CN111177854B - Optimal design method of landing gear retraction mechanism based on direct search method - Google Patents

Optimal design method of landing gear retraction mechanism based on direct search method Download PDF

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CN111177854B
CN111177854B CN201911406511.2A CN201911406511A CN111177854B CN 111177854 B CN111177854 B CN 111177854B CN 201911406511 A CN201911406511 A CN 201911406511A CN 111177854 B CN111177854 B CN 111177854B
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bar
rocker
landing gear
angle
objective function
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周长聪
岳珠峰
刘付超
周昊
周煜棠
李志奇
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Northwestern Polytechnical University
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Abstract

The disclosure relates to the technical field of aviation, in particular to an optimal design method of a landing gear retraction mechanism based on a direct search method. The optimization design method comprises the following steps: selecting a design variable of the landing gear retracting mechanism; determining an objective function of a motion error of the landing gear retracting mechanism based on the design variable; establishing constraint conditions of the landing gear retraction mechanism; based on the constraint condition, the objective function is solved by using a direct search method to obtain the optimal value of the design variable. The optimal design method can solve the optimal value of the design variable of the landing gear retracting mechanism, so that the motion error of the landing gear retracting mechanism reaches the minimum value, and further, guidance is provided for the design and improvement of the landing gear retracting mechanism.

Description

Optimal design method of landing gear retraction mechanism based on direct search method
Technical Field
The disclosure relates to the technical field of aviation, in particular to an optimal design method of a landing gear retraction mechanism based on a direct search method.
Background
Landing gear is the only component for supporting the whole aircraft, and is mainly used for supporting the aircraft during landing, running, ground movement and parking and bearing corresponding gravity loads, so that the landing gear plays an extremely important role in the taking-off and landing process of the aircraft. The landing gear retraction mechanism is used for retracting and releasing the landing gear, and the safety and maneuverability of the aircraft are directly affected.
Currently, the research on the movement error of the landing gear retracting mechanism is relatively lacking, so that guidance cannot be provided for the design and improvement of the landing gear retracting mechanism.
The above information disclosed in the background section is only for enhancement of understanding of the background of the disclosure and therefore it may include information that does not form the prior art that is already known to a person of ordinary skill in the art.
Disclosure of Invention
The invention aims to provide an optimal design method of a landing gear retracting mechanism based on a direct search method, which can solve the optimal value of a design variable of the landing gear retracting mechanism, so that the motion error of the landing gear retracting mechanism reaches the minimum value, and further provides guidance for the design and improvement of the landing gear retracting mechanism.
In order to achieve the above purpose, the present disclosure adopts the following technical scheme:
according to one aspect of the present disclosure, there is provided an optimal design method of a landing gear retracting mechanism based on a direct search method, the optimal design method including:
selecting a design variable of the landing gear retracting mechanism;
determining an objective function of a motion error of the landing gear retracting mechanism based on the design variable;
establishing constraint conditions of the landing gear retraction mechanism;
and solving the objective function by utilizing direct search based on the constraint condition to obtain the optimal value of the design variable.
In one exemplary embodiment of the present disclosure, the planar hinged four-bar mechanism is a double rocker mechanism, the first bar is a driving rocker, the second bar is a connecting bar, the third bar is a driven rocker, and the fourth bar is a frame; the objective function satisfies the following preset formula:
Figure BDA0002348783950000021
wherein f (x) is the objective function; psi phi type i An actual output angle of the double rocker mechanism at an ith position; psi phi type si A required output angle for the double rocker mechanism at an ith position; psi phi type i -ψ si Outputting an angle error for the double rocker mechanism at an ith position; i=1, 2, …, n.
In an exemplary embodiment of the present disclosure, ψ i The following preset formula is satisfied:
Figure BDA0002348783950000022
wherein, psi is 0 The rotation angle of the driven rocker is the rotation angle of the driven rocker when the driven rocker is at the right limit position;
Figure BDA0002348783950000023
the rotation angle of the driving rocker is the rotation angle of the driving rocker when the driven rocker is at the right limit position; />
Figure BDA0002348783950000024
And the rotation angle of the driving rocker at the ith position is set as the rotation angle of the driving rocker at the ith position.
