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In comparison with other types of transmissions currently used, mechanical continuously variable transmissions are capable of providing significant technical and economic advantages, which makes research in this area relevant. This paper presents a mechanical and mathematical method that allows for studying the dynamic processes that take place during operating a controlled mechanical continuously variable transmission with an elastic element and a one-way clutch which provides for transmitting torque to the driven shaft in one direction only.

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Mechanical continuously variable transmissions have high potential for torque conversion, are capable of providing significant technical and economic advantages when used in shafts of technological and other machines, this making investigations in this area to be pertinent. This paper represents a mechanical and mathematical technique, which enables to do research of dynamic processes, that occur in functioning of mechanical continuously variable transmission with a resilient member and free-wheel mechanism, making it possible to transmit torque to a driven shaft only in the same direction. The objective of this paper is to work out a mathematical model of the mechanical system, which determines dynamic force of transmission elements. Computational model of transmission is shown, in obedience to which there was built a mathematical model based on Lagrange equation of second kind with undetermined multipliers. A set of assumptions was made on working out the dynamic system mathematical model. In particular, possibility of excitation of resonant modes in a resilient member was not considered. Moreover, nonlinearity of free-wheel mechanisms was not considered as well as hysteresis losses of energy in on-off use cycle and significant capacity costs in disconnected machinery. In future it is necessary to carry out experimental investigations in order to make transmission dynamics more exact. By the results of simulation modeling regularities were obtained which determine dynamic moments on transmission elements. The results of the investigation may be used for making an output characteristic of transmission, its adaptation with the motor and forecasting of operational features of shafts of different technological equipment.