CN109522622B - Method and system for determining on-orbit load working condition of multi-degree-of-freedom solar cell array - Google Patents
Method and system for determining on-orbit load working condition of multi-degree-of-freedom solar cell array Download PDFInfo
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Abstract
The invention relates to a method and a system for determining the on-orbit load working condition of a multi-degree-of-freedom solar cell array, which comprises the steps of firstly, establishing a finite element model of the solar cell array by adopting finite element software; acquiring a quality matrix of all finite element nodes of an on-orbit rotating part of the solar cell array and a coordinate matrix under a local coordinate system of a rotating point from the finite element model; performing action characteristic analysis on the finite element model by adopting finite element software, and extracting the modal frequency and the modal shape of the model; carrying out dynamic simulation according to an on-orbit dynamic model of an aircraft with a flexible solar cell array and the on-orbit task working condition of the aircraft to obtain modal coordinates, acceleration of an aircraft body, angular acceleration and angular speed; the joint torque is calculated by respectively adopting an elasticity method and Hu Kefa, the consistency of the joint torque is obtained by comparing the two methods, if the consistency indicates that the calculation is correct, the maximum value of the absolute value of the joint torque is obtained, and the load working condition of the solar cell array is obtained, so that the reliability of the on-orbit task of the aircraft is ensured.
Description
Technical Field
The invention relates to a method and a system for determining the on-orbit load working condition of a multi-degree-of-freedom solar cell array, in particular to a method and a system for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array by considering elastic vibration, and belongs to the field of structural loads and mechanical environments of aerospace vehicles.
Background
The solar cell array obtains energy by reflecting sunlight on a large-area and light-weight wing surface, and is an important guarantee for realizing long-time on-orbit operation and task execution of the aircraft, so that the large-flexibility solar cell array aircraft becomes a research hotspot in the aerospace field in recent years. The solar cell array has the structural characteristics of large area, low rigidity and small damping, so that the dynamic characteristics of the solar cell array are complex, once a low-order mode is excited by external interference torque, the normal work of an aircraft is influenced slightly, and the loss of tasks is caused seriously. Therefore, the method has important significance for the elastic vibration research.
In the past, students at home and abroad have more dynamic simulation researches on aircrafts with flexible accessories, particularly more deep researches on excessive vibration control, but less researches on the self elastic load of a solar cell array. Therefore, the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array by considering the elastic vibration has important practical significance.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method and a system for determining the on-orbit load working condition of a multi-degree-of-freedom solar cell array, aiming at the problem that the on-orbit working condition of the multi-degree-of-freedom solar cell array causes elastic vibration under the action of interference force of an attitude control engine of an aircraft, which possibly causes failure of a locking motor, the on-orbit working mode of the aircraft is combed, the attitude motion information and the generalized coordinates of the solar wing aircraft are obtained after dynamic simulation is carried out on the basis of a dynamic model, the rigid body and the elastic load of a joint of the solar cell array are analyzed and researched, and the structure and the mechanism design of the solar cell array are guided.
The above purpose of the invention is mainly realized by the following technical scheme:
a method for determining the on-orbit load working condition of a multi-degree-of-freedom solar cell array comprises the following steps:
establishing a finite element model of the solar cell array by adopting finite element software;
acquiring a mass matrix [ M ] of all finite element nodes of an on-orbit rotating part of the solar cell array and a coordinate matrix [ r ] of the solar cell array under a local coordinate system of a rotating point from a finite element model of the solar cell array;
analyzing the action characteristics of a finite element model of the solar cell array by adopting finite element software, and extracting the modal frequency [ F ] and the modal shape [ phi ] of the model;
according to an on-orbit dynamics model of an aircraft with a flexible solar cell array, carrying out dynamics simulation according to the on-orbit task working condition of the aircraft to obtain a modal coordinate [ q ], an acceleration [ A ], an angular acceleration [ a ] and an angular velocity [ w ];
according to the mode shape [ phi ]]Modal coordinate [ q ]]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]Angular velocity [ w ]]Quality matrix [ M ]]And a coordinate matrix r]Calculating the moment M of the joint by an elastic method a1 、M b1 Calculating the joint moment M by using Hu Kefa a2 、M b2 ；
Comparison M a1 、M b1 And M a2 、M b2 If M is satisfied at the same time a1 And M a2 Coincidence, M b1 And M b2 If they are consistent, M is obtained a1 Or M a2 Maximum value of (1), and M b1 Or M b2 The maximum value of the solar cell array is used as the on-orbit load working condition of the solar cell array.
In the method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array, the established finite element model of the solar cell array comprises a solar cell array sailboard model simulated by a shell unit and a solar cell array mechanism simulated by a beam unit, wherein the solar cell array sailboard model is an on-orbit rotating part of the solar cell array; the boundary condition is root branch fixation.
In the method for determining the on-orbit load condition of the solar cell array with multiple degrees of freedom, MSC.Nastran software is used for acquiring a mass matrix [ M ] of all finite element nodes of the on-orbit rotating part of the solar cell array from a finite element model of the solar cell array, wherein the mass matrix [ M ] is an n multiplied by 1 matrix, and n is the number of all finite element nodes of the on-orbit rotating part of the solar cell array.
