Effects of the Nonlinear Elastic Behavior of Bicycle Chain on Transmission Efficiency

A model for nonfrictional power loss in derailleur-type, bicycle chain drives is developed to identify factors that influence transmission efficiency. Existing treatments of chain drive efficiency consider frictional losses but these do not explain the measured tension dependence of power losses and efficiencies for derailleur-type systems. Based on a nonlinear, spring-mass, mechanical transmission line, the model developed in this work shows that losses can be related to harmonic generation and dispersion in the chain. The nonlinear response leading to harmonic generation results from elastic contact at pin-bushing interfaces while dispersion is related to the periodic nature of the chain construction. Using this approach, the tension-dependence of power loss and efficiency are modeled and the influences of various chain-related characteristics on efficiency are assessed. If Hertzian contact descriptions are used, then the dependence of loss and efficiency on pin-bushing clearance, contact length and modulus can be estimated. Modeled results agree with experiment and show that power loss decreases with increasing chain tension and that efficiency varies nearly linearly with the reciprocal of the chain tension under operational conditions that are typical for bicycle chain drives. Significant increases to the power transmission efficiency of bicycle chain drives in derailleur-based systems could be achieved by altering the geometries and materials of current chain components.