On the Load Distribution and Design of a Chain Drive
Abstract: Three methods are presented to calculate the load distribution in a chain drive containing two sprockets and one chain. The rollers, which are in contact with the sprockets, can move along the tooth flanks and their positions are given by force equilibrium. Since the positions of the rollers, and thereby also the load distribution, depend on the two connecting spans, it has been necessary to include these in all three models. Firstly, the position of the chain in the spans and the rollers in contact with the sprockets are calculated using static condition. The compatibility for the different parts is discussed and a solution procedure is presented in which the boundary conditions are given for when a roller enters or leaves a sprocket. A few special cases are also studied. It is shown that the rollers are in contact with the sprockets at different radii depending on the load, the undeformed pitch of the chain, and the position along the sprocket. The difference in polygon action according to previous model is also studied. This difference is big enough to suspect a significant influence on a dynamic model. The theory is also verified in experiments. Secondly, a chain drive working at higher speed is studied, which means the chain drive must be studied under dynamic oscillations. Therefore the equations of motion are used instead of the static equilibrium for the global system. Since the outer system affects the results, a simplified model of the outer geometry has been used. The moments of inertia in both the sprockets and the surrounding are included in the model but not the inertia forces in the chain. All friction is neglected even if a viscous damping is introduced to get a stabile solution. The response frequencies were shown to coincide with the parametric resonance frequencies, which are multiples of the natural vibration frequency for the chain. It is also shown that the amplitude of the stretching force for other speeds, not equal to a multiple of natural response speed, also increases with higher speeds. Contrary to the amplitude of the stretching force in the span, which increases very much with higher speeds, the error in gear ratio will not increase much with higher speed except for the natural response speeds. Finally, the inertia forces in the chain are taken into account which includes the oscillation in transverse direction as well as in longitudinal direction. The model of the chain part which contacts the sprockets, take care of both the inertias in tangential direction and the centrifugal forces. A chain tensioner has been used to reduce the oscillation on the slack side. The influence of the approximation made is also discussed. The results show that there is a great influence from the mass of the chain on the stretching force in the two spans and most of the transverse vibration comes from the impact force when a new roller comes into contact with a sprocket.
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