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Flexible multibody dynamics : algorithms based on Kane's method
\"This book demonstrates how to formulate the equations of mechanical systems. Providing methods of analysis of complex mechanical systems, the book has a clear focus on efficiency, equipping the reader with knowledge of algorithms that provide accurate results in reduced simulation time. The book uses Kane's method due to its efficiency, and the simple resulting equations it produces in comparison to other methods and extends it with algorithms such as order-n. Kane's method compensates for the errors of premature linearization, which are often inherent within vibrations modes found in a great deal of public domain software. Describing how to build mathematical models of multibody systems with elastic components, the book applies this to systems such as construction cranes, trailers, helicopters, spacecraft, tethered satellites, and underwater vehicles. It also looks at topics such as vibration, rocket dynamics, simulation of beams, deflection, and matrix formulation. Flexible Multibody Dynamics will be of interest to students in mechanical engineering, aerospace engineering, applied mechanics and dynamics. It will also be of interest to industry professionals in aerospace engineering, mechanical engineering and construction engineering\"-- Provided by publisher.
Book
Multibody system transfer matrix method: The past, the present, and the future
The multibody system transfer matrix method (MSTMM), a novel dynamics approach developed during the past three decades, has several advantages compared to conventional dynamics methods. Some of these advantages include avoiding global dynamics equations with a system inertia matrix, utilizing low‐order matrices independent of system degree of freedom, high computational speed, and simplicity of computer implementation. MSTMM has been widely used in computer modeling, simulations, and performance evaluation of approximately 150 different complex mechanical systems. In this paper, the following aspects regarding MSTMM are reviewed: basic theory, algorithms, simulation and design software, and applications. Future research directions and generalization to more applications in various fields of science, technology, and engineering are discussed.
Journal Article
Nonlinear phenomena of contact in multibody systems dynamics: a review
In the present work, an introduction to the contact phenomena in multibody systems is made. The different existing approaches are described, together with their most distinctive features. Then, the term of coefficient of restitution is emphasized as a tool to characterize impact events and the algorithm for calculating the relative indentation between two convex-shaped bodies is developed. Subsequently, the main penalty contact models developed in the last decades are presented and developed, analysing their advantages and drawbacks, as well as their respective applications. Furthermore, some models with specific peculiarities that could be useful to the reader are included. The aim of this work is to provide a resource to the novice researcher in the field to facilitate the choice of the appropriate contact model for their work.
Journal Article
Transfer Matrix Method for Multibody Systems
TRANSFER MATRIX METHOD FOR MULTIBODY SYSTEMS: THEORY AND APPLICATIONS Xiaoting Rui, Guoping Wang and Jianshu Zhang - Nanjing University of Science and Technology, China Featuring a new method of multibody system dynamics, this book introduces the transfer matrix method systematically for the first time.
eBook
Reduced multibody system transfer matrix method using decoupled hinge equations
In the multibody system transfer matrix method (MSTMM), the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations. However, regarding the transfer matrices of hinge elements, typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t. various types of outboard body's output links. This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper. Systematic procedures for chain, tree, closed‐loop, and arbitrary general systems are defined, respectively, to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process. As a result, accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.
Journal Article
Transfer matrix method for multibody systems (Rui method) and its applications
The transfer matrix method for multibody systems, namely the “Rui method”, is a new method for studying multibody system dynamics, which avoids the global dynamics equations of the system, keeps high computational speed, and allows highly formalized programming. It has been widely applied to scientific research and key engineering of lots of complex mechanical systems in 52 research directions. The following aspects regarding the transfer matrix method for multibody systems are reviewed systematically in this paper: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, highlights, tendency, and applications in 52 research directions in over 100 key engineering products.
Journal Article
Efficiency comparison of various friction models of a hydraulic cylinder in the framework of multibody system dynamics
Dynamic simulation of mechanical systems can be performed using a multibody system dynamics approach. The approach allows to account systems of other physical nature, such as hydraulic actuators. In such systems, the nonlinearity and numerical stiffness introduced by the friction model of the hydraulic cylinders can be an important aspect to consider in the modeling because it can lead to poor computational efficiency. This paper couples various friction models of a hydraulic cylinder with the equations of motion of a hydraulically actuated multibody system in a monolithic framework. To this end, two static friction models, the Bengisu–Akay model and Brown–McPhee model, and two dynamic friction models, the LuGre model and modified LuGre model, are considered in this work. A hydraulically actuated four-bar mechanism is exemplified as a case study. The four modeling approaches are compared based on the work cycle, friction force, energy balance, and numerical efficiency. It is concluded that the Brown–McPhee approach is numerically the most efficient approach and it is well able to describe usual friction characteristics in dynamic simulation of hydraulically actuated multibody systems.