In the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array, the coordinate matrix [ r ] under the local coordinate system of the rotating point is an n x 3 matrix, and n is the number of all finite element nodes of the on-orbit rotating part of the solar cell array; firstly, acquiring a coordinate matrix [ r0] of all nodes of an on-orbit rotating part of the solar cell array in a finite element model of the solar cell array under a root coordinate system, and then acquiring the coordinate matrix [ r ] of all nodes under a rotating point local coordinate system by adopting the following conversion formula:
[r]＝[r0]-O
wherein: o is a coordinate matrix of the rotation point under a root coordinate system; the original point of the local coordinate system of the rotating point is the intersection point of the solar cell array sailboard model simulated by the shell unit and the solar cell array mechanism simulated by the beam unit, and each coordinate axis of the local coordinate system of the rotating point is parallel to each coordinate axis under the root coordinate system and has the same direction.
In the method for determining the on-orbit load condition of the multi-freedom-degree solar cell array, the finite element software is adopted to analyze the action characteristics of the finite element model of the solar cell array, and the method for extracting the modal frequency [ F ] and the modal shape [ phi ] of the model comprises the following steps: and when a solver SOL103 in MSC.Nastran software is adopted to analyze the dynamic characteristics of the finite element model of the solar cell array, automatically generating an F06 file, and extracting the modal frequency [ F ] and the modal vibration mode [ phi ] from the F06 file.
In the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array, the on-orbit task working condition of the aircraft comprises orbit transfer and orbit control.
In the method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array, the on-orbit dynamic model of the aircraft with the flexible solar cell array is represented as follows:
wherein:
m-total mass of the aircraft;
B t -a solar wing translational coupling system coefficient matrix;
q-modal generalized coordinates;
f-a control force matrix;
i-an aircraft inertia matrix;
B r -sunA wing rotation coupling system matrix;
t-control moment matrix;
ξ -a damping coefficient matrix;
In the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array, the modal shape [ phi ] is determined]Modal coordinate [ q ]]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]Angular velocity [ w ]]Quality matrix [ M ]]And a coordinate matrix r]Calculating the moment M of the joint by an elastic method a1 、M b1 The method comprises the following steps:
calculating absolute acceleration of all finite element nodes of an on-orbit rotating part of the solar cell array in a finite element model of the solar cell array;
multiplying the absolute acceleration point by a mass matrix [ M ] to obtain the force of all finite element nodes, and solving the moment of all the finite element nodes on the original point of the local coordinate system of the rotation point;
summing all the moments to obtain three components of the inertia moment under the local coordinate system of the rotating point, namely M in the three components a1 、M b1 。
In the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array, the joint moment M is calculated by adopting an elastic method a1 、M b1 The specific method comprises the following steps:
(1) Quality matrix [ M ]]Absolute acceleration a of relative rotation point local coordinate system OXYZ of medium arbitrary point dm m Is represented as follows:
wherein:
a displacement relative to the elastic system OeXeYeZe after the vibration deformation dm, and a combination thereof>
For the angular acceleration of rotation of the aircraft, is>
In order not to take into account the displacement of the elastic oscillation relative to the local coordinate system O 'X' Y 'Z', -the evaluation of the local coordinate system is carried out>
For the ith order modal generalized acceleration,
for the translational acceleration of the aircraft, is>
Is the angle speed of rotation of the aircraft>
The velocity of the elastic system OceXeyeZe after dm is vibrated and deformed, phi i Is the i-th order mode vibration type of the solar cell array>
Is the generalized speed of the ith-order mode of the solar cell array>
Q is the acceleration of the elastic system OeXeYeZe after the vibration deformation of dm i The generalized coordinate is the ith order modal generalized coordinate of the solar cell array;
(2) According to said quality matrix [ M ]]Absolute acceleration of medium arbitrary point dm relative to local coordinate system of rotation point OXYZ
Solving the moment M of the origin O of the local coordinate system OXYZ of the rotating point at the arbitrary point dm OAB ：
Wherein:
is a coordinate matrix r]M is a quality matrix [ M]Mass of any point in;
(3) M for all finite element nodes of on-orbit rotating part of solar cell array OAB Summing to obtain the component M of the Z axis of the summed result in the local coordinate system OXYZ of the rotation point a1 (ii) a M of all finite element nodes of on-orbit rotating part of solar cell array OAB Summing to obtain the component M of the Y axis of the summed result in the local coordinate system OXYZ of the rotation point b1 。
In the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array, the modal shape [ phi ] is determined]Modal coordinate [ q ]]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]Angular velocity [ w ]]Quality matrix [ M ]]And a coordinate matrix r]Calculating the joint moment M by using Hu Kefa a2 、M b2 The specific method comprises the following steps:
calculating a unit stiffness matrix K at an origin O of a local coordinate system OXYZ of a rotation point through finite element software, and calculating the internal force of a moment unit according to the following formula
Wherein:
for a displacement at the origin O of the local coordinate system OXYZ of the rotation point, </or >>
M a2 、M b2 Are respectively as
Moment in a local coordinate system OXYZ of a rotating pointA Z-direction component and a Y-direction component of (a).
