CN112528410A - Undercarriage retraction track determining method and system - Google Patents
Undercarriage retraction track determining method and system Download PDFInfo
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Abstract
The invention provides a method and a system for determining the retraction track of an undercarriage, wherein the method comprises the following steps: determining coordinates q1 of the extreme tip point of the landing gear strut when down, a desired coordinate q2 of the extreme tip point of the landing gear strut when up, a third triangular network and a fourth triangular network in a global coordinate system; constructing a unit vector formula of a rotating shaft according to a coordinate q1 of the extreme end point of the landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is put up in a global coordinate system; and determining the optimal winding and unwinding path according to a unit vector formula of the rotating shaft by adopting an optimization algorithm. Compared with the traditional method relying on manual design, the method can carry out automatic design solution, save the energy of people in the design process, shorten the design time, and can solve the optimal retraction path without depending on experience.
Description
Technical Field
The invention relates to the technical field of orbit planning in aerospace engineering, in particular to a method and a system for determining a retraction track of an undercarriage.
Background
The design of the landing gear device is one of the core technologies of aircraft design through the whole design process of the aircraft. The traditional landing gear design generally adopts a serial design process of 'design-manufacture-test-improvement-design', and the design means is usually based on experience modification and mapping methods and is verified and improved through prototype tests. For an airplane with a larger airplane cabin, the method is feasible, however, in the face of some airplanes with higher requirements on maneuvering performance, such as supersonic airplanes, the traditional landing gear design method cannot meet special requirements such as narrow space, high approach speed and the like, even the combat performance of the hypersonic airplane needs to be sacrificed to realize the function of a landing and landing system, and particularly the problem of the limitation of the landing gear storage space becomes an important bottleneck for restricting the development of the hypersonic aerospace airplane.
With the development of the digital prototype technology, the design sampling, the mechanism motion analysis, the dynamics analysis, the finite element analysis, the optimization design and the like of a complex mechanism are carried out through the multidisciplinary collaborative simulation technology, even the corresponding virtual test is completed, more uncertain factors can be considered in the design stage, the performance of each system can be fully evaluated, the test verification is not needed, the development cost is greatly reduced, and the development period is shortened. But the saved time is only the time of the prototype manufacturing experiment, and the design process still highly depends on the experience and the manual work of people. With the improvement of the performance requirement of the airplane, the complexity of the landing gear mechanism is continuously improved due to a plurality of limiting factors, and the virtual simulation technology is difficult to rapidly provide effective support for the selection of each key parameter at the initial stage of design.
For example, in order to obtain a large lift-drag ratio, the wing body fusion body aircraft adopts thin wings, and the wing aspect ratio is small, so that a cabin for retracting and releasing the undercarriage is narrow, namely the undercarriage is difficult to retract and release, and the aircraft is very easy to interfere with the cabin or engines and other instruments. Aiming at the problems that the solution of the undercarriage recovery path in some practical engineering problems is long, an engineer experience is excessively relied on, an optimal solution is difficult to find, even a solution cannot be found and the like, a method capable of rapidly determining the undercarriage retracting track is urgently needed to be designed at present, and further the problem that a cabin is repeatedly designed due to the non-optimality of the undercarriage retracting mode is avoided.
Disclosure of Invention
Based on the above, the invention aims to provide a method and a system for determining the retraction track of the undercarriage, so as to improve the rapid and automatic solving of the optimal retraction track of the undercarriage.
In order to achieve the aim, the invention provides a method for determining the retraction track of an undercarriage, which comprises the following steps:
step S1: determining coordinates q1 of the extreme tip point of the landing gear strut when down, a desired coordinate q2 of the extreme tip point of the landing gear strut when up, a third triangular network and a fourth triangular network in a global coordinate system;
step S2: constructing a unit vector formula of a rotating shaft according to a coordinate q1 of the extreme end point of the landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is put up in a global coordinate system;
step S3: and determining the optimal winding and unwinding path according to a unit vector formula of the rotating shaft by adopting an optimization algorithm.
Optionally, step S1 specifically includes:
step S11: acquiring a coordinate Q1 of the landing gear mounting point position under an initial coordinate system, a coordinate Q2 of the tail end point of a landing gear support column when the landing gear is put down and an expected coordinate Q3 of the tail end point of the landing gear support column when the landing gear is put up;
step S12: acquiring a first three-dimensional model and a second three-dimensional model; the first three-dimensional model is a three-dimensional model describing an aircraft cabin environment; the second three-dimensional model is a three-dimensional model describing that the undercarriage is in a down state;
step S13: utilizing creo paramicas software to respectively divide the first three-dimensional model and the second three-dimensional model into triangular meshes to obtain a first triangular mesh and a second triangular mesh; the first triangular mesh and the second triangular mesh both comprise a plurality of triangular patches;
step S14: the coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q3 of the extreme end point of the landing gear strut when the landing gear strut is put up, the first triangular mesh and the second triangular mesh are all converted to be under the global coordinate system, and the coordinate Q1 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put up, the third triangular mesh and the fourth triangular mesh are obtained.