In an exemplary embodiment of the present disclosure, ψ 0 、
Figure BDA0002348783950000025
And->
Figure BDA0002348783950000026
The following preset formulas are respectively satisfied:
Figure BDA0002348783950000027
Figure BDA0002348783950000028
Figure BDA0002348783950000029
wherein, I 1 、l 2 、l 3 And l 4 The rod lengths of the driving rocker, the connecting rod, the driven rocker and the frame are respectively.
In one example of the present disclosureIn an embodiment, ψ si The following preset formula is satisfied:
Figure BDA00023487839500000210
wherein alpha is i And beta i The following preset formulas are respectively satisfied:
Figure BDA0002348783950000031
Figure BDA0002348783950000032
in one exemplary embodiment of the present disclosure, the constraints include drive angle constraints and rod length constraints.
In one exemplary embodiment of the present disclosure, the drive angle constraint is:
Figure BDA0002348783950000033
wherein, gamma is the transmission angle of the double rocker mechanism.
In one exemplary embodiment of the present disclosure, the rod length constraint is:
l 2 ≥l 1
l 3 ≥l 1
l 1 +l 4 ≤l 2 +l 3
l 1 +l 2 ≤l 3 +l 4
l 1 +l 3 ≤l 2 +l 4
in one exemplary embodiment of the present disclosure, the direct search method includes a simplex method, a Hooke-Jeeves search method, and a Pavell conjugate direction method.
According to the method for optimizing the design of the landing gear retracting mechanism based on the direct search method, firstly, design variables of the landing gear retracting mechanism are selected; secondly, determining an objective function of the motion error of the landing gear retracting mechanism based on the design variable; subsequently, establishing constraint conditions of the landing gear retraction mechanism; and finally, solving the objective function by using a direct search method based on the constraint condition to obtain the optimal value of the design variable. The optimal design method can solve the minimum value of the design variable of the landing gear retracting mechanism, so that the motion error of the landing gear retracting mechanism reaches the optimal value, and guidance is provided for the design and improvement of the landing gear retracting mechanism.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the disclosure and together with the description, serve to explain the principles of the disclosure. It will be apparent to those of ordinary skill in the art that the drawings in the following description are merely examples of the disclosure and that other drawings may be derived from them without undue effort.
FIG. 1 is a schematic view of a landing gear stowed condition according to an embodiment of the present disclosure.
FIG. 2 is a schematic illustration of an landing gear down state of an embodiment of the present disclosure.
FIG. 3 is a flow chart of a method of optimizing the design of a landing gear extension based on a direct search method in an embodiment of the present disclosure.
Fig. 4 is a schematic structural view of a dual rocker mechanism according to an embodiment of the present disclosure.
FIG. 5 is a comparison of actual output angles and desired output angles at various reference angle points of a dual rocker mechanism prior to optimization in accordance with an embodiment of the present disclosure.
FIG. 6 is a comparison of actual output angles and desired output angles at various reference angle points of a dual rocker mechanism after optimization in accordance with an embodiment of the present disclosure.
Fig. 1 to 2 show: 1. a landing gear retraction mechanism; 11. a first rocker; 12. a connecting rod; 13. a second rocker; 2. a body; 3. and (3) a tire.
In fig. 4: 1. a first link; 2. a second link; 3. a third link; 4. and a fourth link.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. However, the exemplary embodiments may be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure.
The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the disclosed aspects may be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring the main technical ideas of the present disclosure.
Although relative terms such as "upper" and "lower" are used in this specification to describe the relative relationship of one component of an icon to another component, these terms are used in this specification for convenience only, such as in terms of the orientation of the examples described in the figures. It will be appreciated that if the device of the icon is flipped upside down, the "up" component will become the "down" component. Other relative terms such as "high," "low," "top," "bottom," "left," "right," and the like are also intended to have similar meanings.
When a structure is "on" another structure, it may mean that the structure is integrally formed with the other structure, or that the structure is "directly" disposed on the other structure, or that the structure is "indirectly" disposed on the other structure through another structure. The terms "a," "an," "the" are used to indicate the presence of one or more elements/components/etc.; the terms "comprising" and "having" are intended to be inclusive and mean that there may be additional elements/components/etc. in addition to the listed elements/components/etc. The terms "first" and "second" and the like are used merely as labels, and are not intended to limit the number of their objects.