In the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array, M a1 And M a2 Consistent index sequence M a1 And M a2 The error of two corresponding numerical values at the same time is within 5 percent, and the numerical sequence M b1 And M b2 Consistent means M b1 And M b2 The error of two corresponding numerical values at the same time is within 5 percent.
In the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array, matlab software is adopted to solve and solve M a1 Or M a2 Maximum value of (1), and M b1 Or M b2 Maximum value of (2).
A multi-degree-of-freedom solar cell array on-orbit load working condition determining system comprises: the system comprises a finite element model establishing module, a mass coordinate parameter generating module, a dynamic characteristic analyzing module, a dynamic simulation module, a moment solving module and a post-processing module; wherein:
a finite element model building module: establishing a finite element model of the solar cell array by adopting finite element software, and sending the finite element model of the solar cell array to a mass coordinate parameter generation module and a dynamic characteristic analysis module:
the mass coordinate parameter generation module: receiving a finite element model of the solar cell array from a finite element model establishing module, acquiring a mass matrix [ M ] of all finite element nodes of an on-orbit rotating part of the solar cell array and a coordinate matrix [ r ] of a rotating point local coordinate system from the finite element model of the solar cell array, and sending the mass matrix [ M ] and the coordinate matrix [ r ] to a moment solving module;
the dynamic characteristic analysis module: receiving a finite element model of the solar cell array from a finite element model establishing module, analyzing the behavior characteristics of the finite element model of the solar cell array by adopting finite element software, extracting the modal frequency [ F ] and the modal vibration mode [ phi ] of the model, and sending the modal frequency [ F ] and the modal vibration mode [ phi ] to a dynamic simulation module and a torque solving module;
a dynamics simulation module: receiving the modal frequency [ F ] and the modal vibration mode [ phi ] sent by the dynamic characteristic analysis module, carrying out dynamic simulation according to an on-orbit dynamic model of the aircraft with the flexible solar cell array and the on-orbit task working condition of the aircraft to obtain a modal coordinate [ q ], an acceleration [ A ] of the aircraft body, an angular acceleration [ a ] and an angular velocity [ w ], and sending the modal coordinate [ q ], the acceleration [ A ] of the aircraft body, the angular acceleration [ a ] and the angular velocity [ w ] to the moment solving module;
a moment solving module: receiving the modal frequency [ F ] sent by the dynamic characteristic analysis module]Sum mode vibration mode [ phi ]]Quality matrix [ M ] sent by quality coordinate parameter generation module]And a coordinate matrix r]And a modal coordinate [ q ] sent by the dynamics simulation module]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]And angular velocity [ w ]]Calculating the moment M of the joint by an elastic method a1 、M b1 Calculating the joint moment M by using Hu Kefa a2 、M b2 And sending to a post-processing module;
a post-processing module: joint torque M sent by receiving torque solving module a1 、M b1 And joint moment M a2 、M b2 Comparing, if M is satisfied at the same time a1 And M a2 Coincidence, M b1 And M b2 If they are consistent, respectively obtaining M a1 Or M a2 Maximum value of (1), and M b1 Or M b2 And the maximum value of the solar cell array is output outwards as the on-orbit load working condition of the solar cell array.
Compared with the prior art, the invention has the beneficial effects that:
(1) The method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array firstly establishes a finite element model of the solar cell array, obtains the elastic parameters of the on-orbit state of the solar cell array through dynamic simulation, solves the elastic load of the solar cell array joint based on the elastic parameters, solves the difficulty of index design of a solar cell array mechanism, avoids the defect of inaccuracy caused by the adoption of a rigid body algorithm in the past, obviously improves the design precision and efficiency, and ensures the reliability of the on-orbit task of an aircraft.
(2) In the method for determining the on-orbit load working condition of the multi-degree-of-freedom solar cell array, the solar cell array is subjected to simplified modeling, and the simulation of the rigidity of the mechanism and the connection structure and the simulation of the overall quality characteristic are emphatically considered, so that the operation efficiency is simplified.
(3) According to the method for determining the on-orbit load working condition of the solar cell array with multiple degrees of freedom, all working modes of a spacecraft are fully covered in the actual elastic load calculation process, all external factors which possibly cause elastic vibration divergence of the solar cell array are ensured to be within a considered range, and the method has high applicability.
(4) The invention adopts two elastic methods and Hu Kefa as calculation methods to verify each other, thereby ensuring the correctness and the reliability of the method.