Optionally, step S2 specifically includes:
step S21: determining a normal vector under a global coordinate system according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under the global coordinate system, wherein the specific formula is as follows:
wherein q1 is the coordinate of the extreme tip point of the landing gear strut when lowering in the global coordinate system, q2 is the expected coordinate of the extreme tip point of the landing gear strut when retracting in the global coordinate system, (X)f,Yf,Zf) Normal vectors F (X) respectively representing the plane in which the landing gear liesf,Yf,Zf) Three components of (a);
step S22: constructing a unit vector formula of the rotating shaft based on the normal vector, wherein the specific formula is as follows:
where ρ is the projection length of the unit length rotation axis on the global coordinate xy plane, (X)f,Yf,Zf) Normal vectors F (X) of the plane in which the landing gear is locatedf,Yf,Zf) Theta is the angle between the projection of the unit length rotation axis on the global coordinate xy plane and the x-axis, xr、yrAnd zrAre respectively provided withIs a unit vector R (x)r,yr,zr) Three values on each axis, R (x)r,yr,zr) Is a unit vector of the axis of rotation in the global coordinate system from the coordinate q1 of the landing gear strut extreme point when down to the desired coordinate q2 of the landing gear strut extreme point when up.
Optionally, step S3 specifically includes:
step S31: inputting a given theta into a unit vector formula of the rotating shaft to determine a unit vector of the rotating shaft; theta is an angle formed by the projection of the rotating shaft with the unit length on the xy plane of the global coordinate and the x axis;
step S32: determining a rotation matrix of the third triangular network of the landing gear when the third triangular network rotates around the origin for alpha degrees each time based on the unit vector of the rotation axis;
step S33: multiplying the rotation matrix by a coordinate q1 of a tail-end point of a landing gear strut when the landing gear strut is put down under a global coordinate system to obtain the current position of the landing gear;
step S34: calculating the distance between the rotating undercarriage and the cabin environment based on the triangular patch in the third triangular network and the triangular patch in the fourth triangular network;
step S35: judging whether a cosine function value of an included angle between the current position and the target position of the undercarriage is smaller than a first preset value or not; if the distance is smaller than the first preset value, the landing gear is judged to reach the target position, and the minimum distance in the whole lifting process is used as an evaluation index of the retraction path; if the rotation angle is larger than or equal to the first preset value, making α + Φ be α + Φ, and returning to step S32, where Φ is the given rotation angle; the target position is an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear is retracted under a global coordinate system;
step S36: judging whether the evaluation index of the winding and unwinding path is less than or equal to a second preset value or not; if the evaluation index of the retraction path is smaller than or equal to the second preset value, the landing gear is considered to be capable of colliding, and step S37 is executed; if the evaluation index of the retraction path is larger than a second preset value, the undercarriage can be retracted without collision, and the retraction path corresponding to the angle theta is output as the optimal retraction path;
step S37: converting the expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear is folded under the global coordinate system into the spherical coordinate system, and obtaining a new expected coordinate q of the extreme end point of the landing gear strut when the landing gear is foldedx；
Step S38: let q2 be qxAnd returns to "step S2".
Optionally, the expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is folded up under the global coordinate system is converted into the global coordinate system, and a new expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is folded up is obtainedxThe concrete formula is as follows:
wherein (x, y, z) is landing gear spherical coordinate qxThe three-axis coordinate values of (a), r, representing the length of the landing gear itself,
respectively represents the yaw angle and the pitch angle of the landing frame under the coordinate system of the ball marker,
are all translational angle variables.
The invention also provides a landing gear retraction track determining system, which comprises:
a parameter determination module for determining a coordinate q1 of a most terminal point of a landing gear strut when in a down state, an expected coordinate q2 of the most terminal point of the landing gear strut when in a up state, a third triangular network and a fourth triangular network under a global coordinate system;
a unit vector formula building module for building a unit vector formula of a rotating shaft according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under a global coordinate system;
and the optimal winding and unwinding path determining module is used for determining an optimal winding and unwinding path according to a unit vector formula of the rotating shaft by adopting an optimization algorithm.
Optionally, the parameter determining module specifically includes:
a first acquisition unit configured to acquire a coordinate Q1 of a landing gear attachment point position in an initial coordinate system, a coordinate Q2 of a most distal point of a landing gear strut when the landing gear strut is down, and a desired coordinate Q3 of the most distal point of the landing gear strut when the landing gear strut is up;
a second acquisition unit configured to acquire the first three-dimensional model and the second three-dimensional model; the first three-dimensional model is a three-dimensional model describing an aircraft cabin environment; the second three-dimensional model is a three-dimensional model describing that the undercarriage is in a down state;
the triangular mesh dividing unit is used for performing triangular mesh division on the first three-dimensional model and the second three-dimensional model respectively by using creo paramacas software to obtain a first triangular mesh and a second triangular mesh; the first triangular mesh and the second triangular mesh both comprise a plurality of triangular patches;
and the first coordinate conversion unit is used for converting the coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q3 of the extreme end point of the landing gear strut when the landing gear strut is put up, the first triangular mesh and the second triangular mesh under the global coordinate system, and obtaining the coordinate Q1 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put up, the third triangular mesh and the fourth triangular mesh under the global coordinate system.
Optionally, the unit vector formula building module specifically includes:
the normal vector formula building unit is used for determining a normal vector under a global coordinate system according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under the global coordinate system, and the specific formula is as follows:
wherein q1 is a constant value in the global coordinate systemThe coordinates of the extreme tip of the landing gear strut at the time of descent, q2 being the expected coordinates of the extreme tip of the landing gear strut at the time of retraction in the global coordinate system, (X)f,Yf,Zf) Normal vectors F (X) respectively representing the plane in which the landing gear liesf,Yf,Zf) Three components of (a);
the unit vector formula construction unit is used for constructing a unit vector formula of the rotating shaft based on a normal vector, and the specific formula is as follows:
where ρ is the projection length of the unit length rotation axis on the global coordinate xy plane, (X)f,Yf,Zf) Normal vectors F (X) of the plane in which the landing gear is locatedf,Yf,Zf) Theta is the angle between the projection of the unit length rotation axis on the global coordinate xy plane and the x-axis, xr、yrAnd zrAre respectively unit vectors R (x)r,yr,zr) Three values on each axis, R (x)r,yr,zr) Is a unit vector of the axis of rotation in the global coordinate system from the coordinate q1 of the landing gear strut extreme point when down to the desired coordinate q2 of the landing gear strut extreme point when up.
