CN110162921B - Optimization design method for stationary blade joint adjusting mechanism of aircraft engine - Google Patents
Optimization design method for stationary blade joint adjusting mechanism of aircraft engine Download PDFInfo
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- CN110162921B CN110162921B CN201910473153.0A CN201910473153A CN110162921B CN 110162921 B CN110162921 B CN 110162921B CN 201910473153 A CN201910473153 A CN 201910473153A CN 110162921 B CN110162921 B CN 110162921B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
- F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
- F01D17/00—Regulating or controlling by varying flow
- F01D17/10—Final actuators
- F01D17/12—Final actuators arranged in stator parts
- F01D17/14—Final actuators arranged in stator parts varying effective cross-sectional area of nozzles or guide conduits
- F01D17/16—Final actuators arranged in stator parts varying effective cross-sectional area of nozzles or guide conduits by means of nozzle vanes
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention belongs to the technical field of optimization design of a stationary blade joint debugging mechanism of an aeroengine, and particularly relates to an optimization design method of a stationary blade joint debugging mechanism of an aeroengine. Solving a kinematic equation of the two-stage joint debugging mechanism by combining a homogeneous coordinate method and a graphical solution with MATLAB software; deriving a two-stage rocker arm rotation relation equation through a two-stage kinematic equation according to the rotation relation between the two-stage cranks; and performing joint optimization on key components in the two-stage joint debugging mechanism by using a genetic algorithm through a rocker arm rotation relation equation. The joint debugging mechanism meeting the design requirements can be quickly and efficiently designed by the method. The theoretical analysis has higher reliability and persuasion than the simulation analysis; the range of feasible solutions can be obviously expanded through multi-stage combined optimization, and more choices are provided for the design of mechanisms; the intelligent optimization algorithm can remarkably improve the speed and the precision of analysis and solution, improve the design efficiency and shorten the design period.
Description
Technical Field
The invention belongs to the technical field of optimization design of a stationary blade joint debugging mechanism of an aeroengine, and particularly relates to an optimization design method of a stationary blade joint debugging mechanism of an aeroengine.
Background
At present, referring to fig. 1, the structure of the known stationary blade linkage adjusting mechanism at each stage is composed of a crank, a connecting rod, a linkage ring, a support and a rocker arm, wherein the stages are connected by an interstage connecting rod, and the whole mechanism is driven by an actuating cylinder. The interstage connecting rod transmits the driving force of the actuating cylinder to each stage of crank, the crank rotates around a crank rotating shaft and rotates through the connecting rod and the linkage belt to drive the rocker arm to rotate, the stator blade is fixedly connected with one end of the rocker arm, and finally the stator blades of each stage rotate by a specified angle according to a specified motion rule under the driving of the actuating cylinder. However, the spatial motion relationship of the joint adjusting mechanism is complex and the design difficulty is large.
Many of its design and analysis are done by simulation and trial and error methods. For example, liang Shuang of Shenyang engine design research institute in the Navigator industry in 2016 is published in an article in the aeroengine, and a multi-cascade tuning mechanism is analyzed, optimized and designed by a simulation method based on ADAMS software. In 2015, nanjing aerospace university Master Zhang Shuai kinematically solves a joint adjusting mechanism plane model in a graduation paper by using an improved D-H method, and analyzes the motion rule of the joint adjusting mechanism plane model. Zhang Xiaoning and the like published in the aeroengine in 2014 by Shenyang engine design research institute in the aviation industry, namely, in the kinematics simulation of virtual prototype of joint debugging mechanism, ADAMS software is used for performing kinematics simulation analysis on the joint debugging mechanism, then AUTOCAD software is used for solving the rotation rule of each stage of stationary blade of the joint debugging mechanism, and the solved result and the simulation result are compared, so that the correctness of the simulation result and the superiority of the simulation method are proved.
