Modeling of unilateral contact conditions with application to aerospace systems involving backlash, freeplay and friction

This paper describes an analysis procedure for the modeling of backlash, freeplay and friction in flexible multibody systems. The first two effects are formulated in a general manner as unilateral contact conditions in multibody dynamics. The incorporation of the effects of friction in joint elements is also discussed, together with an effective computational strategy. These non-standard effects are formulated within the framework of finite element based multibody dynamics that allows the analysis of complex, flexible systems of arbitrary topology. The versatility and generality of the approach are demonstrated by presenting applications to aerospace systems: the flutter analysis of a wing-aileron system with freeplay, the impact of an articulated rotor blade on its doop stop during engagement operation in high wind conditions, and the dynamic response of a space antenna featuring joints with friction.     

Integrated mechanical and control design of underactuated multibody systems

Multibody systems are called underactuated if they have less control inputs than degrees of freedom, e.g. due to passive joints or body flexibility. For trajectory tracking of underactuated multibody systems often advanced modern nonlinear control techniques are necessary. The analysis of underactuated multibody systems might show that they possess internal dynamics. Feedback linearization is only possible if the internal dynamics remain bounded, i.e. the system is minimum phase. Also feed-forward control design for minimum phase systems is much easier to realize than for non-minimum phase systems. However, often the initial design of an underactuated multibody system is non-minimum phase. Therefore, in this paper a procedure for integrated mechanical and control design is proposed such that minimum phase underactuated multibody systems are obtained. Thereby an optimization-based design process is used, whereby the geometric dimensions and mass distribution of the multibody systems are altered.     

Robust synchronization of uncertain fractional-order chaotic systems with time-varying delay

This paper presents a new technique using a recurrent non-singleton type-2 sequential fuzzy neural network (RNT2SFNN) for synchronization of the fractional-order chaotic systems with time-varying delay and uncertain dynamics. The consequent parameters of the proposed RNT2SFNN are learned based on the Lyapunov–Krasovskii stability analysis. The proposed control method is used to synchronize two non-identical and identical fractional-order chaotic systems, with time-varying delay. Also, to demonstrate the performance of the proposed control method, in the other practical applications, the proposed controller is applied to synchronize the master–slave bilateral teleoperation problem with time-varying delay. Simulation results show that the proposed control scenario results in good performance in the presence of external disturbance, unknown functions in the dynamics of the system and also time-varying delay in the control signal and the dynamics of system. Finally, the effectiveness of proposed RNT2SFNN is verified by a nonlinear identification problem and its performance is compared with other well-known neural networks.     

Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm

In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.

     

Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems

The automatic derivation of motion equations is an important problem of multibody system dynamics. Firstly, an overview of the matrix calculus related to Kronecker product of two matrices is presented. A new matrix form of Lagrangian equations with multipliers for constrained multibody systems is then developed to demonstrate the usefulness of Kronecker product of two matrices in the study of dynamics of multibody systems. Finally, the equations of motion of mechanisms are derived using the proposed matrix form of Lagrangian equations as application examples.     

A parametric study on the dynamic response of planar multibody systems with multiple clearance joints

A general methodology for dynamic modeling and analysis of multibody systems with multiple clearance joints is presented and discussed in this paper. The joint components that constitute a real joint are modeled as colliding bodies, being their behavior influenced by geometric and physical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory together with a dissipative term, is used to evaluate the intrajoint contact forces. Furthermore, the incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also discussed. The suitable contact-impact force models are embedded into the dynamics of multibody systems methodologies. An elementary mechanical system is used to demonstrate the accuracy and efficiency of the presented approach, and to discuss the main assumptions and procedures adopted. Different test scenarios are considered with the purpose of performing a parametric study for quantifying the influence of the clearance size, input crank speed, and number of clearance joints on the dynamic response of multibody systems with multiple clearance joints. Additionally, the total computation time consumed in each simulation is evaluated in order to test the computational accuracy and efficiency of the presented approach. From the main results obtained in this study, it can be drawn that clearance size and the operating conditions play a crucial role in predicting accurately the dynamic responses of multibody systems.     

