Acoustic Modal Testing of Bicycle Rims

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, EI₁₁, 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.