At present, the optimization design of the multi-stage regulating mechanism is mostly carried out through motion simulation, and theoretical analysis is relatively deficient. In the aspect of optimization solution, the optimization solution belongs to serial optimization (namely, the zeroth level is optimized first, and then other levels are optimized by taking the zeroth level as a reference), and multi-level joint optimization is not achieved.
Disclosure of Invention
Technical problem to be solved
Aiming at the existing technical problems, the invention provides an optimal design method of a stationary blade joint adjusting mechanism of an aeroengine.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that:
an optimization design method for a stationary blade joint adjusting mechanism of an aircraft engine comprises the following steps: solving a kinematic equation of the two-stage joint debugging mechanism by combining a homogeneous coordinate method and a graphical method with MATLAB software;
deriving a two-stage rocker arm rotation relation equation through a two-stage kinematic equation according to the rotation relation between the two-stage cranks;
and performing joint optimization on key components in the two-stage joint debugging mechanism by using a genetic algorithm through a rocker arm rotation relation equation.
Preferably, the two-stage joint debugging mechanism comprises a zero-order joint debugging mechanism and a first-order joint debugging mechanism, and the first-order joint debugging mechanism and the zero-order joint debugging mechanism are symmetrical structures;
each cascade adjusting mechanism consists of a crank, a connecting rod, a support, a linkage ring, a rocker arm and a blade, and the stages are connected by an interstage connecting rod;
the crank rotates around a crank rotating shaft, the rocker rotates around a blade rotating shaft, and the linkage ring axially moves along a casing central shaft while rotating around the casing central shaft;
the base coordinate system of the mechanism is established at the rotation center of the zeroth cascade moving ring in the initial state.
Preferably, the component of the chord length rotated by the zeroth rocker arm and the link ring in the x-axis direction is equal, that is, the length of the rocker arm multiplied by the sine value of the rocker arm rotation angle is equal to the radius of the link ring multiplied by the sine value of the link ring rotation angle, that is, S and S are equal to each other 0 Equal;
thereby solving the rotation angle omega of the zero-order rocker arm 0 And angle of rotation beta of link ring 0 The relationship of (1);
in addition, the axial translation displacement t of the linkage ring along the central shaft of the casing can be obtained 0 Is equal to the length of the rocker arm minus the length of the rocker arm multiplied by the cosine of the angle of rotation of the rocker arm.
Preferably, the zero-order crank, the linkage ring, the connecting rod and the rack form a spatial connecting rod mechanism comprising a rotating pair, two spherical hinge pairs and a cylindrical pair;
solving the motion equation of the mechanism by using a rod disassembling method, removing a connecting rod, and solving the crank end points (a) before and after motion by using a homogeneous coordinate method 0 、a 1 ) And the linkage ring end point (b) 0 、b 1 ) The zero-order crank rotation angle theta can be finally deduced by utilizing the rod length condition 0 And angle of rotation beta of the link ring 0 The relation equation between;
the rotation angle omega of the zero-order rocker arm calculated before recombination 0 And angle of rotation beta of link ring 0 The relationship between the two, eliminating the rotation angle beta of the link ring 0 The zero-order crank rotation angle theta can be obtained 0 And angle of rotation omega of rocker arm 0 In relation to (2)And the equation is the motion equation of the zeroth order joint debugging mechanism, and the motion rule of the zeroth order joint debugging mechanism can be analyzed through the equation.
Preferably, the rod length condition is such that the distance between the crank end point and the link end point is constant before and after the movement.
Preferably, the two cranks are connected by an inter-stage connecting rod, and the two cranks, the inter-stage connecting rod and the frame form a parallelogram mechanism, so that the two cranks rotate at the same angle, i.e. theta 0 And theta 1 Equal in size and opposite in direction.