Control structure interaction in the nonlinear analysis of flexible mechanical systems

The effect of the control structure interaction on the feedforward control law as well as the dynamics of flexible mechanical systems is examined in this investigation. An inverse dynamics procedure is developed for the analysis of the dynamic motion of interconnected rigid and flexible bodies. This method is used to examine the effect of the elastic deformation on the driving forces in flexible mechanical systems. The driving forces are expressed in terms of the specified motion trajectories and the deformations of the elastic members. The system equations of motion are formulated using Lagrange's equation. A finite element discretization of the flexible bodies is used to define the deformation degrees of freedom. The algebraic constraint equations that describe the motion trajectories and joint constraints between adjacent bodies are adjoined to the system differential equations of motion using the vector of Lagrange multipliers. A unique displacement field is then identified by imposing an appropriate set of reference conditions. The effect of the nonlinear centrifugal and Coriolis forces that depend on the body displacements and velocities are taken into consideration. A direct numerical integration method coupled with a Newton-Raphson algorithm is used to solve the resulting nonlinear differential and algebraic equations of motion. The formulation obtained for the flexible mechanical system is compared with the rigid body dynamic formulation. The effect of the sampling time, number of vibration modes, the viscous damping, and the selection of the constrained modes are examined. The results presented in this numerical study demonstrate that the use of the driving forees obtained using the rigid body analysis can lead to a significant error when these forces are used as the feedforward control law for the flexible mechanical system. The analysis presented in this investigation differs significantly from previously published work in many ways. It includes the effect of the structural flexibility on the centrifugal and Coriolis forces, it accounts for all inertia nonlinearities resulting from the coupling between the rigid body and elastic displacements, it uses a precise definition of the equipollent systems of forces in flexible body dynamics, it demonstrates the use of general purpose multibody computer codes in the feedforward control of flexible mechanical systems, and it demonstrates numerically the effect of the selected set of constrained modes on the feedforward control law.     

Synchronization control for networked mobile robot systems based on Udwadia–Kalaba approach

This paper addresses the problem of synchronization control for networked multi-mobile robot systems from the perspective of analytical mechanics. By reformulating the task requirement as a constrained motion problem, a unified synchronization algorithm for networked multi-mobile robot systems with or without leaders is proposed in combination with algebraic graph theory and the Udwadia–Kalaba approach. With the proposed algorithm, the networked mobile robot system can achieve synchronization from arbitrary initial conditions for the leaderless case and realize accurate trajectory tracking with explicitly given reference trajectories for the leader-following case. Numerical simulations of a networked wheeled mobile robot system are performed under different network structures and various trajectory requirements to show the performance of the proposed control algorithm.

     

Computational dynamics: theory and applications of multibody systems

Multibody system dynamics is an essential part of computational dynamics a topic more generally dealing with kinematics and dynamics of rigid and flexible systems, finite elements methods, and numerical methods for synthesis, optimization and control including nonlinear dynamics approaches. The theoretical background of multibody dynamics is presented, the efficiency of recursive algorithms is shown, methods for dynamical analysis are summarized, and applications to vehicle dynamics and biomechanics are reported. In particular, the wear of railway wheels of high-speed trains and the metabolical cost of human locomotion is analyzed using multibody system methods.     

Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems

The dynamic modeling and analysis of planar rigid multibody systems that experience contact-impact events is presented and discussed throughout this work. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. Rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the forces and impulses in the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini??s condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb??s law for dry friction. The resulting contact-impact problem is formulated and solved as an augmented Lagrangian approach, which is embedded in the Moreau time-stepping method. The effectiveness of the methodologies presented in this work is demonstrated throughout the dynamic simulation of a cam-follower system of an industrial cutting file machine.     

柔性多体系统刚-柔耦合动力学

首先指出大量复杂系统动力学与控制性态分析与优化等工程问题对柔性多体系统动力学领域的进一步需求,在回顾柔性多体系统动力学研究的若干阶段与当前的研究现状后指出:柔性多体系统刚- 柔耦合动力学的研究是多体系统动力学的一个新的阶段．文末提出了刚- 柔耦合动力学的研究任务。      

动力刚化与多体系统刚—柔耦合动力学

首先指出当前柔性多体系统动力学的大量工程研究背景,在回顾柔性多体系统动力学研究进展后指出动力刚化的现象揭示了刚－柔耦合的零次建模方法的局限,认为进一步深入进行柔性多体系统刚－柔耦合动力学的研究是多体系统动力学研究的新阶段,文末提出了刚－柔耦合动力学的研究任务。     

具有奇异位置的多体系统动力学方程的隐式算法

本文研究了在运动过程中具有奇异位置的多体系统动力学方程的隐式算法，给出了隐式算法所用的Ｊａｃｏｂｉ矩阵，并建立了该矩阵中各子矩阵间的计算关系，提高了计算效率，计算结果表明隐式算法的计算速度和精度明显优于显式算法。     

基于李群局部标架的多柔体系统动力学建模与计算

多柔体系统动力学主要研究由多个具有运动学约束、存在大范围相对运动的柔性部件构成的动力学系统的建模、计算和控制.多柔体系统不仅具有柔体大变形导致的几何非线性,更具有大范围刚体运动引起的几何非线性,其非线性程度远高于计算结构力学所研究的几何非线性问题.本文基于李群局部标架(local frame of Lie group,...     

