A TENSOR METHOD FOR THE DERIVATION OF THE EQUATIONS OF RIGID BODY DYNAMICS

A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.

Monolithic Coupling of the Pressure and Rigid Body Motion Equations in Computational Marine Hydrodynamics

In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.

Modified RATTLE Method for Rigid Body Dynamics in Cartesian Coordinates

In this paper,we describe a modified RATTLE(M-RATTLE)method for rigid body dynamics directly in Cartesian coordinates.The M-RATTLE method introduces a new way of resetting the coordinates to satisfy the constraints at each step,which is designed for the rigid body dynamics calculations in the Cartesian coordinates.M-RATTLE is algebraically equivalent to the RATTLE method and the cost of performing rigid body dynamics by M-RATTLE is independent of the number of constraints.The interaction forces between atoms belonging to the same rigid molecule do not need to be computed and explicit expressions of the constraints of internal degrees of freedom are unnecessary.The performance and sampling results of the proposed method are compared with those of the symplectic splitting method for an isolated rigid benz molecule and for a cluster of twenty-seven benz molecules.

A SYMPLECTIC ALGORITHM FOR DYNAMICS OF RIGID BODY

For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange＇s equations based on dependent generalized momenta. Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants. More importantly, the generalized momenta based Lagrange＇s equations show unique advantages over the traditional Lagrange＇s equations in symplectic integrations.

Implementation of configuration dependent stiffness proportional damping for the dynamics of rigid multi-block systems

The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.

Numerical Solution of Constrained Mechanical System Motions Equations and Inverse Problems of Dynamics

In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

Augmented Eigenvector and Its Orthogonality of Linear Multi-rigid-flexibel-body System

The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, the eigenfunction does not satisfy the orthogonality under ordinary meaning. A new concept--augmented eigenvector is introduced, which is used to overcome the orthogonality problem of eigenvectors of linear multi-rigid-flexible-body system. The constitution method and the orthogonality of augmented eigenvector are expatiated. After the orthogonality of augmented eigenvector is acquired, the coupling of coordinates in dynamics equations can be released, which makes it possible to analyze exactly the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method.

Dynamic model for landsliding monitoring under rigid body assumption

Based on the assumption that the slope bodies are rigid, the dynamic model of the landsiding (forward model) was put forward. According to the dynamic model, the system equations of Kalman filter were constituted. The mechanical status of a slope was hence combined with the monitoring data by Kalman filter. The model uncertainties or model errors could also be considered through some fictitious observation equations. Different from existed methods, the presented method can make use for not only the statistic information contained in the data but also the information provided by the mechanical and geological aspect of slopes. At last a numerical example was given out to show the feasibility of the method. [

花键约束下变形摩擦片角向摆动的数值分析

为了揭示离合器分离状态下摩擦元件变形前后的动力学特性差异,本文研究了花键约束下不同变形程度摩擦片的角向摆动特性,分析了花键界面和翘曲变形对摆动的影响。本文对平直摩擦片进行了力学分析,并建立了平直片角向摆动的动力学模型。在此基础上,对平直片引入薄板的变形函数,考虑几何差异推导出了变形摩擦片的摆动模型。同时,与经典边界条件对比,在摩擦片内径的花键约束处采用了摩擦边界,并且基于几何结构推导出了最大允许摆动角。通过数值仿真,在时域和频域分析了各影响因素对摆动的影响。结果表明:旋转的摩擦片受扰动后,角向摆动频率随转速的增加而增加,而翘曲变形会降低摆动频率。此外,最大摆动角度在低转速时会延长摩擦片摆动的时间,摩擦力则会降低摆动的时间。

