Mathematical model of the control system. Basic research
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Technical task
Design of the actuator motor for the gas steering system
3. Mathematical models of gas and pneumatic steering drives
4. Schematic diagram of the steering track
5. Design of a gas power control system
6. Simulation
Literature
Technical task
Design a proportional gas power control system. The input signal is harmonic with a frequency in the range. In the frequency range of the input signal in all modes of operation, the system must ensure the processing of a useful signal with an amplitude of at least d 0 at phase shifts not exceeding the phase shifts of the aperiodic even with the time constant T of the GSSU.
Basic initial data:
a) transmission coefficient of the system;
b) the maximum angle of deviation of the steering organs d t;
c) estimated time of operation;
d) quantities characterizing the dynamic properties of the system; in the simplest version, this includes the values of the limiting frequency of the input signal u 0, the amplitude d 0 of the signal processed by the drive at the frequency u 0 (the value is usually set in the range 0.8 ... 1.0), the value of the time constant of the equivalent aperiodic link T GSU;
e) loads on the steering bodies - inertial load, set by the moment of inertia of the load J N;
Friction coefficient f;
The coefficient of the hinge moment t sh.
If the coefficient t sh. changes in time, then a schedule of its change in time can be set. In the simplest case, the extreme values of this coefficient are set. Usually the maximum value of the negative load corresponds to the initial moment of operation; at the end, the proportional load is often positive and also has extreme stiffness.
Initial simulation parameters table
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Option No. |
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TK parameters |
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Load moment, Nm |
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Maximum angle, glad |
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Amplitude of Deviation RO, rad |
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Maximum frequency of the input signal, Hz / amplitude, in |
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Friction coefficient N * s / m |
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Mass of moving parts RO kg |
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Gas pressure in ICG bar |
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Gas temperature in ISG degrees С |
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Design of the actuator motor for the gas steering system
pneumatic gas steering motor
1. General information
Pneumatic and gas actuators are widely used in control systems for small aircraft. An alternative to traditional systems with primary energy sources of actuators - systems with gas-cylinder sources of compressed gases and systems with preliminary gasification of various substances - was the creation of devices belonging to a fundamentally new family - systems of air-dynamic steering drives.
Actuators of this class are complex tracking systems of automatic control, which as part of the product during storage, transportation and operation are significantly affected by climatic, mechanical and other external influences. The above-mentioned features of the conditions of use and operating modes, which must be taken into account when developing new systems, make it possible to classify them as mechatronic systems.
When choosing the type and determining the parameters of the BULA steering system, they usually proceed from two control methods: aerodynamic and gas-dynamic. In control systems that implement the first method, the control force is created due to the active influence on the aerodynamic control surfaces of the speed pressure of the incoming air flow. Steering drives are designed to convert electrical control signals into mechanical movement of aerodynamic rudders rigidly connected to the moving parts of the actuator motors.
The executive motor overcomes the articulated loads acting on the rudders, providing the required speed and the required acceleration when processing the given input signals with the required dynamic accuracy.
Control systems that implement the second method include:
Autonomous gas-jet automatic control systems;
Thrust vector control systems (SUVT).
Currently, for the first control method, devices are widely used in which gas is used as an energy source. high pressure... For example, this class of devices includes:
Steering systems with gas cylinder sources of compressed air or air-gas mixture;
Systems with powder pressure accumulators or with other sources of working fluid, which is a product of preliminary gasification of solid and liquid substances.
Such systems have high dynamic characteristics. The noted advantage causes great interest in such steering drive systems on the part of developers and makes them important objects of theoretical and experimental research.
The creation of high-tech steering drives of the BULA control systems is traditionally associated with the search for new circuit and design solutions. A special, radical solution to the problem of creating high-tech steering gears was the use of air flow around the rocket to control the energy. This led to the creation of a new, special class of actuators - air-dynamic steering gears (VDRP), which use the energy of the oncoming gas flow as a primary source of energy, i.e. kinetic energy BULA.
These instructions are devoted to the construction, application and methods of research and design of executive mechatronic modules of control systems of small-sized DULA. It reflects information that can be primarily useful for students of the specialties "Mechatronics" and "Systems of automatic control of aircraft".
2. Device of executive motors
Steering systems include the following functional elements.
1. Devices that ensure the creation of a force effect on the controls:
Power Sources - Primary Energy Sources (Compressed Gas Sources and Sources electrical energy- batteries and turbine generator sources of electrical energy);
Executive motors, kinematically associated with the controls, and elements of energy lines - for example, air and gas filters, check and safety valves, gas pressure regulators for systems with compressed gas cylinder sources, combustion rate controllers for powder pressure accumulators, air intake and discharge devices VDRP and etc.
2. Functional elements that establish the correspondence between the control signal generated in the control system and the required force action - converters and amplifiers of electrical signals, electromechanical converters, of various kinds sensors.
To concretize the areas of research of the tasks facing the development of steering drives, power and control systems are distinguished in their composition (Fig. 1.2).
Rice. 1.2. Aircraft steering gear diagram
The power system combines the functional elements of the steering drive, which are directly involved in converting the energy of the power source into mechanical work associated with the movement of positionally loaded controls. The control system is made up of the functional elements of the steering drive, which provide a change in the controlled value (coordinates of the position of the controls) according to the control law specified or developed during the flight of the aircraft. Despite the somewhat arbitrary nature of the separation of the power and control systems, which is associated with the need to include a number of functional: elements of the steering drive both in the power and in the control system, the practical usefulness of such separation lies in the possibility of a diverse presentation of the steering drive when solving various problems in the development process ...