多体系统Lagrange方程数值算法的研究进展

Lagrange方法是建立多体系统动力学方程的普遍方法之一, 其方程的形式为常微分方程组或微分-代数方程组,数值计算与数 值分析是研究多体系统动力学特性的重要方法。本文简要介绍了多 体系统动 力学方程的第一、二类Lagrange方程和修正的Lagrange方 程的基本形式及这些方程的正则形式,着重介绍了正则方程在数值 计算中的特点,就多体系统Lagrange方程的隐式算法、辛算法和多 体系统动力学特性的数值分析方法(包括数值仿真、 Poincarè映射 和Lyapunov指数的计算方法)的研究现状进行了综述。     

柔性多体系统的递推组集建模与仿真软件的实现

简要地阐述多体系统动力学单向递推组集建模方法，介绍根据这种方法开发而成的仿真软件系统ＤＡＦＭＢ及它的功能与特点。通过双摆算例指出本文提出的模型在计算效率与计算精度方面优于笛卡尔坐标的微分－代数方程。     

车辆纵向非光滑多体动力学建模与数值算法研究

在建立车辆纵向多体系统的动力学模型中, 将车身与车轮视为刚体, 两者通过减振器链接; 将传动系统视为一个圆盘通过扭簧和阻尼器与驱动轮连接; 将车轮与路面间的接触力简化为法向约束力、摩擦力和滚阻力偶,其中摩擦力的模型采用库仑干摩擦模型. 采用笛卡尔坐标作为该系统的广义坐标用于描述该系统的位形, 给出系统单双边的约束方程, 应用第一类拉格朗日方法建立了系统的动力学方程. 由于摩擦与滚阻的非光滑性, 使得该系统动力学方程不连续. 为便于计算, 建立了车轮与路面接触点的相对切向加速度与摩擦力余量的互补条件、车轮角加速度与滚阻力偶余量的互补条件, 以及车轮轮心法向加速度与路面法向约束力的互补条件. 将接触—分离、黏滞—滑移的判断问题转化成线性互补问题的求解, 并给出了具有约束稳定化的基于事件驱动法的数值计算方法. 最后, 应用该方法对车辆纵向多体系统进行了仿真, 分析了输出扭矩、摩擦及滚阻系数对其动力学行为的影响.      

非光滑多体系统动力学数值算法的研究进展

非光滑多体系统动力学数值计算方法是多体系统动力学研究的重要内容之一. 本文介绍了近年来含摩擦与碰撞的非光滑多体系统动力学数值算法方面的研究进展. 首先, 讨论了库仑摩擦模型和修正的库仑摩擦模型, 以及具有单边和双边约束的多体系统中法向约束力的特点. 其次, 回顾了基于连续模型和非连续模型的多体系统动力学方程的数值计算方法, 详细介绍了基于互补概念的非光滑多体系统动力学的事件驱动法和时间步进法, 分析比较了相关的数值算法. 最后, 指出了一些需要进一步研究的问题.     

带约束多体系统动力学方程的隐式算法

研究了带约束多体系统隐式算法,用子矩阵的形式推导出了多体系统正则方程的Ｊａｃｏｂｉ矩阵,它适用于多种隐式算法并给出了隐式Ｒｕｎｇｅ－Ｋｕｔｔａ算法,最后用一算例表明了隐式算法的计算效率和精度明显优于算法。     

含分数阻尼特性元件的多体系统动力学研究

在绝对节点坐标体系下研究了具有分数导数阻尼特性元件的多体系统动力学建模、求解问题. 采用基于绝对节点坐标的无闭锁效应剪变梁单元离散柔性构件,建立了含常数质量矩阵的系统动力学方程, 并采用数值耗散可控的广义a方法求解. 通过数值算例计算,对比研究了算法参数与阻尼项的分数指数对系统动力学响应的影响规律.该方法可以进一步扩展到众多工程实际问题研究中.