A modular formulation for flexible multibody systems including nonlinear finite elements

A formulation for flexible multibody systems (MBS) is investigated, where rigid MBS substructures are coupled with flexible bodies described by a nonlinear finite element (FE) appioach Several aspects that turned out to be crucial for the presented approach are discussed The system describing equations are given in differential algebraic form (DAE), where many sophisticated solvers exist In this paper the performance of several solvers is investigated regarding then suitability for the application to the usually highly stiff DAE The substructures are connected with each other by nonlinear algebraic constraint equations Furthet, partial derivatives of the constraints are tequired, which often leads, to extensive algebraic transfoimations Handcoding of analytically determined derivatives is compared to an appioach utilizing algouthmic differentiation

     

Synthetic analysis of flexible multibody system including a very flexible body

The progress in developing a dynamic analysis solver has different aspects of improvement in the sense of simulating the behavior of the parts. Among them, dynamics in flexible body and large deformable body have been an issue in recent decades. A modal coordinate formulation has been developed and used for analyzing the flexible body dynamics with a commercial dynamic solver, like in ADAMS. Flexible body dynamics using modal coordinates are reliable when the system’s deflection is relatively small, and generally its accuracy depends on how many relevant modes are used for the system. Conversely, to simulate the behavior of the large deflected body, absolute nodal coordinate formulation is derived and developed. The theory presents the mixed equations of motion, which consider both the absolute nodal coordinates and absolute cartesian orientation coordinates to simulate the large deflection. Its reliability is proved by many researches and experimental data. In this study, a dynamic solver which can handle the flexible bodies is developed. Three kinds of bodies, rigid, flexible and large deformable body, can be simulated. Its validity is verified by comparison with a commercial analysis program. For further studies, the constraints and force elements between different coordinates will be developed. Solving efficiency would be another major concern to be improved. This paper was presented at the 4th Asian Conference on Multibody Dynamics(ACMD2008), Jeju, Korea, August 20–23, 2008. Ji Won Yoon received B.S. and M.S. degrees in Mechanical Engineering from Ajou University in 2004 and 2006, respectively. Mr. Yoon is currently a Ph.D student at the School of Mechanical Engineering at Ajou University in Suwon, Korea. He is serving as an instructor for undergraduate students. Mr. Yoon’s research interests are in the area of multibody dynamics, flexible body dynamics, and fatigue analysis.     

Thermal analysis of viscoelastic multibody systems

Thermal analysis of the transient motion of a multibody system, consisting of interconnected rigid, elastic, and viscoelastic components is presented. The configuration of each elastic or viscoelastic body is identified using three sets of modes, rigid-body, reference and normal modes. Rigid-body modes describe translations and large rotations of the body reference. The finite element method is employed to describe body deformations, and reference conditions are imposed in order to define a unique displacement field. Accordingly, normal modes of vibrations of flexible components can be used to reduce the number of elastic coordinates, thus eliminating high-frequency modes of vibration. The system equations of motion are formulated using Lagrange's equation, and nonlinear algebraic equations, describing constraints between adjacent bodies, are coupled to the equations of motion using a Lagrange multiplier technique.     

柔性多体系统动力学理论应用于轧制工业的综述

结合轧制工业的发展现状及柔性多体系统动力学的理论成果,从轧机设备的设计、改造、过程控制、系统特性、接触-碰撞问题的建模、轧制过程中多领域集成化、多体动力学软件的发展等几个方面阐述了将柔性多体系统动力学理论应用于轧制工业的可行性和必要性.     

A study on numerical solution method for efficient dynamic analysis of constrained multibody systems

A new and efficient computational method for constrained multibody systems is proposed. In the proposed method, local parametrization method is employed to apply the same solution method for position, velocity, and acceleration analyses since the coefficient matrices for each analysis have an identical matrix pattern. The skyline solution method is used to overcome numerical inefficiency when solving large scaled equations. Also, subsystem mpartitioning method is derived systematically to perform parallel processing for real time simulation. To show the numerical accuracy and efficiency of the proposed method, three numerical problems are solved.     

