Dynamics Analysis And System Design Of Soft Docking Of Micro/Small Satellites

The soft docking of micro/small paired-satellites shows a significant prospect in the on-orbit operation in order to expand their functions.The contact between the docking probe and the docking cone plays a major role in the docking operation.To accurately model the soft docking of micro/small paired-satellites,contact mechanics is necessary to be considered seriously.In this investigation,the dynamic friction contact of the soft docking was considered using Variational Inequalities(VI).The model of the soft docking of micro/small paired-satellites was developed based on the VI contact solution.The ground-based experiment was conducted to validate the correctness of the proposed modeling methods and the effects of the main factors were analyzed.The feasible domains of the main factors leading to the successful docking were presented to offer a design guideline for the soft docking of micro/small paired-satellites.Details are provided below.Firstly,the basic principle of variational inequalities in solving contact problem was studied and the modeling of the soft docking of micro/small paired-satellites using VI was presented.The basic principle of the VI contact solution includes the inequality contact conditions,the general expressions of the dynamic VI formulations as well as the solution strategy and the numerical implementation.Based on the VI principle,the soft docking of micro/small paired-satellites was modeled and its finite element(FE)solution was stated.The comparison of the simulated results obtained by VI solution and commercial FE software package shows that the traditional FE contact solution is based on penalty functions,which is convenient to insert to the original FE codes without increasing any variable.However,the accuracy of the contact solution given by the commercial FE software package depends on the user-defined contact stiffness.On the contrary,the VI contact solution considers the inequality contact conditions directly using optimization algorithms and gives proper results without any user-defined parameters.Secondly,the analytical solution of the soft docking of micro/small paired-satellites was conducted.The dynamic problem of the soft docking was decomposed into three subproblems that were respectively the rigid-flexible coupling dynamics,the contact between the docking probe and the docking cone,and the vibration description of the docking probe.In the following,the Kane formulations were introduced to solve the subproblem of rigid-flexible coupling dynamics.The Hertz contact theory was adopted to estimate the contact between the docking probe and the inner docking cone.The vibration modes of the docking probe was modified by considering the effect of the complicated boundary conditions.Combining the solutions of these three subproblems,the analytical model of the soft docking of micro/small paired-satellites was developed.The algorithm flow chart of the implementation of coding the analytical model was stated.The analytical model was validated by comparing its results with that from the VI model and the commercial FE software package.Thirdly,the ground-based experiment of the soft docking of micro/small paired-satellites was developed.The design of the ground-based experiment included three sections of overall concept proposal,the measurement of the strain on the docking probe and the measurement of the velocities of the paired-satellites.The design principle and the component of the experiment system were mainly introduced in the section of concept proposal.The installation of the strain gauges and the deduction from the strain to the transverse deflection were presented in the section of strain measurement.The measurement of the translational velocities of the paired-satellites was described in the last section.The ground-based experiment shows the soft docking operation directly and provides a feasible way to validate the proposed models of the soft docking of micro/small paired-satellites.Fourthly,the effects of the main factors of the soft docking were analyzed.From the component of the soft docking system,four items were chosen to be the main factors: 1)the bending stiffness of the docking probe;2)the angle of the docking cone;3)the surface conditions of the docking probe and the inner docking cone;4)the initial relative velocities of the paired-satellites.Then,the independent and the joint effects of these four factors on the contact force,the shape deformation of the docking probe and the trajectory of the docking probe along with the docking cone were discussed.Finally,the design domains of the main factors of the soft docking system were determined.The relative docking velocity and the relative capturing velocity were firstly defined by considering the operational principle of the capturing mechanism used in the docking of micro/small paired-satellites.Accordingly,the following criteria to predict whether a successful or unsuccessful docking will take place are given: 1)the spherical end of the docking probe contacts the docking cone and slides into the capture zone;2)the relative capturing velocity of the paired-satellites is in a certain domain.Based on these criteria,the effects of the probe bending stiffness,the cone angle,the friction coefficient of the candidate contact surfaces and the initial relative velocities of the paired-satellites on the docking and capture results were examined.Using the relative capturing velocity as the design object,the available domains of these four factors were determined.