| Deployable mechanisms are widely used in aviation,aerospace,construction and other fields because they have the advantages of reusage,small volume after folding,and covering larger space after expansion.According to different combinations,the unit mechanism can be assembled into various complex deployable mechanisms,where the scissor deployable mechanisms are composed of scissor-like-elements(SLEs)having the characteristics of large contraction ratio,reliable expansion and folding,high accuracy and good rigidity,so they are often used as space deployable mast,deployable antennas reflectors,and temporary shelters.Also,deployable mechanism is a kind of mechanism structure,that is,in the stage of unfolding and folding,it shows the movement characteristics of the mechanism.However when the mechanism is locked and bears the load,it shows the stability of the structure.Therefore,it is necessary to study the dynamic characteristics and structural stability of deployable mechanism for guaranteeing the smooth motion and reliable bearing loads of the mechanism.In the motion stage,the deployable mechanism is formed by a large number of units through array combination,which lead to the more internal hinges,and more complex structure.Also,the impact characteristics caused by clearance hinge will seriously affect the movement synchrony and deployment precision between different components.In the lock stage,the instability and deformation of deployable mechanism will affect its surface accuracy,and even cause the collapse of the structure.This paper systematically studied the clearance dynamic characteristics of scissor deployable mechanism in the process of motion and the stability of structural configuration after locking.It can provide a theoretical basis for accurately predicting the dynamic characteristics of mechanism with clearance,inhibiting the impact,frictional wear,decrease of motion precision,reduction of mechanism reliability and life caused by clearance,and the buckling characteristics of structural instability,which also can provide an important basis for speeding up the engineering applications of deployable mechanism.The main contents and innovations of this paper are as follows:1.Based on the consistency of the units in the deployable mechanism,the substructure method is incorporated into the dynamics analysis,and the dynamic model and solving method of the ideal scissor linear array deployable mechanism during the motion process are established.In the global coordinate system,according to the geometric constraint,displacement constraint,hinge constraint of SLE,the general motion constraint equation of deployable mechanism is established,which can quickly obtain the dynamic response of the mechanism.Also,it can be extended to a linear array deployable mechanism consisting of any element,which improves the modeling efficiency of mechanism dynamics analysis.In addition,the geometric constraint method is adopted to correct the velocity and position for improving the accuracy of the numerical results.2.A general dynamic equation of scissor deployable mechanism with clearance is established,and the contact impact process between the kinematic pair elements is described mathematically.Also,the contact state,the position of the potential contact point,relative contact velocity and the transformation of the generalized force between the contacts are analyzed.A solution to the numerical stiffness problems which is easy to occur in the numerical solution is put forward.Moreover,the normal and tangential contact forces between the revolute clearance joints are converted to the mass centers of components which are joined by the clearance pair,and the converted contact force and the additional torque are integrated to the generalized force of the deployable mechanism dynamics model,thus the effect of joint clearance is successfully introduced into the dynamic model of deployable mechanism.The effect of clearance size,number of clearance and clearance position on the dynamic behavior of the deployable mechanism is comprehensively analyzed,and the dynamic interaction between clearance joints at different positions and the influence of clearance size on the behavior change of mechanism at different positions are studied.Besides,it is suggested that the appropriate controller can be installed in the sensitive part relative to the clearance for reducing the nonlinear dynamic behavior of the mechanism.3.Based on the "contact-impact-separation" process between the revolute clearance joints,the shortcomings of the Hertz contact model,the Persson contact model and the improved Winkler elastic foundation model are analyzed,and a new hybrid nonlinear contact impact force model is proposed,which uses nonlinear stiffness coefficients to describe the variation of contact stiffness with respect to contact penetration during multi rigid body contact.The nonlinear stiffness coefficient takes into account the coupling relationship between the contact stiffness and the mechanism system,which is closer to the engineering practice.In addition,based on the hybrid model and LuGre friction model,the dynamic model of planar deployable mechanism composed of two SLEs with clearance is established.Compared with the original model,the hybrid contact force model is not limited by the clearance size and the coefficient of restitution during the dynamic analysis,which can predict the dynamic behavior of the mechanical system more accurately.4.According to the linear elastic analysis,equivalent principle and stationary potential principle,stability model(Ⅰ)for the single loaded deployable structure and stability model(Ⅱ)for deployable structure considering self-weight are established respectively.Also,the model(Ⅰ)and model(Ⅱ)are respectively used to study the instability loads of the linear array deployable structures with different number of elements,the results show that the proposed stability models can not only predict the buckling load of deployable structure,but also analyze the influence of the parameters on the stability,and these two stability models are applicable to linear array deployable structure with arbitrary elements.In addition,different buckling parameters,such as the number of elements,deployed angle,and bar length,jointly affect the instability characteristics of deployable structures consisting of SLEs.As the number of units increases or the bar flexibility increases,the structural stability decreases gradually.At the same time,the deployed angle cannot be used alone to judge the basis of structural instability.On the other hand,a modified stability model(Ⅱ)is used to calculate the critical load of a large linear array deployable structure with more number of elements and larger slenderness ratio of the bar.According to engineering requirements,the most stable configuration of scissor deployable structure under the same working condition can be obtained by choosing the appropriate instability parameters,thus the structural buckling can be avoided and a stable structure with maximum carrying capacity can be designed.5.The clearance dynamic characteristics of scissor deployable mechanism in the motion stage and structural stability after locking are studied experimentally.In the experiment of the clearance dynamic characteristics of deployable mechanism,the dynamic output of the acceleration is experimentally tested for different clearance sizes,clearance positions and number of clearances.Compared with the theoretical analysis results,the proposed nonlinear mixed contact force model is verified,and the influence of different parameters on the impact dynamic characteristics of deployable mechanism with clearance is studied.In the stability test,the effect of three major instability parameters on the structural buckling is studied by increasing the number of elements,changing the deployed angle and reducing the bar length.Also,Compared with the theoretical results,the correctness of the proposed new stability model is verified.This work not only provides a method for clearance dynamics analysis and structural stability analysis of deployable mechanisms based on SLEs,but also has a reference value for the dynamic analysis and stability analysis of other types of deployable mechanisms. |
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