A model for the minimum cost configuration problem in flexible manufacturing systems

This paper presents a mathematical programming model to help select equipment for a flexible manufacturing system, i.e., the selection of the types and numbers of CNC machines, washing stations, load/unload stations, transportation vehicles, and pallets. The objective is to minimize equipment costs and work-in-process inventory cost, while fulfilling production requirements for an average period. Queueing aspects and part flow interactions are considered with the help of a Jacksonian-type closed queueing network model in order to evaluate the system's performance. Since the related decision problem of our model can be shown to be NP-complete, the proposed solution procedure is based on implicit enumeration. Four bounds are provided, two lower and two upper bounds. A tight lower bound is obtained by linearizing the model through the application of asymptotic bound analysis. Furthermore, asymptotic bound analysis allows the calculation of a lower bound for the number of pallets in the system. The first upper bound is given by the best feasible solution and the second is based on the anti-starshaped form of the throughput function.     

Sensitivity analysis for estimation of inertial parameters of multibody mechanical systems

As an important issue, we first address in this paper the problem of a regression matrix with non-homogeneous physical units in the parameter estimation of multibody systems. This matrix contains the most important information about the motion of the system. Attention must be paid to this before implementing any parameter estimation algorithm due to the unit inconsistency in matrix multiplication required in such algorithms. A procedure to treat this problem in a proper way will be proposed. An experiment on a six degrees of freedom (DOF) robotic device, whose reference link follows a desired trajectory, is performed. The data collected from the experiment are then used for sensitivity analysis of inertial parameters based on the unit-homogenized regression matrix of the system. In this way, we characterize the influence of each selected inertial parameter on the dynamics of the system using unit-consistent mathematical manipulations.     

适用于程序化建模的风力机混合多体模型研究

研究运用混合多体动力学方法建立风力机柔性叶片的动力学模型。将柔性叶片离散为由带有力元弹簧和阻尼器的有限个超级单元（superelement）;通过约旦变分原理,导出了叶片多体系统的动力学代数一微分方程。计算了一个1．5兆瓦风力机叶片的动力特性和弯曲挠度响应,研究了超级单元的数量对计算结果的影响。算例分析表明,混合多体动力学建模方法能较好地分析和描述柔性叶片弹性变形对其运动特性的影响,为风力机气动弹性稳定性分析和控制系统设计提供了实用的建模和分析方法。     

Non-linear flexible body analysis for mechanical systems

Component mode synthesis method considers only small deformation problems and cannot handle large deformation problems. This paper presents an improved mode synthesis method. Mild geometric nonlinear problems have been solved by considering nonlinear effects in the stiffness matrix.     

On the improvement of a fully recursive formulation for the dynamic analysis of multibody systems

Virtual work in multibody systems is frequently expressed as the inner product of the virtual displacement and the resultant force at the centroid. But provided that the resultant force is converted into the equipollent forces there is no restriction on where the analysis reference point is placed. There are basically three candidate points : the centroid, joint point and the instant global origin. The traditional fully recursive formulation uses the centroid, but the present work verifies that the instant global origin always shows better efficiency (e.g. 86% CPU time of the centroid for quarter car model) and joint point shows the efficiency between that of the centroid and the instant global origin. A discussion on how important it is to define the analysis reference point properly in a fully recursive formulation is also presented.     

The analysis of flexible manufacturing systems for reliability

Flexible manufacturing systems (FMS) constitute a considerable capital investment which must be fully utilised by uninterrupted production. The analysis of reliability at planning and development stages in the implementation of FMS is essential, since it can change both the system design and the operating philosophy to give improvements in the overall system performance. The main objective of this paper is to propose a technique for assessing the reliability of flexible manufacturing systems and further to discuss the unsuitability of the traditional reliability techniques in the study of such systems. It is shown that simulation studies in thereliability of flexible manufacturing can be applied in the analysis of alternative approaches to system design. The key terms, ‘Manufacturing Capability’, ‘Production Efficiency’ and ‘Demanded Production Lead Time Success Ratio’ are introduced as measures which can assess a system's performance. A typical flexible manufacturing cell is then analysed for reliability using predicted reliability data. The effect of equipment redundancy, buffer stock size and production priority rules on the cells performance are finally discussed.     

A high efficient frequency analysis method for closed flexible mechanism systems

Frequency analysis is an important step to predict the dynamic performance of flexible mechanisms. According to the characteristics of the closed flexible mechanisms, an efficient frequency analysis method for planar multi-bar and spatial linkage mechanisms by utilizing free-interface substructure coupling technique, substructure division and the modal basis generation method are presented. Coupling equations for typical substructures are developed. Examples show that the analysis method presented in this paper is effective.     

