CN112685941A - Mechanical thermal stability analysis method for large space load antenna - Google Patents
Mechanical thermal stability analysis method for large space load antenna Download PDFInfo
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Abstract
A method for analyzing the mechanical thermal stability of a large space load antenna solves the problem that the existing large space load antenna has overlarge thermal deformation or non-convergence of thermally induced vibration due to frequent in-and-out ground shadows, and belongs to the field of thermal design of spacecrafts. The invention comprises the following steps: the method comprises the following steps of firstly, acquiring a temperature field of the space load antenna; step two, acquiring thermal response characteristic time and structural response characteristic time according to the temperature field, and determining whether the space load antenna generates thermal vibration or not, if so, turning to step three, otherwise, turning to step four; setting an intelligent rod with a piezoelectric plate between the space load antenna and the satellite main body as a sensor and an actuator, and controlling the intelligent rod by utilizing a PID (proportion integration differentiation) controller according to the thermally induced vibration response; and step four, selecting the most important influence factors of the temperature of the space load antenna, calculating the optimal solution of the most important influence factors by taking the temperature difference of the entrance and the exit of the space load antenna as an optimization target, and then optimizing the space load antenna by combining thermal deformation response.
Description
Technical Field
The invention relates to a method for analyzing the mechanical and thermal stability of a large space load antenna, and belongs to the field of thermal design of spacecrafts.
Background
With the development of aerospace science and technology, space load antennas are developing towards large-scale, large-flexibility and high-precision directions. In the process of in-orbit operation of the large space load antenna, due to frequent in-and-out ground shadows, a phenomenon of large thermal deformation or non-convergence of thermally induced vibration can occur, the load efficiency can be seriously influenced, and even the satellite attitude can be seriously changed. In order to realize the functions of high imaging resolution and high pointing accuracy of the large space load antenna, the generation mechanism of the thermal deformation/thermal vibration is required to be cleared, the amplitude and the frequency spectrum of the thermal deformation/thermal vibration are evaluated, optimized and inhibited, and the optomechanical thermal analysis process of the large space load antenna is improved.
Disclosure of Invention
The invention provides a mechanical thermal stability analysis method for a large space load antenna, aiming at the problem that the existing large space load antenna is too large in thermal deformation or non-convergence of thermal vibration caused by frequent in-and-out ground shadows.
The invention discloses a method for analyzing the mechanical thermal stability of a large space load antenna, which comprises the following steps:
s1, establishing a space load antenna model, and acquiring a temperature field of the space load antenna;
s2, obtaining the temperature of each finite element node of the space load antenna structure according to the obtained temperature field, obtaining thermal response characteristic time and structural response characteristic time, determining whether the space load antenna generates thermal vibration according to the thermal response characteristic time and the structural response characteristic time, obtaining the thermal vibration response and the thermal deformation response if the thermal vibration occurs, and turning to S3, and obtaining the thermal deformation response if the thermal vibration does not occur, and turning to S4;
s3, arranging an intelligent rod with a piezoelectric plate between the space load antenna and the satellite main body as a sensor and an actuator, determining control parameters of a PID controller according to the thermally induced vibration response obtained in S2, controlling the intelligent rod by using the PID controller to realize the suppression of the thermally induced vibration of the space load antenna, and switching to S4;
s4, determining influence factors of the space load antenna temperature, selecting the most important influence factor from the influence factors of the space load antenna temperature by utilizing an orthogonal test, calculating the optimal solution of the most important influence factor by taking the temperature difference of the entrance and the exit of the space load antenna as an optimization target, and optimizing the space load antenna by utilizing the optimal solution and thermal deformation response so as to further realize the suppression of thermal deformation.
Preferably, the method further comprises:
s5, removing rigid body displacement of the space load antenna aiming at the space load antenna of the optical imaging, and then performing lens surface fitting by using a least square method according to the structural characteristic point of the space load antenna and the thermal response of the central point of the structural characteristic point to obtain a polynomial coefficient and the inclination error and the translation error of the reflecting surface; and establishing a model of an original optical system, an optical system with six displacement errors and an optical system with surface change according to the optimized space load antenna and the obtained polynomial coefficient, the inclination error and the translation error of the reflecting surface, and analyzing the change of the optical index of the space load antenna of the optical imaging caused by thermal response.
Preferably, the S1 includes:
s11, establishing a space load antenna model, and obtaining the time and duration of the space load antenna entering and exiting the ground shadow according to the parameters of the satellite orbit;
s12, dividing the structure of the space load antenna into heat grids according to the space load antenna model, wherein each heat grid corresponds to a heat node, and calculating the radiation angle coefficient among the heat grids according to the time and duration of the space load antenna entering and exiting the ground shadow to obtain the external heat flow absorbed and radiated by each heat node;
and S13, obtaining a temperature value of the thermal node along with the change of time, namely a temperature field, according to the space load antenna model, the thermal property of the space load antenna material, the rotation angle of the space load antenna and the size of the external heat flow absorbed and radiated by each thermal node obtained in the step S12.
Preferably, in S2, the method for obtaining the temperature of each finite element node of the space load antenna structure according to the obtained temperature field includes:
and acquiring a temperature matrix, a time matrix, a thermal node matrix and a structural node matrix of the space load antenna according to the space load antenna model and the temperature field, and obtaining the temperature of each finite element node of the space load antenna structure by adopting an interpolation algorithm, wherein the temperature is changed along with the on-orbit running time.
