CN112985530B - Method for adjusting design parameters of fuel metering device based on characteristic equation root track - Google Patents
Method for adjusting design parameters of fuel metering device based on characteristic equation root track Download PDFInfo
- Publication number
- CN112985530B CN112985530B CN202110137607.4A CN202110137607A CN112985530B CN 112985530 B CN112985530 B CN 112985530B CN 202110137607 A CN202110137607 A CN 202110137607A CN 112985530 B CN112985530 B CN 112985530B
- Authority
- CN
- China
- Prior art keywords
- expressed
- valve assembly
- flow
- pressure
- isobaric
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 239000000446 fuel Substances 0.000 title claims abstract description 93
- 238000013461 design Methods 0.000 title claims abstract description 45
- 238000000034 method Methods 0.000 title claims abstract description 31
- 238000013178 mathematical model Methods 0.000 claims abstract description 19
- 238000012546 transfer Methods 0.000 claims abstract description 13
- 238000012545 processing Methods 0.000 claims abstract description 8
- 238000006073 displacement reaction Methods 0.000 claims description 41
- 238000013016 damping Methods 0.000 claims description 8
- 238000010586 diagram Methods 0.000 claims description 8
- 230000006835 compression Effects 0.000 claims description 3
- 238000007906 compression Methods 0.000 claims description 3
- 230000010355 oscillation Effects 0.000 description 13
- 238000004088 simulation Methods 0.000 description 8
- 230000008859 change Effects 0.000 description 7
- 230000007423 decrease Effects 0.000 description 5
- 230000004044 response Effects 0.000 description 4
- 230000009467 reduction Effects 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000033228 biological regulation Effects 0.000 description 1
- 238000002485 combustion reaction Methods 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000004836 empirical method Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000008569 process Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
- G01F9/00—Measuring volume flow relative to another variable, e.g. of liquid fuel for an engine
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Landscapes
- Physics & Mathematics (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computational Mathematics (AREA)
- Fluid Mechanics (AREA)
- Measuring Volume Flow (AREA)
Abstract
The invention discloses a fuel metering device design parameter adjusting method based on a characteristic equation root track, which comprises the following steps: step S1, establishing a dynamics mathematical model; s2, carrying out linearization processing on the dynamic mathematical model by using a small deviation linearization method to obtain a linearization equation; s3, establishing a transfer function model of the fuel metering device by using a linear equation; and step S4, determining key design parameters based on the characteristic equation root track, and improving the stability of the fuel metering device by adjusting the values of the key design parameters. Aiming at the stability problem of the fuel metering device of the aircraft engine, the invention establishes a dynamic mathematical model by using a flow continuity equation and a force balance equation, carries out linear processing on a nonlinear equation of the dynamic mathematical model, and designs a parameter adjusting method for the fuel metering device based on a root track of a characteristic equation, thereby effectively improving the stability of the fuel metering device.
Description
Technical Field
The invention relates to the field of design and debugging of fuel metering devices of aircraft engines, in particular to a fuel metering device design parameter adjusting method based on a characteristic equation root track.
Background
The fuel metering device of the aircraft engine has the main function of metering the flow of fuel supplied to a combustion chamber and realizing the control of the rotating speed of the engine. In the actual use process of the fuel metering device of the engine, unstable problems may occur, for example, the pressure of outlet fuel may oscillate, so that the rotation speed of the engine oscillates, and the engine cannot work normally.
At present, if the engine is unstable, the common method is to change the values of the design parameters in turn according to engineering experience until the stability is improved, the method lacks theoretical guidance, and because the fuel metering device has many design parameters, if the size of the fuel metering device is changed in turn by the empirical method, the engineering quantity is large, and the efficiency is low.
Disclosure of Invention
In view of this, the present invention provides a method for adjusting design parameters of a fuel metering device based on a root trajectory of a characteristic equation, so as to solve the problem of instability of the fuel metering device of an aircraft engine and effectively improve the stability of the fuel metering device.
In order to achieve the purpose, the following technical scheme is provided:
a fuel metering device design parameter adjusting method based on a characteristic equation root track comprises the following steps: the electro-hydraulic servo valve, the metering valve assembly, the isobaric difference valve assembly and the execution valve assembly;
the electro-hydraulic servo valve controls corresponding flow to the metering valve assembly, a metering valve window in the metering valve assembly is pushed to generate certain displacement, a displacement sensor acquires data of the displacement and feeds the data back to the electronic controller, and the electronic controller, the displacement sensor and the electro-hydraulic servo valve form a position control closed loop of the metering valve assembly;
the fuel inlet of the isobaric difference valve assembly is communicated with the fuel inlet of the metering valve assembly to form a first passage, and the fuel inlet of the isobaric difference valve assembly is defined as a first throttling opening;
the metering valve window of the metering valve assembly is communicated with the isobaric difference valve window of the isobaric difference valve assembly sequentially through a second throttling port, a third throttling port and a fourth throttling port; the fourth throttling port is communicated with the oil tank to form a first oil return passage;
the metering valve window of the metering valve assembly is communicated with the fuel inlet of the execution valve assembly, the execution valve assembly is also provided with an execution valve fuel outlet, and the metering valve assembly is communicated with the oil tank through a fifth throttling port to form a second oil return passage;
the method is characterized by comprising the following steps:
step S1, establishing a dynamic mathematical model of the fuel metering device;
s2, carrying out linearization processing on the dynamics mathematical model established in the step S1 by using a small deviation linearization method to obtain a linearization equation;
s3, establishing a transfer function model of the fuel metering device by using the linear equation obtained in the S2;
and S4, analyzing the influence of each design parameter of the fuel metering device on the stability based on the characteristic equation root track, determining a key design parameter which can influence the stability of the fuel metering device and can be adjusted, and improving the stability of the fuel metering device by adjusting the value of the key design parameter.