Because the two-stage joint adjusting mechanism is in a symmetrical relation, the motion laws of the two-stage components are the same, only the motion directions are opposite, and the first-stage crank rotates by an angle theta 1 And angle of rotation beta of the link ring 1 Relation equation and first-stage rocker arm rotation angle omega 1 And angle of rotation beta of link ring 1 The relation equation can be used for deducing the first-stage crank rotation angle theta 1 And rocker arm angle of rotation theta 1 A relational equation, namely a motion equation of the first cascade regulating mechanism;
the motion law of the first cascade adjustment mechanism can be analyzed through the motion equation of the first cascade adjustment mechanism.
By utilizing the condition that the rotation angles of the zero-level crank and the first-level crank are equal, the rotation relation equation of the rocker arm of the two-level joint adjusting mechanism can be deduced through the motion equation of the zero-level and first-level joint adjusting mechanisms.
Preferably, each curve of the two-step rocker arm rotation relationship curve is an arc, and the arc curve can be fitted with a target curve: the method is characterized in that joint optimization is carried out on components in the two-stage mechanism by using a genetic algorithm and taking the fitting degree of an actual curve and a target curve as a target through a rocker arm rotation relation equation of the two-stage joint adjusting mechanism.
Preferably, the purpose of optimization is to enable the rotation angular speed of the two-stage rocker arm to be in a double relation on the basis that the rotation angle of the two-stage rocker arm is in a double relation, and the optimization objects are the length of an adjustable end and the included angle between the adjustable end and a fixed end of the two-stage crank.
(III) advantageous effects
The invention has the beneficial effects that: the invention can analyze the rotation rule of the rocker arm (stationary blade) between each stage and the multiple stages through the motion equation and the relation equation derived from theory, and can carry out combined optimization on the two-stage mechanism through the relation equation. By the method, the joint debugging mechanism meeting the design requirement can be quickly and efficiently designed. The theoretical analysis has higher reliability and persuasion than the simulation analysis; the range of feasible solutions can be remarkably expanded through multi-stage combined optimization, and more choices are provided for the design of a mechanism; the intelligent optimization algorithm can remarkably improve the speed and the precision of analysis and solution, improve the design efficiency and shorten the design period.
Drawings
FIG. 1 is a schematic diagram of a joint debugging entity model according to an embodiment of the present invention;
FIG. 2 is a line model diagram of a two-stage joint debugging mechanism according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a theoretical motion process of a zeroth rocker arm-link ring according to an embodiment of the present invention;
FIG. 4 illustrates an actual motion of the zeroth rocker-link ring according to an embodiment of the present invention;
FIG. 5 illustrates a zeroth order of the link-crank motion process according to an embodiment of the present invention;
FIG. 6 illustrates a two-step crank motion process according to an embodiment of the present invention;
FIG. 7 illustrates a first stage crank-link ring motion process according to an embodiment of the present invention;
FIG. 8 illustrates a first stage link ring-rocker motion process according to an embodiment of the present invention;
FIG. 9 is a graph of a two-step rocker arm rotation angle relationship according to an embodiment of the present invention;
FIG. 10 is a graph of the optimized two-step rocker arm rotation angle relationship provided by an embodiment of the present invention;
FIG. 11 is an enlarged partial view of an optimized post-two step rocker arm rotational angle relationship curve provided in accordance with an embodiment of the present invention.
[ description of reference ]
1: a zero-order crank; 2: a zero-order rocker arm; 3: a connecting rod; 4: a support; 5: a blade; 6: a link ring; 7: an interstage connecting rod; 8: a first stage crank; 9: a first stage rocker arm.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
The invention discloses an optimization design method of a stationary blade joint debugging mechanism of an aeroengine, which solves a kinematic equation of a two-stage joint debugging mechanism by combining a homogeneous coordinate method and a graphical solution with MATLAB software;
deducing a two-stage rocker arm rotation relation equation through a two-stage kinematics equation according to the rotation relation between the two-stage cranks;
and performing joint optimization on key components in the two-stage joint debugging mechanism by using a genetic algorithm through a rocker arm rotation relation equation.
