经历大范围运动和大变形的细梁接触动力学

发布时间：2018-03-04 20:43

本文选题：细梁　切入点：单区域接触　出处：《南京航空航天大学》2016年博士论文　论文类型：学位论文

【摘要】：大型网架式空间结构在微重力环境下展开的过程中,由柔性绳索组成的反射网、张力网不仅经历大范围运动和大变形,而且会发生接触、缠绕甚至打结,导致空间结构在轨展开失败。为了避免这类事故,必须在空间结构设计阶段对柔性绳索的上述复杂动力学行为进行数值仿真和分析。研究柔性绳索的动力学问题一般采用细梁模型。虽然基于绝对坐标描述的梁单元可以正确描述细梁的大范围运动和大变形相互耦合动力学,但应用于细梁接触动力学的研究甚少。目前,对细梁接触动力学的研究主要是两根梁接触与单根梁自接触,且大多采用点对接触模型,不能正确描述细梁之间的多区域接触问题。此外,柔索接触与缠绕时会发生摩擦,如果变形过大还会产生塑性变形,这些都是尚未深入研究的问题。因此,在考虑接触摩擦、局部塑性等因素的前提下,研究经历大范围运动和大变形细梁的接触动力学具有重要的科学意义和工程价值。本文基于绝对节点坐标方法研究了经历大范围运动和大变形的细梁接触动力学问题,主要研究进展如下:(1)基于最小距离准则和主—从梁方法,提出了细梁单区域摩擦接触模型,推导了分别基于罚函数方法与规则化库伦摩擦模型的法向接触力、切向接触力及其雅可比矩阵。将局部坐标系引入到绝对节点坐标的缩减梁单元中,使该单元在接触问题中的应用更加方便。采用广义-α积分算法求解细梁在大范围运动和大变形耦合下的接触动力学问题,通过算例验证了该模型的正确性和处理上述接触问题的可行性。(2)在上述细梁单区域摩擦接触模型的基础上,提出了细梁多区域摩擦接触模型。在该模型中,接触梁的相互嵌入深度是梁局部坐标的函数,每个接触区域包含至少一个局部最小相互嵌入深度点对,由此可确定接触区域的个数。数值仿真结果表明,该模型可成功应用于静力学接触或动力学接触;且基于该模型可有效地对细梁复杂接触碰撞动力学问题进行数值仿真。(3)为了采用LuGre摩擦模型更加准确、高效地描述细梁接触过程中的摩擦力,在若干合理假设的前提下建立了分段解析表达形式的LuGre摩擦模型(LuGre-PAE model)。采用数值算例比较了该模型与常微分方程形式的LuGre摩擦模型(LuGre-ODE model)、规则化库伦摩擦模型(R-Coulomb model)的优缺点,指出LuGre-PAE model不仅能很好地描述Stribeck效应和静摩擦特性,还表现出很好的摩擦诱发迟滞特性。(4)数值结果表明,无论采用LuGre-PAE model还是R-Coulomb model,摩擦力都起到抑制细梁相对滑动、显著降低细梁振荡的效果;而且摩擦系数越大,这种效果越为明显。(5)对细梁引入塑性应变仅依赖于纵向变形的假设,建立了空间弹塑性细梁单元,分析了塑性对接触系统动力学响应的影响。数值结果表明,该单元具有较好的收敛性,与以往文献对比验证了该单元的正确性。塑性会增大细梁的变形,并导致能量耗散;细梁接触时可能会产生较大的局部应变而发生塑性变形,而该塑性变形可抑制细梁由于接触碰撞而产生的剧烈振荡;细梁材料的初始屈服应力越小,上述效果越为明显。(6)为了验证本文提出的细梁多区域摩擦接触模型的正确性,设计研制了三线摆缠绕实验系统。实验结果表明,圆盘角速度的周期随时间有所减小,峰值与谷值随时间均向电机的稳态角速度靠近。通过测定实验系统的参数,采用细梁多区域摩擦接触模型对该实验系统进行了数值仿真,指出产生上述现象的主要原因是圆盘在旋转中受到的空气阻力作用。
[Abstract]:The space structure of large deployable truss in microgravity environment, reflecting network composed of flexible rope, tension net not only has a large range of motion and large deformation will occur, and even lead to contact, winding knot, space structure in orbit failed. In order to avoid this kind of accident, must be in the stage of the complex dynamics of space structure design the behavior of the flexible rope by numerical simulation and analysis of dynamic problems of flexible rope. The commonly used fine beam model. Although the absolute coordinate description based on the beam element can correctly describe the fine beam in large range movement and large deformation coupling dynamics research, but applied to fine beam contact dynamics is rare. At present, research on fine beam contact dynamics is mainly two beam contact and single beam self contact, and most of the points of contact model, can not correctly describe the multi area fine between the beams The contact problem. In addition, the cable will contact with friction winding, if large deformation will produce plastic deformation, these are not yet in-depth study. Therefore, in considering the premise of local plastic contact friction and other factors, research experience large range of motion and deformation of the girder fine contact dynamics it has important scientific significance and engineering value. In this paper, the absolute nodal coordinate method was studied based on the experience of large range of motion and deformation of the thin beam contact dynamics, the main conclusions are as follows: (1) the minimum distance criterion and master-slave beam method based on the proposed fine beam single regional friction contact model is deduced respectively penalty function methods and rules of Kulun friction model based on the method of contact force, tangential contact force and the