Further, the mathematical model of the dynamics is expressed as:
in equation set (1), kdSpring rate, x, expressed as an isobaric differential valve assemblydDisplacement of the valve assembly with equal differential pressure, fydPrecompressed spring force, a, expressed as an isobaric differential valve assemblydArea of the differential pressure valve assembly, p7Expressed as the pressure, p, over the chamber of the isobaric pressure difference valve assembly2Denotes the measured pressure, mdExpressed as the mass of the isobaric difference valve assembly, bdExpressed as damping of the isobaric pressure differential valve assembly, kzExpressed as spring rate, x, of the actuator shutter assemblyzExpressed as the displacement of the actuating flap, fyzExpressed as pre-compression spring force of the actuating valve assembly, azExpressed as the area of the actuating flap, p3Indicating the pressure in the lower chamber of the actuator valve assembly, mzExpressed as the mass of the actuating flap assembly, bzExpressed as damping of the actuating flap assembly, q1Expressed as the flow rate of the metering flap window, q6Expressed as the flow rate of the actuating flap fuel outlet, q4Expressed as the flow of the second restriction, q3Flow indicated as third throttle, czExpressed as the leakage coefficient of the actuator valve assembly, v2Expressed as the volume of the lower chamber of the constant pressure difference valve, betaeExpressed as effective bulk modulus, q10Expressed as the flow of the fourth restriction, q8Expressed as the flow of the isostatically-differential-pressure movable door or window opening, q11Flow, denoted as fifth restriction, v3Expressed as the volume of the lower chamber of the actuator flap, q7Expressed as the flow of the first restriction, v7Expressed as the volume of the upper chamber of the isobaric pressure differential valve assembly.
Further, step S2 specifically includes:
considering the most unstable working condition, performing small deviation linearization processing on the flow expression of each throttling orifice by using a Taylor series expansion method at a rated steady-state working point, and then substituting into the dynamic mathematical model to obtain:
in equation set (2), Kj1Expressed as the flow gain of the metering flap window, Kz6Expressed as the flow gain of the actuating flap fuel outlet, Kp1Expressed as the flow-pressure coefficient, K, of the metering flap windowp3Expressed as the flow-pressure coefficient of the third restriction, Kp4Expressed as the flow-pressure coefficient, K, of the second restrictionp6Expressed as the flow-pressure coefficient, K, of the actuating flap fuel outletp7Expressed as the flow-pressure coefficient, K, of the first restrictionp8Expressed as the flow-pressure coefficient of the isobaric difference valve return, Kp10Expressed as the flow-pressure coefficient, K, of the fourth restrictionp11Flow-pressure coefficient, k, expressed as the fifth restrictiond8Expressed as the flow gain, x, of the isostatic-differential-pressure living door windowjExpressed as the displacement of the metering flap, xzExpressed as the displacement of the actuating flap, v2Expressed as the volume of the lower chamber of the isobaric pressure differential piston assembly, v3Expressed as the volume of the lower chamber of the actuator valve assembly, v7Expressed as the volume of the upper chamber of the isobaric pressure difference valve assembly, p1Expressed as the pressure of the metering flap window, p7Expressed as the pressure over the chamber of the isobaric pressure differential valve assembly.
Further, step S3 specifically includes:
solving the system of equations (2) to obtain the pressure p2、p3、p7And a displacement xd、xzAs variables, a 7 th order closed loop transfer function with variables is obtained:
in the formula (3), b0-b7And a0-a7The transfer function coefficients have specific values, and the values are solved by an equation system (2).
Further, step S4 specifically includes:
step S401, extracting a denominator of the transfer function model as a closed-loop characteristic equation for analysis, and obtaining key design parameters comprises: the area of the third throttling port, the area of the second throttling port, the area of the first throttling port, the area of the fourth throttling port, the area of the fifth throttling port, the spring stiffness of the isobaric differential valve and the spring stiffness of the actuating valve;
and S402, according to the principle of judging stability of the root track of the characteristic equation, changing the seven key design parameters obtained in the step S401 from 0 to positive infinity to obtain a root track diagram corresponding to each key design parameter, and obtaining the optimal design range of the seven key design parameters according to the root track diagram.
The invention has the beneficial effects that:
1. the compressibility, fuel leakage amount, viscous damping and the like of fuel are considered when the mathematical model is established, and the AMESim simulation is compared with the established mathematical model to obtain a simulation result, so that the established nonlinear model has high precision.