Preferably, in S2, the method for determining whether the space-borne antenna thermally-induced vibration occurs according to the thermal response characteristic time and the structural response characteristic time includes:
according to the characteristic time t of thermal responseτAnd a structural response characteristic time tsCalculating a coefficient Boley:
and when Boley >1, determining that the space load antenna generates thermally-induced vibration and thermal deformation, otherwise, only generating thermal deformation and not generating thermally-induced vibration.
Preferably, in S2, the method for acquiring the thermal response characteristic time and the structural response characteristic time includes:
performing modal analysis on the satellite of the space load by using finite element software, outputting a fundamental frequency, and obtaining a structural response characteristic time t according to the fundamental frequencys；
Each finite element of the antenna structure according to space loadObtaining the mean square error of the temperature amplitude curves of all finite element nodes, dividing the range of the mean square error according to a mode of equally dividing intervals, finding out the interval with the most finite element nodes and the number of the finite element nodes, solving the mean value of the mean square error of the interval, finding out the finite element node with the minimum difference with the mean value as a thermal characteristic point, calculating the FFT of the temperature amplitude of the thermal characteristic point, wherein the main frequency after the FFT is the temperature change frequency of the space load antenna, and calculating the thermal response characteristic time t according to the temperature change frequencyτ。
Preferably, in S4, the most important influencing factors are: the ratio of the infrared emissivity of the space-borne antenna material to the solar absorptivity.
Preferably, in S4, the optimal solution of the most important influencing factor is calculated by using a genetic simulated annealing algorithm with the temperature difference between the entrance and the exit of the space-borne antenna as an optimization target.
The invention has the beneficial effects that: the invention provides an integrated analysis method for mechanical and thermal stability aiming at the condition that large thermal deformation or thermal vibration is not converged due to frequent ground shadow entering and exiting of a large space load antenna.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of a first step of the present invention;
FIG. 3 is a schematic diagram illustrating a second step of the present invention;
FIG. 4 is a schematic diagram of the third step of the present invention;
FIG. 5 is a schematic diagram illustrating a fourth step of the present invention;
FIG. 6 is a schematic diagram of the fourth step 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.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
As shown in fig. 1, a method for analyzing machine thermal stability for a large space-borne antenna according to this embodiment includes:
step one, space load on-orbit thermal analysis:
establishing a space load antenna model, and acquiring a temperature field of a space load antenna;
step two, analyzing the on-orbit thermal response of the space load:
obtaining the temperature of each finite element node of the space load antenna structure according to the obtained temperature field, obtaining thermal response characteristic time and structural response characteristic time, determining whether the space load antenna generates thermal vibration according to the thermal response characteristic time and the structural response characteristic time, obtaining thermal vibration response and thermal deformation response if the thermal vibration occurs, turning to the third step, obtaining the thermal deformation response if the thermal vibration does not occur, and turning to the fourth step;
step three, suppressing the on-orbit vibration of the space load:
setting an intelligent rod with a piezoelectric plate between the space load antenna and the satellite main body as a sensor and an actuator, determining control parameters of a PID (proportion integration differentiation) controller according to the thermally induced vibration response obtained in the step two, controlling the intelligent rod by using the PID controller to realize the suppression of the thermally induced vibration of the space load antenna, and turning to the step four;
fourthly, optimizing and analyzing the on-orbit disturbance of the space load:
determining the influence factors of the temperature of the space load antenna, selecting the most important influence factors from the influence factors of the temperature of the space load antenna by utilizing an orthogonal test, calculating the optimal solution of the most important influence factors by taking the temperature difference of the entrance and the exit of the space load antenna as an optimization target, and optimizing the space load antenna by utilizing the optimal solution so as to further realize the suppression of thermal deformation.
The embodiment provides an integrated analysis method for mechanical and thermal stability, which has the advantages of high calculation precision, fast response and strong coupling through on-track thermal analysis, on-track thermal response analysis, on-track thermal disturbance analysis, on-track thermal vibration suppression and on-track optical-mechanical thermal coupling analysis, and meanwhile, the optimization, vibration suppression and optical performance analysis are introduced into the integrated analysis process, so that the interference of an optical system can be reduced while the thermal deformation and the thermal vibration are suppressed.
In a preferred embodiment, as shown in fig. 2, the first step of the present embodiment includes three parts, namely orbit calculation, heat flow calculation outside the space, and temperature field calculation:
and (3) track calculation: establishing a space load antenna model, and obtaining the time and duration of the space load antenna entering and exiting the ground shadow according to the parameters of the satellite orbit;
in the orbit calculation, parameters such as starting time, ending time, step length, a coordinate system, a coordinate type and the like, and factors such as a satellite orbit period, an orbit semimajor axis, an orbit eccentricity, an orbit inclination angle, an orbit ascent point right ascension, an orbit perigee argument, an orbit plano-perigee argument and the like of the large space load antenna are considered, and the orbit calculation is carried out aiming at the large space load antenna structure. The time and the duration of the large space load antenna entering and exiting the ground shadow can be obtained through analysis, and four typical working conditions of sun irradiation, sun shadow inside, sun shadow outside and sun shadow inside are divided according to the actual situation of the track.
