An extensive analysis of the contact phenomenon occuring between a roller chain and sprocket was given by Binder in 1956. Naji and Marshek complemented Binder’s work by presenting a theoretical and experimental investigation of the contact phenomenon under quasi-static conditions during the early 1980’s. The problem is very complex, and significantly complicated due to the non-trivial geometry of the sprocket tooth, manufacturing tolerances, and changes in clearances between components due to wear. Accordingly, several simplifying assumptions were necessary in the previous investigations.

In this paper, a more detailed model of the quasi-static contact phenomenon is developed from first principles. The new model includes the external loading conditions, the curvature difference between the roller and the seating curve, the net error in the chain pitch (defined as the error in the chain pitch minus the error in the sprocket pitch), and Coulomb friction between the tooth and roller, the roller and bushing, and the bushing and pin. No assumption regarding the pressure angle at each contact point is made — rather the pressure angle at each contact point is calculated during the solution. (This is a very significant difference between the present and previous analyses). An efficient strategy for the computation is outlined.

In a companion paper (“Mechanics of Roller Chain - Sprocket Contact: Observations About the Contact Phenomenon and Load Distribution” submitted for presentation at this conference), results generated by the new model are presented and discussed. A comparison with experimental data taken from the literature (Naji and Marshek, 1983) indicates that excellent quantitative prediction of load distribution is possible. Finally, practical observations about chain performance (including effects of manufacturing tolerance and wear, and guidelines for incorporation of idler sprockets) are presented.

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