Optionally, the optimal retraction path determining module specifically includes:
an input unit for inputting a given θ into a unit vector equation of the rotation axis to determine a unit vector of the rotation axis; theta is an angle formed by the projection of the rotating shaft with the unit length on the xy plane of the global coordinate and the x axis;
a rotation matrix determination unit for determining a rotation matrix of the third triangular network of the landing gear each time the third triangular network rotates around the origin by a degree based on the unit vector of the rotation axis;
a multiplying unit, which is used for multiplying the rotation matrix by a coordinate q1 of the extreme point of the landing gear strut when the landing gear is put down under a global coordinate system, so as to obtain the current position of the landing gear;
a distance determining unit, configured to calculate a distance between the rotated landing gear and the cabin environment based on a triangular patch in the third triangular network and a triangular patch in the fourth triangular network after the rotation;
the first judgment unit is used for judging whether a cosine function value of an included angle between the current position and the target position of the undercarriage is smaller than a first preset value or not; if the distance is smaller than the first preset value, the landing gear is judged to reach the target position, and the minimum distance in the whole lifting process is used as an evaluation index of the retraction path; if the angle is larger than or equal to the first preset value, alpha is alpha + phi, and a rotation matrix determining unit is returned, wherein phi is a given rotation angle; the target position is an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear is retracted under a global coordinate system;
the second judging unit is used for judging whether the evaluation index of the folding and unfolding path is less than or equal to a second preset value or not; if the evaluation index of the retraction path is smaller than or equal to a second preset value, the undercarriage is considered to be capable of colliding, and a second coordinate conversion unit is executed; if the evaluation index of the retraction path is larger than a second preset value, the undercarriage can be retracted without collision, and the retraction path corresponding to the angle theta is output as the optimal retraction path;
a second coordinate conversion unit for converting the expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is folded into the global coordinate system, and obtaining a new expected coordinate q of the extreme end point of the landing gear strut when the landing gear strut is foldedx；
An assignment unit for making q2 qxAnd returning to the unit vector formula building module.
Optionally, the expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is folded up under the global coordinate system is converted into the global coordinate system, and a new expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is folded up is obtainedxThe concrete formula is as follows:
wherein (x, y, z) is landing gear spherical coordinate qxThe three-axis coordinate values of (a), r, representing the length of the landing gear itself,
respectively represents the yaw angle and the pitch angle of the landing frame under the coordinate system of the ball marker,
are all translational angle variables.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a method and a system for determining the retraction track of an undercarriage, wherein the method comprises the following steps: determining coordinates q1 of the extreme tip point of the landing gear strut when down, a desired coordinate q2 of the extreme tip point of the landing gear strut when up, a third triangular network and a fourth triangular network in a global coordinate system; constructing a unit vector formula of a rotating shaft according to a coordinate q1 of the extreme end point of the landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is put up in a global coordinate system; and determining the optimal winding and unwinding path according to a unit vector formula of the rotating shaft by adopting an optimization algorithm. Compared with the traditional method relying on manual design, the method can carry out automatic design solution, save the energy of people in the design process, shorten the design time, and can solve the optimal retraction path without depending on experience.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a flowchart of a landing gear retraction track determination method according to embodiment 1 of the present invention;
FIG. 2 is a plane bisecting the distribution angle of the rotating shaft in embodiment 1 of the present invention;
fig. 3 is a structural diagram of a landing gear retraction track determination system according to embodiment 2 of the present invention.
Detailed Description
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 only a part of the embodiments of the present invention, and not all of the embodiments. 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.
The invention aims to provide a method and a system for determining the retraction track of an undercarriage, so as to improve the rapid and automatic solving of the optimal retraction track of the undercarriage.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1
As shown in fig. 1, the invention discloses a method for determining a landing gear retraction track, which comprises the following steps:
step S1: the coordinates q1 of the extreme tip point of the landing gear strut at set-down, the desired coordinates q2 of the extreme tip point of the landing gear strut at set-up, the third triangular network and the fourth triangular network are determined in a global coordinate system.
Step S2: a unit vector equation for the axis of rotation is constructed from the coordinate q1 for the extreme tip point of the landing gear strut when down and the expected coordinate q2 for the extreme tip point of the landing gear strut when up in the global coordinate system.
Step S3: and determining the optimal winding and unwinding path according to a unit vector formula of the rotating shaft by adopting an optimization algorithm.
The individual steps are discussed in detail below:
step S1: determining a coordinate q1 of the extreme end point of the landing gear strut when the landing gear strut is put down, an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is put up, a third triangular network and a fourth triangular network under a global coordinate system, and specifically comprising:
step S11: acquiring a coordinate Q1 of the landing gear mounting point position under an initial coordinate system, a coordinate Q2 of the tail end point of a landing gear support column when the landing gear is put down and an expected coordinate Q3 of the tail end point of the landing gear support column when the landing gear is put up; the initial coordinate system is set according to actual requirements.
Step S12: acquiring a first three-dimensional model and a second three-dimensional model; the first three-dimensional model is a three-dimensional model describing an aircraft cabin environment; the second three-dimensional model is a three-dimensional model describing the landing gear in the down state.