Calculating the heat flow outside the space: dividing heat grids for the structure of the space load antenna according to a space load antenna model, wherein each heat grid corresponds to a heat node, and calculating radiation angle coefficients among the heat grids according to the time and duration of the space load antenna entering and exiting the ground shadow to obtain the external heat flow absorbed and radiated by each heat node;
in the calculation of the external heat flow of the space, the actual satellite model and the shielding condition of each part are considered, relevant parameters such as solar radiation heat flow, earth reflection heat flow, earth radiation heat flow and the like are set, the radiation angle coefficient among grids is calculated after the heat grids are divided, and the size of the external heat flow absorbed and radiated by each heat grid node can be calculated.
And (3) calculating a temperature field: according to the space load antenna model, the thermal property of the space load antenna material and the rotation angle of the space load antenna, and the magnitude of the external heat flow absorbed and radiated by each thermal node obtained in the step S12, the temperature value, namely the temperature field, of the thermal node along with the change of time is obtained.
Only the thermal control coating is adopted for temperature control, and the temperature control principle is as follows: for an insulating plane, the plane is vertically irradiated by the sun, no other heat source is provided, and if only radiant heat exchange is considered, the heat balance equation of the plane is as follows: alpha is alphas·S＝εσT4
In the formula of alphasSurface solar absorptance; s is a solar constant; ε is the surface emissivity; sigma is Boltzmann constant; t is the surface temperature;
then its thermal equilibrium temperature is:
the keplerian orbit definition mode is the most widely used mode, and the specific input parameters used are shown in the following table.
TABLE 1-1 satellite orbital settings input parameters
The Thermal-Desktop software adopts a Monte Carlo and Progressive radio method to calculate external heat flow, and the calculated external heat flow comprises heating of the satellite by the sun, infrared heating of the satellite by the earth and solar reflection heating of the satellite by the earth. The specific modeling process of the thermal analysis is briefly described as follows:
and dividing a thermal grid for the large space load antenna structure. Setting the track, setting the track inclination angle, the track height, the eccentricity and the like. Considering the orbit running state of the satellite in one period, the initial angle is 0 degrees, the end angle is 360 degrees, only considering one orbit period, considering the fact that the six orbits do not change along with the time and the beta angle (the included angle between the sunlight vector and the orbit plane) keeps unchanged for simplifying the calculation and not considering the orbit perturbation; the satellite antenna is set to be oriented to the ground and attitude changes of 36 angles are considered for one orbital period. Adopting a transient solving mode; the change of the temperature under four typical working conditions (generally, four typical working conditions including an in-ground shadow, an out-ground shadow, an illumination area and a ground shadow area are considered) is focused. The SF is submitted to know the time of entering and exiting the ground shadow, the track angle corresponding to the entering and exiting ground shadow, and the like. Material thermal parameters set such as thermal conductivity (Cond) and thermal capacity (Cp) of the material. And (3) setting parameters of the coating, wherein according to the on-orbit state of the satellite and the condition of absorbing external heat flow, the temperature range of each component of the satellite is within the working range of the component, and the infrared absorption rate (Solar absorbance) and the infrared radiance (IR Emissivity) of the material are set.
In order to ensure the continuity of heat conduction among grids, each part needs to establish heat conduction to simulate the heat conduction characteristic among the parts. The thermal conductivity property is set such that the material is thermally conductive. The solar sailboard is arranged to orient the sun in the illumination area so as to ensure the maximum illumination area. And arranging a single-axis orientation by selecting a base point at a main body connecting point, creating a rotating pair, enabling the rotating pair to rotate around a circle to point to the sun, and assembling the solar sail and the connecting beam with the rotating pair so as to realize the sun-facing orientation of the solar sailboard. At 36 attitude change points of the orbit, only the sun-oriented rotation of the solar sailboard is considered, and the relative attitude of the satellite main body and the annular truss antenna is kept unchanged.
In order to ensure that the solar sail does not collide with the satellite main body when rotating, the rotation angle is set to be 0-180 degrees, and the working mode is set to work only in the illumination area.
The first step of the embodiment can obtain the external heat flow condition and the temperature change condition absorbed by each heat node.
In the second step of the present embodiment, a method for determining temperature and thermal vibration at each finite element node of the space load antenna structure is obtained, and a thermal deformation/thermal vibration response is calculated.
Obtaining the temperature of each finite element node of the space load antenna structure:
and acquiring a temperature matrix, a time matrix, a thermal node matrix and a structural node matrix of the space load antenna according to the space load antenna model and the temperature field, operating a self-compiling program adopting a multiple Barnes interpolation algorithm to obtain the temperature of each finite element node of the space load antenna structure, and changing the temperature along with the on-orbit operation time.
The method for judging the thermally induced vibration comprises the steps of searching for a structural thermal characteristic point, calculating the structural thermal response characteristic time and the structural response characteristic time, and providing a solution method of a Boley coefficient. Boley parameter is thermal response characteristic time tTTime t of structural response characteristicSThe ratio of (A) to (B): reflecting the possibility of thermally induced vibration of the space structure, wherein the closer the Boley parameter is to 1, the higher the possibility of thermally induced vibration of the space structure is; conversely, the less likely. When Boley is more than or equal to 1, determining that the space load antenna generates thermally induced vibration and thermal deformation; otherwise, the space load antenna only generates thermal deformation and does not generate thermally induced vibration.
