Acoustic Modal Testing of Bicycle Rims

  • Matthew Ford
  • Patrick Peng
  • Oluwaseyi Balogun


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.


Experimental modal analysis Acoustics Bicycle wheel Structural characterization Smartphone applications 



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)


  1. 1.
    Feng, M., Fukuda, Y., Mizuta, M., Ozer, E.: Citizen sensors for SHM: use of accelerometer data from smartphones. Sensors (Switzerland) 15(2), 2980–2998 (2015). CrossRefGoogle Scholar
  2. 2.
    Morgenthal, G., Höpfner, H.: The application of smartphones to measuring transient structural displacements. J. Civ. Struct. Heal. Monit. 2(3–4), 149–161 (2012). CrossRefGoogle Scholar
  3. 3.
    Kong, Q., Allen, R.M., Schreier, L., Kwon, Y.W.: MyShake: a smartphone seismic network for earthquake early warning and beyond. Sci. Adv. 2(2), e1501055 (2016).
  4. 4.
    Grebenik, J., Zhang, Y., Bingham, C., Srivastava, S.: Roller element bearing acoustic fault detection using smartphone and consumer microphones comparing with vibration techniques. In: 17th Int. Conf. Mechatronics—Mechatronika, Vol. 1, pp. 1–7 (2016)Google Scholar
  5. 5.
    Pepelko, D.: Spoke tension gauge. Available from iTunes App Store (2016)Google Scholar
  6. 6.
    Pippard, A.S., Francis, W.: On a theoretical and experimental investigation of the stresses in a radially spoked wire wheel under loads applied to the rim. Philos. Mag. 11(69), 233–285 (1931). CrossRefzbMATHGoogle Scholar
  7. 7.
    Papadopoulos, J.M.: Method for truing spoked wheels. US Patent 5103414 (1992)Google Scholar
  8. 8.
    Ford, M., Papadopoulos, J.M., Balogun, O.: Buckling of the bicycle wheel. In: Proc. 2016 Bicycl. Mot. Dyn. Conf. (2016).
  9. 9.
    Gavin, H.P.: Bicycle-wheel spoke patterns and spoke fatigue. J. Eng. Mech. 122(8), 736–742 (1996). CrossRefGoogle Scholar
  10. 10.
    Pippard, A.S., Francis, W.: The stresses in a wire wheel under side loads on the rim. Philos. Mag. 14(91), 436–445 (1932). CrossRefzbMATHGoogle Scholar
  11. 11.
    Burgoyne, C., Dilmaghanian, R.: Bicycle wheel as prestressed structure. J. Eng. Mech. 119(3), 439–455 (1993). CrossRefGoogle Scholar
  12. 12.
    Ewins, D.: Modal Testing: Theory and Practice. Wiley, New York (1984)Google Scholar
  13. 13.
    Salawu, O.: Detection of structural damage through changes in frequency: a review. Eng. Struct. 19(9), 718–723 (1997). CrossRefGoogle Scholar
  14. 14.
    Timoshenko, S.P., Young, D.: Vibration Problems in Engineering. D. Van Nostrand Company, New York (1955)Google Scholar
  15. 15.
    Timoshenko, S.P., Gere, J.M.: Theory of Elastic Stability, 2nd edn. McGraw-Hill, New York (1961)Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA

Personalised recommendations