In the gas steering system, the following subsystems can be distinguished:
Primary energy source;
Executive motor;
Gas distribution device with a control electromechanical converter;
Electrical control system - amplifiers, correcting devices, generators of forcing oscillations, etc.;
Primary transducers - sensors of linear and angular displacements of moving parts of mechanical subsystems.
For the classification of gas steering systems, in general, the following classification features can be used:
The type of power system, i.e. type of primary energy source;
The principle of control of aerodynamic rudders;
Control loop type for proportional steering devices;
Executive motor type;
Type of switchgear and control electromechanical converter.
1. Systems with a compressed gas source. The source of high-pressure gas is an air-valve block, which, in addition to a cylinder with compressed air or an air-helium mixture, includes safety, shut-off and distribution and control gas valves and valves for filling and monitoring the pressure in the cylinder. In the technical literature, such systems are often referred to as “pneumatic” systems.
2. Systems with a powder pressure accumulator. In this case, the source of high-pressure gas is a solid propellant powder charge of a special design, which ensures constant productivity of the working fluid - the products of combustion of the charge having a high temperature. In addition to the gas source itself and the device for switching the gas source into operation, such systems may include fuel combustion rate controllers and safety devices. In the technical literature, when describing such systems, the term "hot-gas" or simply "gas" is often used.
3. Electromagnetic steering drives. The basis of such devices is usually an electromechanical converter of a neutral type, which directly carries out a given movement of aerodynamic steering elements.
The executive engine is a device that converts the energy of the compressed gas into the movement of the steering organs, overcoming the force created by the air flow around the BULA.
By design, the following groups of executive motors can be distinguished.
1. Reciprocating - single-acting and double-acting. Devices most often used both in special equipment and in automation systems of technological processes.
Rice. 1. The executive engine of the closed-type hydraulic fracturing system - piston, with one power cylinder.
Fig. 2. Closed-type SGRP executive engine - with two power cylinders.
The operation of the executive engine is controlled by a gas distribution device (GRU).
The purpose of the GRU is to alternately communicate the working cavities of the actuating motor of the drive with a source of compressed gas or with the environment (atmosphere of the on-board compartment of the drive). By the nature of the switching problem being solved, GRUs are generally divided into devices:
With control "at the entrance" - the area of the inlet openings in the working cavities is changed;
With control "at the outlet" - the area of the outlet openings from the working cavities is changed;
With inlet and outlet control - both inlet and outlet areas change.
3. Mathematical models of gas and pneumatic steering drives
In the mathematical modeling of the steering gas drive system (SRGP), as an element of the control system of the BULA, functioning in the air flow around it, the area of research is a set of geometric, electromechanical parameters and parameters of the working fluid - air or other compressed gas, as well as the state function of electromechanical, aerogasdynamic processes and management processes occurring in all the variety of cause-and-effect relationships. With the transformations of some types of energy into others, the presence of distributed fields and the structurally complex representation of real mechanisms in the considered physical area of research, the creation of mathematical models that provide the required degree of reliability of engineering calculations is achieved through the introduction of theoretically and experimentally substantiated idealizations. The level of idealization is determined by the goals of the created software.
Steering drive mathematical model:
p 1, p 2 - gas pressure in the cavity 1 or 2 of the steering drive,
S P - area of the steering drive piston,
T 1, T 2 - the temperature of the gas in the cavity 1 or 2 of the steering drive,
T cn - the temperature of the walls of the steering gear,
V is the speed of the steering piston,
F pr - spring compression force,
h - coefficient of viscous friction,
Hinge load factor,
M is the reduced mass of moving parts.
Rice. 3 Typical graphs of transient processes.
4. Schematic diagram of the steering track
The steering tract of the gas power control system can be built with mechanical, kinematic, electrical feedback or not have the main feedback. In the latter case, the drive usually operates in relay mode ("yes - no"), and in the presence of feedback, in proportional mode. In this development, steering paths with electric feedback will be considered. The error signal in these paths can be amplified by either a linear or a relay amplifier.
A schematic diagram of a steering section with a linear amplifier is shown in Fig. 5.
Rice. 4. Diagram of the steering tract
The diagram shows: W F (p), W Z (p), W p (p), W o (p) -transfer functions of the correcting filter, electromechanical converter, drive, feedback circuit, respectively. The gain of a linear amplifier in this circuit is included as a multiplier in the EMI gain.
The choice of the drive parameters is made in such a way that in a given range of frequencies and amplitudes of the processed signal there is no limitation on the coordinates x and X. In this regard, nonlinearities in the form of limitations on these values are not taken into account when forming the steering path.
5. Design of a gas power control system
Design methodology
The type of the actuator and the schematic diagram of the steering section are selected. The type of drive is determined based on the requirements and operating conditions. With long operating times and high temperatures T p, a drive circuit with output control is preferable. To select a schematic diagram, it is advisable to carry out a preliminary study of various schemes, to estimate approximately their capabilities (operational, dynamic, weight, dimensions) and choose the best option... Such a problem, consisting in the approximate calculation of the characteristics of the GSSU of various schemes, should be solved at the initial stage of the development of the system. In some cases, the type of circuit diagram can be unambiguously selected already at the initial stage of work and specified in the terms of reference.
Generalized drive parameters are calculated. The methodology for this calculation is determined by the type of the selected steering circuit diagram. Here is the methodology applied to the electric feedback steering tract:
a) the value of the load factor y is selected:
Maximum value of the pivot load factor;
M t is the maximum moment created by the drive,
where l is the shoulder of the mechanical transmission.