Characteristic time t of thermal responseτAnd a structural response characteristic time tsThe obtaining method comprises the following steps:
performing modal analysis on the satellite of the space load by using finite element software, outputting a fundamental frequency, and obtaining a structural response characteristic time t according to the fundamental frequencys；
Obtaining the mean square error of the temperature amplitude curve of all finite element nodes according to the temperature of each finite element node of the space load antenna structure, dividing the range of the mean square error in an interval-dividing mode, finding out the interval with the most finite element nodes and the number of the finite element nodes, solving the mean value of the mean square error of the interval, finding out the finite element node with the minimum difference with the mean value as a thermal characteristic point, calculating the FFT of the temperature amplitude of the thermal characteristic point, taking the main frequency after the FFT as the temperature change frequency of the space load antenna, and calculating the thermal response characteristic time t according to the temperature change frequencyτ。
As shown in fig. 3, in the calculation of thermal deformation/thermal vibration response, if it is determined that thermal vibration does not occur, the influence of the inertia term can be ignored in the solving process, the analyzing step is set to be quasi-static, and the thermal deformation response of the large space load antenna under the action of the thermal load is solved; if the large-scale space load antenna is judged to generate the thermally induced vibration, the influence of an inertia term can not be ignored in the solving process, the analyzing step is set as a dynamic analysis, and the thermally induced vibration response of the large-scale space load antenna under the action of the thermal load is solved.
The finite element modeling for thermal deformation/thermal vibration analysis is briefly described as follows:
and importing the bdf file into abaqus to ensure that the section attribute, the material attribute and the interaction relation are established in the model, the grid division cannot be divided again, and temperature values under each finite element node are generated after the TD interpolation program runs. A step of statics or dynamics analysis is created.
Since the satellite body can be used as a central rigid body, i.e. the satellite body can be used as a boundary condition of the flexible attachment without thermal deformation, a fixed constraint condition is applied to the root of the connecting beam. The temperature application method is to apply temperature field load, the specific operation method is to create each finite element node as a point set by modifying an inp file, and to apply a temperature amplitude value varying with time to each point set. The inp statements that need to be modified are explained separately below:
creating a point set and traversing each finite element node; establishing an amplitude curve as a time function, and determining a time change range and a time interval as follows, if a quasi-static analysis model is adopted, considering that a temperature value is linearly changed in a slope manner between amplitudes: traversing each finite element node; and creating a temperature field, connecting the point set and the amplitude curve, and traversing each finite element node. Running a self-compiled program, checking whether an unavailable node exists or not, and whether a temperature field is combined with each amplitude curve and other error-prone links, and applying a temperature value which changes along with time to each finite element node. After the operation is submitted, a cloud picture of the change of the temperature field of the flexible accessory along with time can be obtained through post-processing.
In the third step of this embodiment, set up a smart pole that has the piezoelectric patch as sensor and actuator between space load antenna and satellite main part, to the thermal vibration mechanics environment, propose smart pole + PID control: and reading a result file (. odb) after the finite element software Abaqus performs modal analysis, running a self-compiling program, and generating a specified format file (. f06) containing the first n-order modal information (vibration mode). And inputting the rotational inertia of the satellite and inputting control parameters. And running a self-compiling program to finish the loading of the time sequence and the thermally-induced vibration reaction force/reaction moment. And calculating PID control parameters. And operating a self-compiling program, and calculating to obtain an open-loop response (without control) and a closed-loop response (with PID control) to draw a comparison graph of the thermally induced corner response and the thermally induced displacement response along with the change curve of time/frequency.
In the field of vibration control, the piezoelectric material has good force-electricity coupling characteristics, can be used as a sensor and an actuator, is usually adhered or embedded in a structure when being used as the actuator, and is integrated with the structure, so the piezoelectric material is very suitable for vibration control of a flexible member. The device is sensitive to the change of the external environment, and can quickly respond to the change of the external environment to adjust the self adaptive environment. The intelligent rod of the embodiment is formed by combining sensitive materials and a base body structure, and the structure has a strong application market in the field of aerospace. Current smart materials are piezoelectric materials, shape memory alloys, galvanic and magneto-rheological materials, magnetic and electrostrictive materials, and the like. Piezoelectric-type materials have their own unique advantages over other smart materials, particularly for applications in structural vibration modulation. The flexible mechanical arm, the satellite antenna, the telescopic wing and other flexible mechanisms with stretching structures in the space have smaller rigidity, lighter mass and smaller environmental damping, so that the mechanisms are easy to generate continuous vibration in the processes of external disturbance and attitude rotation adjustment, and in the special environment of space, once the structure generates vibration, the vibration is difficult to stop under the self damping action, and the stability and the positioning accuracy of the system are influenced. Some of the vibrations with lower order and smaller amplitude are difficult to attenuate in an undamped environment such as the outer space, the piezoelectric material has the particularity of force-electricity coupling under an uncontrolled condition, and the piezoelectric material can be used as a sensor and an actuator and is very suitable for being applied to the field of vibration control;
generally, the piezoelectric material can be adhered to the surface of the structure or embedded into the structure to form a whole with the structure, and the piezoelectric material is sensitive and light, and is often applied to vibration suppression with a flexible mechanism.