3. The method provided by the invention has higher efficiency. Because the fuel metering device of the aircraft engine is a complex hydraulic system, the related parameters are more and more complex, and the influence of each parameter on the stability of the system is different, if the current method is used for sequentially changing each design parameter according to engineering experience, a large amount of time is spent, and by using the fuel metering device design parameter adjusting method based on the root track of the characteristic equation, the influence of each parameter on the stability of the system can be directly obtained, so that the parameters which have no influence or less influence on the stability of the system are skipped, and the parameters which have greater influence on the stability are adjusted according to the analysis result of the root track, so that the stability of the system is improved.
4. The invention establishes a mathematical model of the fuel metering device and obtains the influence of each design parameter on the system stability through the root track of the characteristic equation, thereby having certain guiding significance in designing other similar fuel metering devices.
Drawings
FIG. 1 is a schematic diagram of a fuel metering device in an embodiment of the present invention;
FIG. 2 is an AMESim simulation model of a fuel metering device in an embodiment of the present invention;
FIG. 3 is a steady state characteristic of displacement of the fuel metering device versus the metering valve assembly in an embodiment of the present invention;
FIG. 4 is a step response of a fuel metering device to displacement of a metering valve assembly in an embodiment of the present invention;
FIG. 5 shows the constant differential pressure valve spring rate k in an embodiment of the present inventiondA root trajectory as a parameter;
FIG. 6 is a graph of amplitude of outlet pressure oscillations versus differential pressure valve spring rate k in an embodiment of the present inventiondA change in (c);
FIG. 7 is a graph of the isobaric difference valve spring rate k in an embodiment of the present inventiondThe effect on steady state error;
FIG. 8 is an area a of the first restriction in an embodiment of the invention7A root trajectory as a parameter;
FIG. 9 is a graph of amplitude of outlet pressure oscillations with area a of the first orifice in an embodiment of the present invention7A change in (c).
In the figure:
1-metering valve window, 2-metering valve assembly, 3-third throttling port, 4-second throttling port, 5-execution valve assembly, 6-execution valve fuel outlet, 7-first throttling port, 8-isobaric difference valve oil return port, 9-isobaric difference valve assembly, 10-fourth throttling port and 11-fifth throttling port.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
Referring to fig. 1 to 9, the present embodiment provides a method for adjusting design parameters of a fuel metering device based on a root trajectory of a characteristic equation based on a fuel metering device (as shown in fig. 1), the method comprising: an electro-hydraulic servo valve, a metering valve assembly 2, an isobaric valve assembly 9 and an actuator valve assembly 5.
The metering valve assembly 2 is mainly used for controlling the fuel quantity of the engine by adjusting the opening degree of the metering valve window 1, and the flow quantity of the metering valve window 1 can be calculated by the following formula:
in the formula (1), CdFor the flow coefficient, A is the opening area of the metering flap window 1, which is specified by the valve element displacement x in the metering flap assembly 2jDetermination of Δ p1ρ is the fuel density for the differential pressure before and after metering. Assumed flow coefficient CdAnd the fuel density rho are constant, according to the formula, if delta p is kept1Is constant, then the flow rate is only related to the valve core displacement xjIt is related.
The electro-hydraulic servo valve controls corresponding flow to the metering valve assembly 2, the metering valve window 1 in the metering valve assembly 2 is pushed to generate certain displacement, the displacement sensor acquires data of the displacement and feeds the data back to the electronic controller, and the electronic controller, the displacement sensor and the electro-hydraulic servo valve form a position control closed loop of the metering valve assembly 2.
The position ring is a relatively independent module, the function of the position ring is to enable the valve core of the metering valve assembly 2 to generate certain displacement, the steady-state control precision and the dynamic response speed of the position ring can completely meet the requirement of fuel regulation, and the small closed ring is easy to stabilize as long as the open-loop gain is not too large.
The position ring is generally not a critical factor affecting the stability of the fuel metering device.
The fuel inlet of the isobaric difference valve assembly 9 is communicated with the fuel inlet of the metering valve assembly 2 to form a first passage, and the fuel inlet of the isobaric difference valve assembly 9 is defined as a first throttling opening 7;
the metering valve window 1 of the metering valve assembly 2 is communicated with the isobaric difference valve window 8 of the isobaric difference valve assembly 9 sequentially through a second throttling port 4, a third throttling port 3 and a fourth throttling port 10; the fourth throttling orifice 10 is communicated with an oil tank to form a first oil return passage;
the metering valve window 1 of the metering valve assembly 2 is communicated with a fuel inlet of the execution valve assembly 5, the execution valve assembly 5 is also provided with an execution valve fuel outlet 6, and the metering valve assembly 2 is communicated with an oil tank through a fifth throttling port 11 to form a second oil return passage.
