Selection of design parameters of the system for changing the supply of power supplies for hydraulic systems of aircraft

. The article develops a mathematical model of the variable flow pump of the aircraft power supply, designed to simulate the operation of the power supply depending on the speed of the sustainer engine, oil temperature, pressure and supply (removable power). In addition, a control algorithm has been developed that provides the required quality of the transient process, which is achieved by installing additional hydraulic resistances between the servo piston cavity, the drain hydraulic line and the control spool, which change the flow characteristic of the pump and contribute to the fastest attenuation of the transient process and reduce its


Introduction
The efficiency of aircraft hydraulic systems largely depends on the characteristics of the power supply unit, which is the main, most loaded functional section of the hydraulic system, designed to convert mechanical or electrical energy into hydraulic. Due to the fact that the installed power of the pumps exceeds the power consumed by the hydraulic system, reducing losses in the power sources of hydraulic systems in aircraft flight modes at low flow rates is an urgent problem [1].
Therefore, much attention is currently paid to the choice of the structure and characteristics of the pumps included in the power supply unit of the aircraft hydraulic system, which has a large number of hydropower consumers, in order to obtain minimal losses and, consequently, reduce heat generation in hydraulic systems.
For the correct choice of the structure of the hydraulic system and units included in a single power supply, it is necessary to conduct simulation modeling of the operation of the power supply, depending on the speed of the propulsion engine, oil temperature, pressure and supply (removable power) [2].
In aircraft hydraulic systems, the change in feed is carried out by changing the working volume of the hydraulic machine. Hydraulic systems with variable flow pumps have better dynamic, weight and performance characteristics than systems with constant flow pumps [3].
Changing the displacement of a piston pump is usually carried out by changing the geometric stroke of the piston or by changing the stroke of the piston. In the practice of pump engineering, the first method is most common, when by changing the angle of inclination of the washer or cradle of the cylinder block in axial piston pumps and the eccentricity in radial piston and vane pumps, a change in the geometric stroke, and, consequently, the working stroke of the pistons is achieved [4].
The control mechanisms, along with the mechanisms for supplying and distributing the flow of the working fluid, are of decisive importance for the performance of the pump as a whole.
Putting the pump into zero flow mode in the event of a failure of the control system is tantamount to a complete and instantaneous failure of the pump. If a failure occurs at maximum pump flow, which will operate in constant flow mode after failure, then the maximum pressure in the system will be limited by a safety valve. The excess of the working fluid will be bypassed through the safety valve into the tank, which will cause the fluid to overheat and lead to the failure of the hydraulic system or its individual components [5].
In addition, the changeover mechanism affects the dynamic performance of the hydraulic system and pump, so careful design and high quality workmanship are essential.

Model and method
The design diagram of the power supply control system is shown in fig. 1. When the pump is operating in a supply mode close to zero, it is possible to overheat the pump (especially with high tightness) due to heat caused by mechanical losses and internal overflows, as a result of which there is practically no heat removal by the circulating liquid [6]. On fig. Figure 2 shows a typical dependence of the specific theoretical pump flow on the discharge pressure, provided that the volumetric efficiency of the pump = 0,9, and the pressure difference between zero and maximum feeds is