The method specifically comprises the following steps:
fig. 2 is a line model of a two-stage joint debugging mechanism, and only the zeroth level is labeled for the sake of clarity. The zeroth level and the first level are in a symmetrical structure, and the two levels are connected through an interstage connecting rod. Each stage of joint adjusting mechanism consists of a crank, a connecting rod, a linkage ring, a support and a rocker arm. The movement is as follows: the crank rotates around the crank rotating shaft, the rocker rotates around the blade rotating shaft, and the linkage ring axially moves along the central shaft of the casing while rotating around the central shaft of the casing. The basic coordinate system XOY of the mechanism establishes the center of rotation of the zeroth cascade of the rotating ring in the initial state. The coordinate systems used in this application all obey the right-hand rule. And in the solving process, the linkage ring and the support are viewed as a whole and are recorded as the linkage ring (support).
1.1 equation of motion of zeroth order
The derivation of the zeroth order equation of motion adopts a mode of combining a graphical method and a homogeneous coordinate method.
1.1.1 zeroth order rocker-link ring part
In the joint-regulating mechanism, the rocker arm is in the plane X 2 O 2 Y 2 Middle winding Z 2 Rotation angle omega of shaft (blade rotation axis) 0 . Linkage surrounding Y-axis (central axis of casing) rotation angle beta 0 While translating a distance t along the negative direction of the Y axis 0 (i.e., the origin of coordinates is changed from O to O 1 ). Because the rotating shaft of the rocker arm is vertical to the rotating shaft of the link ring, the end point f of the rocker arm rotates for a certain angle theoretically 1 And is separated from the connection point f on the link ring as shown in fig. 3. In fact, slight deformation of the rocker arm itself compensates for the difference in the Z coordinate between the two points, as shown in fig. 4.
In theory or practice, f 1 The point is always equal to the X component of the f point coordinate, namely the projection of the chord length rotated by the rocker arm and the chord length rotated by the linkage ring in the X-axis direction (S is respectively 0 And S) are equal. Namely:
S 0 ＝S (1)
neglecting the effect of slight deformation of the rocker arm, one can obtain:
S 0 ＝r 0 sinω 0 (2)
S＝R 0 sinβ 0 (3)
obtaining the rotation angle beta of the zeroth-order linkage ring by the formula (1), the formula (2) and the formula (3) 0 And rocker arm angle of rotation omega 0 The relationship of (1):
R 0 sinβ 0 r 0 sinω 0 (4)
wherein:
R 0 -a zero-order link ring radius;
r 0 -a zeroth order rocker arm length;
β 0 -a zeroth order link ring rotation angle;
ω 0 zero order rocker angle of rotation.
1.1.2 zeroth cascade dynamic Ring-crank part
As shown in fig. 5, the crank is in plane X 4 O 4 Y 4 Middle winding Z 4 Rotation angle theta of shaft (crank rotation axis) 0 . Angle of rotation beta of link ring (support) around Y axis 0 While translating a distance t along the negative Y-axis direction 0 。
The adjustable ends of the linkage ring (support), the connecting rod and the crank are also provided with a frame to form the deviceA revolute pair, two spherical hinge pairs and a cylindrical pair space four-bar mechanism (RSSC). The analysis is carried out by a rod-detaching method, namely, the connecting rod is detached. Solving the end point a of the crank before movement by using a homogeneous coordinate method 0 Connecting point b of linkage ring (support) and connecting rod before movement 0 And the end point a of the crank after the exercise 1 And a connecting point b of the linkage ring (support) and the connecting rod after movement 1 Coordinates in the base coordinate system XOY. And establishing a relation equation between the crank rotation angle and the linkage ring rotation angle according to the unchanged length of the linkage before and after movement.
From FIG. 5, b 0 The coordinates of a point in the base coordinate system XOY are:
b 0 ＝[0 0 H 0 ] T (5)
wherein: h 0 - - - -point O to point b 0 Of the distance of (c).