In the device, two ends of the equal pressure difference valve assembly 9 are respectively communicated with the oil pressure in front of and behind the metering valve assembly 2, and the functions of the device are as follows: the change of the pressure difference is sensed, and the valve core of the constant pressure difference valve assembly 9 generates corresponding displacement according to the pressure difference at the two ends, so that the area of an oil return opening 8 of the constant pressure difference valve assembly is changed, and the pressure p of the lower cavity of the execution valve assembly 5 is controlled3So that the valve core of the actuating valve assembly 5 produces corresponding displacement, thereby changing the opening area of the fuel outlet 6 of the actuating valve and further controlling the middle chamber, namely the measured pressure p2And finally, the pressure difference of the front and the back of the metering valve assembly 2 is kept unchanged, so the fuel metering device is essentially in pressure difference closed-loop control, and the steady-state control precision, the dynamic characteristic and the output stability of the fuel metering device mainly depend on parameters such as a spring, a damping hole and the like.
The method comprises the following steps:
s1, according to the working principle of the fuel metering device, a force balance equation and a flow continuity equation are used for establishing a dynamic mathematical model, and the dynamic mathematical model is compared with an AMESim simulation result to verify the accuracy of the established mathematical model;
in particular, since the dynamic response of the servo valve position loop is very fast, its dynamic behavior is ignored. According to the working principle of the fuel metering device, a force balance equation and a flow continuity equation of each throttling opening of the isobaric difference valve assembly 9 and the execution valve assembly 5 are established:
in equation set (2), kdSpring rate, x, expressed as an isobaric differential valve assemblydDisplacement of the valve assembly with equal differential pressure, fydPrecompressed spring force, a, expressed as an isobaric differential valve assemblydArea of the differential pressure valve assembly, p7Expressed as the pressure, p, over the chamber of the isobaric pressure difference valve assembly2Denotes the measured pressure, mdExpressed as the mass of the isobaric difference valve assembly, bdExpressed as damping of the isobaric pressure differential valve assembly, kzExpressed as spring rate, x, of the actuator shutter assemblyzExpressed as the displacement of the actuating flap, fyzExpressed as pre-compression spring force of the actuating valve assembly, azExpressed as the area of the actuating flap, p3Indicating the pressure in the lower chamber of the actuator valve assembly, mzExpressed as the mass of the actuating flap assembly, bzExpressed as damping of the actuating flap assembly, q1Expressed as the flow rate of the metering flap window, q6Expressed as the flow rate of the actuating flap fuel outlet, q4Expressed as the flow of the second restriction, q3Flow indicated as third throttle, czExpressed as the leakage coefficient of the actuator valve assembly, v2Expressed as the volume of the lower chamber of the constant pressure difference valve, betaeExpressed as effective bulk modulus, q10Expressed as the flow of the fourth restriction, q8Expressed as the flow of the isostatically-differential-pressure movable door or window opening, q11Flow, denoted as fifth restriction, v3Expressed as the volume of the lower chamber of the actuator flap, q7Expressed as the flow of the first restriction, v7Expressed as the volume of the upper chamber of the isobaric pressure differential valve assembly.
FIG. 2 is an AMESim simulation model of the fuel metering device, and since the AMESim modeling only needs structural parameters, the steady-state accuracy of the nonlinear model is verified by taking the simulation result as the reference. FIGS. 3 to 6 show the AMESim sum for the case of a displacement of the metering valve varying from 0 to 10mm when the inlet pressure is 90bar and the outlet pressure is 70barOutput flow q of MATLAB fuel metering device4Equal differential pressure valve assembly 9 displacement xdAnd performing a shutter assembly 5 displacement xzThe result of comparison of the steady-state characteristics of the equal parameters relative to the displacement of the metering valve assembly 2 shows that the nonlinear model has higher steady-state accuracy.
S2, carrying out linearization processing on the dynamics mathematical model established in the step S1 by using a small deviation linearization method to obtain a linearization equation;
specifically, considering the most unstable operating condition (high pressure and large flow rate), at the rated steady-state operating point, the flow expression of each throttling orifice is subjected to small-deviation linearization processing by using a Taylor series expansion method, and then the flow expression is substituted into a force balance equation and a flow continuity equation, and for the sake of simplicity, the increment of the flow expression at a certain steady-state point is still represented by the variable per se:
in equation set (3), Kj1、Kz6The flow gains of the metering valve window and the execution valve fuel outlet are respectively, and the flow gains are approximately constant because other throttling devices are fixed throttling holes; kj1Expressed as the flow gain of the metering flap window, Kz6Expressed as the flow gain of the actuating flap fuel outlet, Kp1Expressed as the flow-pressure coefficient, K, of the metering flap windowp3Expressed as the flow-pressure coefficient of the third restriction, Kp4Expressed as the flow-pressure coefficient, K, of the second restrictionp6Expressed as the flow-pressure coefficient, K, of the actuating flap fuel outletp7Expressed as the flow-pressure coefficient, K, of the first restrictionp8Expressed as the flow-pressure coefficient of the isobaric difference valve return, Kp10Expressed as the flow-pressure coefficient, K, of the fourth restrictionp11Flow-pressure coefficient, k, expressed as the fifth restrictiond8Expressed as the flow gain of the isobaric differential motion window and door opening; to sum up kpiFor the flow-pressure coefficient of the restriction i, the specific value is calculated from the correlation coefficient in equation set (2)And (5) calculating.