子母无人机多体分离气动特性模拟

子母机多体分离过程中气动干扰特性的分析是集群无人机发射技术的重要研究方向。基于动态嵌套非结构多面体网格技术,耦合求解流场非定常N-S方程与刚体六自由度运动方程,实现了子母机多体分离过程的精确模拟。首先,对母机的气动干扰区和子母机的分离方式进行分析,其次,计算得到整体状态时子母机以及子机与子机之间的气动干扰特性,最后,根据多体分离过程中子机运动状态的变化情况,进行安全特性评估。研究结果表明:相对于减速分离,加速分离能够快速脱离气动干扰区,安全性更高,并且随着子机数量的增加,子机机翼的距离不断减小,在一定程度上减弱了子机的翼尖涡对翼面的影响,增大了子机的升力。

基于LAGRANGE方程的深水钻井隔水管–水下井口系统动力分析

为了探究大质量、大刚度防喷器组(blowout preventers,BOPs)对深水钻井隔水管系统动态相应预测精度的影响,根据细长钻井隔水管与刚性防喷器组的结构特点,提出两者刚柔耦合的概念,采用能量法推导隔水管–防喷器组–水下井口系统的动能和势能,采用LAGRANGE方法建立耦合系统动力学理论模型,采用科学计算软件和Newmark-β直接积分法对动力学模型进行数值计算。以南海某深水钻井隔水管为例,开展基于耦合动力学模型的隔水管系统动态响应分析。结果表明,采用本文理论模型得到的隔水管不同位置的节点位移、单元弯矩、上部和下部挠性接头转角时程曲线、整体侧向位移包络线和弯矩包络线等与ABAQUS仿真结果均吻合良好,最大误差为8.8%。此方法可为深水钻井隔水管和水下井口系统动态分析提供参考。

无人机火箭助推机构分离安全性研究

为提高火箭助推式无人机起飞时助推机构的分离安全性,提出一种可自动安全分离的无人机火箭助推机构。以某型号无人机为例,运用理论力学与刚体运动学知识建立以分离安全性最优为目标的助推机构理论模型,得出助推机构中关键参数的设计依据并建立助推机构的三维模型。运用刚体动力学分析方法得到助推机构的分离运动轨迹,搭建包含助推机构和模拟无人机部分的实验系统,验证助推机构分离轨迹和分离姿态与仿真结构有一致的变化趋势。研究结果表明,该助推机构在分离过程中可有效规避安全隐患,提高分离安全性。

轮-阜机构的动力学模拟

受滚木运输的启发,设计了一种轮-阜复摆互动机构,通过在两个平面上分别构造摆轮和凸台阵列,可实现平面之间的平稳滑动。为了研究滑动中接触面间法向力和切向力的关系,建立了轮-阜机构的系统动力学微分方程,并基于Runge-Kutta方法提出一种迭代算法对之求解,计算摆轮和凸台相互碰撞所产生的滑动阻力。数值仿真结果表明,合理设置轮-阜机构的几何参数,可以减少接触面相互滑动中的能量损耗,从而大幅提高法向载荷和等效切向阻力之间的比值。在理论分析的基础上,制造了相应的实物模型进行实验验证,结果显示该机构可以实现平稳的滑动,且切向驱动力可低于法向载荷的百分之一,从而验证了该机构的可行性。

基于多体动力学模型的柴油机曲轴振动特性分析

为了减少发动机故障分析曲轴系统的扭转振动,建立了由活塞、连杆、曲轴、飞轮和硅油阻尼器组成的曲轴系统三维模型。利用多体动力学仿真软件ADAMS,建立了由多自由度组成的刚性混合动力发动机系统的多体动力学模型,对其进行扭振响应仿真,对曲轴的扭振进行分析。该仿真结果具有较高的精度,该计算方法具有一定的工程应用价值。