Step S13: utilizing creo paramicas software to respectively divide the first three-dimensional model and the second three-dimensional model into triangular meshes to obtain a first triangular mesh and a second triangular mesh; the first triangular mesh and the second triangular mesh both comprise a plurality of triangular patches; and storing the first triangular mesh and the second triangular mesh in an STL file format or an OBJ file format.
Step S14: converting a coordinate Q2 of the extreme point of the landing gear strut when the landing gear strut is put down, an expected coordinate Q3 of the extreme point of the landing gear strut when the landing gear strut is put up, a first triangular mesh and a second triangular mesh under a global coordinate system to obtain a coordinate Q1 of the extreme point of the landing gear strut when the landing gear strut is put down, an expected coordinate Q2 of the extreme point of the landing gear strut when the landing gear strut is put up, a third triangular mesh and a fourth triangular mesh under the global coordinate system; the third triangular network is an LG triangular network, and the fourth triangular network is an RE triangular network.
That is, a global coordinate system is constructed with the coordinate Q1 of the landing gear attachment point position as the origin. And subtracting the coordinate of Q1 from the coordinate of each vertex of each patch in the first triangular mesh to generate a third triangular mesh, and subtracting the coordinate of Q1 from the coordinate of each vertex of each patch in the second triangular mesh to generate a fourth triangular mesh under the global coordinate system.
Step S2: constructing a unit vector formula of a rotating shaft according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under a global coordinate system, wherein the unit vector formula specifically comprises the following steps:
step S21: determining a normal vector under a global coordinate system according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under the global coordinate system, wherein the specific formula is as follows:
wherein q1 is the coordinate of the extreme tip point of the landing gear strut when lowering in the global coordinate system, q2 is the expected coordinate of the extreme tip point of the landing gear strut when retracting in the global coordinate system, (X)f,Yf,Zf) Normal vectors F (X) respectively representing the plane in which the landing gear liesf,Yf,Zf) Three components of (a).
Step S22: constructing a unit vector formula of the rotating shaft based on the normal vector, wherein the specific formula is as follows:
where ρ is the projection length of the unit length rotation axis on the global coordinate xy plane, (X)f,Yf,Zf) Normal vectors F (X) of the plane in which the landing gear is locatedf,Yf,Zf) Theta is the angle between the projection of the unit length rotation axis on the global coordinate xy plane and the x-axis, xr、yrAnd zrAre respectively unit vectors R (x)r,yr,zr) Three values on each axis, R (x)r,yr,zr) Is a unit vector of the axis of rotation in the global coordinate system from the coordinate q1 of the landing gear strut extreme point when down to the desired coordinate q2 of the landing gear strut extreme point when up.
For a rotation axis in three-dimensional space, given a mode length, it can be described by a two-dimensional vector. Here, the rotation axis is a unit vector, and the specific formula is: r (x)r,yr,zr) And is and
wherein x isr、yrAnd zrThree values on each axis.
Determining a rotating shaft satisfying a condition; the conditional formula is as follows:
wherein the content of the first and second substances,
unit vector R (x) of rotation axisr,yr,zr) In the short-hand form of (1),
is a normal vector F (X)f,Yf,Zf) Abbreviation of (a), xr、yrAnd zrAre respectively unit vectors R (x)r,yr,zr) Three values on each axis, (X)f,Yf,Zf) Respectively represent normal vectors F (X)f,Yf,Zf) Three components of (a).
All the rotating axes satisfying the condition are necessarily distributed on an angular bisector, as shown in fig. 2, the specific formula of the angular bisector is as follows:
Xfx+Yfy+Zfz＝0；
wherein (X)f,Yf,Zf) Respectively represent normal vectors F (X)f,Yf,Zf) Q1 is the coordinate of the landing gear strut extreme point at set-down in the global coordinate system, and q2 is the desired coordinate of the landing gear strut extreme point at set-up in the global coordinate system. The rotation axis distribution plane can be obtained by passing a normal vector of the plane through the origin of coordinates Q1.
Step S3: determining an optimal winding and unwinding path according to a unit vector formula of the rotating shaft by adopting an optimization algorithm, and specifically comprising the following steps:
the optimization algorithm is a gradient descent algorithm, a conjugate gradient descent algorithm, a heuristic algorithm, a genetic algorithm, an adam algorithm or a simulated annealing algorithm.
Step S31: inputting an angle theta formed by the projection of a given unit length rotating shaft on a global coordinate xy plane and an x axis into a unit vector formula of the rotating shaft to determine a unit vector of the rotating shaft; unit vector R (x) of each landing gear's axis of rotationr,yr,zr) One for each landing gear, that is, one for each theta.
Step S32: determining a rotation matrix of a third triangular network of the landing gear when the third triangular network rotates around the origin for alpha degrees each time based on the unit vector of the rotation axis, wherein the specific formula is as follows:
wherein alpha is a specific degree of rotation of the undercarriage triangular network LG around the origin each time, and xr、yrAnd zrAre respectively unit vectors R (x)r,yr,zr) Three values on each axis.
Step S33: multiplying the rotation matrix by a coordinate q1 of a tail-end point of a landing gear strut when the landing gear strut is put down under a global coordinate system to obtain the current position of the landing gear;
step S34: calculating the distance between the rotating undercarriage and the cabin environment based on the triangular patch in the third triangular network and the triangular patch in the fourth triangular network; that is to say: and taking the distance between two triangular patches closest to each other in the two sets as the distance between the undercarriage and the cabin environment, wherein the triangular patches of the third triangular network form one set after rotation, and the triangular patches of the fourth triangular network form the other set.