To verify the dynamic accuracy of the equation linearization, the valve assembly 2 is measured for a displacement xjAt a steady-state operating point of 9mm, an inlet pressure of 90bar and an outlet pressure of 70bar, a Δ x is added to the displacement of the metering valve assembly 2jSimulating by using MATLAB (matrix laboratory) for the step signal of 0.1mm, and comparing the output flow q of the metering device before and after the linearization of the equation6The front and back pressure difference delta p of the metering valve assembly 21Equal differential pressure valve assembly 9 displacement xdAnd performing a shutter assembly 5 displacement xzEtc., the results are shown in fig. 4. Due to the strong non-linearity of the fuel metering device, the equation after linearization has some error from the dynamic response of the original equation, but the two generally agree. Since stability analysis itself requires a certain margin, the above linearization error does not affect the analysis result.
S3, establishing a transfer function model of the fuel metering device by using the linear equation obtained in the S2;
specifically, the system of equations (3) is solved to obtain the pressure p2、p3、p7And a displacement xd、xzAs variables, a 7 th order closed loop transfer function with variables is obtained:
in the formula (4), b0-b7And a0-a7The coefficient is a transfer function coefficient and has a specific numerical value, and the numerical value is obtained by solving an equation set (3); in this embodiment, b0-b7And a0-a7The specific numerical values of (A) are:
a09.8667 x 103，a1Is 69.3641, a2Is 1.8167, a3Is 0.0098, a41.2112 x 10-5，a52.8833 x 10-9，a62.1954 x 10-13，a74.8677 x 10-18，b01.5078 x 104,b1Is 102.9986, b2Is 2.5461, b3Is 0.0097, b49.4396 x 10-6，b51.0588 x 10-9，b62.7464 x 10-14，b7Is 0.
And S4, analyzing the influence of each design parameter of the fuel metering device on the stability based on the characteristic equation root track, determining a key design parameter which can influence the stability of the fuel metering device and can be adjusted, and improving the stability of the fuel metering device by adjusting the value of the key design parameter.
Specifically, step S4 includes:
step S401, extracting the denominator of the transfer function model as a closed-loop characteristic equation for analysis, and finding that 7 adjustable design parameters influencing the system stability are available: area a of the third orifice3Area a of the second orifice4Area a of the first orifice7Area a of the fourth orifice10Area a of the fifth orifice11Spring rate k of equal differential pressure valvedAnd spring rate k of the actuating flapz；
And S402, according to the principle of judging stability of the characteristic equation root track, changing the 7 parameters of the fuel metering device from 0 to positive infinity to obtain a root track diagram corresponding to each key design parameter, and acquiring the optimal design range of the seven key design parameters according to the root track diagram.
More specifically, the spring rate k of the constant pressure difference valve isdAnd the area a of the first orifice7These two parameters are illustrated as examples.
Spring rate k of constant pressure difference valvedChanges from 0 to positive infinity (original value of 4.8 × 10)4N/m), the root locus of the closed-loop eigen equation is on the complex plane as shown in fig. 5, where the circle represents a zero, the cross represents a pole, and the point B is kdTake the original value of 4.8 × 104The position of the root at N/m, point A is kdExpansion to 4.84X 104The position of the root at N/m, the C point is kdThe reduction is 4.75 multiplied by 104The position of the root at N/m. According toAccording to the principle of judging stability of the characteristic equation according to the locus, when the equation has a pole on the right half complex plane, the system cannot be stable, and the point B is on the right half complex plane, so that the fuel metering device is unstable, and the outlet flow and the pressure have oscillation phenomena.
According to the root locus diagram, k can be judged within a certain rangedGradually increasing the pressure, so that the point B gradually moves leftwards, the oscillation amplitude of the outlet flow and the pressure is gradually reduced, and when the point B passes through the virtual axis and enters the left half-complex plane, the system is in a stable state, and the oscillation phenomenon theoretically completely disappears; k is a radical ofdThe gradual decrease will cause point B to move to the right and the oscillation amplitude will increase.
At the original value of 4.8X 104On the basis of N/m, increasing and decreasing kdThe change of the oscillation amplitude is observed through MATLAB simulation, and the result is shown in FIG. 6, and k can be seendIncreasing, the oscillation amplitude decreases and vice versa. This is consistent with the conclusions drawn from the root trace plot.
However, kdCannot be too large because of the following kdThe steady state error of the control of the isobaric pressure difference valve assembly 9 will also increase. FIG. 7 shows the output values (differential pressures) of the isobaric pressure difference valve assembly 9 at different kdThe curve under value that varies with the displacement of the metering shutter assembly 2 (corresponding to the flow rate). Visible increase kdThe balance between stability and steady-state accuracy is considered.
The area a of the first restriction 7 was found7The influence on the stability is very obvious and is not monotonous in a change relationship. In FIG. 8 and FIG. 9, a is7Root track from 0 to positive infinity and a7Output oscillation amplitude that varies around the original value. In FIG. 8, point B is a7Take original value 8.171 × 10-7m2The position of the root of the hour, point A being a7The reduction is 3.109 multiplied by 10-6m2The position of the root of time, point C is a7Expanded to 7.234 × 10-7m2The position of the root of time, D is a7Expanded to 5.049 × 10-6m2The position of the root of the time.
