On the Load Distribution and Design of a Chain Drive

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

A dynamic analysis of the oscillations in a chain drive

A model is presented in which the oscillations, and the forces thus produced, in a chain drive, working at moderate and high speed, can be calculated. Since the outer system affects the result it has been necessary to include this in the model. The mass of the chain is included in the model and both the gravitational forces and the inertia forces in the chain are taken into account. The elasticity in the links is included. The sprockets are connected by two spans, both of which have to be included in the model to fulfill the equilibrium equations for the rollers in contact with the sprockets. The position of the chain is given by the geometric conditions as well as the equilibrium condition. On the slack side a chain tensioner is used to reduce the tansverse oscillation, which occur at higher speeds

A method to determine the dynamic load distribution in a chain drive

This paper presents a method to calculate the forces in a chain and, thus, the resulting load distribution along the sprockets in a chain transmission working at a moderate or high speed. When the chain drive is loaded, the rollers that contact the sprockets will move along the flanks to different height positions. There are mainly two different ways to determine the actual positions: to assume the positions or to use force equilibrium and to calculate the positions. To find the correct solution the geometry and the force equilibrium are used which will give each roller's position, along the flank. This method demands knowledge of all parts of the chain, even the slack part. Therefore it has been necessary to model both the connecting tight and the slack spans in which power between the two sprockets is transmitted. The gravitational force acting at the chain has been included in the complete model so that the position of the rollers and the forces in the links at the slack span can be calculated. The elastic deformation in the chain has also been included. The moment of inertia in the two sprockets and in the outer geometry has been taken into account, but not the inertia forces in the chain

A method to determine the static load distribution in a chain drive

A model of how to calculate the load distribution for a chain drive is presented. In the model the complete standard geometry is used without any assumptions. The rollers which are in contact with the sprockets can move freely along the tooth flanks and their positions are given be force equilibrium. Since the positions of the rollers and thereby also the load distribution are dependent on the two connecting spans, these necessary tight and slack spans have been included in the model. The elastic deformation in the chain is included as well as the gravitational force