Jacobi matrix. The introduction of the local coordinate system to reduce the absolute nodal coordinate beam element, the element in contact The application is more convenient. Using generalized-a algorithm for solving integral fine beams in the range of motion and deformation under coupling dynamic contact problems, through a numerical example to verify the feasibility of the model is correct and the contact problem. (2) based on the fine beam single regional friction contact model. The fine beam multi region contact model. In this model, each embedded depth of the contact beam is a function of the beam local coordinates, each contact region includes at least one local minimum point of mutual embedding depth, which can determine the number of contact area. The results of numerical simulation show that the model can be successfully applied to the static contact or contact dynamics; and based on the dynamic numerical simulation of the model can be effective in the fine beam complex contact collision. (3) in order to use the LuGre friction model is more accurate and effective to describe fine beam connection The friction contact process, the analytic expression of LuGre friction model in the form of on the basis of some reasonable assumptions under the (LuGre-PAE model). The numerical examples of LuGre friction model of the model with ordinary differential equations (LuGre-ODE model), the rules of Kulun friction model (R-Coulomb model) pointed out the advantages and disadvantages. LuGre-PAE model Stribeck not only can describe the effect well and static friction characteristics, friction induced hysteresis also showed very good. (4) the numerical results show that, regardless of the LuGre-PAE model or R-Coulomb model, the friction force to suppress the fine beam relative sliding, significantly reduce the fine beam oscillation effect; and the greater the friction coefficient and this effect was more obvious. (5) the plastic strain depends only on the assumption that the introduction of longitudinal deformation of thin beams, established the spatial elastic-plastic thin beam element, analysis of the plastic dynamic response of contact system Should the effect. The numerical results show that the unit has a good convergence performance, verify the correctness of the unit compared to previous papers. The plastic deformation will increase the fine beam, and leads to energy dissipation; may produce large local strain and the plastic deformation of thin beam contact, and the plastic deformation can inhibit the slender beam due to contact vibration; the initial fine beam material yield stress is small, the effect is more obvious. (6) in order to verify the correctness of the proposed fine beam multi region contact model, designed and developed a winding line three pendulum experiment system. The experimental results show that cycle disk angular velocity decreases with time, peak and valley value with time to the steady-state motor angular velocity near. Through parameter determination of experimental system, using fine beam multi regional friction contact model in the numerical simulation of the experimental system were pointed out. The main reason for the above phenomenon is the effect of the air resistance on the disc in the rotation.

【学位授予单位】：南京航空航天大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O343.3

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