By means of a root trace map, canTo judge that within a certain range, a7Gradually reducing the vibration amplitude of the outlet flow and pressure, so that the point B can gradually move leftwards, and the system is in a stable state after the point B passes through the virtual axis and enters the left half complex plane, and theoretically, the vibration phenomenon completely disappears; a is7Gradually increases, the distance from the B point to the imaginary axis increases and then decreases, but the B point is always positioned on the right half plane, so the a point is positioned on the right half plane7And gradually increasing, the oscillation amplitude will increase first and then decrease.
At original value 8.171 × 10-7m2On the basis of (a), increase and decrease7The change of the oscillation amplitude is observed by MATLAB simulation, and the result is shown in FIG. 9, and a7Decreasing, the oscillation amplitude decreases; a is7And increasing, wherein the oscillation amplitude is increased firstly and then reduced. This is consistent with the conclusions drawn from the root trace plot. Thus it can be seen that a7The original value is just in the value range with poor stability, so that the stability of the fuel metering device can be effectively improved by changing the design parameter.
Similarly, the influence of the remaining 5 parameters on stability can be analyzed by root-trace method.
The invention is not described in detail, but is well known to those skilled in the art.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (5)
1. A fuel metering device design parameter adjusting method based on a characteristic equation root track comprises the following steps: the electro-hydraulic servo valve, the metering valve assembly (2), the isobaric difference valve assembly (9) and the execution valve assembly (5);
the electro-hydraulic servo valve controls corresponding flow to the metering valve assembly (2), a metering valve window (1) in the metering valve assembly (2) is pushed to generate certain displacement, a displacement sensor acquires data of the displacement and feeds the data back to the electronic controller, and the electronic controller, the displacement sensor and the electro-hydraulic servo valve form a position control closed loop of the metering valve assembly (2);
the fuel inlet of the isobaric difference valve assembly (9) is communicated with the fuel inlet of the metering valve assembly (2) to form a first passage, and the fuel inlet of the isobaric difference valve assembly (9) is defined as a first throttling opening (7);
the metering valve window (1) of the metering valve assembly (2) is communicated with the isobaric difference valve window (8) of the isobaric difference valve assembly (9) sequentially through a second throttling port (4), a third throttling port (3) and a fourth throttling port (10); the fourth throttling port (10) is communicated with the oil tank to form a first oil return passage;
the metering valve window (1) of the metering valve assembly (2) is communicated with a fuel inlet of the execution valve assembly (5), the execution valve assembly (5) is also provided with an execution valve fuel outlet (6), and the metering valve assembly (2) is communicated with the oil tank through a fifth throttling port (11) to form a second oil return passage;
the method is characterized by comprising the following steps:
step S1, establishing a dynamic mathematical model of the fuel metering device;
s2, carrying out linearization processing on the dynamics mathematical model established in the step S1 by using a small deviation linearization method to obtain a linearization equation;
s3, establishing a transfer function model of the fuel metering device by using the linear equation obtained in the S2;
and S4, analyzing the influence of each design parameter of the fuel metering device on the stability based on the characteristic equation root track, determining a key design parameter which can influence the stability of the fuel metering device and can be adjusted, and improving the stability of the fuel metering device by adjusting the value of the key design parameter.
2. The fuel metering device design parameter adjusting method based on the characteristic equation root track as claimed in claim 1, characterized in that the expression of the dynamic mathematical model is as follows:
in equation set (1), kdSpring rate, x, expressed as an isobaric differential valve assemblydDisplacement of the valve assembly with equal differential pressure, fydPrecompressed spring force, a, expressed as an isobaric differential valve assemblydArea of the differential pressure valve assembly, p7Expressed as the pressure, p, over the chamber of the isobaric pressure difference valve assembly2Denotes the measured pressure, mdExpressed as the mass of the isobaric difference valve assembly, bdExpressed as damping of the isobaric pressure differential valve assembly, kzExpressed as spring rate, x, of the actuator shutter assemblyzExpressed as the displacement of the actuating flap, fyzExpressed as pre-compression spring force of the actuating valve assembly, azExpressed as the area of the actuating flap, p3Indicating the pressure in the lower chamber of the actuator valve assembly, mzExpressed as the mass of the actuating flap assembly, bzExpressed as damping of the actuating flap assembly, q1Expressed as the flow rate of the metering flap window, q6Expressed as the flow rate of the actuating flap fuel outlet, q4Expressed as the flow of the second restriction, q3Flow indicated as third throttle, czExpressed as the leakage coefficient of the actuator valve assembly, v2Expressed as the volume of the lower chamber of the constant pressure difference valve, betaeExpressed as effective bulk modulus, q10Expressed as the flow of the fourth restriction, q8Expressed as the flow of the isostatically-differential-pressure movable door or window opening, q11Flow, denoted as fifth restriction, v3Expressed as the volume of the lower chamber of the actuator flap, q7Expressed as the flow of the first restriction, v7Expressed as the volume of the upper chamber of the isobaric pressure differential valve assembly.
