# Efficiency Estimation of Roller Chain Power Transmission System
## 1 Introduction
The results of efficiency were in the range of 9-99% in high torque transmission. [PERSON] [12] and [PERSON] [13] in 2001 modeled a complete chain transmission with two sprockets and a chain with tight and slack spans. Damping force is considered as an important factor in the tight span that transmits the most power, and it is assumed to be proportional to the relative velocity between the two end points at the tight side. In 2004, [PERSON] and [PERSON] [14] demonstrated that the efficiency of the chain is significantly influenced by the center distance between two sprocket axes, and showed that chain center distance is a key design parameter for motorcycles, although experimental verification was not achieved. [PERSON], [PERSON] et al. [15], in 2018, estimated the drive transmission efficiency of the roller chain according to the sliding friction force among the pin, bush, and roller of a chain; however, the experimental test was only validated in the condition of low rotational speed. In 2018, [PERSON] et al. developed a method that determined the transmission energy consumed to accelerate a rotating chain system [16,17,18,19]. In addition, chain efficiency was estimated by measuring the time of angular acceleration in the rotation axis of the drive shaft with and without load during the speeding-up of a chain drive. This method, however, could not discern the characteristics of a steady-state for a chain system, such as various affected parameters. In computing the roller chain system efficiency, energy loss should be always considered. While some energy stored as elastic deformation of components is recovered, other energy losses due to friction and damping cannot be recovered. [PERSON] et al. [3] estimated the bicycle chain drive efficiency based on the energy losses due to sliding friction. Theoretical efficiency of the chain system was found to be between 97 and 99%, however, the results from the experiment and theoretical analysis showed some discrepancy. In order to estimate the energy losses based on damping force, [PERSON], [PERSON] and [PERSON] [12] proposed a method to determine the load distribution during power transmission considering the damping factor. The damping force was modeled according to the damping coefficient and rotational speed of the chain span. The aim of the present study is to estimate the efficiency of the roller chain transmission system considering energy losses due to sliding friction and damping force in the tight span. The sliding frictional force between the pin, the bush, and the roller was established. The dynamics between links with lateral offset owing to the derailleur system are also modeled. In addition, the damping force between the driving sprocket and the driven sprocket in the tight span is considered theoretically according to the choice of damping coefficient. The effects of rotational speed, torque, offset angle, and damping coefficient are analyzed. The test stand of the roller chain power transmission system is set up to verify the estimated efficiency. The results demonstrate the experimental measurements of the efficiency of the roller chain drive under various operation conditions to validate the theoretical estimation.