Transverse vibrations of power transmission chains

On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the string-like case

“…It should be noticed that for m = 1 this system of ordinary differential equations is reduced to system (22). In this section we will study system (22), which is a coupled system of infinitely many ordinary differential equations.…”

“…In [21] the author also studied the case where one end of the moving string is subjected to an harmonic excitation to represent the case of a belt traveling from an eccentric pulley to a smooth pulley. Whereas the case where both ends of the string are excited is studied in [22]. In that paper a moving string model is used to study the transverse vibrations of power transmission chains.…”

“…In that paper a moving string model is used to study the transverse vibrations of power transmission chains. In all of these papers [19][20][21][22], the belt velocity is assumed to be constant. This paper is organized as follows.…”

Kinematic and dynamic modeling and approximate analysis of a roller chain drive

“…Since the limits of integration in (20) and (22) are time dependent, the usual process of deriving the governing equations [10] using integrations by parts is not possible, and the use of Leibniz rule for differentiation of integrals is required, as in [39]. This gives:…”

“…the review [19]. The study of sprocket and chain span motion introduced in [20,21] and subsequent studies [22] are based on the assumption that the driven sprocket angular velocity varies time-harmonically at the tooth frequency, due to the excitation coming from the variable velocity ratio between driver and driven sprocket. Comprehensive models are derived for belt drives [23] and engine timing chain drives [24], with non-linear transverse and longitudinal motion of the chain spans coupled to the displacements of pulleys/sprockets with flexible supports.…”