3. The fuel metering device design parameter adjusting method based on the characteristic equation root track as claimed in claim 2, wherein the step S2 specifically comprises:
considering the most unstable working condition, performing small deviation linearization processing on the flow expression of each throttling orifice by using a Taylor series expansion method at a rated steady-state working point, and then substituting into the dynamic mathematical model to obtain:
in equation set (2), Kj1Expressed as the flow gain of the metering flap window, Kz6Expressed as the flow gain of the actuating flap fuel outlet, Kp1Expressed as the flow-pressure coefficient, K, of the metering flap windowp3Expressed as the flow-pressure coefficient of the third restriction, Kp4Expressed as the flow-pressure coefficient, K, of the second restrictionp6Expressed as the flow-pressure coefficient, K, of the actuating flap fuel outletp7Expressed as the flow-pressure coefficient, K, of the first restrictionp8Expressed as the flow-pressure coefficient of the isobaric difference valve return, Kp10Expressed as the flow-pressure coefficient, K, of the fourth restrictionp11Flow-pressure coefficient, k, expressed as the fifth restrictiond8Expressed as the flow gain, x, of the isostatic-differential-pressure living door windowjExpressed as the displacement of the metering flap, xzExpressed as the displacement of the actuating flap, v2Expressed as the volume of the lower chamber of the isobaric pressure differential piston assembly, v3Expressed as the volume of the lower chamber of the actuator valve assembly, v7Expressed as the volume of the upper chamber of the isobaric pressure difference valve assembly, p1Expressed as the pressure of the metering flap window, p7Expressed as the pressure over the chamber of the isobaric pressure differential valve assembly.
4. The fuel metering device design parameter adjusting method based on the characteristic equation root track as claimed in claim 3, wherein the step S3 specifically comprises:
solving the system of equations (2) to obtain the pressure p2、p3、p7And a displacement xd、xzAs variables, a 7 th order closed loop transfer function with variables is obtained:
in the formula (3), b0-b7And a0-a7The transfer function coefficients have specific values, and the values are solved by an equation system (2).
5. The fuel metering device design parameter adjusting method based on the characteristic equation root track as claimed in claim 4, wherein the step S4 specifically comprises:
step S401, extracting a denominator of the transfer function model as a closed-loop characteristic equation for analysis, and obtaining key design parameters comprises: the area of the third throttling port, the area of the second throttling port, the area of the first throttling port, the area of the fourth throttling port, the area of the fifth throttling port, the spring stiffness of the isobaric differential valve and the spring stiffness of the actuating valve;
and S402, according to the principle of judging stability of the root track of the characteristic equation, changing the seven key design parameters obtained in the step S401 from 0 to positive infinity to obtain a root track diagram corresponding to each key design parameter, and obtaining the optimal design range of the seven key design parameters according to the root track diagram.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110137607.4A CN112985530B (en) | 2021-02-01 | 2021-02-01 | Method for adjusting design parameters of fuel metering device based on characteristic equation root track |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110137607.4A CN112985530B (en) | 2021-02-01 | 2021-02-01 | Method for adjusting design parameters of fuel metering device based on characteristic equation root track |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112985530A CN112985530A (en) | 2021-06-18 |
| CN112985530B true CN112985530B (en) | 2022-04-22 |
Family
ID=76346600
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110137607.4A Active CN112985530B (en) | 2021-02-01 | 2021-02-01 | Method for adjusting design parameters of fuel metering device based on characteristic equation root track |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112985530B (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103439880A (en) * | 2013-08-30 | 2013-12-11 | 上海电力学院 | PID parameter setting method based on MCP standard transfer function |
| CN105140935A (en) * | 2015-08-12 | 2015-12-09 | 浙江工业大学 | Design method of wide-area time-lag proportion-integration-differentiation (PID) damping controller with high damping value for power system |
| CN109347385A (en) * | 2018-09-14 | 2019-02-15 | 华中科技大学 | Recursive model reference adaptive algorithm adaptive rate parameter tuning method |
Family Cites Families (17)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| BR9604813A (en) * | 1995-04-10 | 1998-06-09 | Siemens Ag | Method for determining the mass flow of air inside cylinders of an internal combustion engine with the help of a model |
| WO1997039182A1 (en) * | 1996-04-18 | 1997-10-23 | Valmet Corporation | Method for overall regulation of the headbox and/or the former of a paper machine or equivalent |
| CN102364308A (en) * | 2011-10-17 | 2012-02-29 | 南京航空航天大学 | Method and device for measuring mass flow of jet flow |
| CN102629293A (en) * | 2012-03-29 | 2012-08-08 | 昆明理工大学 | Simulation calculation method for additional mechanical damping of hydropower set |