Since the computer and various microcontroller chips enter the control field, the computer or microcontroller chip replaces an analog PID control circuit to form a control system, not only can the PID control algorithm be realized by software, but also the logic functions of the computer and the microcontroller chip can be utilized, so that the PID control is more flexible. After the analog PID control rule is properly converted, a microcontroller or a computer is used as an operation core, and PID control and correction are realized by using a software program, namely digital (software) PID control. Since the digital control is a sampling control, it can only calculate the control amount according to the deviation value of the sampling time, and thus it is necessary to perform discretization processing on the continuous PID control algorithm. For a real-time control system, although the working state of an object is continuous, if the sampling is measured and controlled at discrete moments, the object can be represented as a discrete model, and when the sampling period is short enough, the discrete control form can be close to the continuous control form, so that the same control effect can be achieved.
A basic structure of a typical control system includes an input, a sampling, a controller, a controlled object, and an output, where r (t) is an input set value, c (t) is an actual output value, e (t) is a deviation signal, and the control amount is composed of a difference between the input set value and the actual output value, i.e., e (t) r (t) -c (t).
In an analog control system, the basic input-output relationship of the PID control law can be expressed by a differential equation as follows:
or frequency domain representation:
the following equations can be used in computer simulation and numerical control systems:
where at is the time step of the discrete system.
The PID controller combines three basic control links: a proportional control link Kp, an integral control link Ki/s and a differential control link Kd × s. When the controller operates, the proportion (P), the integral (I) and the derivative (D) of the error signal are linearly combined to form a control amount, and the controlled object is controlled, so the controller is called a PID controller.
The three basic control links have the characteristics that:
and P proportion control: the controller immediately generates a control action to reduce the deviation once the deviation is generated, which is proportional to an error signal reflecting the control system. When the signal is converted, the proportional controller only changes the amplitude of the signal and does not change the phase of the signal, and the open loop gain of the system can be improved by adopting proportional control, so that the proportional controller is a main control part of the system. It should be noted that an excessive scaling factor may cause a relatively large overshoot of the system and may cause oscillations that deteriorate the stability.
I integral control: integral control is mainly used for eliminating static error and improving the non-difference of a system, but can aggravate the oscillation of the system, increase overshoot and damage the dynamic performance, generally does not act independently, and is combined with PD control. The strength of the integration depends on the integration time constant Ti, the larger the time constant, the weaker the integration and vice versa.
D, differential control: reflects the variation trend (change rate) of the error signal and can introduce an effective early-period correction signal into the system before the error signal becomes too large, thereby accelerating the operation speed of the system and reducing the regulation time. The differential control can predict the change of the system, increase the damping xi of the system, improve the phase angle margin and play a role in improving the dynamic performance of the system, but the differential has a great amplification effect on interference, and the overlarge differential can aggravate the system oscillation and reduce the signal-to-noise ratio of the system.
In order to achieve control purposes and achieve control indexes, a proper control algorithm needs to be selected. Common control methods include feedback control, feed forward control, P control, PD control, PI control, PID control, etc., wherein PID control is one of the most widely used control methods. The PID composite control can integrate the characteristics of the control rules, so that the system can obtain good dynamic and steady-state performance at the same time.
As shown in fig. 4, the smart bar implementation for thermally induced vibration suppression using structural mode information according to the present embodiment:
and reading a result file (. odb) after the finite element software Abaqus performs modal analysis, running a self-compiling program, and generating a specified format file (. f06) containing the first n-order modal information (vibration mode). Input the moment of inertia of the satellite (the moment of inertia of the whole satellite (kg. m)2) When the solar sail and the truss are both unfolded, 3 × 3 matrix is used for inputting at least three main moments of inertia), and control parameters are input, including: control bandwidth, overshoot, damping ratio, interference node number, response node number, control moment node number, and sensor node number. And running a self-compiling program to finish the loading of the time sequence and the thermally-induced vibration reaction force/reaction moment. The time sequence being a 1 x n matrix including suppression of thermally induced vibrationsStart time, end time and time step. And running a self-compiling program to calculate PID control parameters. And operating a self-compiling program, and calculating to obtain an open-loop response (without control) and a closed-loop response (with PID control) to draw a comparison graph of the thermally induced corner response and the thermally induced displacement response along with the change curve of time/frequency.
In the fourth step of the present embodiment: as shown in fig. 5, the disturbance optimization of the large space loading structure mainly discusses the influence of various physical parameters of the structure on the on-orbit thermal stability of the satellite-borne antenna, because internal disturbance (mainly an internal heat source of the satellite-borne antenna), the angular coefficients of each surface relative to the sun and the planet, and the radiation energy of the sun and the planet are determined according to flight missions and cannot be easily changed. And listing thermal object parameters influencing the temperature field of the satellite in orbit, performing an orthogonal test to give the most important thermal object parameters, taking the temperature difference of the antenna in and out of the earth shadow as an optimization target, and repeatedly calling Matlab and ThermalDesktop by utilizing a genetic simulation annealing algorithm to calculate an optimal solution.
Factors influencing the temperature field and the temperature gradient distribution of the satellite-borne antenna are many, and unknown parameters can be encountered in the analysis and calculation process, so that it is difficult to give an exact and quantitative thermal analysis result. The node thermal balance equation of the antenna is as follows:
the mathematical symbols involved in the formula have the following meanings:
Er0: average reflection density of the earth's surface;
Fj: the jth node area;
Bkj: the part of the energy radiated by the node k and absorbed by the node j is called an absorption factor, and the factor can be calculated and solved by an analysis method;
kkj: the coefficient of thermal conductivity between nodes k and j;
φ1j,φ2j,φ3j: the geometrical angular coefficients of the node j with respect to the sun, the earth's albedo and the infrared radiation, which are functions of time, depend on the position and attitude of the space-borne antenna on the orbit and on the shape of the space-borne antenna.