Drawings
FIG. 1 is a flow chart of a method for determining an on-orbit load condition of a multi-degree-of-freedom solar cell array according to the invention;
FIG. 2 is a schematic diagram of the on-orbit load condition determination system for a multi-degree-of-freedom solar cell array of the invention;
FIG. 3 is a schematic diagram of a finite element model of a solar cell array constructed according to the present invention;
FIG. 4 is a diagram showing the result of analysis of the dynamic characteristics of the solar cell array according to the present invention;
FIG. 5 is a schematic diagram of the present invention considering the relative movement of a certain point of the elasticity of the battery array;
FIG. 6 is a schematic view of the position of the aircraft body and solar array according to the present invention;
FIG. 7 is a schematic view of the position of the solar cell array A, B shaft of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
as shown in fig. 1, the method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array of the present invention is a flowchart, and the method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array includes the following steps:
establishing a finite element model of the solar cell array by adopting finite element software based on the structure, the mechanism scheme and the quality characteristics of the solar cell array; in an optional embodiment of the invention, MSC.Nastran software is adopted to establish a finite element model of the solar cell array, the established finite element model comprises a solar cell array sailboard model simulated by a shell unit and a solar cell array mechanism simulated by a beam unit, and the method also comprises the step of configuring a mass center of mass of the solar cell array to a design state by adopting a non-structural mass unit, wherein the solar cell array sailboard model is an on-orbit rotating part of the solar cell array, and the boundary condition is root fixed branch. Fig. 3 is a schematic diagram of a finite element model of a solar cell array constructed according to the present invention.
And (II) acquiring a mass matrix [ M ] of all finite element nodes of the on-orbit rotating part of the solar cell array and a coordinate matrix [ r ] of the on-orbit rotating part of the solar cell array in a local coordinate system of the rotating point from the finite element model of the solar cell array.
In an optional embodiment of the invention, a mass matrix [ M ] of all finite element nodes of the on-orbit rotating part of the solar cell array is obtained from a finite element model of the solar cell array through MSC.Nastran software, wherein the mass matrix [ M ] is an n x 1 matrix, and n is the number of all finite element nodes of the on-orbit rotating part of the solar cell array.
A coordinate matrix [ r ] under the local coordinate system of the rotating point is an n multiplied by 3 matrix, and n is the number of all finite element nodes of the on-orbit rotating part of the solar cell array; firstly, acquiring a coordinate matrix [ r0] of all nodes of an on-orbit rotating part of the solar cell array in a finite element model of the solar cell array under a root coordinate system, and then obtaining the coordinate matrix [ r ] of all the nodes under a rotating point local coordinate system by adopting the following conversion formula:
[r]＝[r0]-O
wherein: o is a coordinate matrix (1 multiplied by 3 matrix) of the rotation point under the root coordinate system; the origin O of the local coordinate system of the rotation point xyz is the intersection point of the solar cell array sailboard model simulated by the shell unit and the solar cell array mechanism simulated by the beam unit, and each coordinate axis of the local coordinate system of the rotation point xyz is parallel to each coordinate axis under the root coordinate system and has the same direction.
And step three, performing action characteristic analysis on the finite element model of the solar cell array by adopting finite element software, and extracting the modal frequency [ F ] and the modal shape [ phi ] of the model.
In an optional embodiment of the invention, commercial software msc. Nastran SOL103 is adopted to analyze the behavior of the finite element model of the solar cell array, and the modal frequency [ F ] (m × 1,m is the modal order) and the modal vibration mode [ phi ] (m × n × 6) of the model are extracted, and in an optional embodiment of the invention, the modal damping is 0.005.
Fig. 4 is a graph showing the analysis result of the solar cell array of the present invention, and it can be seen from fig. 4 that the first-order mode of the solar cell array is 0.47Hz.
And (IV) combing the working conditions of the main tasks according to the on-orbit task of the aircraft, and classifying the working conditions into on-orbit engine switch combinations, wherein the on-orbit task working conditions of the aircraft can be divided into orbit transfer and orbit control, and the on-orbit engine switch combinations are related to the actual engine configuration of the aircraft.
And (V) carrying out dynamics simulation according to an on-orbit dynamics model of an aircraft with a flexible solar cell array and the on-orbit mission working condition of the aircraft to obtain a modal coordinate [ q ] (m multiplied by t multiplied by 1,t is a time step), an acceleration [ A ] (t multiplied by 3) of the aircraft body, an angular acceleration [ a ] (t multiplied by 3) and an angular velocity [ w ] (t multiplied by 3).
An on-orbit dynamics model of an aircraft with a flexible solar cell array is generally characterized as follows:
generally, the aircraft is assumed to be a rigid body, the deformation of the flexible accessory solar cell array is very small, and the aircraft dynamic equation expressed by the vector can be simplified as follows:
in the formula:
m-total mass of the aircraft;
B t -a solar wing translational coupling system coefficient matrix 3 × n;
q-modal generalized coordinates (n × 1);
f-control force matrix (3 × 1);
i-aircraft inertia matrix (3 × 3);
B r -a solar wing rotational coupling system matrix 3 × n;
t-control moment matrix (3 × 1);
ξ -a matrix of damping coefficients (nx 1);
n-modal order.