Journal Article
Dynamic topology optimization of flexible multibody systems
Flexible multibody system (FMBS) refers to a mechanical system, which consists of flexible components and kinematic pairs, and undergoes both overall motions and deformations. FMBS serves as a useful dynamic model for many advanced industrial products, such as flexible robots, helicopter rotors and deployable space antennas. Traditionally, the design of flexible components in an FMBS mainly relies on the trial-and-error method, which is time-consuming and cannot guarantee the best design. In addition, the optimization design of the flexible components in an FMBS usually uses a component-based approach without accounting for the interaction between a component to be optimized and the FMBS of concern. Yet, when a component gets more and more flexible, the interaction between the component and the FMBS plays a nonnegligible role in optimization and requires the FMBS-based optimization. This feature article presents the basic ideas and methods for the dynamic topology optimization of an FMBS mainly based on the studies of the authors over the past decade. The article focuses on four emerging topology optimization problems of an FMBS as follows, (i) topology optimization of dynamic responses and dynamic characteristics, (ii) fully coupled and weakly coupled optimizations, (iii) topology optimization of time-varying systems, and (iv) optimization designs and prototype tests of flexible robots. Together with concluding remarks, the article addresses some open problems of the dynamic topology optimization of an FMBS for future researches.
Journal Article
An interval uncertainty propagation method using polynomial chaos expansion and its application in complicated multibody dynamic systems
This paper is devoted to the construction of a nonintrusive interval uncertainty propagation approach for the response bounds evaluation of multibody systems. The motivation for this effort is twofold. First, the traditional methods using the Taylor inclusion function and interval arithmetic usually lead to the wrapping effect. Second, the real-life multibody dynamics models are mostly large systems, which are highly rigid, nonlinear, and discontinuous; however, many conventional, intrusive interval analysis methods are not suitable for such large, complicated multibody systems. To end these, a polynomial chaos inclusion function using Legendre orthogonal basis is presented for analyzing such multibody dynamics models with interval uncertainty, where the Galerkin projection method is adopted to compute the Legendre polynomial coefficients. The capacity of the Legendre polynomial inclusion function to alleviate the wrapping effect is proved by a mathematical example. Through sampling, the nonintrusive algorithm expresses the original multibody dynamics system with interval uncertainty as the deterministic differential algebraic equations, followed by calculation using the general numerical integration method. The response bounds at each time step are predicted using the truncated Legendre polynomial expansion. A benchmark test based on three methods is analyzed to demonstrate the effectiveness of this approach. Moreover, an artillery multibody dynamics model created in ADAMS/Solver can reproduce a suite of experimental results, and is then specifically investigated to illustrate the superiority of this method in large, complicated multibody dynamic systems.
Journal Article
Hybrid multibody system method for the dynamic analysis of an ultra‐precision fly‐cutting machine tool
The dynamics of an ultra‐precision machine tool determines the precision of the machined surface. This study aims to propose an effective method to model and analyze the dynamics of an ultra‐precision fly‐cutting machine tool. First, the dynamic model of the machine tool considering the deformations of the cutter head and the lathe head is developed. Then, the mechanical elements are classified into M subsystems and F subsystems according to their properties and connections. The M‐subsystem equations are formulated using the transfer matrix method for multibody systems (MSTMM), and the F‐subsystem equations are analyzed using the finite element method and the Craig–Bampton reduction method. Furthermore, all the subsystems are assembled by combining the restriction equations at connection points among the subsystems to obtain the overall transfer equation of the machine tool system. Finally, the vibration characteristics of the machine tool are evaluated numerically and are validated experimentally. The proposed modeling and analysis method preserves the advantages of the MSTMM, such as high computational efficiency, low computational load, systematic reduction of the overall transfer equation, and generalization of its computational capability to general flexible‐body elements. In addition, this study provides theoretical insights and guidance for the design of ultra‐precision machine tools.
Journal Article