The embodiment of the disclosure provides an optimal design method of a landing gear retraction mechanism based on a direct search method, which is used for optimizing the landing gear retraction mechanism in an airplane.
As shown in fig. 1 and 2, the landing gear retraction mechanism 1 of the embodiments of the present disclosure may be a double rocker mechanism, in particular, the double rocker mechanism may include a first rocker 11 (driving lever), a connecting rod 12, and a second rocker 13 (driven lever), wherein:
the first rocker 11 and the second rocker 13 are hinged to the body 2, the connecting rod 12 is hinged to the first rocker 11 and the second rocker 13, and the tyre 3 is rotatably connected to the hinge of the connecting rod 12 and the second rocker 13. As shown in fig. 1, when the first rocker 11 (active lever) rotates in a direction away from the tire 3, the first rocker 11 (active lever) drives the connecting rod 12 to drive the tire 3 to move upwards, so that the landing gear is retracted; as shown in fig. 2, when the first rocker 11 (active lever) rotates in a direction approaching the tire 3, the first rocker 11 (active lever) drives the connecting rod 12 to drive the tire 3 to move downwards, so as to realize the landing gear lowering.
As shown in fig. 3, the method for optimally designing the landing gear retraction mechanism based on the direct search method according to the embodiment of the present disclosure may include the following steps:
step S110, selecting design variables of the landing gear retraction mechanism;
step S120, determining an objective function of the movement error of the landing gear retracting mechanism based on the design variable;
step S130, establishing constraint conditions of the landing gear retraction mechanism;
and step S140, solving the objective function by using a direct search method based on the constraint condition to obtain the optimal value of the design variable.
According to the method for optimizing the design of the landing gear retracting mechanism based on the direct search method, firstly, design variables of the landing gear retracting mechanism are selected; secondly, determining an objective function of the motion error of the landing gear retracting mechanism based on the design variable; subsequently, establishing constraint conditions of the landing gear retraction mechanism; and finally, solving the objective function by using a direct search method based on the constraint condition to obtain the optimal value of the design variable. The optimal design method can solve the optimal value of the design variable of the landing gear retracting mechanism, so that the motion error of the landing gear retracting mechanism reaches the optimal value, and guidance is provided for the design and improvement of the landing gear retracting mechanism.
The following describes in detail each component of the optimization design method provided in the embodiment of the present disclosure with reference to the accompanying drawings:
in step S110, a design variable of the landing gear extension is selected.
As shown in fig. 4, the landing gear retraction mechanism of the embodiment of the present disclosure may be simplified as a planar hinge four-bar mechanism that may include a first bar 1, a second bar 2, a third bar 3, and a fourth bar 4 hinged two by two, with the bar lengths of the first bar 1, the second bar 2, the third bar 3, and the fourth bar 4 being design variables.
Specifically, the planar hinge four-bar mechanism is a double-rocker mechanism, and at this time, the first bar 1 may be a driving rocker, the second bar 2 may be a connecting bar, the third bar 3 may be a driven rocker, and the fourth bar 4 may be a frame.
Thus, the design variable of the landing gear retraction mechanism of an embodiment of the present disclosure may be represented by an X, an
Figure BDA0002348783950000061
Wherein l 1 、l 2 、l 3 And l 4 The rod lengths of the driving rocker (the first rod 1), the connecting rod (the second rod 2), the driven rocker (the third rod 3) and the frame (the fourth rod 4) are respectively.
In step S120, an objective function of the landing gear retraction mechanism movement error is determined based on the design variables.
The objective function of the motion error of the landing gear retraction mechanism in the embodiment of the present disclosure may satisfy the following preset formula:
Figure BDA0002348783950000071
wherein f (x) is an objective function; psi phi type i The actual output angle of the double rocker mechanism at the ith position; psi phi type si The required output angle of the double rocker mechanism at the ith position is obtained; psi phi type i -ψ si The output angle error of the double rocker mechanism at the ith position is obtained; i=1, 2, …, n.