The coordinate system 3 is obtained by rotating the coordinate system 1 about the Y-axis. The transformation T from coordinate system XOY to coordinate system 3 o3 Comprises the following steps:
T o3 ＝Trans(0，-t 0 ，0)Rot(Y，-β 0 ) (6)
wherein: t is t 0 ＝r 0 (1-cosω 0 )。
Point b 1 Homogeneous coordinate in coordinate system 3 is [ 0H ] 0 1] T Then point b 1 The homogeneous coordinates in the base coordinate system XOY are:
from the formula (7), the point b can be obtained 1 Coordinates b in the base coordinate system XOY 1 。
Similarly, the transformation T from the coordinate system XOY to the coordinate systems 5 and 6 can be obtained o5 、T o6 Further, a is obtained 0 、a 1 The coordinates of the points. The coordinate systems 5, 6 are both surrounded by Z from the coordinate system 4 4 The shaft (crank rotating shaft) is rotated by a certain angle. Then:
wherein:
α 0 -the angle between the fixed end and the adjustable end of the zero order crank;
h 0 zero order crank center of rotation O 4 Distance to point O;
L 0 -a zeroth order crank throw length.
Wherein: theta 0 Zero crank angle degree.
Point a 0 Homogeneous coordinates in the coordinate system 5 and point a 1 Homogeneous coordinates in the coordinate system 6 are all [ L ] 0 0 0 1] T . Then point a 0 、a 1 The homogeneous coordinates in the base coordinate system XOY are respectively:
a is obtained from the respective expressions (10) and (11) 0 、a 1 。
The length of the connecting rod is not changed before and after movement, namely:
(a 0 -b 0 ) T (a 0 -b 0 )＝(a 1 -b 1 ) T (a 1 -b 1 ) (12)
the zeroth-order crank rotation angle theta can be obtained by solving the equation (12) 0 And the link ring rotatesAngle beta 0 The relationship (c) in (c). Combining formula (12) with formula (4) and eliminating the rotation angle beta of the linkage ring 0 And obtaining a zero-order motion equation:
1.1.3 zeroth order crank-first order crank part
As shown in FIG. 6, the two-step crank fixing end, the inter-step connecting rod and the frame form a parallelogram, and the zero-level crank fixing end rotates by an angle delta 0 Angle delta from the first crank fixing end 1 Are equal. Namely:
δ 0 ＝δ 1 (14)
and because the fixed end and the adjustable end of the crank are integrated, the rotating angles of the fixed end and the adjustable end are equal. Namely:
δ 0 ＝θ 0 (15)
δ 1 ＝θ 1 (16)
obtaining the rotation angle theta of the adjustable end of the zeroth-order crank by the formulas (14), (15) and (16) 0 The rotation angle theta with the adjustable end of the first-stage crank 1 Are equal in size. Namely:
θ 0 ＝θ 1 (17)
1.2 first order equation of motion
The two-stage joint debugging mechanism is of a symmetrical structure, so that the solving method for the zeroth level is also suitable for the first level.
1.2.1 first stage crank-link Ring segment
As shown in FIG. 7, similar to the zeroth order, the first order crank is in plane X 7 O 7 Y 7 Middle winding Z 7 Angle of rotation theta of shaft (i.e. crank axis of rotation) 1 . Angle of rotation beta of link ring (support) about Y axis 1 While translating the distance t along the positive direction of the Y axis 1 . Similarly, the linkage ring (support), the connecting rod, the adjustable end of the crank and the frame of the first stage form a spatial four-bar mechanism (RSSC).
Method for solving first-stage crank before movement by using homogeneous coordinate methodEnd point c 0 And a connecting point d of the link ring (support) and the connecting rod 0 End point c of the first crank stage after the exercise 1 And a connecting point d of the link ring (support) and the connecting rod 1 Coordinates in the base coordinate system XOY. And (3) establishing an equation by using the length of the connecting rod before and after movement to deduce the relation between the rotation angle of the first-stage linkage ring and the rotation angle of the crank.
