Design and justification of hydrostatic transmission parameters for special transport vehicles

. Traditionally, hydrostatic transmissions of specialised transport vehicles use piston hydraulic machines to move the vehicle, as well as to operate attachment systems and units. For a wide range of special vehicles used in agriculture and municipal services, movement requires the power of the drive motor, comparable to the power of gear hydraulic machines. Gear hydraulic machines are less demanding on the quality, viscosity, and purity of the working fluid, are cheaper, and are easier to operate. Regulation of speed of an output shaft of gear hydraulic motors, as a rule, is provided by the throttle method that considerably reduces the general efficiency of a hydraulic drive. In the article the project of hydrostatic transmission on the basis of gear hydraulic machines with "volumetric" way of regulation is offered, the basis of which is the combination of work of two hydraulic motors (gerotor and gear with external gearing) with connection of output shafts of hydraulic motors to axes of gear differential. The basic calculation dependencies for determining the operating parameters of transmission hydraulic machines are given.


Introduction
The use of hydrostatic transmission (hereinafter -HST) in agricultural machinery has its advantages and disadvantages that determine the feasibility of its application.Among the main advantages we can note the convenience of placing the drive of driving wheels instead of the traditional mechanical transmission with friction clutch, convenience of vehicle control (high controllability during driving, when turning and turning), rational use of engine power, especially at low speeds.In addition, when travelling on soft soils, the driving wheels retain constant torque, which ensures high cross-country ability of the vehicle [1].
HST is used as part of combine harvesters and potato harvesters, self-propelled sprayers, specialised tractors and other self-propelled agricultural machinery (Fig. 1).The drive power of the pump as part of the HST (drive motor power) has a wide range.For example, the engine power of the Lida-1300 combine harvester is 260 hp, self-propelled sprayer OVS-4224 -212 hp, mini-tractor Kioti NX 6020 CH (South Korea) -60 hp For the majority of self-propelled machinery, the engine power is consumed not only to drive the HST pump, but also to drive the pump to ensure the operation of hydraulically driven attachments.In 2016, John Deere company introduced the 3025E 25 hp compact all-purpose tractor with a dual-range hydrostatic transmission that eliminates clutching and provides quick and easy directional changes (Figure 2).The aim of the work is to investigate the possibility of using gear hydraulic machines as part of HST, to develop a basic hydraulic scheme of hydrostatic transmission, to determine the main parameters of the hydraulic machines included in its composition.

