using measured frequency response functions (FRFs) from a structural system with free-free boundary conditions. The eRCF is estimated using FRF measurements involving impact testing in which a four by four (4x4) FRF matrix is acquired at four separate, symmetric locations on a structure. This is in contrast to a traditional, static torsion test that involves constraints applied to two of these four locations and a static torque applied to the other two of these four locations. The traditional, static torsion test requires extensive instrumentation and a two day test procedure while the eRCF method involves minimal instrumentation over several hours. Added masses can be utilized to acquire additional statistical data that estimates the same compliance (stiffness). The theoretical background is presented along with both modeling and experimental cases involving a rectangular plate structure
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Abbreviations
- Symbol:
-
Description
- σ :
-
Standard deviation
- \(\Delta \) :
-
Static deflection (in)
- \(\Theta \) :
-
Angular deflection (rad)
- f max :
-
Maximum frequency of the stiffness parameter estimation band (Hz)
- f min :
-
Minimum frequency of the stiffness parameter estimation band (Hz)
- L f :
-
Front spacing (in)
- L r :
-
Rear spacing (in)
- F :
-
Generalized force magnitude (lb f)
- M :
-
Generalized moment magnitude (lb f in)
- \(\left [\mathsf{H}(\omega )\right ]\) :
-
FRF matrix (\(\mathsf{\frac{X} {F} }\))
- K T :
-
Static torsional stiffness (lb f in∕deg)
- {V} :
-
Moment scaling vector
- DOF 1:
-
Left front DOF, z direction
- DOF 2:
-
Right front DOF, z direction
- DOF 3:
-
Left rear DOF, z direction
- DOF 4:
-
Right rear DOF, z direction
- DOF 5:
-
Left mid-span DOF, z direction
- DOF 6:
-
Right mid-span DOF, z direction
- eRCF(ω):
-
Enhanced Rotational Compliance Function
- eFRF(ω):
-
Enhanced Frequency Response Function
References
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Acknowledgements
The authors would like to acknowledge the contributions and support from Helmut Schneeweiss and Luc Cremers of BMW AG, München, Germany.
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Pasha, H.G., Allemang, R.J., Phillips, A.W., Young, A., Poland, J. (2015). Estimation of Torsional Compliance (Stiffness) from Free-Free FRF Measurements: eRCF Theory. In: De Clerck, J. (eds) Experimental Techniques, Rotating Machinery, and Acoustics, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-15236-3_12
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DOI: https://doi.org/10.1007/978-3-319-15236-3_12
Publisher Name: Springer, Cham
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