See d in FIG. 7 0 The coordinates of a point in the base coordinate system XOY are:
d 0 ＝[0 L H 1 ] T (18)
wherein:
l- - - - - -point O to point O 11 The distance of (a);
H 1 - - - -Point O 11 To point d 0 The distance of (d);
the coordinate systems 8, 9 are both surrounded by the coordinate system 7 by Z 7 The axis (crank rotation axis) is rotated by a predetermined angle, and the coordinate system 10 is rotated around the Y-axis (casing center axis) by the coordinate system 12. The transformation from coordinate system XOY to coordinate systems 8, 9, 10 is then:
wherein:
a 1 -the angle between the adjustable end and the fixed end of the first stage crank;
h 1 a first-stage crank rotation center O 7 To O 11 The distance of (d);
L 1 -first stage crank adjustable end length.
Wherein: theta 1 First stage crank rotation angle.
T o10 ＝Trans(0，L，0)Trans(0，t 1 ，0)Rot(Y，β 1 ) (21)
Wherein: t is t 1 ＝r 1 (1-cosω 1 )。
Point c 0 Homogeneous coordinates and point c in coordinate system 8 1 Homogeneous coordinates in the coordinate system 9 are all [ L ] 1 0 0 1] T Point d of 1 Homogeneous coordinate in the coordinate system 10 is [ 0H ] 1 1] T . Then point c 0 、c 1 、d 1 The homogeneous coordinates in the base coordinate system XOY are:
the point c is obtained from the formulae (22), (23) and (24) 0 、c 1 、d 1 In that
Coordinates in the base coordinate system XOY.
The length of the front and rear connecting rods is unchanged after rotation. Namely:
(c 0 -d 0 ) T (c 0 -d 0 )＝(c 1 -d 1 ) T (C 1 -d 1 ) (25)
1.2.2 first Cascade moving Ring-Rocker arm section
As shown in FIG. 8, the rocker arm is at X 13 O 13 Y 13 In plane around Z 13 Rotation angle omega of shaft (i.e. blade rotation axis) 1 . The link ring being rotated about the Y-axis (i.e. the central axis of the casing) by an angle beta 1 While translating the distance t along the positive direction of the Y axis 1 。
Neglecting the deformation of the rocker arm during the movement,the chord length rotated by the rocker arm is equal to the projection of the chord length rotated by the linkage ring in the X-axis direction and is S 1 . Namely:
R 1 sinβ 1 ＝r 1 sinω 1 (26)
wherein:
R 1 -first stage link ring radius;
r 1 -first stage rocker arm length;
β 1 -first stage link ring rotation angle;
ω 1 -first rocker angle of rotation.
The first order equation of motion can be solved by equations (25), (26):
1.3 two-stage rocker arm rotation equation
And connecting the zero-order motion equation with the first-order motion equation to immediately obtain a two-stage rocker arm rotation relation equation. In order to make the dependent variable and independent variable of the equation displayed more clearly, the zero-order rocker arm rotation angle omega is set 0 = x; zero order crank angle theta 0 = t; first-stage rocker arm rotation angle omega 1 = y; as can be seen from the equation (17), when the first crank rotation angle is equal to the zero crank rotation angle, the first crank rotation angle θ 1 And = t. As shown in equation (28), the two-stage rocker arm rotation relation equation is a parameter equation using the zero-order rocker arm rotation angle x as an independent variable, the first-stage rocker arm rotation angle y as a dependent variable, and the two-stage crank rotation angle t as a parameter.
2. Joint debugging mechanism optimization calculation
The optimization algorithm used was the genetic algorithm [18-19]; the optimization objects are four variables of the length of the adjustable end of the crank and the included angle between the adjustable end of the crank and the fixed end in the two-stage adjusting mechanism; the optimization aim is to ensure that the rotation angular speed of the two-stage rocker arm keeps a double relation as much as possible on the basis of the double relation of the rotation angles of the two-stage rocker arm.