Step S35: judging whether a cosine function value cos beta of an included angle between the current position and the target position of the undercarriage is smaller than a first preset value or not; if the distance is smaller than the first preset value, the landing gear is judged to reach the target position, and the minimum distance in the whole lifting process is used as an evaluation index of the retraction path; the target position is an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear is retracted under a global coordinate system; if the rotation angle is greater than or equal to the first preset value, let α be α + Φ, which is the given rotation angle, and return to "step S32". The target position is the desired coordinate q2 of the extreme tip point of the landing gear strut at stow in the global coordinate system.
Step S36: judging whether the evaluation index of the winding and unwinding path is less than or equal to a second preset value or not; if the evaluation index of the retraction path is smaller than or equal to the second preset value, the landing gear is considered to be capable of colliding, and step S37 is executed; if the evaluation index of the retraction path is larger than the second preset value, the undercarriage can be retracted without collision, and the retraction path corresponding to the angle theta is output as the optimal retraction path.
The geometric meaning of the evaluation index f is that when the undercarriage rotates along the optimal path obtained by the given parameters, the shortest distance D exists between the undercarriage and the optimal path when the undercarriage is closest to the cabin environment on the whole path. If the evaluation index is less than or equal to the second predetermined value, this indicates movement along the path, and the landing gear may collide, indicating that the path is not feasible. In this embodiment, the first preset value and the second preset value are both set according to actual requirements.
In the optimization of the previous step, the optimal parameter θ can be calculated, but the selected optimal parameter path still has the possibility of generating a scene that the landing gear cannot be received and the collision occurs. This means that if the landing gear is retracted in a spatially rotating manner according to the initially given stow-desired position q2, and therefore needs to be further optimized, for a partially stowable scenario, the shortest distance f between the landing gear and the cabin environment needs to be less than the second preset value, if the designer moves along the optimal path according to the optimal parameter θ. The optimal track is better through fine adjustment of the final upper receiving expected position q2, or the landing gear can avoid the income of collision under the condition that the optimal track obtained in the previous step can not avoid the collision, and the specific steps are as follows:
step S37: converting the expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear is folded under the global coordinate system into the spherical coordinate system, and obtaining a new expected coordinate q of the extreme end point of the landing gear strut when the landing gear is foldedxThe concrete formula is as follows:
wherein (x, y, z) is landing gear spherical coordinate qxThe three-axis coordinate values of (a), r, representing the length of the landing gear itself,
respectively represents the yaw angle and the pitch angle of the landing frame under the coordinate system of the ball marker,
are all translational angle variables. R in the formula,
And
is determined from the initially given desired coordinate q2 of the extreme point of the landing gear strut when the landing gear is retracted and up in the global coordinate system. The spherical coordinate system is constructed by taking the mounting point of the undercarriage as an origin.
Step S38: let q2 be qxAnd returns to "step S2".
Example 2
As shown in fig. 3, the present invention also provides a landing gear retraction trajectory determination system, the system comprising:
a parameter determination module 301 for determining the coordinates q1 of the extreme point of the landing gear strut at set down, the desired coordinates q2 of the extreme point of the landing gear strut at set up, the third triangular network and the fourth triangular network in a global coordinate system.
And a unit vector formula building module 302 for building a unit vector formula of the rotation axis according to the coordinate q1 of the extreme tail point of the landing gear strut when the landing gear strut is put down and the expected coordinate q2 of the extreme tail point of the landing gear strut when the landing gear strut is put up in the global coordinate system.
And the optimal deploying and retracting path determining module 303 is configured to determine an optimal deploying and retracting path according to a unit vector formula of the rotating shaft by using an optimization algorithm.
As an implementation manner, the parameter determining module 301 of the present invention specifically includes:
a first acquisition unit for acquiring a coordinate Q1 of a landing gear mounting point position in an initial coordinate system, a coordinate Q2 of a most distal point of a landing gear strut when down, and a desired coordinate Q3 of the most distal point of the landing gear strut when up.
A second acquisition unit configured to acquire the first three-dimensional model and the second three-dimensional model; the first three-dimensional model is a three-dimensional model describing an aircraft cabin environment; the second three-dimensional model is a three-dimensional model describing the landing gear in the down state.
The triangular mesh dividing unit is used for performing triangular mesh division on the first three-dimensional model and the second three-dimensional model respectively by using creo paramacas software to obtain a first triangular mesh and a second triangular mesh; the first triangular mesh and the second triangular mesh both include a plurality of triangular patches.
And the first coordinate conversion unit is used for converting the coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q3 of the extreme end point of the landing gear strut when the landing gear strut is put up, the first triangular mesh and the second triangular mesh under the global coordinate system, and obtaining the coordinate Q1 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put up, the third triangular mesh and the fourth triangular mesh under the global coordinate system.
As an implementation manner, the unit vector formula constructing module 302 of the present invention specifically includes:
the normal vector formula building unit is used for determining a normal vector under a global coordinate system according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under the global coordinate system, and the specific formula is as follows:
wherein q1 is the coordinate of the extreme tip point of the landing gear strut when lowering in the global coordinate system, q2 is the expected coordinate of the extreme tip point of the landing gear strut when retracting in the global coordinate system, (X)f,Yf,Zf) Normal vectors F (X) respectively representing the plane in which the landing gear liesf,Yf,Zf) Three components of (a).
