Experimental examination of bicycle chain forces

Abstract

ABSTRACTmThis paper presents the results of an investigation evaluating the forces present in a statically loaded bicycle chain prior to and beyond sprocket engagement. Comparisons are made with previous investigations that have been limited to industrial chains and sprockets. The chain drive system for a bicycle differs from the industrial standard types not only in its size but in its operation. A high degree of lateral flexibility is required in the bicycle chain for it to operate with noncoplanar sprockets having an effective misalignment of 3 deg or more. The experimental analysis in this paper considers chain loads for a range of sprocket sizes and angles of misalignment. Results indicate that localized bending arising from misalignment between chain and sprocket can increase or decrease the strain on the side plates by a substantial fraction of the direct strain due to chain tension. The work presented here is part of a more general study of bicycle chain efficiency for competition applications.KEY WORDS--Bicycle chain, bicycle sprocket, strain gage, mechanicsIn conjunction with Hans Renold's bush roller chain patented in 1880, the English bicycle manufacturer Starley became the first to produce what would become known as the "safety bicycle." The advantages of using the chain as a drive system quick!y became apparent, and the fundamental engineering details of the chain have remained essentially unchanged to this day. Two further inventions allowed the chain to become even more useful for the bicyclist. The first of these, a bushingless chain, permitted lateral flexibility, allowing the chain to run on a series of parallel sprockets of different sizes. The second was the derailleur gear mechanism, which shifts the chain between these sprockets. As part of a program of experiments investigating the efficiency of the bicycle chain, it was decided to analyze the forces experienced by a link as it approaches and then engages a driving sprocket in an effort to locate where some of the efficiency losses occur.The wide range of applications for industrial chains has yielded a substantial literature over the past 20 years or so, the major proportion of which relates more to chain application and durability than fundamental analysis of forces and transmission efficiency. Industrial chains tend to operate under more favorable conditions than their bicycle counterparts (e.g., coplanar sprockets, enclosed lubrication and steadystate running), thereby resulting in higher transmission efficiencies; hence, the need for such detailed analysis has not been great. However, another factor in this bias is the undoubted complexity in analyzing the basic mechanics of operation of a modern chain drive system.The distribution of chain load from tight to slack side depends fundamentally on the size of the sprocket, the amount of chain wrapped around it, the tooth pressure angle and the materials used. Much of the founding work on chain and sprocket mechanics was developed by Binder 1 in 1956. This classical work analyzes the dist...

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

“…Consequently, the fundamental arrives at the distal portion of the chain sooner than the second harmonic and, in doing so, alters the chain-sprocket interaction for the second harmonic by changing the orientation of the sprocket tooth relative to the link and decreasing the load transfer. Kidd et al modeled load transfer from chain to sprocket using the geometric progression load distribution (GPLD) method allowing for calculation of link tension during sprocket engagement/departure [4]. They also made static measurements of link tension as a function of angular orientation (sprocket relative to chain line) to confirm the validity of the GPLD model.…”

“…Their estimates indicated that 96%-99% efficiency could be obtained for sprockets typically used for bicycles but no measurements of chain drive efficiency were presented. Kidd et al [4] modeled and measured forces in bicycle chain links during engagement and departure to provide information necessary to estimate efficiency but these models were not used to do so. Work by Lodge and Burgess [5] assessed the efficiency of bush roller chains, including bicycle chains, by modeling frictional losses and measuring efficiencies using a drive system that isolated losses in the chain drive itself.…”

“…A trial solution for the displacement of the nth particle with the following form is assumed: (4) a" is the amplitude of the harmonic wave on the chain with angular frequency ca and propagation constant k, t is time, x" is the position of the nth mass, and b" is the amplitude of the second harmonic wave that is generated through the nonlinear behavior of the chain. Linear systems allow arbitrary displacements to be represented using Fourier techniques, but these cannot be employed where d is the spacing between masses.…”

The roller chain lubricated with ferrofluids

“…Kidd et al. 11 studied the results of an investigation evaluating the forces present in a statically loaded bicycle chain prior to and beyond sprocket engagement. Sujata et al.…”

Multibody Dynamics Formulation for Modeling and Simulation of Roller Chain Using Spatial Operator

“…Sheu [12] proposed a vector approach for analyzing the friction kinetostatics and the transmission efficiency. The forces in the chain links were measured experimentally by Kidd et al [13] and showed that sprocket misalignment leads to localized bending of the chain links. Marshek et al [14] showed that the misalignment leads to rubbing of the links with the sprockets.…”