基于绝对节点坐标法的介电弹性体驱动柔性双层板结构动力学模型
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摘要
基于绝对节点坐标法,引入介电弹性体本构方程,提出了一种以介电弹性体为驱动板、柔性材料为从动板的新型柔性双层板结构动力学模型,利用数值仿真研究了不同材料参数和激励电压对复合结构动力学特性的影响,对软体机器人驱动器选择和设计提供一定参考。仿真结果表明,复合双层板单元结构在一定大小的驱动电压的激励下会产生周期性变形,在各个方向的运动周期与驱动电压无关,保持复合单元的材料参数不变,其末端最大位移与驱动电压呈近似线性正相关;相同电压激励下,弹性模量越高的复合单元末端运动的周期越小,最大位移也越小,其结构的刚度和稳定性越强。当驱动电压过高,从动板单元材料超弹性系数过小时,复合单元柔性过大,末端运动出现将失稳现象。
In this paper, a plate-plate coupled element with dielectric elastomer as driven plate and flexible material as follower plate is proposed based on absolute nodal coordinate formulation and the constitutive model of dielectric elastomer. The influences of material properties and the voltage excitation on the dynamical behaviors of the coupled element are studied, which shall shed light on the design and selection of soft robot actuator. The results of numerical simulation show that the plate-plate structure will deform under the excitation voltage of a certain degree, its free end movement is periodic, and the movement in all directions is independent of the voltage, given constant material properties of the coupled element, the maximum displacement of the its free end is positively and linearly correlated to the excitation voltage. When at the same excitation voltage, as the elastic modulus increases, the movement cycle and maximum displacement of its free end decrease, the plate-plate coupled element shows higher stability and stiffness. When the excitation voltage is too high and the super-elasticity coefficient of the follower plate is too small, the coupled element's free end movement will appear to be unstable.
In this paper, a plate-plate coupled element with dielectric elastomer as driven plate and flexible material as follower plate is proposed based on absolute nodal coordinate formulation and the constitutive model of dielectric elastomer. The influences of material properties and the voltage excitation on the dynamical behaviors of the coupled element are studied, which shall shed light on the design and selection of soft robot actuator. The results of numerical simulation show that the plate-plate structure will deform under the excitation voltage of a certain degree, its free end movement is periodic, and the movement in all directions is independent of the voltage, given constant material properties of the coupled element, the maximum displacement of the its free end is positively and linearly correlated to the excitation voltage. When at the same excitation voltage, as the elastic modulus increases, the movement cycle and maximum displacement of its free end decrease, the plate-plate coupled element shows higher stability and stiffness. When the excitation voltage is too high and the super-elasticity coefficient of the follower plate is too small, the coupled element's free end movement will appear to be unstable.
引文
[1]杨位东.卷绕式介型EAP驱动单元性能的提高与应用[D].南京:南京航空航天大学,2014.
[2]陈花铃,王永泉,盛俊杰,等.电活性聚合物材料及其在驱动器中的应用研究[J].机械工程学报,2013,49(16):205-214.
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[11]温雯,汤朋朋,陈建魁.柔性膜材收卷内应力分布分析[J].机械设计与研究,2017,33(2):38-42.
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[14]SUO Z,ZHAO X,GREEN W H.A nonlinear field theory of deformable dielectrics[J].Journal of the Mechanics and Physics of Solids,2008,56(2):467-486.
[15]刘立武,李金嵘,吕雄飞,等.电活性介电弹性体的本构理论和稳定性研究进展[J].中国科学:技术科学,2015,45(5):450-463.
[16]刘立武.电活性介电弹性体的本构理论和稳定性[D].哈尔滨:哈尔滨工业大学,2011.
[17]陈家照,黄闽翔,王学仁,等.几种典型材料本构模型及其适用性[J].材料导报:纳米与新材料专辑,2015(S1):118-120.
[18]王子文.基于介电型EAP材料的柔性驱动器的驱动特性研究[D].北京:北京理工大学,2016:27-35.
[19]MAQUEDA L G,SHABANA A A.Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams[J].Multibody System Dynamics,2007,18(3):375-396.
[2]陈花铃,王永泉,盛俊杰,等.电活性聚合物材料及其在驱动器中的应用研究[J].机械工程学报,2013,49(16):205-214.
[3]郭闯强,吴春亚.介电弹性材料驱动器在机器人中的应用进展[J].哈尔滨工业大学学报,2016,48(1):0367-6234.
[4]ARAROMI O A,GAVRILOVICH I,SHINTAKE J,et al.Towards a deployable satellite gripper based on multisegment dielectric elastomer minimum energy structures[C]//Proceedings of SPIE-The International Society for Optics and Engineering,Smart Structures and Materials 2014-Electroactive Polymer Actuators and Devices(EAPAD).San Diego:SPI,2014:90562G.
[5]CARRERA E.Historical review of zig-zag theories for multilayered plates and shells[J].Applied Mechanics Reviews,2003,56(3):287-308.
[6]ZHAO C,YU H,ZHENG B,et al.New stiffened plate elements based on the absolute nodal coordinate formulation[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-body Dynamics,2017,231(1):213-229.
[7]SHABANA A A.Definition of the slopes and the finite element absolute nodal coordinate formulation[J].Multibody System Dynamics,1997,1(3):339-348.
[8]SHABANA A A,Christensen A P.Three-dimensional absolute nodal coordinate formulation:plate problem[J].International Journal for Numerical Methods in Engineering,1997,40(15):2775-2790.
[9]MIKKOLA A M,SHABANA A A.A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications[J].Multibody System Dynamics,2003,9(3):283-309.
[10]杨东武,段宝岩,狄杰建.柔性机构的动力学综合法建模与分析[J].机械设计与研究,2004,20(6):22-24.
[11]温雯,汤朋朋,陈建魁.柔性膜材收卷内应力分布分析[J].机械设计与研究,2017,33(2):38-42.
[12]TOMMASI D,PUGLISI G.Taut states of dielectric elastomer membranes[J].International Journal of Non-linear Mechanics,2011,47,355-361.
[13]GOULBOURNE N.Cylindrical dielectric elastomer actuators reinforced with inextensible fibers[C].Proc.Of SPIE,2006,6168(61680A):1-10.
[14]SUO Z,ZHAO X,GREEN W H.A nonlinear field theory of deformable dielectrics[J].Journal of the Mechanics and Physics of Solids,2008,56(2):467-486.
[15]刘立武,李金嵘,吕雄飞,等.电活性介电弹性体的本构理论和稳定性研究进展[J].中国科学:技术科学,2015,45(5):450-463.
[16]刘立武.电活性介电弹性体的本构理论和稳定性[D].哈尔滨:哈尔滨工业大学,2011.
[17]陈家照,黄闽翔,王学仁,等.几种典型材料本构模型及其适用性[J].材料导报:纳米与新材料专辑,2015(S1):118-120.
[18]王子文.基于介电型EAP材料的柔性驱动器的驱动特性研究[D].北京:北京理工大学,2016:27-35.
[19]MAQUEDA L G,SHABANA A A.Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams[J].Multibody System Dynamics,2007,18(3):375-396.