The required drive power depends on the choice of y. The optimal value y opt corresponding to the minimum required drive power can be determined as a solution to the cubic equation
The numerical value for opt usually lies in the range of 0.55 ... 0.7. When atom is assigned, the value is assigned in the range 1.2? 1.3. The value of the ratio and depends on the type of the selected actuator. So. for actuators with a gas distributor of the nozzle - damper type,; for actuators with jet lance,.
The parameter q, depending on the value, must correspond to regime I. Its value is determined either from the results of thermal calculation, or from the data of experiments with analytical devices. Here we will assume that the law of variation of the parameter q with time is given in the form of an approximating dependence for various values of the ambient temperature.
The value b 0 - the amplitude of movement of the EMF armature for the steering tract with a linear amplifier is taken equal to y m, i.e. , and for systems with a relay amplifier operating in PWM mode on a switchgear, the value is taken in the range of 0.7? 0.8;
b) at the selected value of the value y, the maximum torque developed by the drive is calculated:
c) the required value of the angular velocity Ш т provided by the drive is determined.
The value of Ut is found from the conditions for the gas drive to process a harmonic signal with a frequency of um and an amplitude of q 0. The amplitude of the movement of the EMF armature b 0 is assumed to be the same as in the previous calculation.
In the low frequency region (), the dynamics of the drive with a relatively low inertia of the mechanical link can be described by an aperiodic link. You can get the following expressions:
For aperiodic link
From the last dependence after the transformations, we obtain the formula for calculating the required value of U max:
The design parameters of the drives are calculated.
The shoulder of the mechanical transmission l, the diameter of the piston of the power cylinder D P, the amount of free travel of the drive X t are determined.
Fig.5 Structural diagram of the ID.
When determining the shoulder l, it is necessary to set the ratio between the free stroke of the piston and its diameter.
For reasons of compactness of the developed design of the power cylinder, the ratio can be recommended.
When X = X t, the maximum torque generated by the drive must be several times greater than the maximum torque from the load, i.e.
Taking into account the accepted ratio, from the last equality we obtain the dependence
The maximum pressure drop in the cavities of the power cylinder Ap max depends on the value of p p, the type and ratios of the geometric dimensions of the switchgear, as well as on the intensity of heat transfer in the cavities. When calculating the value of l, it is possible to roughly take for drives with a nozzle-flap type gas distributor Dp max = (0.55? 0.65) p p, when using a jet distributor Dp max = (0.65? 0.75) p p.
When calculating the value of l, the value of Ap max must correspond to mode I.
For relatively small values of d max
In the course of calculations, all linear geometric dimensions should be rounded in accordance with the requirements of standards.
Calculate the parameters of the drive gas distribution device. This calculation is based on the condition that in the worst case, i.e. in mode I, the drive speed was not lower than, where Ш т is the value of the angular speed. Here will be given methods for calculating the geometric parameters for two constructive varieties of gas distributors: with a jet tube and with a nozzle and a damper. The first of the named valves implements the regulation of the gas flow according to the principle "inlet and outlet". In this case, the maximum steady-state speed of the drive is determined by the relationship
From what follows
When calculating the dependence, the values of T p and q must correspond to regime I.
Taking into account the size ratios characteristic of this distributor, take,.
The rational ratio of the areas with and a provides the best energy capabilities of the drive and lies within the limits. From these considerations, the value of C is found. Having calculated the values of a, c, it is necessary to determine the main geometric dimensions of the distributor.
Rice. 6. Design diagram of the "jet tube" gas distributor.
The diameter of the distributor inlet window is determined from the condition
where the flow rate m = 0.75 ... 0.85.
The magnitude of the maximum displacement of the end of the jet tube, a is the length of the jet tube.
At known meaning x m calculate the values b and d.
The gas distribution device of the "nozzle-flap" type realizes the regulation of the gas flow "at the outlet".
Ad hoc
Therefore:
When calculating, the attitude should be taken. The values of T p and q correspond to regime I.
Rice. 7 Design diagram of the "nozzle-flap" gas distributor.
The nozzle diameter d c is selected so that the effective area is at least 2 times the maximum area of the outlet:
With the selected value of d c, the value of b is found: b = mрd c; calculate the maximum value of the coordinate x t and the value
After the development of the design of the gas distribution device, the loads on its moving parts are determined and the EMF is designed or selected. The required flow rate of the working fluid is also determined, which is necessary for the design (or selection) of the power source.
With known design and operational parameters of the drive, the parameters of its jet scheme for both mode I and mode II can be determined from the dependence (I), after which a steering tract can be formed.
The formation of the contour of the steering tract is carried out taking into account the extreme modes of its operation. At the first stage of formation, the frequency characteristics of an open loop in mode I are plotted (the value of the coefficient k 3 is temporarily unknown).
Based on the requirement for the dynamic accuracy of the closed loop, we find the permissible value of the phase shift at the frequency u0:
c z (u 0) = arctan u 0 T GSSU.
With a known value of the value of the phase shift for an open loop c p (u 0), determined as a result of constructing the frequency characteristics, and a certain value of c s (u 0), we find the required value of the amplitude characteristic A p (u 0) of an open system at a frequency u 0. For this purpose, it is convenient to use the closure nomogram. After that, the amplitude characteristic of the circuit in mode I proved to be unambiguously determined, and therefore, the value of the open-loop coefficient K p is also determined.
Since the correcting filter has not yet been introduced into the circuit, the value of K p is determined by the relationship K p = k e K n k oc. The value of the feedback factor can be determined by the closed loop gain:. Then you can calculate the value of the coefficient k e:, and then calculate the required value of the gain of the voltage amplifier
6. Simulation
Using the data from the table, let us first simulate the system in the PROEKT_ST.pas program. Having thus calculated the suitability of the system parameters, we will continue the simulation in PRIVODKR.pas and calculate the response time in it.
Let's fill in the tables based on the obtained parameters:
Raise the temperature:
Let's lower the pressure:
Raise the temperature (under reduced pressure)
Main literature
1. Goryachev OV Fundamentals of the theory of computer control: textbook. allowance / O. V. Goryachev, S. A. Rudnev. - Tula: Publishing house of Tula State University, 2008 - 220 p. (10 copies)
2. Pupkov, K.A. Methods of classical and modern theory of automatic control: textbook for universities: in 5 volumes. Vol.5. Methods of modern theory of automatic control / K.A. Pupkov [and others]; ed. K.A. Pupkova, N. D. Egupova. - 2nd ed., Rev. and add. - M.: MSTU im. Bauman, 2004 .-- 784 p. (12 copies)
3. Suitodanov, B.K. Tracking drives: in 3 volumes. Vol.2. Electric servo drives / E.S.Bleiz, V.N.Brodovsky, V.A.Vvedensky and others / Edited by B.K. Chemodanov. - 2nd ed., Rev. and add. - M.: Bauman Moscow State Technical University, 2003 .-- 878p. (25 copies)
4. Electromechanical systems: textbook. allowance / G.P. Eletskaya, N.S. Ilyukhina, A.P. Pankov. -Tula: Publishing house of Tula State University, 2009.-215 p.
5. Gerashchenko, A.N. Pneumatic, hydraulic and electric drives of aircraft based on wave actuators: textbook for universities / A.N. Gerashchenko, S.L. Samsonovich; edited by A.M. Matveenko - M.: Mashinostroenie, 2006. - 392p. (10 copies)
6. Nazemtsev, A.S. Hydraulic and pneumatic systems. Part 1, Pneumatic drives and automation equipment: Textbook / A.S. Nazemtsev - M.: Forum, 2004 .-- 240p. (7 copies)
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2.5.1. Control object model.
Aircraft motion relative to the longitudinal axis occurs under the action of the aerodynamic moment and is described by the differential equation:
In this equation:
Moment of inertia about the longitudinal axis;
Angular speed of rotation about the longitudinal axis;
M x- aerodynamic moment about the longitudinal axis.
The quantity M x is determined from the relation
where: - high-speed head,
S - wing area,
l- wingspan,
m x = m x(w x, d e) - dimensionless torque coefficient,
r- air density,
V- flight speed,
d e- deflection of ailerons.
To obtain a linear model of the control object, we resort to the standard procedure for linearizing equation (2.1.) With respect to the steady-state value w x* and d e*, which we will consider unperturbed, and which satisfies the equation
. (2.2.)
At the same time, we assume that changes in altitude and flight speed insignificantly affect the parameters of angular motion, due to which variations in altitude and speed during linearization are not taken into account, and, accordingly, the magnitude of the velocity head is constant.
Increment of variable parameters:
,
and equation (2.1.) for the disturbed motion:
Taking into account relation (2.2.), We obtain the linearized equation of motion of the aircraft relative to the longitudinal axis
(2.3.)
In aerodynamics of aircraft, the following designations are adopted:
where:, - dimensionless coefficients.
Taking into account these designations, equation (2.3.) Takes the form:
(2.4.)
Passing to the form of notation accepted in the theory of automatic control, we get:
(2.5)
It should be noted here that due to the zero values of the steady motion, the values of the increments and in equation (2.4.) Coincide with the very values of these variables.
Let us introduce the notation for dynamic coefficients:
- damping coefficient;
- coefficient of efficiency of ailerons.
As a result, equation (2.5.) Or the mathematical model of the control object in angular motion relative to the longitudinal axis is represented by a linear differential equation
(2.6.)
.
Let's denote:
and we obtain in these notation a mathematical model of the control object in the form of a system of linear differential equations:
which reduces to one linear second-order equation
, (2.8.)
which corresponds to the transfer function of the control object
, (2.9)
in which the input signal is aileron deflection d e, and at the weekend - the roll angle, as shown in Fig. 2.8.
Rice. 2.8. Transfer function of the control object
2.5.2. Steering drive mathematical model.
The mathematical model of the steering drive is an integrating link with a negative rev 
communication, the block diagram of the model is shown in Fig. 2.9.
Rice. 2.9. Structural diagram of the steering drive model
The operation of the steering drive is described by the differential equation:
, (2.10.)
and the transfer function can be obtained from structural diagram
, (2.11.)
2.5.3. Mathematical model of measuring devices
which means that the measured values of the roll angle and the yaw rate do not differ from their true values.
2.5.4. Control law.
The regulator, shown on the functional diagram of the autopilot in the roll channel (Fig. 2.7.), Is a device that implements the control law, i.e. generates a control signal to the input of the steering gear s e depending on the values of the roll angle g and the angular velocity. This amount of information about the output variables of the control object allows you to apply a PD - a controller (proportional-differential), the transfer function of which
, (2.12.)
and the control law formed by him has the form
The coefficients are called gear ratios(according to the positional and damping signals, or according to the free gyroscope and the damping gyroscope). It is the gear ratios within the fixed configuration of the control system that are the tool with which you can achieve the desired quality of the control system. By changing the values of the gear ratios (or, in other words, by adjusting them), you can improve the operation of the control system, achieving the desired quality of its work.
2.5.5. Mathematical model of the contour
stabilization of the aircraft in the roll channel.
Developed in this section (2.5.) Mathematical models of individual elements of the functional diagram of the roll stabilization loop (Fig. 2.7.) Make it possible to construct a mathematical model of the aircraft angular motion control system in the roll channel.
This mathematical model is shown in Fig. 2.10. and its research is the main task of the course work
Introduction.
Chapter 1. Analytical review of the RP LA.
1.1 State and development prospects of the aircraft RP.
1.2 Analysis of structural and layout diagrams of the RP.
1.3 Analysis of mathematical models of electro-hydraulic RP.
1.4 The relevance of the research, the purpose and objectives of the work.
Chapter 2. Mathematical model of RP with SGRM.
2.1 Features of mathematical modeling of SGRM.
2.2 The influence of the main nonlinearities of the EGU on the characteristics of the RM.
2.3 Nonlinear mathematical model of RP.
2.4 Analysis of the results of numerical simulation of RP.
Chapter 3. Improving the quality of the dynamic characteristics of the steering gear-control system. 93
3.1 Features of RP operation and determination of factors affecting performance indicators.
3.2 Simulation modeling of DGS in the Ansys CFX.Ill package
3.3 The influence of the rigidity of the power wiring on the characteristics of the RP.
Chapter 4. Experimental research of the aircraft RP.
4.1 Experimental stand for research of the aircraft RP.
4.2 Investigation of the influence of inertial load and the rigidity of the SGRM fastening on the dynamic characteristics of the aircraft RP.
4.3 Methodology for calculating the RP using simulation.
4.4 Comparative analysis the results of numerical modeling and experimental studies of the aircraft RP.
Recommended list of dissertations
Methodological foundations for improving the design of jet hydraulic steering gears 2010, Doctor of Technical Sciences Mesropyan, Arsen Vladimirovich
Jet hydraulic steering gears with correction devices 2006, Candidate of Technical Sciences Arefiev, Konstantin Valerievich
Method for calculating a jet-cavitation hydraulic steering gear using methods of mathematical and physical modeling 2010, Candidate of Technical Sciences Tselischev, Dmitry Vladimirovich
Identification of jet hydraulic steering gears 2000, Candidate of Technical Sciences Mesropyan, Arsen Vladimirovich
Modeling and optimization of hydromechanical systems of mobile machines and technological equipment 2008, Doctor of Technical Sciences Rybak, Alexander Timofeevich
Dissertation introduction (part of the abstract) on the topic "Improving the dynamic characteristics of the steering drive of the aircraft based on simulation"
The improvement of aircraft (JIA) entails increased requirements for the reliability, speed and durability of steering gears (RP) operating in harsh operating conditions. Scientific and production organizations both abroad and in the domestic industry are conducting research to improve the RP and devices that meet the conditions of their work at JIA.
The JIA RP is a set of electro-hydraulic and mechanical devices that allow developing the required characteristics with high speed (the time to reach the mode is less than 0.6 s) and accuracy (the overshoot value is no more than 10%). The functioning of the J1A RP occurs in rather difficult operating conditions: the effect of vibration loads, abrupt impacts during uncoupling of the rocket stages, nonlinear characteristics of the friction forces of the rods and rockers and the inertia forces of the rotary control nozzle (PSC) with a constantly changing hinge moment, difficult climatic conditions and problems of long-term storage ...
The maximum possible tactical and technical characteristics of unmanned JIAs are achieved, among other things, thanks to numerous design and research works, which include bench tests and RP simulation. Simulation of RP using modern mathematical modeling and C / iD-design packages allows to reduce time and financial costs in the development and subsequent fine-tuning of RP for unmanned JIA, eliminating trial and error. Experimental studies make it possible to analyze the correspondence of the results of numerical modeling to the adequacy of the real object.
In this work, a simulation model of the JIA RP has been developed based on the results of processing and generalization of experimental data obtained at OJSC State Rocket Center named after Academician V.P. Makeev "and in the educational and scientific innovation center" Hydropneumoautomatics "at the Department of Applied Hydromechanics of the Ufa State Aviation Technical University.
Purpose and objectives of the work
Improvement of the dynamic characteristics of the steering gear of the aircraft based on simulation.
1. Development of a mathematical model of the RP and analysis of the results of numerical modeling;
2. Carrying out experimental studies of RP and comparing their results with the results of numerical modeling;
4. Development of the calculation method using the simulation model of the aircraft RP.
Research methods are based on fundamental methods of mathematical modeling of physical processes occurring in the JIA RP during operation, methods statistical analysis experimental characteristics of RP and methods of computational experiment.
Scientific novelty of the main results of the work
For the first time in the mathematical model of the JIA RP with a jet hydraulic amplifier (SGU), it is proposed to use a nonlinear model of backlash in a mechanical transmission and an empirical model of the hysteresis of the control characteristic of an electromechanical converter, which made it possible to increase the reliability of the results of numerical simulation.
For the first time, the inverse problem of the influence of the non-rigidity of the power wiring on the change in the hydrodynamic moment of the reverse jets acting on the jet pipe was solved, as a result of which the stability zone of the RP decreases. As a result of the studies carried out, recommendations were obtained for reducing the hydrodynamic moment of the reverse jet.
For the first time, the range of change in the transmission coefficient of the RP DA was determined, at which its stable operation is observed. Analysis of the results of numerical modeling and the results of experimental studies made it possible to identify the stability zone of the RP DA as a function of the stiffness of the power wiring and the parameters of the RM.
The practical significance lies in the fact that the developed method for calculating the RP of an aircraft makes it possible to study stability, accuracy and speed, taking into account the operational loads acting on it. The complex of applied programs, executed in a mathematical package, makes it possible to carry out a numerical study of a simulation model of a steering drive and to compare the results obtained with experimental data. Are brought to the defense
1. Mathematical model of RP J1A;
2. Results of a numerical study of the JIA RP simulation model;
3. Results of experimental studies of RP JIA;
4. New inkjet scheme hydraulic distributor(SGR), which allows to increase the reliability and speed of the aircraft RP by reducing the hydrodynamic effect of the reverse jet on the jet tube.
Approbation of work
The main theoretical provisions and practical results of the work were reported and discussed at the All-Russian Youth Scientific and Technical Conference "Problems of Modern Engineering" (Ufa, 2004), at international conference"Global Scientific Potential" (Tambov 2006), at the Russian Scientific and Technical Conference dedicated to the 80th anniversary of the Corresponding Member. RAS, professor P.P. Mavlyutova "Mavlyutov readings" (Ufa 2006), at the competition for young specialists in the aerospace industry (Moscow, RF CCI, committee for the development of aviation and space technology, 2008).
The basis for the work is the research plan of the state budget research "Research of thermophysical and hydrodynamic processes and the development of the theory of promising high-energy motors and power plants" (2008-2009), No. 01200802934, State contracts No. P317 of 28.07.2009 "Development of calculation methods and improvement steering drives of rocket engines "and No. P934 dated 20.08.2009 *" Electro-hydraulic control system of variable solid fuel propulsion system of multiple switching on "in the direction of" Rocket engineering "of the federal target1 program" Scientific and pedagogical personnel of innovative Russia "for 2009-2013.
Publications
The main research results on the topic of the dissertation are presented in 16 publications, including 3 articles in the publications recommended by the Higher Attestation Commission. the analysis of published works on the study of the JIA RP, methods of their calculation and design is presented.
Published theoretical research and experimental studies of the authors A.I.: Bazhenova, N.S. Gamynina, S.A. Ermakova, I.S. Shumilova, V.M. Fomicheva, V.A. Kornilov ,. V.V. Malysheva, V.A. Polkovnikova, V.A. Chashchina. The analysis of the research results made it possible to refine the linear mathematical model of the RM, which is used in the RP J1A. On domestic aircraft of the third generation, the RP includes RM, developed at JSC State Missile Center. Academician V.P. Makeev ". The development and testing of the RP, carried out by the specialists of the rocket center, confirmed that the PM, which meets all the parameters of work, is a hydraulic jet steering machine (SGRM).
Scientific and technical review of research on RP by I.S. Shumilova, D.N. Popova, V.F. Kazmirenko, V.I. Goniodsky, A.S. Kochergina, N.G. Sosnovsky, M.V. Siukhina, V. Ya. Bocharova made it possible to develop a calculation methodology and a JIA RP simulation method. The presented frequency characteristics of the RP and dependencies, which take into account the rigidity of the power wiring, the stiffness of the hydraulic cylinder fastening, the variable modulus of the volumetric elasticity of the working fluid, made it possible to refine the linear mathematical model of the RP.
Throughout the development of military aviation, research based on engineering methods has played a colossal role in ensuring reliability, durability, and speed of response. In the works of authors such as V.M. Apasenko, R.A. Rukhadze, V.I. Varfolomeev, M.I. Kopytov, I.M. Gladkov, I.Kh. Farkhutdinov, various design schemes of the RP are presented, each of which has its own advantages and disadvantages. Constructive diagrams allow you to determine the kinematic diagram and the design diagram of the RP.
In the works of scientists of the Department of Applied Hydromechanics of the Ufa State Aviation Technical University, such authors as E.G. Gimranov, V.A. Tselishchev, R.A. Sunarchin, A.V. Mesropyan, A.M. Rusak, as well as in the works of foreign authors: M. Nordin, Gutman Per-Olof, Hong-guang Li, Guang Meng, F. Ikhouane, JE Hurtado, J. Rodellar, nonlinear mathematical models of electrohydraulic and mechanical devices operating in harsh operating conditions have been developed ...
The conducted analytical review shows that often the trial and error method in the design of the JIA RP is not only one of the most effective methods, but also by an expensive method, and linear mathematical models do not adequately describe the real object, especially under the loaded operating mode of the RP. The developed nonlinear mathematical models make it possible to bring the results of numerical modeling closer to the physical processes that occur during the operation of the JIA RP.
The second chapter presents the mathematical model of the JIA RP. RP with SGRM, which is currently used in JIA rocket engines, meets all the requirements for speed and power characteristics. During the work of the JIA RPs, which include SGRM, complex physical processes take place. Thus, complex hydrodynamic processes arise in the jet cascade, which lead to the ejection of the working fluid, to the negative effect of the hydrodynamic reverse jet, to hysteresis in the control characteristic "EMF - jet tube", etc. dry friction, non-rigidity of the power wiring, which negatively affect the performance of dynamic characteristics (accuracy, stability and controllability). The developed mathematical model of the JIA RP in numerical modeling allows obtaining results with a high degree of adequacy to the real object.
In the third chapter, the issues of improving the quality of the dynamic characteristics of the JIA RP are presented. With the help of numerical modeling of the developed "mathematical model of RP" JIA, it is possible to analyze the influence of certain parameters, which include the inertial load, the rigidity of the power wiring, the size of the backlash in the mechanical transmission, the hysteresis in the control characteristics of the "EMF - jet tube", etc. This examines the quality indicators of dynamic characteristics: overshoot, regulation time, time to reach the first maximum and amplitude of oscillations.