2.1 optimization procedure
Under the condition that the rotation angle of the two-stage crank is pi/6, the target rotation angle of the zero-stage rocker arm is pi/18, and the target rotation angle of the first-stage rocker arm is pi/9. Length range L of adjustable end of zero-order crank 0 = 30-60 mm, range alpha of included angle between fixed end and adjustable end of zero-order crank 0 = 0-pi, length range L of adjustable end of first-stage crank 1 = 30-60 mm, and the included angle range alpha between the adjustable end and the fixed end of the first-stage crank 1 And (h) = 0-pi. Other parameters are as follows: r 0 ＝350mm；r 0 ＝40mm；H 0 ＝390mm；
h 0 ＝360mm；R 1 ＝350mm；
H 1 ＝390mm；
h 1 ＝360mm；r 1 ＝40mm。
By substituting the parameters into the equation for the two-step rocker arm rotation relationship of equation (28), a two-step rocker arm rotation relationship curve can be drawn, as shown in FIG. 9
Fig. 9 shows 64 curves, each curve representing a set of curves of the two-stage rocker arm rotation relationship for a combination of variables to be optimized (length of the adjustable end and angle between the adjustable end and the fixed end of the two-stage crank). Each combination meets the requirement of making the two-stage rocker arm rotate twice (the zero-stage rocker arm rotates by pi/18, and the first-stage rocker arm rotates by pi/9). The angular speed of rotation of the two-stage rocker arm keeps twice relation as much as possible all the time, even if the curve of the angular speed of rotation of the two-stage rocker arm is infinitely close to a straight line with the slope of 2. The length L of the adjustable end of the zero-order crank is adjusted by using the genetic algorithm 0 The included angle a between the adjustable end and the fixed end of the zero-level crank 0 The length L of the adjustable end of the first-stage crank 1 Adjustable end and fixing of the first stage crank
End angle alpha 1 And (3) carrying out optimization solution, wherein a group of optimal solutions obtained after multiple times of optimization are shown in table 1:
TABLE 1 optimal solution for joint tuning mechanism
And (4) bringing the optimal solution into a formula (28) two-stage rocker arm rotation relation equation to draw a two-stage rocker arm rotation relation curve. As shown in fig. 10 and 11:
as shown in fig. 10, the actual rotation curve of the two-step rocker arm completely coincides with the target curve. Therefore, the solution meets the condition that the rotating angular speed of the two-stage rocker arm is kept 2 times as much as possible on the premise of ensuring that the rotating angle of the two-stage rocker arm is doubled.
The technical principles of the present invention have been described above in connection with specific embodiments, which are intended to explain the principles of the present invention and should not be construed as limiting the scope of the present invention in any way. Based on the explanations herein, those skilled in the art will be able to conceive of other embodiments of the invention without inventive step, which shall fall within the scope of the invention.
Claims (5)
1. An optimal design method for a stationary blade joint adjusting mechanism of an aeroengine is characterized by comprising the following steps: solving a kinematic equation of the two-stage joint debugging mechanism by combining a homogeneous coordinate method and a graphical solution with MATLAB software;
deducing a two-stage rocker arm rotation relation equation through a two-stage kinematics equation according to the rotation relation between the two-stage cranks;
performing joint optimization on key components in the two-stage joint debugging mechanism by applying a genetic algorithm through a rocker arm rotation relation equation;
the two-stage joint debugging mechanism comprises a zeroth-level joint debugging mechanism and a first-level joint debugging mechanism, and the first-level joint debugging mechanism and the zeroth-level joint debugging mechanism are of symmetrical structures;
each cascade adjusting mechanism consists of a crank, a connecting rod, a support, a linkage ring, a rocker arm and a blade, and the stages are connected by an interstage connecting rod;
the crank rotates around a crank rotating shaft, the rocker rotates around a blade rotating shaft, and the linkage ring axially moves along a casing central shaft while rotating around the casing central shaft;
establishing a base coordinate system of the mechanism at a rotation center of a zero-order linkage ring in an initial state;