From the energy equation, it can be seen that the temperature distribution of the upper surface of the antenna is a complex function of a number of variables, i.e.
The above variable parameters can be basically divided into three groups.
A first set of parameters S is set for the first,
Er0,Qj… is the radiant energy of the sun and planet and the internal heat source of the satellite antenna. These quantities depend on the flight mission and they cannot be changed arbitrarily. For example, in a flight mission in space near the earth, the solar constant, earth albedo and infrared radiation energy are constant, while in flight near other planets, there is a set of determined solar and planet radiation densities. The distribution of the internal heat source basically depends on the performance and the working state of the electromagnetic radiation of the satellite-borne antenna, is determined by the flight mission, and can change along with time.
The second set of parameters is phi1j,φ2j,φ3j… angular coefficients of the geometrical relationship of the surface of the space antenna with respect to the position and attitude of the sun, the planet. They depend on the orbit of the flight of the spacecraft and on the attitude of the spacecraft in inertial space. The orbit and attitude parameters are also determined by the mission of the spacecraft and are generally not variable at will. The orbit parameters allow a certain range of variation in some cases, such as the launch time of some spacecraft, the eccentricity of the elliptical orbit, etc. But the choice is very small. Since the spacecraft is constantly moving in space, the set of parameters is generally followed byTime and thus the temperature of the on-board antenna will also change over time.
The third set of parameters is αsj,εej,εij,Gjcj,kkj,…,Bkj… the thermophysical properties of the reflector of the space-borne antenna depend on its material properties and surface state. These parameters need to be selected and reasonably adjusted during design to ensure that the on-orbit thermal equilibrium temperature of the reflecting surface of the satellite-borne antenna is within the allowable temperature range. Because the satellite-borne antenna has a typical thermo-mechanical-electric coupling problem during in-orbit operation, how to adjust the thermal physical properties to minimize the temperature difference generated by the reflecting surface so as to ensure the profile precision of the antenna and the electrical performance index of normal operation, which is an engineering design problem with practical significance.
In the embodiment, under the condition that the operation orbit and the posture of the large space load antenna are fixed, the main factors influencing the surface temperature and the root mean square error of the antenna are researched by carrying out an orthogonal test and changing the material property and the surface state of the large space load antenna. On the basis of an orthogonal test result, the infrared radiance and the solar absorptivity of the antenna thermal control coating are taken as design variables, the difference of the average temperature of the antenna when the antenna enters and exits the ground shadow is taken as a target function, and a mathematical model of the on-orbit thermal performance and structure coupling optimization design of the antenna is established by considering the search space limitation of the design variables; and optimally designing the in-orbit thermal performance parameters of the large-deflection SAR antenna by adopting a hybrid genetic algorithm.
The test shows that the flying orbit and the flying attitude of the antenna are fixed, and the material property and the surface state of the satellite-borne deployable antenna are changed to research the main factors influencing the temperature.
And inspecting the index, namely the temperature change rate of the antenna molded surface entering and exiting the ground shadow.
Factors and levels: because the thermal parameters of the material influencing the temperature of the antenna are mainly parameters such as absorption-emission ratio, thermal conductivity and specific heat capacity of the surface of the material, the embodiment selects the ratio of infrared radiance to solar absorptivity, the thermal conductivity and the specific heat capacity, the three factors are subjected to orthogonal tests, and each factor is examined at three levels.
From the worst, the ratio of the infrared radiance to the solar absorptivity has the greatest influence on the temperature of an index, compared with the bad level, the influence on the average temperature change of an in-and-out ground shadow is far higher than that of other parameters, the influence on the heat conductivity and the specific heat capacity is basically on one level, and the change of the infrared radiance and the solar absorptivity has smaller influence on the temperature field distribution of the profile of the antenna, so that the conclusion can be drawn that the ratio of the infrared radiance to the solar absorptivity is the main factor influencing the surface temperature of the antenna under the condition that the orbit and the attitude of the antenna in flight are fixed. The embodiment optimizes thermal disturbance by using a genetic simulated annealing algorithm according to the ratio of the infrared radiance to the solar absorptivity.
The genetic simulated annealing algorithm is an optimization algorithm formed by combining a genetic algorithm and a simulated annealing algorithm. The genetic algorithm has poor local searching capability, but has strong capability of grasping the whole searching process and strong local searching capability of the simulated annealing algorithm, and can avoid the searching process from falling into a local optimal solution, but the simulated annealing algorithm has little knowledge about the condition of the whole searching space, so that the searching process is inconvenient to enter the most promising searching area, and the operating efficiency of the simulated annealing algorithm is low. However, if the genetic algorithm and the simulated annealing algorithm are combined to make up for each other, a new global search algorithm with excellent performance may be developed, which is the basic idea of the genetic simulated annealing algorithm.
Similar to the overall operation process of the basic genetic algorithm, the genetic simulated annealing algorithm is a search process of starting a global optimal solution from a group of initial solutions generated randomly, and generates a new group of individuals through genetic operations such as selection, intersection, mutation and the like, and then independently performs the simulated annealing process on each generated individual, and the result is used as the individual in the next generation group. This run is iteratively repeated until a certain termination condition is met.