The unit vector formula construction unit is used for constructing a unit vector formula of the rotating shaft based on a normal vector, and the specific formula is as follows:
where ρ is the projection length of the unit length rotation axis on the global coordinate xy plane, (X)f,Yf,Zf) Normal vectors F (X) of the plane in which the landing gear is locatedf,Yf,Zf) Theta is the angle between the projection of the unit length rotation axis on the global coordinate xy plane and the x-axis, xr、yrAnd zrAre respectively unit vectors R (x)r,yr,zr) Three values on each axis, R (x)r,yr,zr) Is a unit vector of the axis of rotation in the global coordinate system from the coordinate q1 of the landing gear strut extreme point when down to the desired coordinate q2 of the landing gear strut extreme point when up.
As an implementation manner, the optimal retraction path determining module 303 of the present invention specifically includes:
an input unit for inputting a given θ into a unit vector equation of the rotation axis to determine a unit vector of the rotation axis; theta is an angle formed by the projection of the rotating shaft with the unit length on the xy plane of the global coordinate and the x axis;
a rotation matrix determination unit for determining a rotation matrix for each rotation of the third triangular network of the landing gear by a number of degrees around the origin, based on the unit vector of the rotation axis.
And the multiplying unit is used for multiplying the rotation matrix by a coordinate q1 of the extreme point of the landing gear strut when the landing gear is put down under a global coordinate system to obtain the current position of the landing gear.
And the distance determining unit is used for calculating the distance between the rotated undercarriage and the cabin environment based on the triangular patch in the third triangular network and the triangular patch in the fourth triangular network.
The first judgment unit is used for judging whether a cosine function value of an included angle between the current position and the target position of the undercarriage is smaller than a first preset value or not; if the distance is smaller than the first preset value, the landing gear is judged to reach the target position, and the minimum distance in the whole lifting process is used as an evaluation index of the retraction path; if the angle is larger than or equal to the first preset value, making alpha be alpha + phi, and returning to a rotation matrix determining unit, wherein phi is a given rotation angle change alpha degree; the target position is the desired coordinate q2 of the extreme tip point of the landing gear strut at stow in the global coordinate system.
The second judging unit is used for judging whether the evaluation index of the folding and unfolding path is less than or equal to a second preset value or not; if the evaluation index of the retraction path is smaller than or equal to a second preset value, the undercarriage is considered to be capable of colliding, and a second coordinate conversion unit is executed; if the evaluation index of the retraction path is larger than the second preset value, the undercarriage can be retracted without collision, and the retraction path corresponding to the angle theta is output as the optimal retraction path.
A second coordinate conversion unit for converting the expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is folded into the global coordinate system, and obtaining a new expected coordinate q of the extreme end point of the landing gear strut when the landing gear strut is foldedxThe concrete formula is as follows:
wherein (x, y, z) is landing gear spherical coordinate qxIII of (2)An axis coordinate value, r, representing the length of the landing gear itself,
respectively represents the yaw angle and the pitch angle of the landing frame under the coordinate system of the ball marker,
are all translational angle variables.
An assignment unit for making q2 qxAnd returning to the unit vector formula building module.
Example 3
In the embodiment, the optimal design calculation of the movement path of the undercarriage is carried out by taking the design of the undercarriage retracting mechanism of the hypersonic aircraft as an example. The design of the air inlet structure, the airborne equipment and the heat insulation layer of the aircraft enables the storage space of the landing gear to be extremely narrow, so that the design of the retraction path of the landing gear is very difficult. The model of the embodiment is simplified as follows, for the landing gear itself, only the strut and tire parts are reserved by simplifying unnecessary additional mechanisms, and the model is obtained, for the complex cabin environment composed of the air inlet channel, the aircraft engine, the skin outside the aircraft and the like, by cutting the cabin section of the landing gear installation position part and considering that the cabin door is in the open state, the complex connection part is covered by the enveloping body.
And S1, performing meshing on the obtained landing gear model (first three-dimensional model) and the obtained obstacle cabin model (second three-dimensional model) by using creo paraicas software, and exporting the obtained landing gear model and the obtained obstacle cabin model into an STL file. The following triangular network is generated. The angles 0 degrees and the string heights 1000mm are selected, the undercarriage is divided into 150 patches, and the angles 0.0 degrees and the string heights 800mm are selected to divide the intercepted cabin sections into 634 patches.
S2, the initial ideal stow position coordinate vector is q2(0.00,0.00,2500) mm, the corresponding tip position of the landing gear when in the down position, the vector coordinate is q1(2201.37,1180.98, -94.09) mm. With the ideal stowed position vector q2(0.00,0.00,2500) mm as the target position and the corresponding tip position vector q1(2201.37,1180.98, -94.09) mm when the landing gear is in the down position, the normal vector to the rotor axis plane can be found to be R (-0.6113, -0.3279, 0.7203). Thus, the landing gear axis of rotation can be derived from the normal vector of the plane.
S3, optimizing the parameter theta through optimization algorithms such as adam and the like, wherein the value of the parameter is [0,2 pi ]]And finally obtaining the result of
S4. selecting two angles,
the direction angle coordinate of the current ideal target position qx can be obtained to be (28.21, -2.15) through a direction angle-Cartesian coordinate conversion formula. Taking the point as the starting point of optimization, the adam algorithm is used for optimization, and the following results are obtained as shown in table 1:
TABLE 1 results obtained by optimization
The landing gear has a small angular deviation from the original target position, so that the shortest distance between the aircraft cabin and the motion recovery path can obtain the optimal result under the radian limit.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A landing gear retraction trajectory determination method, the method comprising:
step S1: determining coordinates q1 of the extreme tip point of the landing gear strut when down, a desired coordinate q2 of the extreme tip point of the landing gear strut when up, a third triangular network and a fourth triangular network in a global coordinate system;
step S2: constructing a unit vector formula of a rotating shaft according to a coordinate q1 of the extreme end point of the landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is put up in a global coordinate system;
step S3: and determining the optimal winding and unwinding path according to a unit vector formula of the rotating shaft by adopting an optimization algorithm.