| CN102980622B (en) * | 2012-11-06 | 2015-06-17 | 中国航空工业集团公司沈阳发动机设计研究所 | Design and adjusting method for fuel oil metering device starting flow characteristics |
| EP2735852A1 (en) * | 2012-11-26 | 2014-05-28 | Endress + Hauser Flowtec AG | Scalable and continuous auto-zeroing method for AC driven magneto-inductive flowmeters |
| US9976405B2 (en) * | 2013-11-01 | 2018-05-22 | Baker Hughes, A Ge Company, Llc | Method to mitigate bit induced vibrations by intentionally modifying mode shapes of drill strings by mass or stiffness changes |
| CN103984237B (en) * | 2014-06-04 | 2016-08-17 | 西北工业大学 | Axial symmetry aircraft triple channel Adaptive Control System Design method based on movement state comprehensive identification |
| CA2934585C (en) * | 2014-07-23 | 2017-10-17 | Zhongshan Broad-Ocean Motor Co., Ltd. | Air volume measurement method for fan motor |
| US10024835B2 (en) * | 2015-07-29 | 2018-07-17 | Advanced Sensors Limited | Apparatus for measuring a higher concentration of fluorescent materials in a liquid |
| CN206277497U (en) * | 2016-11-30 | 2017-06-27 | 长沙矿山研究院有限责任公司 | A kind of sand storehouse automatic uniform pulp making device |
| CN106777944B (en) * | 2016-12-07 | 2019-06-18 | 中国南方电网有限责任公司 | A kind of governor parameter setting method of the Hydropower Unit through direct current transmitting system |
| JP6731666B2 (en) * | 2017-12-19 | 2020-07-29 | 国立大学法人神戸大学 | Design support device, design support method, and design support program |
| CN108445920A (en) * | 2018-05-31 | 2018-08-24 | 国家电网公司 | A kind of solar energy equipment and its control method |
| CN109358634B (en) * | 2018-11-20 | 2020-07-07 | 南京航空航天大学 | Robust self-adaptive control method for hypersonic aircraft |
| CN111507012B (en) * | 2020-04-26 | 2023-04-14 | 太原科技大学 | Method for establishing gas dissolution theoretical mathematical model of rolling shear hydraulic system |
| CN111914365A (en) * | 2020-08-04 | 2020-11-10 | 南京航空航天大学 | Variable-cycle engine modeling method and variable-cycle engine component level model |
-
2021
- 2021-02-01 CN CN202110137607.4A patent/CN112985530B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103439880A (en) * | 2013-08-30 | 2013-12-11 | 上海电力学院 | PID parameter setting method based on MCP standard transfer function |
| CN105140935A (en) * | 2015-08-12 | 2015-12-09 | 浙江工业大学 | Design method of wide-area time-lag proportion-integration-differentiation (PID) damping controller with high damping value for power system |
| CN109347385A (en) * | 2018-09-14 | 2019-02-15 | 华中科技大学 | Recursive model reference adaptive algorithm adaptive rate parameter tuning method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112985530A (en) | 2021-06-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108757192B (en) | Diesel engine electronic control speed regulation and test method based on fuzzy variable structure | |
| CN111666648B (en) | Method for simulating dynamic characteristics of aircraft engine | |
| CN110794687B (en) | Electro-hydraulic servo system self-adaptive state constraint control method based on interference compensation | |
| CN111006843B (en) | Continuous variable speed pressure method of temporary impulse type supersonic wind tunnel | |
| CN112415891A (en) | Adaptive output feedback asymptotic control method for electro-hydraulic servo system | |
| CN104734588A (en) | Biomass gas internal combustion generator set rotation speed control method | |
| CN111475889B (en) | Physical and data-driven aeroengine digital twin modeling method | |
| CN111308889B (en) | Adaptive integral robust control method of spray rod system | |
| Wang et al. | Modeling, control, and experimental validation of a transient hydrostatic dynamometer | |
| CN110647111B (en) | Output-discreteness-considered non-linear active disturbance rejection control method for electro-hydraulic servo system | |
| CN113389646A (en) | Engine supercharging pressure control method and device | |
| CN112985530B (en) | Method for adjusting design parameters of fuel metering device based on characteristic equation root track | |
| CN113359485B (en) | Method for controlling output feedback preset performance of electro-hydraulic servo system | |
| CN110794708A (en) | Spray rod system testing method based on VeriStation and Simulink combined simulation | |
| Ali et al. | IJFP-2018-0015-robust control design for an inlet metering velocity control system of a linear hydraulic actuator | |
| CN106988906A (en) | The method and airflow control of the position of the choke valve in air inlet pipe for controlling combustion motors | |
| Fales | Stability and performance analysis of a metering poppet valve | |
| CN115061512A (en) | Flow control method and device based on adjustable venturi tube | |
| Gabdrafikov et al. | Efficiency improvement methodology for functioning of Machine-tractor diesel unit with electronic positional regulation of fuel supply | |
| CN113803179B (en) | Engine control method and device and electronic equipment | |
| CN115454007A (en) | Closed-loop control system and method for constant pressure valve of fuel servo of aircraft engine | |
| Miljić et al. | Model based tuning of a variable-speed governor for a distributor fuel-injection pump | |
| CN115573820A (en) | Aero-engine fuel servo equal differential pressure control system and method | |
| CN100516485C (en) | Heavy Pressure charging thin combustion natural gas engine fuel supply controller | |
| CN116146357B (en) | Feedforward control method of electric fuel pump |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |