Acoustic Modal Testing of Bicycle Rims

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Abstract

The stiffness, strength, and safety of a bicycle wheel depend critically on the stiffness of its rim. However, the complicated cross-sections of modern bicycle rims make estimation of the stiffness by geometric methods very difficult. We have measured the radial bending stiffness and lateral-torsional stiffness of bicycle rims by experimental modal analysis using a smartphone microphone. Our acoustic method is fast, cheap, and non-destructive, and estimates the radial bending stiffness, \(EI_{11}\), to within 8% and the torsional stiffness, GJ, to within 11% as compared with a direct mechanical test. The acoustic method also provides a direct measurement of the coupled lateral-torsional effective stiffness, which is necessary for calculating many useful properties of bicycle wheels such as stiffness, buckling tension, and the influence of spoke tensioning. For a complete bicycle wheel, the lateral stiffness can be determined by a superposition of equivalent springs for each mode in series, where each mode stiffness contains a rim stiffness and spoke stiffness combined in parallel. We give example calculations on two realistic bicycle wheels using our experimentally derived rim properties to show how stiff spokes can compensate for a flexible rim, while a very stiff rim doesn’t necessarily result in a stiff wheel.

Keywords

Experimental modal analysis Acoustics Bicycle wheel Structural characterization Smartphone applications 

Notes

Acknowledgements

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1324585. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. This research was also supported by a Grant-In-Aid of Research from Sigma Xi. We would like to thank Dr. Joel Fenner for his help performing the diametral compression tests, and Professor Jonathan Siegel and the Department of Communication Sciences and Disorders at Northwestern for the use of their anechoic chamber. We are also grateful to Professor Jim Papadopoulos for many enlightening discussions on bicycle wheel mechanics.

Supplementary material

10921_2018_471_MOESM1_ESM.pdf (584 kb)
Supplementary material 1 (pdf 583 KB)

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA

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