Wherein, psi is i The following preset formula can be satisfied:
Figure BDA0002348783950000072
in the psi- 0 Is the rotation angle of the driven rocker (the third rod 3) when the driven rocker (the third rod 3) is at the right limit position, and ψ 0 The following preset formula is satisfied:
Figure BDA0002348783950000073
Figure BDA0002348783950000074
is the rotation angle of the driving rocker (the first rod 1) when the driven rocker (the third rod 3) is at the right limit position, and +.>
Figure BDA0002348783950000075
The following preset formula is satisfied:
Figure BDA0002348783950000076
Figure BDA0002348783950000077
is the angle of rotation of the active rocker (first lever 1) in the ith position and +.>
Figure BDA0002348783950000078
The following preset formula is satisfied:
Figure BDA0002348783950000079
and psi is si The following preset formula can be satisfied:
Figure BDA00023487839500000710
/>
wherein alpha is i And beta i The following preset formulas are respectively satisfied:
Figure BDA00023487839500000711
Figure BDA00023487839500000712
in step S130, constraints of the landing gear retraction mechanism are established.
In designing landing gear retraction mechanisms (double rocker mechanisms), two general constraints are considered: one is the requirement of the transmission angle of the double rocker mechanism during movement, and the other is to ensure that the double rocker mechanism meets the rod length condition, that is, the constraints of the landing gear retracting mechanism in the embodiment of the disclosure include the transmission angle constraint and the rod length constraint.
The transmission angle constraint condition is mainly used for enabling the transmission of the double-rocker mechanism to be flexible and reliable, and meets the following preset formula:
γ min ≤γ≤γ max
wherein, gamma min And gamma max The following preset formulas are respectively satisfied:
Figure BDA0002348783950000081
Figure BDA0002348783950000082
thus, the drive angle constraints are:
Figure BDA0002348783950000083
for example, γ can be set min ＝45°、γ max =135°, the transmission angle constraint can be as follows:
Figure BDA0002348783950000084
Figure BDA0002348783950000085
of course, use of gamma min And gamma max The setting is not particularly limited here, and other angles are set.
For the rod length constraint, the constraint needs to be established according to the conditions existing in the double rocker mechanism, as follows:
l 2 ≥l 1
l 3 ≥l 1
l 1 +l 4 ≤l 2 +l 3
l 1 +l 2 ≤l 3 +l 4
l 1 +l 3 ≤l 2 +l 4
wherein l 1 、l 2 、l 3 And l 4 Respectively isThe lever lengths of the driving rocker (first lever 1), the connecting lever (second lever 2), the driven rocker (third lever 3) and the frame (fourth lever 4).
The following constraint conditions can be obtained after finishing:
g 3 (x)＝l 1 -l 2 ≤0
g 4 (x)＝l 1 -l 3 ≤0
g 5 (x)＝l 1 +l 4 -l 2 -l 3 ≤0
g 6 (x)＝l 1 +l 2 -l 3 -l 4 ≤0
in step S140, the objective function is solved by using a direct search method based on the constraint condition to obtain an optimal value of the design variable.
In order to maximize the accuracy of the motion of the double rocker mechanism, it is desirable to minimize the objective function, and thus the motion error of the double rocker mechanism.
The direct search method is suitable for highly nonlinear objective functions, especially for the case that the objective functions have no derivative or the derivative is difficult to calculate, and many problems in practical engineering are nonlinear, so the direct search method is an effective solution. Common direct search methods include simplex, hooke-Jeeves (step-by-step acceleration), pavell (Pavell) conjugate direction, and the like, which are not listed here.
For example, the rod lengths of the first link 1, the second link 2, the third link 3, and the fourth link 4 may be selected to be 10cm, 42cm, 20cm, and 50cm, respectively, while the lower limits of the rod lengths of the first link 1, the second link 2, the third link 3, and the fourth link 4 are defined as 8cm, 35cm, 20cm, and 45cm, respectively, the upper limits of the rod lengths of the first link 1, the second link 2, the third link 3, and the fourth link 4 are selected to be 13cm, 45cm, 30cm, and 50cm, respectively, and n in the objective function is selected to be 10, and the objective function is solved by using a simplex method, a Hooke-Jeeves search method (step acceleration method), and a Pavell (Pavell) conjugate direction method, respectively, and the optimization results are shown in table 1:
table 1 optimization results for different methods
Figure BDA0002348783950000091
As can be seen from Table 1, the objective function value of the double rocker mechanism is reduced from 0.0185 to 0.0033 (using simplex method or Hooke-Jeeves search method) to 0.0036 (using Pavell conjugate direction method), and the optimization effect is obvious. Meanwhile, since the time taken for the simplex method is the shortest, it is preferable that the simplex method solves the objective function of the double-rocker mechanism, and as can be seen from fig. 5 and 6, the actual output angle (actual angle) after the optimization by the simplex method is close to the required output angle (required angle), and the obtained optimized values are 11.1708cm, 40.5927cm, 24.8405cm and 48.7393cm, respectively.
