【作者】 缪建成；

【导师】 陈关龙；

【作者基本信息】 上海交通大学 ， 车辆工程， 2008， 博士

【摘要】 柔性多体动力学(Flexible multibody dynamics,FMD)发展已近40年,建模理论仍未尽善尽美,并面临进一步突破的难题;与建模理论相比,FMD计算技术和实验技术的研究更显得极为匮乏,尚有相当多的问题需要进一步深入探讨。本文在建立柔性多体系统(Flexible multibody system,FMS)缩并模型的基础上,针对其求解分析问题进行了深入的研究,分别基于中心差分法和Newmark法提出了适用于FMD问题求解的子循环算法,该类算法的提出对FMD计算理论的发展将起到积极的推动作用,柔性多体动力学计算方法的研究工作包括以下几个方面:1、应用有限元方法离散空间任意柔性体,通过浮动坐标系描述柔性体上任意点的坐标位置,并将其变形表达为广义模态坐标,建立了完备的FMS方程;将广义坐标变量分解为独立变量和非独立变量,得到了缩并型的FMS方程,在此基础上,深入分析了FMD问题求解中存在的特殊性,针对FMS方程固有的刚性问题,提出了应用子循环原理对常用的FMS方程计算方法进行修正,从而在提高FMD问题求解效率的同时,有效地处理FMS微分方程的刚性问题。2、基于中心差分算法,通过将缩并型FMS方程中的待求变量分解为长、短周期变量域,采用不同的步长进行时域积分,推导出同步更新公式和子步更新公式,建立了适用于缩并型FMS方程求解的中心差分子循环算法,并应用直接积分逼近算子方法进行了该算法的稳定性分析,证明只要各积分域步长不超过其临界步长,该算法能保持良好的稳定性。在中心差分子循环算法中,子步循环是显式过程,因此,该算法仍存在一定程度的误差累积现象,然而算例表明,中心差分子循环算法可以在保持恰当计算精度的同时,大幅度提高了FMS方程的求解效率。3、基于Newmark算法,采用类似的处理措施对子循环算法进行了修正,建立了适用于FMS方程求解的Newmark子循环计算公式,通过实时检查系统的能量平衡状态,并摄动修正积分步长,使子循环积分过程保持了良好的稳定性,得到了合理的数值计算结果。与中心差分子循环算法比较,Newmark子循环算法的同步更新过程和子步更新过程都进行了隐式迭代,消除了数值积分过程中的误差累积现象,算例表明,修正的Newmark子循环算法无论在计算精度方面还是在计算效率方面,都优于中心差分子循环算法。FMD理论已普遍应用于星载可展天线展开过程的仿真分析中,但是在陆基车载可展天线设计中却尚未得到普遍应用,本文分别建立了车载可展天线的FMS模型、多刚体模型及有限元模型,分别将FMS模型计算结果与有限元模型计算结果、多刚体模型计算结果进行了对比分析,给出了相应的比较结论,这些结论对进一步拓展FMD理论的工程应用领域具有一定的参考意义。1、建立了可展天线结构的有限元模型和FMS模型,分别对其进行了有限元分析和FMD分析,结果表明天线阵面在运动过程中,有限元分析结果与FMD分析结果之间存在一定的差异性;有限元分析计算仅仅得到了天线在大范围运动过程中由于自重及外载荷作用下的阵面变形状态,变形的时域曲线连续光滑且无波动现象,而FMD分析结果却明显反映出,由于天线的大范围运动惯性,造成了阵面的小幅度弹性变形,这种弹性变形的反过来影响了天线大范围运动的轨迹,体现了大范围运动和小幅度变形之间的耦合现象,这一分析结果更加符合天线阵面在运动过程中的实际状态。2、分别采用可展天线多刚体模型和FMS模型,对其展开过程进行了多刚体分析和FMD动态分析,结果表明天线阵面FMD分析的结果与多刚体分析结果之间存在显著的差异,应用FMD逆动力学分析技术求得的内、外侧展开油缸驱动力大小悬殊,显示出天线不同位置的变形不一致性会给油缸造成不同的反作用力。通过FMD计算得到的天线转角和变形结果与实际现象保持了高度的一致性,而采用多刚体系统模型计算的展开油缸驱动力却导致展开转角和变形出现了不合实际的越界现象。这一结果表明对大型可展柔性天线的动力学分析而言,多刚体系统动力学有明显的不足之处。同时,为验证子循环算法对复杂FMS模型计算的有效性,应用子循环算法进行了天线展开过程的动态响应分析计算,比较结果显示了FMD子循环算法的普适性。3、分别对天线系统倒竖过程和工作旋转过程进行了基于FMD的动态响应计算分析,分析结果显示:无论是否考虑风载荷作用,由于天线阵面运动的巨大惯性以及结构的柔性,阵面在运动初期均出现剧烈的变形波动现象,在稳态工作时,由于风载荷作用的周期变化特性,阵面变形也出现显著的周期性,这种周期性的变形状态,将导致天线系统电磁特性出现一定程度的精度下降,这一分析结果说明在进行大型阵面天线结构设计时,必须充分重视系统的惯性作用以及外界变化载荷的作用,对阵面结构进行适当的刚度加强,以满足天线系统足够的工作可靠性和精度要求。更多还原

【Abstract】 Study of Flexible multi-body dynamics (FMD) has been developed nearly 40 years. Theory of the FMD modeling still doesn’t reach perfect condition and involves in difficult of farther breakthrough. Comparing with the modeling theory, studies of computational strategies and experiment technologies are more weakness. There are a lot of problems which wait for further more discussion.Based on modeling a condensed formulation of FMD problem, this paper makes a deep study of its analysis problem and presents subcycling algorthms, which are suitable for the FMD problem, based on the central difference method and the Newmark algorithm respectively. This will actively promote development of the FMD computational theory. Research of the FMD computational methods includes several contents as following.1、Applying the FEM method to discrete an arbitrary spatial flexible body, describing position of a point in the body by means of a float frame and measuring deformation of the body in a generalized mode coordinate style, a self-contained FMS formulation was established based on the second Lagrange equation. Separating the generalized variables to a group of independent variables and a group of dependent variables, a condensed FMS equation was established. Based on this result, Special problems, which exist in solution process of a FMS equation, are deeply analyzed. In order to deal with stiffness of the FMS differential equation, we proposed to modify the algorithms, which are frequently used in FMD problems, based on subcycling principles. Thereby, solution efficiency of the FMD problem can be enhanced and stiffness of the differential equation can be effectively managed at the same time.2、Based on the central difference method, separating unknown variables of the condensed FMS equation in larger cycling domain and smaller cycling domain and using different step sizes to integrate these variables, common update formula and sub-step update formula are carried out and a central-difference-based sub-cycling algorithm, which is suitable for FMD problems, was established. An integral approximation operator method is used for analyzing stability of the sub-cycling algorithm. It is proved that the algorithm can hold stable property only if the step sizes in each domain do not exceed their critical limits. Due to sub-step cycles of the central-difference-based sub-cycling algorithm are explicit processes, there is still error accumulation phenomenon in the algorithm. However, numerical examples indicate that the central-difference-based sub-cycling algorithm can enhance the computational efficiency greatly without intensely dropping of the precision.3、Also, based on the Newmark algorithm, modifying the sub-cycling by means of similar manner mentioned above, a Newmark-based sub-cycling, which is suitable for FMD problems, was presented. By means of checking energy balance status and changing the step sizes during the integral process, favourable stability of the sub-cycling can be preserved and reasonable numerical results can be obtained. Compared with the central-difference-based sub-cycling algorithm, the implicit iterative processes are performed whether in the common-update or in the sub-step-update. Accordingly, error accumulation phenomenon is eliminated during the numerical integrate process. Numerical examples indicate that the Newmark-based sub-cycling is more efficient and more precise than the central-difference-based sub-cycling algorithm.FMD theory has been largely applied in simulation of deploying process of artificial satellite mounted antennas. However, this application has not been expanded to design of mobile-mounted deployable antenna. This paper established FEM model, multi rigid body model and FMS model of a mobile-mounted deployable antenna. Comparing computational results from the FMS model with that from the FEM model and that from the multi rigid body model, we got some relative conclusions. These conclusions have a little reference values for further developing engineering application domain of the FMD theory.1、FEM model and FMS model of a large mobile-mounted deployable antenna were respectively established. FEM analysis and FMD analysis are separately performed for the two models. Comparison of the results illustrate that some differences exist between the FEM analysis and the FMD analysis during motion process of the antenna frame. The FEM analysis only got hold of deformation condition of the frame resulting from its deadweight and external loads during a large range motion. Time-domain deformation curve is continued, slippy and without fluctuate phenomenon. On the contrary, the FMD analysis reflected evidently that a small range oscillating deformation was produced due to motion inertia of the frame. And this oscillation also affected motion trajectory of the frame by contraries. This interaction exhibited coupling between large range motion and small range deformation of the frame. And this result is more according with actual condition of the frame during motion process.2、Deploying process of the antenna frame were analyzed by means of the multi rigid-bodies model and the FMS model respectively. A notable difference was displayed between the two results. Driving forces of frame deploying oil-cylinders, which were resulted from anti-dynamic analysis technique, revealed evident relativity between loads and locations. Rotation angle and deformation result from the FMS model are also according with actual phenomenon enough. On the contrary, Rotation angle and deformation result from the multi rigid-bodies model induced a bound exceeded phenomenon, which is unnatural. This result indicates that the multi rigid-bodies model is shortage for dynamic analysis of a large deployable flexible antenna. At the same time, to validate applicable property of the sub-cycling on a complicated FMS model, the Newmark integral and the Newmark-based sub-cycling were used to calculate dynamic response of the antenna, respectively. It shows that the subcycling algorithms can be used in a broad application area.3、Inverse uprighting process and circumrotating process of the antenna frame were analyzed by means of the multi rigid-bodies model and the FMS model respectively. Results showed that whether wind loads are taken into account, a startup oscillation phenomenon usually existed during the motion process due to large inertia and flexibility of the frame. During circumrotating service status, deformation oscillation displayed distinctive periodicity due to periodic variety of the wind loads. This periodic deformation conditions will induce a dropping precision of electromagnetism of the antenna system. This result informed us that the inertia and the external variational loads need to be sufficiently regarded for design of a large frame antenna. To satisfy enough reliability and precision of an antenna, structure of the frame need to be strengthened appropriately.更多还原