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The processes that occur in the transmissions of tractor units and self-propelled agricultural machines under various modes of movement and in the process of regulation are characterized by complex dependencies that are studied analytically or experimentally. Various methods are known for obtaining mathematical models. One of them is the classical direct description method. Another is the use of passive and active methods of regression analysis. It is rational to use both methods, the combination of which makes it possible to obtain the necessary mathematical model. Volumetric hydraulic drive (OGP) is increasingly used in transmissions of modern tractors and self-propelled agricultural machines. The presented article discusses the mathematical description of axial piston hydraulic machines. A study of transient processes was carried out and their assessment was carried out to determine the loads arising in the transmission of the machine with a stepwise change in the load, the gear ratio of the OGP and constant fuel supply when the unit is accelerated from a standstill. The unit acceleration mode was studied while driving on plowing and during transport operations for the following parameters and such initial conditions: rotation speed of the hydraulic motor shaft and engine shaft; torque on the motor shaft; hook load; pressure in the OGP pressure line. The dynamic characteristics of hydraulic machines, fluid leaks and its elastic properties, as well as variable values of the hydraulic drive efficiency are taken into account. The simulation results are compared with experimental studies. The objects of research were: a model of a caterpillar tractor T-150E with independent full-flow OGP of the left and right sides; mock-up of a wheeled r oot harvester with independent OGP sides of the rear driving wheels. Depending on the operating modes with unsteady motion, the following control options are possible, providing high performance at a certain level of dynamic loads, or minimum dynamic loads when the time factor is not prevalent. Optimal control is also promising when additional parameters are included in the goal function.

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