Improvement of the efficiency of hydraulic power steering

The purpose of the study is to increase the reliability of the steering system. The article reflects scientifically based recommendations for improving the design of steering. The research method is theoretical studies performed on the basis of the provisions, laws and methods of theoretical mechanics, hydraulics, heat engineering, power flow theory and mathematical analysis. The article presents the results of theoretical studies on the temperature regimes of a hydraulic power steering (HPS), the results of which establish the analytical relation between the temperature pressure of the working fluid and the efficiency coefficient of the HPS. As a result, knowing the temperature of the working fluid, it is possible to determine the efficiency of the HPS in any of its operating modes. The analysis shows that in order to increase the efficiency of the HPS it is necessary to lower the temperature of the HPS working fluid. To this end, a device is developed aimed at improving the efficiency of the cooling fluid in the power steering and allowing increasing the efficiency of the HPS.


Introduction
The achievement of significant economic success in the agro-industrial complex (AIC) of Russia is largely determined by the reliability of the agricultural equipment.
The main part of the AIC of RF is equipped with trucks with hydraulic power. One of the problems of the HPS design according to the data of L L Ginzburg (1972) is to increase its temperature regime as a result of a long action at the extreme positions of the steering wheel. Maintaining normal temperature regimes of the HPS significantly affects the reliability of the machine.
As it is shown by the analysis of materials on the steerability in the works of native and foreign scientists: E M Gonikberg and A A Golbreykh (1969); L L Ginzburg (1959); V V Osepchugov and A K Frumkin (1989), the process of heat generation in the HPS was not fully considered, no patterns of heat release in the HPS from structural and operational parameters were identified, and there were no uniform principles for choosing an economical and efficient HPS circuit [1][2][3].
Thus, the creation of new scientifically based decisions at the design stage will make it possible to predict the conformity of the steering controls to the requirements and take measures aimed at improving the design of the steering control [4].

Materials and methods
In the article, the design scheme is based on the hydraulic scheme of the HPS of Ural 4320-0010-31. Analysis of the calculation methods showed that the HPS is a complex system in which transformations of mechanical, hydraulic and heat flows take place, each of which is calculated according to its own laws [5][6][7]. In this regard, to determine the uniform principles for calculating the HPS, the power flow theory developed by A S Antonov (1981). According to this theory, the HPS can be represented in the For the formation of the design scheme, the moment M (Nm) is taken as the power factor of the mechanical flow, and the angular velocity of the shaft ω (rad/s) is taken as the speed factor. The mass flow rate of the fluid q (kg/s) is taken as the power factor of the hydraulic flow, and the head H (m) is taken as the speed factor. The full heat capacity of the mass flow rate of a liquid W (W/°C) is taken as the power factor of the heat flow, and the temperature of the liquid T (°C) is taken as the speed factor of the heat flow.
The product of power and speed factors allows you to respectively obtain the power factor of the mechanical flow or the mechanical power N = Mω, the power factor of the hydraulic flow or the hydraulic power N G = qH, the power factor of the heat flow or the power of the heat flow Q = WT, W.
According to the power flow theory, the whole variety of transforming devices included in the design scheme can be conditionally represented by three types of nodal points: branching, kinetic, and generalized. At the branching nodal point only force factors are transformed, and in kinetic nodal point speed factors are transformed. The generic nodal point is the union of kinetic and branching nodal points. It is simultaneously the transformation of power and speed factors.
The analytic model of the HPS (Figure 1) includes the following nodal points: 1) Kinetic: an oil pump tank, a radiator -a device for improving the efficiency of the HPS cooling fluid, a distributor, a filter; 2) Generic: an engine, a vane-type pump, a power cylinder, a resistor.
For each flow, we separately compose the equation of balance continuity at the nodal points. To compile the balance equations, we use the second and third principles of the power flow theory. According to the second principle of the power flow theory, the sum of the velocity factors of a closed power flow is zero.
Or in general terms: where Uк is the speed factor of K-flow; n is the number of flows.
The speed factor transformation (temperature) for the kinetic nodal points in a closed power circuit of an oil pump tank, a radiatora device to improve the cooling efficiency of the HPS fluid, a distributor, a filter and generic nodal points of a vane-type pump and a main cylinder will be determined accordingly: where Тp, Тd, Тmc, Тr, Тf, Тot are temperature values of the pump, the distributor, the main cylinder, the radiatorthe device to improve the cooling efficiency of the HPS fluid, the filter and the oil tank, correspondingly, °С.  The HPS energy balance will be: All hydraulic power losses are converted to heat. Thus, the obtained calculation scheme reflects in general the processes of transformation of mechanical, hydraulic and heat flows of HPS, as their speed and power factors are interconnected by the second and third principles of the power flow theory.

Results
Direct determination of HPS efficiency is complicated by the fact that it is theoretically and practically very difficult to determine losses at all points of HPS characteristics [8][9][10]. The point of the characteristic that can be determined by calculation reliably is the point of maximum efficiency.
In general, the equation for the total power losses of the HPS is: Since the value of Nout in formula (14) is unknown, we express this equation in terms of efficiency, thereby determining the analytical relationship between power loss and power efficiency factor of the HPS.
To further description of the mathematical model including parameter ∑ ∆N in formula (16), the whole variety of power losses is converted into heat (Prokofyev, V.N., 1960). That is, the article puts forward the hypothesis that the total losses in the steady-state modes of operation of the HPS are equal to the amount of heat that must be removed from the hydraulic booster , HPS NQ    (17) Parameter QHPS does not include the amount of heat required to heat the working fluid and parts of the HPS, as well as the amount of convection discharged into the environment. That is, it is assumed that the percentage of QHPS is much larger than the listed components of heat dissipation.
Thus, the purpose of the mathematical model is to determine the amount of heat removed in steady- The variable parameters of the mathematical model of the mechanical flow are: the angular velocity of the pump shaft ωp, the speed of the piston rod Vr, the input power Nin, and for the heat flow it is the amount of heat QHPS, withdrawn from the HPS [11,12].
In the deterministic process, when the velocity temperature fields of coolants do not change, there is no need to solve the heat balance equation in a differential form (Shukhman, S.B., et al., 2007).
Using the equations of continuity of heat fluxes at nodal points, we create the system of equations: where Сwf is the specific heat of the working fluid, J/kg•°С; q is the working fluid consumption, kg/s. Thus, using the systems of equations of thermal and hydraulic power balances as a result of transformations, a functional dependence of the steady temperature head of the working fluid of the HPS was obtained (24).
Next, we establish the analytical relationship between the temperature pressure of the working fluid and the efficiency of the HPS. To do this, we use the dependence (15), substituting the quantity of heat diverted from the HPS instead of ∑∆N. As a result, we get: