Transversal vibration analysis of resonance condition and frequency for orchard chain ropeway system

Abstract: To suppress the transverse vibration of an axially moving chain system with concentrated inertial masses in hilly orchard, the important factors affecting frequency characteristic of moving chain and their interaction are required to be studied. Based on the string theory and dynamics of chain transmission, the differential equation of transverse vibration was developed in the Laplace domain and the critical transport velocity was obtained in this paper. The stable condition for transport velocity corresponding to resonance was determined by considering the polygon effect causing speed variation when the moving chain link engaging with supporting end. With solutions for the second-order homogeneous partial differential equation, the effects of initial tension, transport velocity and load mass on the frequency of transverse vibration were numerically and experimentally analyzed. The difference between measured data and calculated data yielded values from 1.4% to 27.6% for various transport velocities, from 6.1% to 14.2% for various load masses, and from 14.7% to 24.3% for various initial tensions. The results show that the frequency of transverse vibration of axially moving chain increases with the increase in initial tension. The negative effect of transport velocity and load mass on vibration frequency in the case of forced nonlinear vibration is found. The proposed differential equation is proved valid to predict the effects of operation parameters on vibration frequency. It is conformed that this approach to transverse vibration of an axially moving chain can be used for parameter optimization under a certain constraint condition. The solution provides the theoretical basis for the vibration analysis and stability control of moving chain by consideration of wind-induced and rain-induced effects.