The use of modern Ansys CFX and Solid Works packages makes it possible to simulate the RP using the finite element method, the main technical base for the materials used in modern mechanical engineering and a mathematical model of the flow of an incompressible fluid in the flow path of the SGRM. The results of the analysis of theoretical and experimental studies are presented and a functional diagram of the SGRM is proposed, which makes it possible to reduce the dead zone in the control characteristic by reducing the hydrodynamic effect of the reverse jet on the jet tube.
The fourth chapter presents an analysis of the results of theoretical and experimental studies of the JIA RP. To conduct experimental research in the course of an innovative project as a result of joint activities of the USATU and JSC “GRTs im. Academician V.P. Makeev ”a stand was developed to study the static and dynamic characteristics of the JIA RP. The stand allows you to obtain data on such characteristics as the flow-drop characteristic of the SRM, the movement of the jet tube, the PM piston and the inertial load in real time, as well as frequency characteristics under various operating conditions of the RP. As a result of the refinement of the mathematical model, the error in the calculations of numerical modeling and experimental research is no more than 5%, which is acceptable for the engineering methodology for calculating the RP JIA.
The work was carried out under the guidance of Doctor of Technical Sciences, Professor V.A. Tselischev and Ph.D., associate professor A.V. Mesropyan. The results presented in this work and presented for defense were obtained personally by the author of the thesis.
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Conclusion of the thesis on the topic "Hydraulic machines and hydraulic pneumatic units", Gallyamov, Shamil Rashitovich
MAIN RESULTS AND CONCLUSIONS
JIA RPs are constantly being improved in terms of design and functionality. The improvement of JIA leads to an increase in the requirements for the reliability, speed and durability of RPs under harsh operating conditions. Reducing the cost during the development and subsequent fine-tuning to the required characteristics of the JIA RP is achieved by using modern means computer-aided design and simulation, with the use of numerous studies on this topic. The operation of the RP occurs in rather difficult conditions: the effect of vibration loads, abrupt effects of a static load during undocking of the rocket stages, the effect of frictional forces of rods and rockers and inertia forces of the CCD with a constantly changing hinge moment. Therefore, special attention, during its design "is paid to the design of the power wiring stiffness, the design of the RM and the testing of the RP with the most approximate simulated operating conditions. The stiffness of the RP power wiring significantly affects its characteristics.
Today, there are various methods for calculating and designing the JIA RP, which are based on the numerical solution of linear and nonlinear equations describing various physical processes. It is necessary to use such a technique when calculating the RP, which allows taking into account all possible phenomena occurring during the operation of the RP. Such phenomena can be a backlash in the mechanical wiring, a dead zone in the control characteristic, the lack of rigidity of the RM housing, the rigidity of the power wiring of the JIA RP, the hydrodynamic effect on the moving elements of the jet cascade, etc.
For the numerical experiments of the aircraft RP, a mathematical model was developed, which makes it possible to carry out numerical experiments of the RP at the initial stage of development. In contrast to the existing mathematical models, in the developed mathematical model of the aircraft RP, nonlinearities were additionally taken into account, which significantly affect its characteristics. Such nonlinearities include backlash in the mechanical transmission, hysteresis in the control characteristic of the EMF of the SGRM, the dependence of the hydrodynamic moment of the reverse jet on the movement of the jet tube acting on the jet tube of the SGRM.
In numerical modeling using the developed mathematical model of the aircraft RP, an analysis was made of the influence of some factors on the quality indicators of dynamic characteristics, among which one can single out overshoot, control time, maximum piston movement and inertial load, etc. , = 104.106 N / m, the overshoot value decreases by 50%, and the regulation time tp with a stiffness less than s, = 106 N / m exceeds the permissible values (tp< 0.6.0.7 с). Следовательно, для рассматриваемого РП ЛА с однокаскадной СГРМ не допускается, чтобы жёсткость силовой проводки была меньше чем с. = 106 Н/м. Анализ результатов численного моделирования выявил значительное влияние эмпирического коэффициента магнитного гистерезиса Р на величину перерегулирования о. Коэффициент р определяет величину ширины петли гистерезиса. Так в случае, когда выполняется условие Р<840Н/(Ам), величина перерегулирования а достигает 100%, что не допустимо для РП ЛА. В результате проведённых исследований было выявлено, что данного РП JIA величина (3 может изменяться в пределах 1500 Н/(Ам) - 2000 НУ(Ам).
In the study of the characteristics of the JIA RP, the inverse problem of the influence of the non-rigidity of the power wiring of the RP on the change in the physical processes occurring during the outflow of a high-pressure jet from the conical nozzle of the SGU was solved. With a change in the stiffness of the power wiring of the RP, a pressure pulsation occurs in the cavities of the HZ PM, which leads to a change in the r / d moment acting on the jet tube.
In order to determine the r / d torque, which negatively affects the control characteristic, the DGS was simulated in the Ansys CFX package. As a result of the research carried out, the dependence of the change in the r / d torque on the movement of the jet tube for a single-stage RM was obtained, and a study was also carried out on the effect of the r / d. moment on the jet tube on the dynamic characteristics. The change in the r / d moment of the reverse jet is not proportional to the displacement of the jet tube PM. In the absence of the r / d effect of the reverse stream on the jet tube at an oscillation frequency of 15 Hz, stable operation of the JIA RP is observed. In this case, the transmission coefficient of the RP is less than 1.5 (for<1.5). В случае г/д воздействия запаздывание инерционной нагрузки относительно поршня ГЦ РМ происходит при значениях сх = 6 107 Н/м и Л = 1.2 10-4 м. С целью снижения г/д момента обратной струи была разработана функциональная схема СГУ, доработанная на основе существующего изобретения, которая позволяет компенсировать г/д момент, действующий на струйную трубку, и уменьшить зону нечувствительности.