Step six, according to the mode vibration mode [ phi ]]Modal coordinate [ q ]]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]Angular velocity [ w ]]Quality matrix [ M ]]And a coordinate matrix r]Calculating the moment M of the joint by an elastic method a1 、M b1 Calculating the joint moment M by using Hu Kefa a2 、M b2 。
(6.1) wherein the joint moment M is calculated by the elasticity method a1 、M b1 The principle of (1) is as follows:
calculating absolute acceleration of all finite element nodes of an on-orbit rotating part of the solar cell array in a finite element model of the solar cell array;
multiplying the absolute acceleration point by the mass matrix [ M ] to obtain the force of all finite element nodes, and solving the moment of all finite element nodes on the original point of the local coordinate system of the rotating point;
summing all the moments to obtain three components of the inertia moment under the local coordinate system of the rotating point, namely M in the three components a1 、M b1 。
The specific method comprises the following steps:
considering the elasticity of the battery array and the rigid body of the aircraft body, calculating the absolute acceleration of each point of the battery array according to the linear acceleration, the angular velocity and the elastic motion of the aircraft body, superposing the mass of each point, taking the distance from the A, B intersection point position, and summing to obtain the inertia moment of the A, B shaft. As shown in fig. 7, which is a schematic diagram of the positions of the axes A, B of the solar cell array of the present invention, it can be seen from fig. 7 that the a axis is parallel to the Z axis in the local coordinate system of the rotation point, xyz, and the B axis is parallel to the Y axis in the local coordinate system of the rotation point, xyz.
FIG. 5 is a schematic diagram showing the relative movement of a certain point of the cell array in consideration of the elasticity of the mass point dm, and the displacement r of the mass point dm with respect to the elastic system OXeYeZee after the vibration deformation of the mass point dm e Relative velocity v e Relative acceleration a e Relative angular velocity w e Relative angular acceleration
The generalized coordinate is q.
(6.1.1), quality matrix [ M]Absolute acceleration a of relative rotation point local coordinate system OXYZ of medium arbitrary point dm m Is represented as follows:
wherein:
a displacement relative to the elastic system OeXeYeZe after the vibration deformation dm, and a combination thereof>
In the form of an aircraft rotation angular acceleration +>
In order not to take into account the displacement of the elastic vibration relative to the local coordinate system O 'X' Y 'Z', ->
For the ith order modal generalized acceleration,
for the translational acceleration of the aircraft, is>
For the angle speed of rotation of the aircraft, in combination with>
The velocity of the elastic system OceXeyeZe after dm is vibrated and deformed, phi i For the ith order mode vibration mode of the solar cell array>
For the solar cell array in the ith-order mode generalized speed>
Q is the acceleration of the elastic system OeXeYeZe after the vibration deformation of dm i The generalized coordinate is the ith order modal generalized coordinate of the solar cell array.
(6.1.2) according to the quality matrix [ M []Absolute acceleration of medium arbitrary point dm relative to local coordinate system OXYZ of rotation point
Solving the moment M of the origin O of the local coordinate system OXYZ of the rotating point at the arbitrary point dm OAB ：
Wherein:
is a coordinate matrix [ r]M is a quality matrix [ M]The mass of any point in;
(6.1.3) M of all finite element nodes of on-orbit rotating part of solar cell array OAB Summing to obtain the component M of the Z axis of the summed result in the local coordinate system OXYZ of the rotation point a1 (ii) a M for all finite element nodes of on-orbit rotating part of solar cell array OAB Summing to obtain the component M of the Y axis of the summation result in the local coordinate system OXYZ of the rotation point b1 。
(6.2) calculating the Joint Torque M by using Hu Kefa a2 、M b2 The specific method comprises the following steps:
calculating a unit stiffness matrix K at an origin O of a local coordinate system OXYZ of a rotation point through finite element software, and calculating the internal force of a moment unit according to the following formula
Wherein:
there are six components, three of which are forces and three of which are moments;
M a2 、M b2 Are respectively as
Local coordinate system OXY of moment at rotation pointThe Z-direction component and the Y-direction component in Z.
Step seven, comparing the number series M a1 、M b1 And the sequence M a2 、M b2 If M is satisfied at the same time a1 And M a2 Coincidence, M b1 And M b2 If they are consistent, respectively obtaining M a1 Or M a2 Maximum value of (1), and M b1 Or M b2 The maximum value of the solar cell array is used as the on-orbit load working condition of the solar cell array.
M above a1 And M a2 Consistent index sequence M a1 And M a2 The error of two corresponding numerical values at the same time is within 5 percent, and the numerical sequence M b1 And M b2 By consistent is meant M b1 And M b2 The error of two corresponding numerical values at the same moment is within 5 percent. If the difference is not consistent, the finite element model and the on-orbit dynamic model of the solar cell array need to be modified.
M can be solved and solved by Matlab software a1 Or M a2 Maximum value of (1), and M b1 Or M b2 Of (2) is calculated.
FIG. 6 is a schematic view of the aircraft body and solar array according to the present invention; fig. 7 is a schematic axial position diagram of the solar cell array A, B of the present invention, and it can be seen from fig. 7 that the a axis is parallel to the Z axis of the local coordinate system of rotation point, and the B axis is parallel to the Y axis of the local coordinate system of rotation point, xyz.
