Aim. Development of a mathematical model of dynamic processes in speed change devices with multistage gear differential transmissions with closed-loop hydraulic systems on an example of a concrete design. Method. A device with a multistage differential has been considered, in which the gear wheel - the ring gear of the first stage is connected to the sun gear wheel of the second stage, the gear wheel - the ring gear of the second stage is connected to the sun gear wheel of the third stage, and so on, depending on the number of steps. Speed control is performed at the expense of carriers of each stage by means of the closed hydraulic systems established on them. On the basis of the Lagrange equation of the second kind the equations of dynamics of such devices depending on conditions of their work have been derived and solved. Results. The mathematical dynamic model have been obtained of gear differential motion with the possibility of controlling the movement of reserved hydraulic systems in order to provide the necessary law of load change on the driven link - ring gear, and the results can be the basis for quantitative analysis of power dependencies of mechanical drive with hydraulic control. Scientific novelty. For the first time a dynamic model of a speed change device in mechanical drives of machines with a multistage gear differential has been built, which allows to determine the speed of the drive link and select the required closed-loop hydraulic system to control the speed of its driven link. Practical significance. The results obtained can be the basis for a quantitative analysis of the power dependences of a mechanical drive with hydraulic control through the carriers, when the torque of the resistance changes periodically over a long period of time; or the magnitude of the impact torque of the resistance after a sharp increase remains unchanged for a long time; or the magnitude of the impact torque of the resistance after a sharp increase is maintained for a short time; or the actuator stops immediately due to significant overload.
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