Kinematics and Dynamics of Roller Chain Drives

There are two main subjects of this work: Kinematic and dynamic modeling and analysis of roller chain drives. In the kinematic analysis we contribute first with a complete treatment of the roller chain drive modeled as a four-bar mechanism. This includes a general, exact and approximate analysis with a clear derivation of the seating and release configurations, as well as the driven sprocket angular position, velocity and discontinuous acceleration. The approximate analysis allows for simple expressions describing the seating and release configurations and shows the influence of main design parameters which is useful for predicting the characteristic loading of the roller chain drive. As a completely novel contribution, a kinematic model and analysis is presented which includes both spans and sprockets in a simple chain drive system. A general procedure for determination of the total wrapping length is presented, which also allows for exact sprocket center positions for a chain with a given number of links. Results show that the total chain wrapping length varies periodically with the tooth frequency. These results are of practical importance to both the design, installation and operation of roller chain drives. For the analysis of roller chain drive dynamics we present a novel model of a chain drive that couples the vibrations of the chain spans and the driven sprocket. This also includes contributions to the studies of axially moving materials, as the chain is modeled as a string with a variable length supported by moving boundaries. A stationary operating state is introduced for the dynamic model and employing a perturbation method for the analysis of the approximate model results show a multitude of internal and external resonance conditions, thereby identifying critical operating conditions for real chain drives. Examples are presented of both decoupled and coupled motion. Together, the kinematic and dynamic model and analytical results provides a framework for numerical and experimental investigations of roller chain drive motion and deepens the understanding of roller chain drive operation.