The genetic simulated annealing algorithm can be described as follows:
a. an evolution algebra counter is initialized: t → 0;
b. randomly generating an initial population p (t);
c. evaluating the fitness of the population P (t);
d. individual crossover operation: p' (t) ← crossplayer [ P (t) ];
e. individual mutation operation: p "(t) ← details [ P" (t) ];
f. individual simulated annealing operation P '(t) ← Simulaned annealing [ P' (t) ];
g. assessing fitness of population P' (t);
h. individual selection and copy operation: p (t +1) ← Re reduction [ P (t) u P' "(t) ];
and (4) judging termination conditions: if the termination condition is not satisfied: t ← t +1, go to the d step, continue the evolution process; if the termination condition is met, outputting the current optimal individual, and ending the algorithm.
The following briefly describes the process of iteratively iterating Matlab and ThermalDesktop with a self-compiled program:
in order to reflect the full orbit situation, the objective function selects the temperature change rate of the antenna entering and exiting the earth shadow in an orbit period from the global adaptability consideration of the optimization result.
FT＝∫∫∫vBTDε0dV (formula 1-9)
I1＝[1 1 1 0 0 0]T(formulae 1 to 10)
ε0＝I1α Δ T (formulas 1 to 11)
In the formula of0Strain induced for varying temperature, FTThe strain matrix is an external force generated by temperature change, D is an elastic constitutive matrix, and B is a unit strain matrix.
Because the force generated by the temperature change is in direct proportion to the thermal strain which is in direct proportion to the temperature change, under the condition that the thermal expansion coefficient of the material is not changed, the force generated by the temperature is in direct proportion to the temperature change, and the temperature change at the time of entering and exiting the terrestrial shadow is selected as an objective function in the optimization.
And (3) value taking of each parameter of the optimization program, and a genetic algorithm: the population number, the maximum evolution algebra, the cross rate, the variation rate and the chromosome length of two design variables are as follows; and (3) simulating an annealing algorithm: initial annealing temperature, number of temperature iterations, markov chain length, end temperature.
The optimization program is realized as follows: and establishing a variable TDcontrol by combining Matlab and TD in an ActiveX mode, and establishing an interface for operations such as variable assignment, calculation submission, result output and the like by remotely controlling the TD by a Matlab command in the ActiveX mode. Two variables are set in the SF to control the variables of the circulating temperature calculation, namely the solar absorptivity and the infrared radiance, and the specific values of the variables are generated into individual values of each generation by a genetic algorithm. And changing the assignment of the two variables each time the loop is performed, submitting the assignment to calculation, and outputting the antenna structure temperature value corresponding to the time when the ground shadow enters or exits. These temperature values will be stored in the (. txt) text with time step as a filename suffix for subsequent use by programs based on Matlab genetic algorithm and simulated annealing algorithm toolkits.
The space load antenna of the present embodiment includes an optical imaging antenna and other types of antennas (such as microwave load), and for the optical imaging antenna, the present embodiment further includes the fifth step: aiming at an optical imaging space load antenna, removing rigid body displacement of the space load antenna, and performing lens surface fitting by using a least square method according to structural characteristic points of the space load antenna and thermal response of central points of the structural characteristic points to obtain polynomial coefficients and inclination errors and translation errors of a reflecting surface; and establishing a model of an original optical system, an optical system with six displacement errors and an optical system with surface change according to the optimized space load antenna and the obtained polynomial coefficient, the inclination error and the translation error of the reflecting surface, and analyzing the change of the optical index of the space load antenna of the optical imaging caused by thermal response.
As shown in fig. 6, in the present embodiment, the thermal response of the structural feature point and the center point is used, and after the rigid displacement is removed, the lens surface fitting is performed by the least square method, thereby obtaining the polynomial coefficient, and the tilt error and the translation error of the reflection surface. Three optical systems were modeled using the optical analysis software CodeV: an original optical system, an optical system with six displacement errors, and an optical system with surface variations. And performing optical performance analysis by using the three optical systems, wherein the optical performance analysis comprises RMS wavefront errors, image point images, MTF and the like.
The displacement error of the thermal deformation to the block mirror comprises the axial translation amount and the radial translation amount. The amount of thermal distortion to the tilt error of the segmented mirror can be seen as (x) due to the fact that the segmented mirror surrounds the center of the segmented mirrori，yi，zi) Three axes of rotation (α, β, γ). The sub-mirrors at each position after blocking are relatively independent, the splicing main mirror is not in common phase due to the sub-mirror position error (sub-mirror displacement error and sub-mirror inclination error) caused by thermal deformation, and the position error of each sub-mirror needs to be analyzed to obtain a relation curve graph between different position errors and optical system imaging.
And performing surface fitting on the lens by using the solved thermal response of the structural characteristic points and the central point and a least square method after rigid displacement is removed to obtain polynomial coefficients and the inclination error and the translation error of the reflecting surface.
And finishing the definition of the preset value after entering CodeV. The surface properties of each lens are set, including surface type, Y radius, lens thickness, glass type, refraction mode, shape and size of the Y half aperture, etc. After the setting is finished, real ray tracing and three-dimensional light path checking can be carried out. The performance change conditions of the optical system under two working conditions of the displacement of six degrees of freedom of the reflector and the change of the profile of the reflector under the action of the thermal load are analyzed.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.