薄壁四点接触球轴承-腕部关节系统接触动力学分析

在机器人实际工况中,针对含有薄壁四点接触球轴承的机器人腕部关节系统的运动稳定性问题,对腕部系统模型进行了简化设计和仿真研究。在考虑薄壁结构的弹性变形和动态接触作用耦合影响的基础上,建立了刚柔耦合工业机器人腕部关节系统模型,分析了不同受载工况和正反转驱动下的变形规律和动态特性。首先,基于多体动力学和Hertz接触理论,设计了包含薄壁四点接触球轴承和中空轴及基座的腕部关节系统刚柔耦合接触动力学仿真模型;然后,考虑薄壁中空轴、基座、轴承套圈和保持架的结构弹性变形、钢球和套圈滚道、保持架的动态接触作用,研究了机器人腕部关节系统两种实际工况对保持架和钢球角速度、保持架和薄壁基座振动位移、钢球与套圈的动态接触力的影响;最后,计算分析了两种工况下腕部关节系统的动态载荷规律和振动响应特性。研究结果表明:在相对较大的径向载荷作用下,保持架和钢球会出现打滑现象,速度呈现周期波动,保持架和基座具有更好的运动稳定性,其薄壁轴承内部载荷降低,主副接触对均承担联合载荷,轴承内部载荷稳定性也更好。该仿真模型及结果可以为薄壁腕部关节系统的动力学分析与设计提供参考。

复合驱动并联机构的动力学建模与仿真分析

针对一种PUU-2PRRS 5自由度复合驱动并联机构的刚体动力学建模问题,采用拉格朗日法结合虚功原理建立刚体动力学模型并进行仿真分析。首先,在考虑存在次闭环的情况下,采用闭环矢量法对并联机构进行运动学分析,推导出机构各构件质心的线速度和角速度;其次,采用拉格朗日法结合虚功原理建立复合驱动并联机构的刚体动力学模型,为复合驱动并联机构驱动力的求解及后续动力学仿真分析奠定了基础;最后,基于MATLAB软件和ADAMS软件对该并联机构进行动力学仿真分析,在给定相同末端轨迹的情况下,对比两种软件得到的驱动力变化曲线,仿真结果验证了所建动力学模型的正确性。文中不仅为PUU-2PRRS 5自由度复合驱动并联机构控制系统的搭建打下了基础,也为其他复合驱动并联机构的动力学建模分析提供了理论依据。

6RSS仿人并联咀嚼机器人的刚性动力学建模分析

目的:对设计的6RSS仿人并联咀嚼机器人进行刚性动力学建模分析。方法:首先,推导刚性动力学建模所需的运动变量(包括平动/转动速度和加速度)函数。其次,使用牛顿-欧拉法则建立机器人的刚性动力学模型。最后,在机器人受到咀嚼反力情况下,跟踪口腔健康志愿者的咀嚼运动轨迹,并开展数值计算。结果:数值计算结果表明,机器人的驱动力矩和约束力出现峰值的时刻和咀嚼反力出现峰值的时刻一致。结论:外力对机器人的逆动力学有较大影响,该研究为机器人的运动控制以及优化设计提供了理论依据。

数值模拟技术在高坠案法医学分析中的应用

高坠案的焦点、难点是推演重建坠落轨迹,分析损伤机制,为综合判断坠落性质提供依据,并将结论向死者家属等非专业人士进行直观、有效的解释。近年来,得益于数值运算方法发展和计算能力提高等有利条件,数值模拟技术在损伤生物力学研究领域取得了一定进展。该技术具有模拟结果客观化、直观化、参数化以及可重复等优势,为分析研究人体坠落轨迹及坠落伤等开辟了新的途径。高坠数值模拟技术主要有两种方法,一种是基于多刚体动力学方法进行坠落轨迹的推演重建;另一种是基于有限元方法进行坠落伤的推演重建。本文综述了近年来国内外数值模拟技术在高坠案中的应用研究,展示了该技术应用于高坠案法医分析的潜力。

剪刀叉顶升机构的铰接力分析

本文根据虚功原理对剪刀叉顶升机构的液压缸推力进行了理论推导,并利用有限元分析软件进行了刚体动力学仿真验证,确认理论计算公式的正确性。同时通过仿真,得到剪刀叉结构各运动副处铰接力的特点及其变化规律。据此为剪刀叉顶升机构设计提供重要的参考。