Research and results
In static modes of operation of the pump, when its parameters do not change over time, consider the balance of the servo piston of the regulator It is obvious that at △ < 0 = 0 we have = 0 and then = , = , = 1. In this case, the pump operates in constant flow mode and at a constant temperature and shaft speed. ( ) pump efficiency is determined by volume loss ( ), depending on discharge pressure [7] = (1 − △ ) = ( − △ ) .
Where -dynamic viscosity of the fluid. In the pressure range 0 <△ < 0,9 theoretical pump flow remains constant = , and in the pressure range 0,9 <△ < 1 the theoretical flow of the pump varies from = до = . Depending on the conductance ratio Gn and Gc depends on the type of flow characteristic of the pump with a variable supply with a regulator of a differential-throttle type (Fig. 3).
The cost balance equation has the form If there is a hydraulic accumulator in the power supply instead of the flow rate associated with the compressibility of the working fluid △ on the right side of the equation, it is required to take into account the flow of the accumulator △ [8]. The flow through the control system in accordance with the designations in fig. 2 can be defined as follows: Thus, for the design calculation, we obtain When taking into account the compressibility of the liquid and leakage, the differential equation for the movement of the piston of the servo cylinder Leakage and compressibility costs and , depend on the discharge pressure, and the remaining flow rates of the working fluid may depend on both the discharge pressure and the pressure in the accumulator, depending on the specific power supply circuit diagram [9,10].
On fig. 4 shows the dependence of the change in the relative conductivity of the throttles on the discharge pressure. The design scheme of the control spool is shown in fig. 1. The linear dependence of relative throttles on discharge pressure can be represented as On Fig. 5 shows the dependence of the pressure in the cavity of the servo piston on the value of the discharge pressure. The obtained boundary conductivities make it possible to determine, similarly to the dependences obtained earlier, the values of the coefficients , .
In some pumps, to obtain a given slope of the load characteristic, the spring cavity of the spool is connected not to the drain hydraulic line, but to the working cavity of the servo cylinder, i.e. introduce additional feedback on the pressure in the regulator servo cylinder.
The pressure drop within which the control mechanism operates is usually 6…8% pmax [11]. Such a characteristic of the pump can be achieved by profiling the working slots of the control spool or by installing constant throttles in the control and drain hydraulic lines. In this case, the throttle system consists of two pressure dividers, one of which is formed by variable throttles of the spool valve, and the other by constant throttles.
The parameters of the regulation mechanism and the feed mechanism are interconnected. The specific theoretical feed is determined geometric dimensions of the hydraulic machine. For axial piston hydraulic machine with rotating cylinder block and freely supported pistons In this case, the stroke of the servo piston corresponds to the stroke of the piston of the cylinder block The force of resistance to the movement of the servo piston is equal to In aircraft pump control systems, the spring sets the regulator to the maximum stop and the spring force must significantly exceed the given moment of resistance. The maximum flow rate through the control system will be considered equal to = .
Conductivity ratio With large moments of inertia of the control mechanism and the swash plate, the inertial load must also be taken into account [13,14]. Next, we determine the maximum area of \u200b\u200bthe working window of the throttles for draining and forcing the control spool We select the total conductivity of the throttles for drain and discharge within When the spool is moved in the process of regulation, the conductivities of the throttles for drain and discharge change On fig. 6 shows the calculation scheme for determining the moment on the regulating body.
The moment relative to the axis of rotation of the inclined washer from the forces of fluid pressure on the bottom and inertial forces is equal to the piston is equal to  The total moment on the swashplate relative to the axis of its rotation is equal to Depending on the direction of movement of the piston, the friction forces can either increase the reaction value of the washer or decrease it. As a result of the action of the system of forces in the supports of the regulatory body, reactions occur 1 and 2 , causing friction in the bearings and the corresponding moment , which is added to the moment of friction of the shoes relative to the center of the sphere of the plunger head [15]. Thus, the total moment is equal to where -distance from the surface of the washer to the center of the sphere. When the pump shaft rotates in the discharge cavity, due to the odd number of pistons and the displacement of the indicator diagram in the direction of rotation of the pump shaft, a moment pulsating with a piston frequency occurs, i.e. the moment of the resultant pressure force relative to the axis of the trunnions is a sign-alternating sawtooth function with an oscillation period = [17]. Due to the high frequency of oscillations, the relatively large mass of the swash plate and the friction in the bearings, this moment is not able to cause oscillations of the washer [18].
The average torque can be made equal to zero (symmetrical swashplate loading) or setting the swashplate to the maximum feed position by shifting the axis of rotation. In aircraft pumps, the servo piston spring sets the swash plate to the maximum flow stop when designing the control system, the problem arises of choosing the parameters of this spring.
At the stage of preliminary design, the calculation of the parameters of the control system presents certain difficulties, and when choosing the power of the actuator, they proceed from experimental data [20]. The moment on the regulating body can be taken equal to the moment on the machine shaft, and the total force acting on the swash plate from the side of the pistons is equal to ∑ = ∑ 1 and is applied at a point lying from the axis of symmetry of the washer at a distance of about 0,7 . According to the received force and the point of its application, it is possible to determine the reactions of the washer supports and calculate the journal bearings [21].
The bearings of the regulating body operate at very low turning speeds and a significant pulsating load, therefore, when calculating the torque on the regulating body, the friction coefficient is taken equal to 0,008…0,015.

Conclusion
Thus, a mathematical model of the variable flow pump of the aircraft power supply has been developed, the regulator of which is made two-stage with servo action, taking into account the mass of the actuator of the regulator, the mass of the spool valve and its flow characteristics, the resistance of the supply and drain control lines. The swash plate is loaded with a pulsating moment from the pistons, the frequency of which corresponds to the piston frequency of the hydraulic machine. The asymmetry of the swashplate loading is related to the position of the pistons on the washer and changes when the cylinder block is rotated, and the moment does not exceed 10% of the maximum theoretical moment on the pump shaft. The required quality of the transient process is achieved by installing additional hydraulic resistance between the cavity of the servo piston, the drain hydraulic line and the control spool. These resistances change the flow characteristic of the pump and contribute to the fastest attenuation of the transient and a decrease in its oscillation.