Main Part
The main disadvantages limiting the application of HST are: -lower efficiency in comparison with mechanical transmission (about 80-85 %); -application of axial and radial piston hydraulic machines as part of HST, which significantly increases the cost of HST and requirements to the quality of working fluid, especially in the cold season.
The reason for the decrease in supply of piston hydraulic machines, which is a sign of emerging failure, is mechanical wear of piston and distributive friction pairs of hydraulic machines, leading to a decrease in volumetric efficiency.For the majority of HST the criterion of limit state is the reduction of volumetric efficiency of hydraulic machines at nominal modes by more than 20 % [2].The reasons of volumetric efficiency reduction during operation of agricultural machinery equipped with HST are: -high load modes at a long period of operation in conditions of increased ambient temperatures; -quality and purity of the working fluid.
The structural diagram of HST is presented in Fig. 3.As a rule, HST working fluid circulation is a closed circuit [3].The open circuit of HST working fluid circulation is much less common.The disadvantages of HST also include the complexity of the transmission, as additional systems are required for its functioning: -system for regulating the supply of working fluid from the pump to the hydraulic motor to regulate the speed of the hydraulic motor shaft; -system of cooling and filtration of the working fluid (operation of the system of filtration and cooling consists in partial draining of the working fluid from the low-pressure circuit in the volume equal to approximately 10% of the total volume of the working fluid per minute, which also creates difficulties with its cooling and filtration); -an overload protection system, which is a standard feature of any hydrostatic transmission; -a make-up system, which requires the installation and drive of an additional low-pressure pump, usually a gear pump.
Due to the complexity of the closed-loop system, there is interest in organising the operation of the HST in open-loop mode [6].This simplifies the system somewhat in terms of cooling and filtration, but does not reduce the complexity of the HST.In order to simplify the system both in cost and in operation mode, it is possible to build HST on the basis of gear hydraulic machines for low power vehicles (according to preliminary calculations, up to 40 hp).The proposed scheme of such a transmission is shown in Fig. 4. The following designations are adopted in the diagram: HP -pump; HM1, HM3gerotor hydraulic motors; HM2, HM4 -external gear hydraulic motors; V1 -proportional distributor; EV2, EV3 -directional distributors; A -soft starter; CO -cooler; F1, F2filters; CV1 and CV2 -check valves; 1, 2 -gear differential.
Distributor V1 in the initial position provides supply of working fluid to hydraulic motors HM1 with the largest working volume, which ensures the minimum speed of the vehicle.When the spool valve is shifted, the working fluid is redistributed between the hydraulic motors, which leads to a change in the rotation speed of the differential output shaft.Distributors EV2 and EV3 are designed to create a reversible flow of working fluid.By switching on only, for example, distributor EV2, the shafts of hydraulic motors HM1, HM3 and hydraulic motors HM2, HM4 are counter-rotated.This achieves the creation of low vehicle speeds and the control range will be between 0 and n_min.As hydraulic motors HM1 and HM3, providing the start of vehicle movement, gerotor hydraulic motors should be accepted, as they have, unlike gear hydraulic motors with external meshing, high starting torque and a significant working volume [4].
Application of transmission on the basis of gear hydraulic machines is expedient for use in the designs of a number of agricultural machinery, construction and municipal equipment [5].For example, in the design of municipal harvesting machines of the UKM-2500 type with hydrostatic transmission, produced by the company "Rusbiznesavto", Kurgan (Fig. 5).Unfavourable conditions of winter period, operation at summer temperatures adversely affect the operation of piston hydraulic machines.Gear hydraulic machines are much easier to operate in terms of quality and viscosity of the working fluid.
The efficiency of the transmission will be determined by the ratio of the working volumes of gerotor and gear hydraulic motors, the output shafts of which are connected to the input shafts of the differential.At the stage of the highest speed of the vehicle will provide a gear hydraulic motor, the working volume of which is equal to: is dynamic wheel radius;   -maximum vehicle speed;  2 -shaft speed of the gear hydraulic motor at the highest vehicle speed;  2 -supply of the working fluid from the pump to the hydraulic gear motor;  2 -volumetric efficiency of gear hydraulic motor.The oil supply from the HP pump will be equal to the oil supply to the hydraulic gear motor at the highest vehicle speed: here:   -hydraulic gear motor displacement;   -pump shaft speed;   -pump volumetric efficiency.Pump shaft speed is equal to drive motor shaft speed: Then the working volume of the gear hydraulic motor will be equal to: In the obtained expression (4) the dynamic wheel radius, and the highest speed of the vehicle are set during its design.We also set the nominal engine shaft speed (for example, it is possible to take for a diesel engine   = 1700 revolutions per minute (rpm)).Taking into account that all parameters of equation (4) will have some definite value, it is possible to write down the relation between the working volumes of the gear hydraulic motor and pump: The gerotor hydraulic motor shaft speed determines the movement of the vehicle at a certain minimum speed: where  1 defines gerotor hydraulic motor shaft revolutions;  1 and  ℎ -angular speed of rotation of the gerotor hydraulic motor shaft and drive wheel shaft, respectively;   is minimum vehicle speed.The working volume of the gerotor hydraulic motor will be equal to: here  1 -supply of working fluid from the pump to the gerotor hydraulic motor;  1 -volumetric efficiency of gerotor hydraulic motor.The oil supply from the pump will be equal to the oil supply to the gerotor hydraulic motor when the vehicle is started: Then the working volume of the gerotor hydraulic motor will be equal to: The ratio between the working volumes of the pump and the gerotor motor will be as follows: The ratio of working volumes of the gerotor hydraulic motor and gear hydraulic motor with external meshing is obtained from relations ( 5) and (10): After determining the working volumes of hydraulic machines included in the HST, we determine the pump delivery according to expression (2) or (8), as the working fluid delivery from the pump in the mode of minimum or maximum speed of the vehicle at nominal speed of the drive motor will be equal to each other.Change of vehicle speed is carried out due to redistribution of working fluid flow between hydraulic motors with different working volumes.
Dependence of flow rates on hydraulic motors  1 and  2 , as well as the total flow rate without taking into account leakage losses in hydraulic machines, equal to the pump flow rate   , of the differential output shaft speed, can be graphically represented in the form shown in Fig. 6. 6.When the distributor spool valve V1 is shifted, the total flow rate at the hydraulic motors without taking leakage into account will be constant.The total efficiency of any hydraulic motor included in the transmission is determined by the known relation: here   and   -torque and angular speed at the output shaft of the hydraulic motor, respectively;   and   -pump pressure and flow rate.The torque and angular velocity at the shaft of any hydraulic motor will be as follows: {   =     ; = 2  60 ; (13) here   -is the tractive force on the driving wheel of the vehicle.
After converting expression (12) we obtain the formula for determining the pump pressure: In the presented formulas the volumetric and total efficiency of hydraulic machines are taken on the basis of known values of efficiency of hydraulic machine types.After performed calculations and selection of hydraulic machine parameters it is necessary to carry out corrective calculation.The power of the drive motor can be easily determined using the expression for determining the total efficiency of the pump, which is equal to the ratio of the power of the working fluid to the power of the drive motor.The presented parameter calculations do not take into account the differential gear ratio.Possible design variants of the differential were not considered in the article.

Conclusions
The wide application of hydrostatic transmission in the design of a number of special machines, on the one hand, determines such directions of further development of HST as increasing efficiency, improvement of hydraulic machine designs, application of hydraulic accumulators in transmissions as a source of energy recovery.On the other hand, HST development can be considered from the point of view of design simplification, reduction of production and operating costs.Application of gear hydraulic machines as part of HST is possible and expedient from the point of view of HST manufacturing and production operation cost reduction.The application of volumetric method of regulation for gear hydraulic machines by means of gear differential allows to provide sufficient efficiency of transmission.The presented hydraulic scheme of HST on the basis of gear hydraulic machines has no analogues, allows to ensure the operation of the transmission.The proportional distributor, which provides volumetric regulation, is subject to theoretical calculation with experimental research.
The mathematical dependences presented determine the possibility of a preliminary calculation of the working volumes of hydraulic machines with further specification in accordance with standard values.The pressure produced by the pump is determined according to the load during the movement of the transport machine.The power of the drive motor should take into account both the movement of the vehicle and the possibility of creating special systems with hydraulic drive powered by an additional pump on the basis of the machine.The presented calculations do not reflect pressure losses when supplying the working fluid from the pump to the hydraulic motors.

Fig. 3 .
Fig. 3. HST structural diagram:   ,   -torque and motor shaft speed;   ,   -torque and rotational speed of the hydraulic motor shaft;   ,   -pump pressure and flow rate;   ,  pressure and supply to the hydraulic motor

Fig. 4 .
Fig. 4. Hydraulic scheme of HST based on gear hydraulic machines

Fig. 2 .
Fig. 2. Dependence of flow rates on hydraulic motors on rotation speed of the differential output shaft:   and   -maximum and minimum flow rate at hydraulic motors;  -softstarter operating area;  -V1 distributor operating area