Modular Modeling And Coupling Dynamics Of Liquid-Filled Flexible Spacecraft

Modern high-tech spacecraft continues to develop in the direction of multi-tasking and modularization.The size of solar array becomes larger and the number of flexible appendages carried is gradually increasing,as well as the quality of the equipment.When the spacecraft performs orbital maneuver and attitude adjustment,and the drive mecha-nism drives the flexible appendages to maneuver,the flexible appendages are deformed and vibrated.At the same time,the reaction force generated by the deformation and vi-bration of the flexible appendages will also affect the stability of the spacecraft operation and attitude,as well as the smooth maneuvering of the driving mechanism.From the above,the spacecraft with maneuvering appendages is a rigid-flexible coupling system.Accurate establishment of the system dynamics equation can not only reveal the dynamic characteristics of the spacecraft system,but also provide theoretical basis and preliminary research for the design of the system control law.In this paper,a modular dynamic mod-eling method based on Kane’s equation is proposed for the complex rigid-liquid-flexible coupling dynamic system of spacecraft.（1）The parametric modeling method based on system identification of sloshing force and sloshing moment is used to derive the dynamic equation of liquid-filled spheri-cal tank under small amplitude sloshing.The liquid in the tank is assumed as ideal fluid,the modal coordinate function and the governing equation of the liquid sloshing in the cylindrical liquid-filled tank are derived based on the potential flow theory.According to the Fourier-Bessel series expansion condition,the solution domain of the rotationally symmetric liquid-filled tank is transformed to the solution domain of the cylindrical tank by using the unknown arbitrary continuous function.And the parametric model of liquid sloshing in a rotationally symmetric tank with undetermined coefficients is established.The computational fluid dynamics software is used to calculate the sloshing force and sloshing moment response of the liquid-filled spherical tank,and the unknown parame-ters of the system are identified in the MATLAB program.By comparing the output re-sponse of the liquid sloshing system with the output response of the corresponding para-metric model,the accuracy and applicability of the parametric modeling method are veri-fied.（2）For the solar panels on the spacecraft,the finite element method is used to estab-lish the four-node quadrilateral plate element model for the flexible appendage.The de-scription of the vibration deformation of the flexible appendage is based on the small de-formation and Kichhroff-Love thin plate theory,that is,only the normal deformation and the rotation angle relative to the axis k_{i 1} and k_i2 of the local reference frame are con-sidered.According to the displacement function,the shape function of the plate element is derived,and the stiffness matrix,mass matrix and equivalent load matrix of the plate element are obtained by integration based on the shape function.The above type of ele-ment matrix is combined according to the node sorting number,and the dynamic equation of the flexible appendage is constructed simultaneously.The accuracy of the formula derivation and the program is verified by comparing the results of static loading experi-ment,modal analysis results and dynamic responses by programming and FEM software.（3）Considering the model of typical spacecraft configuration,the reference frames are defined to describe the motion of each component.The velocity vectors of each component in inertial reference frame are obtained by the time derivative of the vector diameters of each component in the inertial reference frame.Based on the velocity vec-tors,the independent partial velocity and partial angular velocity are selected as the gen-eralized rate,that is,the system degree of freedom in the Kane’s equation.The velocity vector is further derived to obtain the acceleration vectors,and then the generalized iner-tial force and generalized active force of the spacecraft system are calculated.The dy-namic equations of the spacecraft system are obtained by combining the projections of the generalized inertial force and the generalized active force in the direction of the par-tial velocity and the partial angular velocity.（4）The MATLAB program corresponding to the derivation is compiled.The rig-id-flexible coupling of spacecraft system with flexible appendages and the rig-id-liquid-flexible coupling dynamic effect of liquid-filled flexible spacecraft are solved by programming.The influence of the installation position on the dynamic characteristics of the spacecraft system is compared and analyzed.The eccentric installation of the ap-pendage will make the rigid body and liquid sloshing behavior of the spacecraft center more complicated.The simulation results are similar to the literature examples,which verifies the accuracy of the modular modeling method.Finally,a variety of typical actual working conditions,such as orbital acceleration,solar wind disturbance and relative rota-tion of accessories,are selected to calculate the dynamic response of each component of spacecraft system under such working conditions.The simulation results show that the main body motion of the spacecraft interacts with the liquid sloshing of the tank and the vibration of the flexible appendages,showing the complex dynamic characteristics of the spacecraft system.The dynamic characteristics of the spacecraft are preliminarily studied,which provides a theoretical basis for the design of the complex precise control law.