the components of chord lengths rotated by the zero-order rocker arm and the linkage ring in the X-axis direction are equal, namely the length of the rocker arm multiplied by the sine value of the rotation angle of the rocker arm is equal to the radius of the linkage ring multiplied by the sine value of the rotation angle of the linkage ring, namely S and S are equal to each other 0 Equal;
thereby solving the rotation angle omega of the zero-order rocker arm 0 And angle of rotation beta of the link ring 0 The relationship of (1);
in addition, the axial translation displacement t of the linkage ring along the central shaft of the casing can be obtained 0 The size of the angle is equal to the length of the rocker arm minus the cosine value of the length multiplied by the rotation angle of the rocker arm;
the zero-order crank, the linkage ring, the connecting rod and the rack form a spatial connecting rod mechanism comprising a rotating pair, two spherical hinge pairs and a cylindrical pair;
solving the motion equation of the mechanism by using a rod-disassembling method, removing a connecting rod, and solving the crank end points (alpha) before and after motion by using a homogeneous coordinate method 0 、a 1 ) And the linkage ring end point (b) 0 、b 1 ) The zero-order crank rotation angle theta can be finally deduced by utilizing the rod length condition 0 And angle of rotation beta of link ring 0 The relation equation between;
the rotation angle omega of the zero-order rocker arm calculated before recombination 0 And angle of rotation beta of link ring 0 The relationship between the two, eliminating the rotation angle beta of the link ring 0 The zero-order crank rotation angle theta can be obtained 0 And angle of rotation omega of rocker arm 0 The equation of the relationship (b) of (c), namely the motion equation of the zeroth-order joint debugging mechanism, can be used for analyzing the motion rule of the zeroth-order joint debugging mechanism.
2. The method for optimally designing the stationary blade joint-adjusting mechanism of the aircraft engine as claimed in claim 1, wherein the rod length condition is that the distance between the crank end point and the link ring end point before and after the movement is constant.
3. The optimum design method for the aero-engine stationary blade joint debugging mechanism according to claim 2 wherein the two-step cranks are connected by an inter-step connecting rod, the two-step cranks, the inter-step connecting rod and the frame form a parallelogram mechanism so that the two-step cranks have the same rotation angle, i.e. θ 0 And theta 1 Equal in size and opposite in direction;
because the two-stage joint adjusting mechanism is in a symmetrical relation, the motion laws of the two-stage components are the same, only the motion directions are opposite, and the first-stage crank rotates by an angle theta 1 And angle of rotation beta of the link ring 1 Relation equation and first-stage rocker arm rotation angle omega 1 And angle of rotation beta of link ring 1 The relation equation can be used for deducing the first-stage crank rotation angle theta 1 And the rotation angle omega of the first-stage rocker arm 1 A relational equation, namely a motion equation of the first cascade mechanism;
the motion rule of the first cascade adjustment mechanism can be analyzed through the motion equation of the first cascade adjustment mechanism;
by utilizing the condition that the rotation angles of the zero-level crank and the first-level crank are equal, the rotation relation equation of the rocker arm of the two-level joint adjusting mechanism can be deduced through the motion equation of the zero-level and first-level joint adjusting mechanisms.
4. The optimization design method of the aircraft engine stationary blade joint debugging mechanism according to claim 3,
each curve of the rotation relation curve of the two-stage rocker arm is an arc line, and the arc curve can be fitted with a target curve: the method is characterized in that the joint optimization is carried out on the components in the two-stage mechanism by using a genetic algorithm and taking the fitting degree of an actual curve and a target curve as a target through a rocker arm rotation relation equation of the two-stage joint adjusting mechanism.
5. The method for optimally designing the stationary blade joint-adjusting mechanism of the aircraft engine as claimed in claim 4, wherein the optimization aims to ensure that the rotating angular speed of the two-stage rocker arm is doubled on the basis of the doubling of the rotating angle of the two-stage rocker arm, and the optimization objects are the length of the adjustable end and the included angle between the adjustable end and the fixed end of the two-stage crank.
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