Claims (8)
1. A method for analyzing the mechanical thermal stability of a large space load antenna is characterized by comprising the following steps:
s1, establishing a space load antenna model, and acquiring a temperature field of the space load antenna;
s2, obtaining the temperature of each finite element node of the space load antenna structure according to the obtained temperature field, obtaining thermal response characteristic time and structural response characteristic time, determining whether the space load antenna generates thermal vibration according to the thermal response characteristic time and the structural response characteristic time, obtaining the thermal vibration response and the thermal deformation response if the thermal vibration occurs, and turning to S3, and obtaining the thermal deformation response if the thermal vibration does not occur, and turning to S4;
s3, arranging an intelligent rod with a piezoelectric plate between the space load antenna and the satellite main body as a sensor and an actuator, determining control parameters of a PID controller according to the thermally induced vibration response obtained in S2, controlling the intelligent rod by using the PID controller to realize the suppression of the thermally induced vibration of the space load antenna, and switching to S4;
s4, determining influence factors of the space load antenna temperature, selecting the most important influence factor from the influence factors of the space load antenna temperature by utilizing an orthogonal test, calculating the optimal solution of the most important influence factor by taking the temperature difference of the entrance and the exit of the space load antenna as an optimization target, and optimizing the space load antenna by utilizing the optimal solution and thermal deformation response so as to further realize the suppression of thermal deformation.
2. The method for analyzing the mechanical thermal stability of the large space loading antenna according to claim 1, further comprising:
s5, removing rigid body displacement of the space load antenna aiming at the space load antenna of the optical imaging, and then performing lens surface fitting by using a least square method according to the structural characteristic point of the space load antenna and the thermal response of the central point of the structural characteristic point to obtain a polynomial coefficient and the inclination error and the translation error of the reflecting surface; and establishing a model of an original optical system, an optical system with six displacement errors and an optical system with surface change according to the optimized space load antenna and the obtained polynomial coefficient, the inclination error and the translation error of the reflecting surface, and analyzing the change of the optical index of the space load antenna of the optical imaging caused by thermal response.
3. The method for analyzing the mechanical thermal stability of the large space loading antenna according to claim 1, wherein the step S1 includes:
s11, establishing a space load antenna model, and obtaining the time and duration of the space load antenna entering and exiting the ground shadow according to the parameters of the satellite orbit;
s12, dividing the structure of the space load antenna into heat grids according to the space load antenna model, wherein each heat grid corresponds to a heat node, and calculating the radiation angle coefficient among the heat grids according to the time and duration of the space load antenna entering and exiting the ground shadow to obtain the external heat flow absorbed and radiated by each heat node;
and S13, obtaining a temperature value of the thermal node along with the change of time, namely a temperature field, according to the space load antenna model, the thermal property of the space load antenna material, the rotation angle of the space load antenna and the size of the external heat flow absorbed and radiated by each thermal node obtained in the step S12.
4. The method for analyzing the mechanical and thermal stability of the large space loading antenna according to claim 1, wherein in step S2, the method for obtaining the temperature of each finite element node of the space loading antenna structure according to the obtained temperature field comprises:
and acquiring a temperature matrix, a time matrix, a thermal node matrix and a structural node matrix of the space load antenna according to the space load antenna model and the temperature field, and obtaining the temperature of each finite element node of the space load antenna structure by adopting an interpolation algorithm, wherein the temperature is changed along with the on-orbit running time.
5. The method for analyzing the mechanical thermal stability of the large space loading antenna according to claim 4, wherein in the step S2, the method for determining whether the space loading antenna generates the thermally-induced vibration according to the thermal response characteristic time and the structural response characteristic time comprises the following steps:
according to the characteristic time t of thermal responseτAnd a structural response characteristic time tsCalculating a coefficient Boley:
and when Boley >1, determining that the space load antenna generates thermally-induced vibration and thermal deformation, otherwise, only generating thermal deformation and not generating thermally-induced vibration.
6. The method for analyzing the mechanical thermal stability of the large space loading antenna according to claim 5, wherein in S2, the method for obtaining the thermal response characteristic time and the structural response characteristic time comprises:
performing modal analysis on the satellite of the space load by using finite element software, outputting a fundamental frequency, and obtaining a structural response characteristic time t according to the fundamental frequencys；
Obtaining the mean square error of the temperature amplitude curve of all finite element nodes according to the temperature of each finite element node of the space load antenna structure, dividing the range of the mean square error in an interval-dividing mode, finding out the interval with the most finite element nodes and the number of the finite element nodes, solving the mean value of the mean square error of the interval, finding out the finite element node with the minimum difference with the mean value as a thermal characteristic point, calculating the FFT of the temperature amplitude of the thermal characteristic point, taking the main frequency after the FFT as the temperature change frequency of the space load antenna, and calculating the thermal response characteristic time t according to the temperature change frequencyτ。
7. The method for analyzing the mechanical thermal stability of the large space loading antenna according to claim 1, wherein in the step S4, the most important influencing factors are as follows: the ratio of the infrared emissivity of the space-borne antenna material to the solar absorptivity.
8. The method for analyzing mechanical thermal stability of a large space-borne antenna according to claim 7, wherein in step S4, the optimal solution of the most important influencing factors is calculated by using a genetic simulated annealing algorithm with the temperature difference between the entrance and the exit of the space-borne antenna as an optimization target.
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