2. The landing gear retraction trajectory determination method according to claim 1, wherein step S1 specifically includes:
step S11: acquiring a coordinate Q1 of the landing gear mounting point position under an initial coordinate system, a coordinate Q2 of the tail end point of a landing gear support column when the landing gear is put down and an expected coordinate Q3 of the tail end point of the landing gear support column when the landing gear is put up;
step S12: acquiring a first three-dimensional model and a second three-dimensional model; the first three-dimensional model is a three-dimensional model describing an aircraft cabin environment; the second three-dimensional model is a three-dimensional model describing that the undercarriage is in a down state;
step S13: utilizing creo paramicas software to respectively divide the first three-dimensional model and the second three-dimensional model into triangular meshes to obtain a first triangular mesh and a second triangular mesh; the first triangular mesh and the second triangular mesh both comprise a plurality of triangular patches;
step S14: the coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q3 of the extreme end point of the landing gear strut when the landing gear strut is put up, the first triangular mesh and the second triangular mesh are all converted to be under the global coordinate system, and the coordinate Q1 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put up, the third triangular mesh and the fourth triangular mesh are obtained.
3. The landing gear retraction trajectory determination method according to claim 1, wherein step S2 includes:
step S21: determining a normal vector under a global coordinate system according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under the global coordinate system, wherein the specific formula is as follows:
wherein q1 is the coordinate of the extreme tip point of the landing gear strut when lowering in the global coordinate system, q2 is the expected coordinate of the extreme tip point of the landing gear strut when retracting in the global coordinate system, (X)f,Yf,Zf) Normal vectors F (X) respectively representing the plane in which the landing gear liesf,Yf,Zf) Three components of (a);
step S22: constructing a unit vector formula of the rotating shaft based on the normal vector, wherein the specific formula is as follows:
where ρ is the projection length of the unit length rotation axis on the global coordinate xy plane, (X)f,Yf,Zf) Normal vectors F (X) of the plane in which the landing gear is locatedf,Yf,Zf) Theta is the angle between the projection of the unit length rotation axis on the global coordinate xy plane and the x-axis, xr、yrAnd zrAre respectively unit vectors R (x)r,yr,zr) Three values on each axis, R (x)r,yr,zr) Is a unit vector of the axis of rotation in the global coordinate system from the coordinate q1 of the landing gear strut extreme point when down to the desired coordinate q2 of the landing gear strut extreme point when up.
4. The landing gear retraction trajectory determination method according to claim 1, wherein step S3 includes:
step S31: inputting a given theta into a unit vector formula of the rotating shaft to determine a unit vector of the rotating shaft; theta is an angle formed by the projection of the rotating shaft with the unit length on the xy plane of the global coordinate and the x axis;
step S32: determining a rotation matrix of the third triangular network of the landing gear when the third triangular network rotates around the origin for alpha degrees each time based on the unit vector of the rotation axis;
step S33: multiplying the rotation matrix by a coordinate q1 of a tail-end point of a landing gear strut when the landing gear strut is put down under a global coordinate system to obtain the current position of the landing gear;
step S34: calculating the distance between the rotating undercarriage and the cabin environment based on the triangular patch in the third triangular network and the triangular patch in the fourth triangular network;
step S35: judging whether a cosine function value of an included angle between the current position and the target position of the undercarriage is smaller than a first preset value or not; if the distance is smaller than the first preset value, the landing gear is judged to reach the target position, and the minimum distance in the whole lifting process is used as an evaluation index of the retraction path; if the rotation angle is larger than or equal to the first preset value, making α + Φ be α + Φ, and returning to step S32, where Φ is the given rotation angle; the target position is an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear is retracted under a global coordinate system;
step S36: judging whether the evaluation index of the winding and unwinding path is less than or equal to a second preset value or not; if the evaluation index of the retraction path is smaller than or equal to the second preset value, the landing gear is considered to be capable of colliding, and step S37 is executed; if the evaluation index of the retraction path is larger than a second preset value, the undercarriage can be retracted without collision, and the retraction path corresponding to the angle theta is output as the optimal retraction path;
step S37: converting the expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear is folded under the global coordinate system into the global coordinate system to obtain the extreme end point of the landing gear strut when the landing gear is foldedNew desired coordinates qx；
Step S38: let q2 be qxAnd returns to "step S2".
5. A landing gear retraction trajectory determination method according to claim 4, wherein the desired coordinate q2 of the extreme end point of the landing gear leg during retraction on the global coordinate system is transformed into the global coordinate system, and a new desired coordinate q of the extreme end point of the landing gear leg during retraction on the landing gear is obtainedxThe concrete formula is as follows:
wherein (x, y, z) is landing gear spherical coordinate qxR represents the length of the undercarriage itself, theta,
Respectively represents the yaw angle and the pitch angle of the landing frame under the coordinate system of the ball marker,
Δ θ is the translation angle variable.
6. A landing gear retraction trajectory determination system, the system comprising:
a parameter determination module for determining a coordinate q1 of a most terminal point of a landing gear strut when in a down state, an expected coordinate q2 of the most terminal point of the landing gear strut when in a up state, a third triangular network and a fourth triangular network under a global coordinate system;
a unit vector formula building module for building a unit vector formula of a rotating shaft according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under a global coordinate system;
and the optimal winding and unwinding path determining module is used for determining an optimal winding and unwinding path according to a unit vector formula of the rotating shaft by adopting an optimization algorithm.