Fatigue analysis of the main frame of over head transportation vehicles using flexible multibody dynamics

The industrial over head transportation vehicle is a guided railway vehicle that is attached overhead and transports cargo, hoisting it up and down from the factory ceiling. The vehicle is widely used in many industries, such as automobile and liquid crystal display (LCD), because it can carry freight very safely and quickly to destinations. This kind of freight transportation usually operates for several months to a few years, carrying large amounts of products. Accidently, the vehicle often fails during operation because of a part’s plastic deformation from large loads. Furthermore, periodic dynamic loads cause fatigue accumulation, which leads to OHT failure. This failure is directly connected to significant economic loss during mass production processes. Therefore, the prediction of fatigue life for the important parts becomes an important task. In this study, the fatigue life of an OHT main frame was calculated and predicted by using a flexible multibody dynamic model. The development of a flexible multibody dynamic model and the procedure of fatigue life prediction were presented. To predict the fatigue lives of parts of interest, the prediction procedure required three kinds of data: Dynamic stress time history from a dynamic analysis, material properties of the parts, and stress-life curves of the parts. Using a finite element model and a multibody model, a flexible multibody model was developed. To ensure the reliability of the model, displacement and strain measurement tests were conducted. After verification of the reliability, the fatigue life of the main frame was predicted.     

Modal analysis of constrained multibody systems undergoing constant accelerated motions

The modal characteristics of constrained multibody systems undergoing constant accelerated motions are investigated in this paper. Relative coordinates are employed to derive the equations of motion, which are generally nonlinear in terms of the coordinates. The dynamic equilibrium position of a constrained multibody system needs to be obtained from the nonlinear equations of motion, which are then linearized at the dynamic equilibrium position. The mass and the stiffness matrices for the modal analysis can be obtained from the linearized equations of motion. To verify the effectiveness and the accuracy of the proposed method, two numerical examples are solved and the results obtained by using the proposed method are compared with those obtained by analytical and other numerical methods. The proposed method is found to be accurate as well as effective in predicting the modal characteristics of constrained multibody systems undergoing constant accelerated motions.     

多刚体系统运动学分析的自然坐标法及在悬架运动学分析中的应用

本文介绍了一种适用于计算机分析的多刚体系统运动学分析的自然坐标法。利用自然坐标描述多刚体系统时,只需要一些点和一些单位向量,刚体的约束方程和运动副的约束方程组成了多刚体系统的运动学约束方程。约束方程均为线性或二次方程,因此求解方便。文中利用该方法分析了Maepherson悬架的轮胎横向滑移量、主倾内倾角等与车轮上、下跳动距离的关系。     

Reliability analysis of flexible manufacturing systems

High productivity is the primary goal of flexible manufacturing systems (FMSs) in which semi-independent workstations are integrated using automated material-transport systems and hierarchical local networks. Availability of various subsystems and of the system as a whole is a prerequisite for achieving functional integration as well as high throughput. An FMS also has inherent routing and operation flexibilities that provide it with a certain degree of fault tolerance. A certain volume of production can thus be maintained in the face of subsystem (i.e., machines, robots, material handling system, etc.) failures. In this article, we propose two reliability measures, namely, part reliability (PR) and FMS reliability (FMSR) for manufacturing systems and present algorithms to evaluate them. We also consider the dynamic or time-dependent reliability analysis as a natural generalization of the static analysis. The methods outlined use an algorithm that generates process-spanning graphs (PSGs), which are used to evaluate the reliability measures.     

Sensitivity analysis approach to multibody systems described by natural coordinates

The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.     

Performance analysis of flexible material handling systems for the apparel industry

Flexible material handling systems (FMHS) have been widely used to enhance productivity involved with product proliferation, and thus far, only fixed-track material handling systems such as Eton systems in the apparel industry are commonly used. This paper explores the potential advantages of a FMHS using free-ranging automated-guided vehicles with a local positioning system for the apparel industry. First, the free-ranging FMHS (FRMHS) for the apparel industry has been designed. Then, through Monte Carlo simulation and analytical models, the performance in terms of manufacturing system effectiveness, workstation utilization, and the total transportation distance of the FRMHS are compared with those of the fixed-track system. Based on our analysis, the current proposed FRMHS can have significant advantages over the fixed-track system.     

A decision-making framework model for evaluating flexible manufacturing systems using digraph and matrix methods

In the present work, a methodology based on digraph and matrix methods is developed for evaluation of alternative flexible manufacturing systems. A ‘flexible manufacturing system selection index’ is proposed that evaluates and ranks flexible manufacturing systems for a given industrial application. The methodology is illustrated by an example.