As shown in fig. 2, the schematic diagram of the system for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array of the invention is shown, and the system for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array of the invention comprises a finite element model establishing module, a mass coordinate parameter generating module, a dynamic characteristic analyzing module, a dynamic simulation module, a moment solving module and a post-processing module; wherein:
and the finite element model establishing module is used for establishing a finite element model of the solar cell array by adopting finite element software and sending the finite element model of the solar cell array to the mass coordinate parameter generating module and the dynamic characteristic analyzing module.
And the mass coordinate parameter generation module is used for receiving the finite element model of the solar cell array from the finite element model establishment module, acquiring the mass matrix [ M ] of all finite element nodes of the on-orbit rotating part of the solar cell array and the coordinate matrix [ r ] of the rotating point in the local coordinate system from the finite element model of the solar cell array, and sending the mass matrix [ M ] and the coordinate matrix [ r ] to the moment solving module.
And the dynamic characteristic analysis module is used for receiving the finite element model of the solar cell array from the finite element model establishing module, adopting finite element software to carry out dynamic characteristic analysis on the finite element model of the solar cell array, extracting the modal frequency [ F ] and the modal shape [ phi ] of the model, and sending the modal frequency [ F ] and the modal shape [ phi ] to the dynamic simulation module and the moment solving module.
And the dynamic simulation module is used for receiving the modal frequency [ F ] and the modal vibration mode [ phi ] sent by the dynamic characteristic analysis module, carrying out dynamic simulation according to the on-orbit dynamic model of the aircraft with the flexible solar cell array and the on-orbit task working condition of the aircraft to obtain a modal coordinate [ q ], an acceleration [ A ], an angular acceleration [ a ] and an angular velocity [ w ] of the aircraft body, and sending the modal coordinate [ q ], the acceleration [ A ], the angular acceleration [ a ] and the angular velocity [ w ] to the moment solving module.
A moment solving module for receiving the modal frequency [ F ] sent by the dynamic characteristic analysis module]Sum mode shape [ phi ]]Quality matrix [ M ] sent by quality coordinate parameter generation module]And coordinate matrix r]And a modal coordinate [ q ] sent by the dynamics simulation module]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]And angular velocity [ w]Calculating the moment M of the joint by an elastic method a1 、M b1 Calculating the joint moment M by using Hu Kefa a2 、M b2 And sent to a post-processing module.
A post-processing module for receiving the joint moment M sent by the moment solving module a1 、M b1 And joint moment M a2 、M b2 Comparing, if M is satisfied at the same time a1 And M a2 Coincidence, M b1 And M b2 If they are consistent, M is obtained a1 Or M a2 Maximum value of (1), and M b1 Or M b2 And the maximum value of the solar cell array is output outwards as the on-orbit load working condition of the solar cell array.
The specific functions of each module are described in the above description of the method, and are not described herein again.
The method is based on the structure, the mechanism scheme and the quality characteristics of the solar cell array, a finite element model of the solar cell array is established, and the boundary condition is root fixed support; acquiring a quality matrix of all finite element nodes of an on-orbit rotating part of the solar cell array and a coordinate matrix of a rotating point local coordinate system by a finite element method; adopting commercial software MSC.Nastran SOL103 to analyze the dynamic characteristics, extracting modal frequency and modal vibration mode, and determining modal damping; according to the on-orbit task of the aircraft, the working conditions of the main task are combed, and the on-orbit engine is classified into an on-orbit engine switch combination; according to an on-orbit dynamics model of the aircraft with the flexible solar cell array and main task working conditions, carrying out dynamics simulation to obtain parameters such as modal coordinates, acceleration of the aircraft body, angular acceleration, angular speed and the like; respectively adopting an elasticity method and Hu Kefa to calculate joint torque; the two methods are compared to obtain the consistency of the joint moment, if the two methods are consistent, the calculation is correct; and solving the maximum value of the absolute value of the joint moment to obtain the load working condition of the solar cell array.