In the course of the joint work of the employees of JSC “GRTs im. V.P. Makeev "and employees of the Department of Applied Hydromechanics of USATU, an experimental stand was developed to study the static and dynamic characteristics of the JIA RP. The experimental stand allows conducting research with imitation of a constant positional load, which can vary from 0 to 5000 N and an inertial load, which can have values of 0, 45 and 90 kg. The developed mathematical model of the JIA RP is adequate to the real object, since the error in comparing the results of numerical modeling and the results of experimental studies is no more than 5%;
When analyzing the results of numerical and experimental studies, such characteristics were obtained as the flow-drop characteristic of the PM, the characteristic of the dead zone when the actuator is exposed to a positional load and in its absence, the characteristic of the change in the flow coefficient at different positions of the jet tube, the AFC of the piston of the PM and the inertial load. An analysis of the comparison of the results of numerical modeling and the results of experimental studies made it possible to develop a method for calculating the RP with a single-stage SGRM. The developed technique makes it possible to obtain characteristics when calculating the RP at the initial design stage. The developer can optionally use the developed mathematical model of the JIA RP: use it as a black box without changing the structure or make some changes in the numerical study of the aircraft RP. So, it is possible to make changes in the flow-drop characteristic of the RM, change the empirical coefficients used, change the loading mode of the aircraft RP.
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The block diagram of the electric motor-driven steering gear model is shown in Figure 4.5. The rudder together with the boat should be considered the load.
Figure 4.5 - Block diagram of the rudder electric drive model
Shifting the steering wheel to a corner α causes (Figure 4.6) lateral movement (drift with an angle β drift) and rotation of the vessel around three mutually perpendicular axes: vertical (yaw with an angular velocity ω p), longitudinal (roll) and transverse (trim). In addition, due to an increase in the resistance of the water to the movement of the vessel, its linear speed is somewhat reduced. v.
Figure 4.7 shows the static characteristics of the torque on the rudder stock M B = f(α ) from the transfer angle α it for different rudders when the ship moves forward and backward. These characteristics are non-linear and also depend on the speed of movement. v ship. If the vessel is drifting, the angle α replace the rudder with an angle ( α+β ) between the plane of the rudder blade and the flow of incoming water. Thus, in the influence of the rudder on the electric motor of the rudder drive, in addition to the actual angle α shifting, you must also take into account the parameters of the ship's movement - the angle β drift and line speed v... This means that to analyze the electric rudder drive, it is necessary to consider the ACS with the ship's heading (Figure 4.8), which includes the autopilot ( AR), steering gear ( RM) and the ship. The steering gear consists of a steering wheel and a motor that drives it into rotation. The vessel is presented in the form of two structural blocks with transfer functions for control W Y(R) and by indignation W B(R). The drive motor can be DPT or IM with frequency control. The power source for the DCT can be either a controlled rectifier or a direct current generator. The AD is powered from the frequency converter.
Figure 4.6 - Trajectory of movement when turning the vessel and its parameters
Figure 4.7 - Static characteristic of the rudder
In the stabilization mode of the vessel turning process, if we assume that its linear speed v is constant, and the dependence of the lateral force and hydrodynamic moment acting on the body on the drift angle β is linear, and neglect the angles of roll and trim, then the system of equations describing the dynamics of the vessel's motion will have the form
(4.3)
where F(t) Is a function. taking into account the effect on the vessel of disturbing effects of waves, wind, current, etc .;
a 11, ..., a 23- coefficients depending on the shape of the hull and the load of the vessel.
Figure 4.8. Structural diagram of the ACS heading the vessel
If we exclude from system (4.3) the signal β , then a differential equation will be obtained that relates the value of the course Ψ with an angle α turn of the rudder and a disturbing signal F(t):
where T 11,…. T 31- time constants determined through the coefficients a 11, ..., a 23;
k Y and k B- coefficients of transfer of the ACS by the heading of the vessel, also determined through the coefficients a 11, ..., a 23.
In accordance with (4.4), the control transfer functions W Y(R) and by indignation W B(R) have the form
The equation of the mechanics of the electric motor of the steering device has the form
or 
(4.6)
where i- the gear ratio of the gearbox between the engine and the steering wheel;
M S- the moment of resistance, determined through the moment M B on the rudder stock by expression
Moment M B on the rudder stock according to Fig. 4.7 is a non-linear function of the angle α .
(4.7)
In general, the mathematical model of the electric steering, taking into account the vessel and the autopilot, is nonlinear and is described, at least, by a system of equations (4.4), (4.5) and (4.6). The order of this system is seventh.
Questions for self-control
1. Explain the composition and interaction of the elements of the structural diagram of the electric drive of the steering device.
2. Explain the parameters characterizing the process of turning the vessel caused by the rudder shift.
3. Why should the electric steering gear model take into account the parameters of the vessel?
4. What equations and in what variables describe the process of the ship's movement with a turn?
5. Give the expression of the transfer functions of the vessel for steering and disturbance with turn on the heading.
6. Justify the type and order of the mathematical model of the steering electric drive.
