Mathematical Modeling of the Transfer of Energy Forces from the Engine through Hydro Transmission and Hydro Differential to Executive Bodies

Mathematically simulated energy transfers from the energy source to the chassis through hydro transmissions and hydro differential. The developed unified mathematical model of a dynamic system allows, at the design stage, of many branched drive mechanisms, including transmission hydraulic and hydraulic differential actuators, to explore dynamic processes and select rational parameters.


Introduction
The results of experimental studies of experimental structures indicate a high dynamic load during transient processes of moving off, shifting gears and locking hydraulic differentiation, as well as in steady-state motion modes of mobile machines, which limits the durability of the elements of power mechanisms [1].
This determines the need for in-depth research aimed at reducing dynamic loading.
At present, the available theoretical and experimental data for previously de-

Problem Definition
One of the promising areas for improving the designs of wheeled vehicles and creating high-performance equipment is the use of volumetric hydraulic drives as a drive for the drive wheels of the undercarriage system. At present, industrial and agricultural mobile energy equipment (wheeled and tracked tractors) has been improved and has reached the level of mobile power facilities (MPF).
MPF universal and unified tractor. It can simultaneously hang and fasten several different many operating machines in front, side and rear. In this case, there will be a lot of branching of the transmission of power from the engine to the actuators. In particular, energy is transmitted to the undercarriage, working actuators-to the drive shaft, a number of active working bodies. To describe these phenomena by mathematical expression is considered an important task.
Taking into account the influencing factors in the design of many branched mechanisms, including the flexibility of the working fluid and hydraulic drive elements, allows the design stage to provide a high technical level, reduce the amount of testing by increasing the reliability of calculations.
The creation of many branched mechanisms of a high technical level is hampered by the fact that the magnitudes of the influence of the flexibility of the working fluid, the elements of the hydraulic drive and the links of the mechanisms on its dynamic loading are insufficiently investigated. The influence of the flexibility of the working fluid and hydraulic drive elements on the optimal values of the parameters of the boom lifting mechanisms and the handle drive has not been taken into account.
The development of more accurate mathematical models of working processes of hydraulic mechanisms taking into account leaks in the hydraulic system, operation of safety systems, pliability of the working fluid and hydraulic drive elements makes it possible to fully and objectively determine the loads overcome by a many-branched mechanism during operation, and therefore evaluate the pressure state of the links, including number and in transient conditions. Usually, traditionally, after the transmission gearbox, the differential, semi-axle and front-wheel reducer is installed. All these mechanisms serve to reduce the power during transmission from the hydraulic motor to the wheel.
In the thesis [2], the hypothesis about the destruction of metal-ceramic disks of friction elements, the control system of hydromechanical transmission due to the occurrence of resonant modes, caused by high-frequency disturbances generated by the torque converter, is put forward and substantiated. Based on the results of the study, an improved method of friction elements is presented.
Energy transfer previously performed on all mathematical models is described To write a single mathematical model, we accept the following assumptions: oscillation phenomena in all mechanisms and nodes are not taken into account; sustainability is not considered; not studied external perturbing all sorts of phenomena.

Describe the Transfer of Energy from the Engine to Branched Mechanisms Involving Hydraulic Transmission
Equations describing the rotational motion of mechanisms from the engine  11 11  11  11  11  11  11  3  3  23  2  3  23  2  3  2 And consider hydraulic transmissions from hydraulic leaks and leakages.  , e e -hydraulic compliance pressure pump parts; R-created efforts RJ; γ -angle of rotation of the pump control device; r-leakage ratio of RJ; 1 2 , V V -volume in pressure and drain cavities; E-volume modulus of elasticity RJ; 45 k -damping coefficient of hydraulic motor shaft; 45 e -hydraulic compliance of the working part of the motor; 23 34 , e e -hydraulic compliance of pressure and drain lines between the pump and the hydraulic unit; 56 k -shaft damping ratio of the active executive body; 56 с -circumferential rigidity of the shaft of the active executive body; , n y c c -hydraulic leakage and leakage rates; 1 2 , p p -pressure in the pressure and discharge lines; 1 2 , p p   -time derivatives of pressure in the pressure and discharge lines; nkl p -pressure setting of the make-up valve; nkl r -specific flow through the return pick valve; n k -coefficient specific feed pump; gm q -specific consumption of here, m-saturation coefficient tire tread; q-normal tire pressure on the ground;

Describes Energy Transfer in Hydro Differential
According to the calculation scheme (4H, 4gm links) ( Figure 1) and accepted assumptions, the mathematical model of the hydro differential action will be the system of equations [4] ( ) ( ) World Journal of Mechanics -flow coefficient and the density of the RJ.
In the system of Equation (1), the first two equations reflect the rotation of the pump and the hydraulic motor, the third one-the flow rate of the fluid, the fourth one-the fluid flow in the throttle of the accumulator, the fifth-the change in pressure in the hydro accumulator.
In the absence of a hydro accumulator, the system of Equation (1) is simpli- Initial conditions System of Equation (2)    4 v ϕ -reduced speed high-speed hydraulic motors of hydro differential.

Conclusions
A single mathematical model of the transfer of energy from the engine through a multi-branched transmission mechanism to the executive bodies is described by the expression of the transfer of energy from the joint work of mechanical and hydraulic actuators. The developed mathematical model of a dynamic system allows, at the design stage, of many branched drive mechanisms, including transmission hydraulic and hydraulic differential actuators, to explore dynamic processes and choose rational parameters of hydraulic drive compliance, time and damping coefficient, which are variable by selecting kinematic dynamic parameters, hydraulic motors working volume, the volume of the injection line and the reduced mass of inertia. A unified mathematical model of the transfer of energy from the engine through many branched transmission mechanisms to the executive bodies take into account the hydraulic transmission and hydraulic differential.