The above description is only for the best mode of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (12)
1. A method for determining the on-orbit load working condition of a multi-degree-of-freedom solar cell array is characterized by comprising the following steps: the method comprises the following steps:
establishing a finite element model of the solar cell array by adopting finite element software;
acquiring a mass matrix [ M ] of all finite element nodes of an on-orbit rotating part of the solar cell array and a coordinate matrix [ r ] of the solar cell array under a local coordinate system of a rotating point from a finite element model of the solar cell array;
analyzing the action characteristics of a finite element model of the solar cell array by adopting finite element software, and extracting the modal frequency [ F ] and the modal shape [ phi ] of the model;
according to an on-orbit dynamics model of an aircraft with a flexible solar cell array, carrying out dynamics simulation according to the on-orbit task working condition of the aircraft to obtain a modal coordinate [ q ], an acceleration [ A ], an angular acceleration [ a ] and an angular velocity [ w ];
according to the mode shape [ phi ]]Modal coordinate [ q ]]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]Angular velocity [ w ]]Quality matrix [ M ]]And a coordinate matrix r]Calculating the moment M of the joint by an elastic method a1 、M b1 Calculating the joint moment M by using Hu Kefa a2 、M b2 ；
Comparison M a1 、M b1 And M a2 、M b2 If M is satisfied at the same time a1 And M a2 Coincidence, M b1 And M b2 If they are consistent, M is obtained a1 Or M a2 Maximum value of (1), and M b1 Or M b2 The maximum value of the solar cell array is used as the on-orbit load working condition of the solar cell array;
according to the mode shape [ phi ]]Modal coordinate [ q ]]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]Angular velocity [ w ]]Quality matrix [ M ]]And coordinate matrix r]Calculating the moment M of the joint by an elastic method a1 、M b1 The method comprises the following steps:
calculating absolute acceleration of all finite element nodes of the on-orbit rotating part of the solar cell array in a finite element model of the solar cell array;
multiplying the absolute acceleration point by a mass matrix [ M ] to obtain the force of all finite element nodes, and solving the moment of all the finite element nodes on the original point of the local coordinate system of the rotation point;
summing all the moments to obtain three components of the inertia moment under the local coordinate system of the rotating point, namely M in the three components a1 、M b1 。
2. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: the established solar cell array finite element model comprises a solar cell array sailboard model simulated by a shell unit and a solar cell array mechanism simulated by a beam unit, wherein the solar cell array sailboard model is an on-orbit rotating part of a solar cell array; the boundary condition is root branch fixation.
3. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: acquiring a quality matrix [ M ] of all finite element nodes of the on-orbit rotating part of the solar cell array from the finite element model of the solar cell array through MSC.Nastran software, wherein the quality matrix [ M ] is an n multiplied by 1 matrix, and n is the number of all finite element nodes of the on-orbit rotating part of the solar cell array.
4. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: a coordinate matrix [ r ] under the local coordinate system of the rotating point is an n multiplied by 3 matrix, and n is the number of all finite element nodes of the on-orbit rotating part of the solar cell array; firstly, acquiring a coordinate matrix [ r0] of all nodes of an on-orbit rotating part of the solar cell array in a finite element model of the solar cell array under a root coordinate system, and then obtaining the coordinate matrix [ r ] of all the nodes under a rotating point local coordinate system by adopting the following conversion formula:
[r]＝[r0]-O
wherein: o is a coordinate matrix of the rotation point under the root coordinate system; the original point of the local coordinate system of the rotating point is the intersection point of the solar cell array sailboard model simulated by the shell unit and the solar cell array mechanism simulated by the beam unit, and each coordinate axis of the local coordinate system of the rotating point is parallel to each coordinate axis under the root coordinate system and has the same direction.
5. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: the method for analyzing the action characteristics of the finite element model of the solar cell array by adopting finite element software and extracting the modal frequency [ F ] and the modal shape [ phi ] of the model comprises the following steps: and when a solver SOL103 in MSC.Nastran software is adopted to analyze the dynamic characteristics of the finite element model of the solar cell array, automatically generating an F06 file, and extracting the modal frequency [ F ] and the modal vibration mode [ phi ] from the F06 file.
6. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: the on-orbit mission working condition of the aircraft comprises orbit transfer and orbit control.
7. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: the on-orbit dynamic model of the aircraft with the flexible solar cell array is represented as follows:
wherein:
m is the total mass of the aircraft;
B t -a solar wing translational coupling system coefficient matrix;
q-modal generalized coordinates;
f-control force matrix;
i, an aircraft inertia matrix;
B r -a solar wing rotational coupling system matrix;
t-control moment matrix;
xi-damping coefficient matrix;
8. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: calculating joint moment M by adopting elastic method a1 、M b1 The specific method comprises the following steps:
(1) Quality matrix [ M ]]Absolute acceleration a of relative rotation point local coordinate system OXYZ of medium arbitrary point dm m Is represented as follows:
wherein:
a displacement of the elastic system OeXeYeZe after dm is deformed by vibration, and/or a combination thereof>
Is the angular acceleration of the rotation of the aircraft,
in order not to take into account the displacement of the elastic oscillation relative to the local coordinate system O 'X' Y 'Z', -the evaluation of the local coordinate system is carried out>
For an i-th mode generalized acceleration>
For the translational acceleration of the aircraft, is>
Is the angle speed of rotation of the aircraft>
The velocity of the elastic system OceXeyeZe after dm is vibrated and deformed, phi i Is the i-th order mode vibration type of the solar cell array>
Is the generalized speed of the ith-order mode of the solar cell array>
Q is the acceleration of the elastic system OeXeYeZe after the vibration deformation of dm i The generalized coordinate is the ith-order modal coordinate of the solar cell array;
(2) According to said quality matrix [ M]Absolute acceleration of medium arbitrary point dm relative to local coordinate system OXYZ of rotation point
Solving the moment M of the origin O of the local coordinate system OXYZ of the rotating point at the arbitrary point dm OAB ：
Wherein:
is a coordinate matrix [ r]M isQuality matrix [ M]The mass of any point in;
(3) M of all finite element nodes of on-orbit rotating part of solar cell array OAB Summing to obtain the component M of Z axis in the local coordinate system OXYZ of the rotating point a1 (ii) a M of all finite element nodes of on-orbit rotating part of solar cell array OAB Summing to obtain the component M of the Y axis of the summation result in the local coordinate system OXYZ of the rotation point b1 。
9. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: according to the mode shape [ phi ]]Modal coordinate [ q ]]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]Angular velocity [ w ]]Quality matrix [ M ]]And a coordinate matrix r]Calculating the joint moment M by using Hu Kefa a2 、M b2 The specific method comprises the following steps:
calculating a unit stiffness matrix K at an origin O of a local coordinate system OXYZ of a rotation point through finite element software, and calculating the internal force of a moment unit according to the following formula
Wherein:
for a displacement at the origin O of the local coordinate system OXYZ of the point of rotation, <' > H>
M a2 、M b2 Are respectively as
The Z-direction component and the Y-direction component of the moment in the local coordinate system of the rotation point, oyx.
10. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: the M is a1 And M a2 Consistent index sequence M a1 And M a2 The error of two corresponding numerical values at the same time is within 5 percent, and the numerical sequence M b1 And M b2 By consistent is meant M b1 And M b2 The error of two corresponding numerical values at the same time is within 5 percent.
11. The method for determining the on-orbit load condition of the multi-degree-of-freedom solar cell array according to claim 1, characterized in that: solving and obtaining M by adopting Matlab software a1 Or M a2 Maximum value of (1), and M b1 Or M b2 Maximum value of (2).
12. A multi-degree-of-freedom solar cell array on-orbit load working condition determining system is characterized in that: the method comprises the following steps: the system comprises a finite element model establishing module, a mass coordinate parameter generating module, a dynamic characteristic analyzing module, a dynamic simulation module, a moment solving module and a post-processing module; wherein:
a finite element model building module: establishing a finite element model of the solar cell array by adopting finite element software, and sending the finite element model of the solar cell array to a mass coordinate parameter generation module and a dynamic characteristic analysis module:
a mass coordinate parameter generation module: receiving a finite element model of the solar cell array from a finite element model establishing module, acquiring a mass matrix [ M ] of all finite element nodes of an on-orbit rotating part of the solar cell array and a coordinate matrix [ r ] of a rotating point local coordinate system from the finite element model of the solar cell array, and sending the mass matrix [ M ] and the coordinate matrix [ r ] to a moment solving module;
the dynamic characteristic analysis module: receiving a finite element model of the solar cell array from a finite element model establishing module, analyzing the behavior characteristics of the finite element model of the solar cell array by adopting finite element software, extracting the modal frequency [ F ] and the modal vibration mode [ phi ] of the model, and sending the modal frequency [ F ] and the modal vibration mode [ phi ] to a dynamic simulation module and a torque solving module;
a dynamics simulation module: receiving the modal frequency [ F ] and the modal vibration mode [ phi ] sent by the dynamic characteristic analysis module, carrying out dynamic simulation according to an on-orbit dynamic model of the aircraft with the flexible solar cell array and the on-orbit task working condition of the aircraft to obtain a modal coordinate [ q ], an acceleration [ A ], an angular acceleration [ a ] and an angular velocity [ w ] of the aircraft body, and sending the modal coordinate [ q ], the acceleration [ A ], the angular acceleration [ a ] and the angular velocity [ w ] to the torque solving module;
a moment solving module: receiving the modal frequency [ F ] sent by the dynamic characteristic analysis module]Sum mode vibration mode [ phi ]]Quality matrix [ M ] sent by quality coordinate parameter generation module]And a coordinate matrix r]And a modal coordinate [ q ] sent by the dynamics simulation module]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]And angular velocity [ w]Calculating the moment M of the joint by an elastic method a1 、M b1 Calculating the joint moment M by using Hu Kefa a2 、M b2 And sending to a post-processing module;
a post-processing module: joint torque M sent by receiving torque solving module a1 、M b1 And joint moment M a2 、M b2 Comparing, if M is satisfied at the same time a1 And M a2 Coincidence, M b1 And M b2 If they are consistent, respectively obtaining M a1 Or M a2 Maximum value of (1), and M b1 Or M b2 The maximum value of the solar cell array is used as the on-orbit load working condition of the solar cell array to be output outwards;
according to the mode vibration mode [ phi ]]Modal coordinate [ q ]]Aircraft body acceleration [ A ]]Angular acceleration [ a ]]Angular velocity [ w ]]Quality matrix [ M ]]And coordinate matrix r]Calculating the moment M of the joint by an elastic method a1 、M b1 The method comprises the following steps:
calculating absolute acceleration of all finite element nodes of an on-orbit rotating part of the solar cell array in a finite element model of the solar cell array;
multiplying the absolute acceleration point by a mass matrix [ M ] to obtain the force of all finite element nodes, and solving the moment of all finite element nodes on the original point of the local coordinate system of the rotating point;
summing all the moments to obtain inertia moment under the local coordinate system of the rotating pointThree components of (a) to (b), i.e. M therein a1 、M b1 。
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