It is to be understood that the disclosure is not limited in its application to the details of construction and the arrangement of components set forth in the disclosure. The disclosure is capable of other embodiments and of being practiced and carried out in various ways. The foregoing variations and modifications are within the scope of the present disclosure. It should be understood that the present disclosure disclosed and defined herein extends to all alternative combinations of two or more of the individual features mentioned or evident from the text and/or drawings. All of these different combinations constitute various alternative aspects of the present disclosure. The embodiments described herein explain the best modes known for practicing the disclosure and will enable others skilled in the art to utilize the disclosure.

Claims (5)

1. An optimization design method of a landing gear retraction mechanism based on a direct search method is characterized by comprising the following steps of:
selecting a design variable of a landing gear retraction mechanism, wherein the landing gear retraction mechanism is a plane hinge four-bar mechanism, the plane hinge four-bar mechanism comprises a first bar, a second bar, a third bar and a fourth bar which are hinged in pairs, and the bar lengths of the first bar, the second bar, the third bar and the fourth bar are the design variable;
determining an objective function of a motion error of the landing gear retracting mechanism based on the design variable, wherein the plane hinge four-bar mechanism is a double-rocker mechanism, the first bar is a driving rocker, the second bar is a connecting bar, the third bar is a driven rocker, and the fourth bar is a frame; the objective function satisfies the following preset formula:
Figure FDA0004162814270000011
wherein f (x) is the objective function; psi phi type i An actual output angle of the double rocker mechanism at an ith position; psi phi type si A required output angle for the double rocker mechanism at an ith position; psi phi type i -ψ si Outputting an angle error for the double rocker mechanism at an ith position; i=1, 2, …, n;
ψ i the following preset formula is satisfied:
Figure FDA0004162814270000012
wherein, psi is 0 The rotation angle of the driven rocker is the rotation angle of the driven rocker when the driven rocker is at the right limit position;
Figure FDA0004162814270000013
the rotation angle of the driving rocker is the rotation angle of the driving rocker when the driven rocker is at the right limit position; />
Figure FDA0004162814270000014
The rotation angle of the driving rocker at the ith position is set;
ψ 0 、
Figure FDA0004162814270000015
and->
Figure FDA0004162814270000016
The following preset formulas are respectively satisfied:
Figure FDA0004162814270000017
Figure FDA0004162814270000018
Figure FDA0004162814270000019
wherein, I 1 、l 2 、l 3 And l 4 The rod lengths of the driving rocker, the connecting rod, the driven rocker and the rack are respectively;
establishing constraint conditions of the landing gear retraction mechanism, wherein the constraint conditions comprise a transmission angle constraint condition and a rod length constraint condition;
and solving the objective function by using a direct search method based on the constraint condition to obtain the optimal value of the design variable.
2. The optimization design method according to claim 1, wherein ψ is si The following preset formula is satisfied:
Figure FDA0004162814270000021
wherein alpha is i And beta i The following preset formulas are respectively satisfied:
Figure FDA0004162814270000022
Figure FDA0004162814270000023
3. the optimization design method according to claim 1, wherein the transmission angle constraint condition is:
Figure FDA0004162814270000024
wherein, gamma is the transmission angle of the double rocker mechanism.
4. The optimization design method according to claim 1, wherein the rod length constraint condition is:
l 2 ≥l 1
l 3 ≥l 1
l 1 +l 4 ≤l 2 +l 3
l 1 +l 2 ≤l 3 +l 4
l 1 +l 3 ≤l 2 +l 4 。
5. the optimization design method according to claim 1, wherein the direct search method includes a simplex method, a Hooke-Jeeves search method, and a Pavell conjugate direction method.
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