7. The landing gear retraction trajectory determination system according to claim 6, wherein the parameter determination module specifically comprises:
a first acquisition unit configured to acquire a coordinate Q1 of a landing gear attachment point position in an initial coordinate system, a coordinate Q2 of a most distal point of a landing gear strut when the landing gear strut is down, and a desired coordinate Q3 of the most distal point of the landing gear strut when the landing gear strut is up;
a second acquisition unit configured to acquire the first three-dimensional model and the second three-dimensional model; the first three-dimensional model is a three-dimensional model describing an aircraft cabin environment; the second three-dimensional model is a three-dimensional model describing that the undercarriage is in a down state;
the triangular mesh dividing unit is used for performing triangular mesh division on the first three-dimensional model and the second three-dimensional model respectively by using creo paramacas software to obtain a first triangular mesh and a second triangular mesh; the first triangular mesh and the second triangular mesh both comprise a plurality of triangular patches;
and the first coordinate conversion unit is used for converting the coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q3 of the extreme end point of the landing gear strut when the landing gear strut is put up, the first triangular mesh and the second triangular mesh under the global coordinate system, and obtaining the coordinate Q1 of the extreme end point of the landing gear strut when the landing gear strut is put down, the expected coordinate Q2 of the extreme end point of the landing gear strut when the landing gear strut is put up, the third triangular mesh and the fourth triangular mesh under the global coordinate system.
8. The landing gear retraction trajectory determination system according to claim 6, wherein the unit vector formula construction module specifically comprises:
the normal vector formula building unit is used for determining a normal vector under a global coordinate system according to a coordinate q1 of a tail end point of a landing gear strut when the landing gear strut is put down and an expected coordinate q2 of the tail end point of the landing gear strut when the landing gear strut is put up under the global coordinate system, and the specific formula is as follows:
wherein q1 is the coordinate of the extreme tip point of the landing gear strut when lowering in the global coordinate system, q2 is the expected coordinate of the extreme tip point of the landing gear strut when retracting in the global coordinate system, (X)f,Yf,Zf) Normal vectors F (X) respectively representing the plane in which the landing gear liesf,Yf,Zf) Three components of (a);
the unit vector formula construction unit is used for constructing a unit vector formula of the rotating shaft based on a normal vector, and the specific formula is as follows:
where ρ is the projection length of the unit length rotation axis on the global coordinate xy plane, (X)f,Yf,Zf) Normal vectors F (X) of the plane in which the landing gear is locatedf,Yf,Zf) Theta is the angle between the projection of the unit length rotation axis on the global coordinate xy plane and the x-axis, xr、yrAnd zrAre respectively unit vectors R (x)r,yr,zr) Three values on each axis, R (x)r,yr,zr) Is a unit vector of the axis of rotation in the global coordinate system from the coordinate q1 of the landing gear strut extreme point when down to the desired coordinate q2 of the landing gear strut extreme point when up.
9. The landing gear retraction trajectory determination system according to claim 6, wherein the optimal retraction path determination module specifically comprises:
an input unit for inputting a given θ into a unit vector equation of the rotation axis to determine a unit vector of the rotation axis; theta is an angle formed by the projection of the rotating shaft with the unit length on the xy plane of the global coordinate and the x axis;
a rotation matrix determination unit for determining a rotation matrix of the third triangular network of the landing gear each time the third triangular network rotates around the origin by a degree based on the unit vector of the rotation axis;
a multiplying unit, which is used for multiplying the rotation matrix by a coordinate q1 of the extreme point of the landing gear strut when the landing gear is put down under a global coordinate system, so as to obtain the current position of the landing gear;
a distance determining unit, configured to calculate a distance between the rotated landing gear and the cabin environment based on a triangular patch in the third triangular network and a triangular patch in the fourth triangular network after the rotation;
the first judgment unit is used for judging whether a cosine function value of an included angle between the current position and the target position of the undercarriage is smaller than a first preset value or not; if the distance is smaller than the first preset value, the landing gear is judged to reach the target position, and the minimum distance in the whole lifting process is used as an evaluation index of the retraction path; if the rotation angle is larger than or equal to the first preset value, enabling alpha to be alpha + phi, and returning to a rotation matrix determining unit, wherein phi is a given rotation angle; the target position is an expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear is retracted under a global coordinate system;
the second judging unit is used for judging whether the evaluation index of the folding and unfolding path is less than or equal to a second preset value or not; if the evaluation index of the retraction path is smaller than or equal to a second preset value, the undercarriage is considered to be capable of colliding, and a second coordinate conversion unit is executed; if the evaluation index of the retraction path is larger than a second preset value, the undercarriage can be retracted without collision, and the retraction path corresponding to the angle theta is output as the optimal retraction path;
a second coordinate conversion unit for converting the expected coordinate q2 of the extreme end point of the landing gear strut when the landing gear strut is folded into the global coordinate system, and obtaining a new expected coordinate q of the extreme end point of the landing gear strut when the landing gear strut is foldedx；
An assignment unit for making q2 qxAnd returning to the unit vector formula building module.
10. The method of claim 9A landing gear retraction trajectory determination system, wherein the desired coordinate q2 of the extreme end point of the landing gear strut when the landing gear is retracted and retracted in the global coordinate system is converted into the global coordinate system, and a new desired coordinate q of the extreme end point of the landing gear strut when the landing gear is retracted is obtainedxThe concrete formula is as follows:
wherein (x, y, z) is landing gear spherical coordinate qxR represents the length of the undercarriage itself, theta,
Respectively represents the yaw angle and the pitch angle of the landing frame under the coordinate system of the ball marker,
Δ θ is the translation angle variable.
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