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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
Matrix Methods in the Design Analysis of Mechanisms and Multibody Systems
This book is an integrated approach to kinematic and dynamic analysis. The matrix techniques presented are general and fully applicable to two- or three-dimensional systems. They lend themselves to programming and digital computation and can act as the basis of a usable tool for designers. Techniques have broad applicability to the design analysis of all multibody mechanical systems. The more powerful and more flexible the approach, and the less specialisation and reprogramming required for each application, the better. The matrix methods presented have been developed using these ideas as primary goals. Matrix methods can be applied by hand to such problems as the slider-crank mechanism, but this is not the intent of this text, and often the rigor required for such an attempt becomes quite burdensome in comparison with other techniques. The matrix methods have been extensively tested, both in the classroom and in the world of engineering industry.
eBook
Flexible Multibody Dynamics
Arun K. Banerjee is one of the foremost experts in the world on the subject of flexible multibody dynamics. This book describes how to build mathermatical models of multibody systems with elastic components. Examples of such systems include the human body itself, construction cranes, cares with trailers, helicopers, spacecraft deploying antennas, tethered satellites, and underwater maneuvering vehicles. This book provides methods of analysis of complex mechanical systems that can be simulated in less computer time than other methods. It equips the reader with knowledge of algorithms that provide accurate results in reduced simulation time.
eBook
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
A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems
This study is aimed at examining and comparing several friction force models dealing with different friction phenomena in the context of multibody system dynamics. For this purpose, a comprehensive review of present literature in this field of investigation is first presented. In this process, the main aspects related to friction are discussed, with particular emphasis on the pure dry sliding friction, stick–slip effect, viscous friction and Stribeck effect. In a simple and general way, the friction force models can be classified into two main groups, namely the static friction approaches and the dynamic friction models. The former group mainly describes the steady-state behavior of friction force, while the latter allows capturing more properties by using extra state variables. In the present study, a total of 21 different friction force models are described and their fundamental physical and computational characteristics are discussed and compared in details. The application of those friction models in multibody system dynamic modeling and simulation is then investigated. Two multibody mechanical systems are utilized as demonstrative application examples with the purpose of illustrating the influence of the various frictional approaches on the dynamic response of the systems. From the results obtained, it can be stated that both the choice of the friction force model and friction parameters involved can significantly affect the simulated/modeled dynamic response of mechanical systems with friction.
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
Theoretical modeling and numerical solution methods for flexible multibody system dynamics
Flexible multibody system dynamics (MSD) is one of the hot spots and difficulties in modern mechanics. It provides a powerful theoretical tool and technical support for dynamic performance evaluation and optimization design of a large number of complex systems in many engineering fields, such as machinery, aviation, aerospace, weapon, robot and biological engineering. How to find an efficient accurate dynamics modeling method and its stable reliable numerical solving algorithm are the two core problems of flexible MSD. In this paper, the research status of modeling methods of flexible MSD in recent years is summarized first, including the selection of reference frames, the flexible body’s kinematics descriptions, the deductions of dynamics equation, the model reduction techniques and the modeling methods of the contact/collision, uncertainty and multi-field coupling problems. Then, numerical solution technologies and their latest developments of flexible MSD are discussed in detail. Finally, the future research directions of modeling and numerical computation of flexible MSD are briefly prospected.
Journal Article
A new numerical method for the tribo-dynamic analysis of cylindrical roller bearings
This paper proposes a new numerical method for the tribo-dynamic analysis of the CRB by coupling the roller–raceway mixed EHL model and the motion equations of the CRB multibody system. The mixed EHL model is established by an implicit solution of the empirical EHL film thickness expression and Greenwood–Tripp asperity contact formula. The CRB motion equations are derived using Lagrange multibody dynamics methodology. The proposed model improves the previous CRB dynamics models by considering the roller–raceway mixed EHL contact. Based on this model, the tribo-dynamic characteristics of CRB system and the effects of radial load, rotation speed and lubricant viscosity are analyzed. The results show that the asperity interaction accounts for 90% of the friction but a small fraction of the total contact force. The roller-inner raceway friction causes the inner ring to move horizontally, leading to a saw-like fluctuation of the contact forces within the contact zone. Moreover, a higher radial load leads to a smaller vertical motion amplitude of the inner ring. The asperity contact force shows a nonlinear decrease as the rotation speed and lubricant viscosity increase. In addition, the high rotation speed tends more to cause skidding (more than 4%). This model provides a new option for the tribo-dynamic simulations of the CRB system.
Journal Article
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.
Journal Article
Model reduction for constrained mechanical systems via spectral submanifolds
Dynamical systems are often subject to algebraic constraints in conjunction with their governing ordinary differential equations. In particular, multibody systems are commonly subject to configuration constraints that define kinematic compatibility between the motion of different bodies. A full-scale numerical simulation of such constrained problems is challenging, making reduced-order models (ROMs) of paramount importance. In this work, we show how to use spectral submanifolds (SSMs) to construct rigorous ROMs for mechanical systems with configuration constraints. These SSM-based ROMs enable the direct extraction of backbone curves and forced response curves and facilitate efficient bifurcation analysis. We demonstrate the effectiveness of this SSM-based reduction procedure on several examples of varying complexity, including nonlinear finite-element models of multibody systems. We also provide an open-source implementation of the proposed method that also contains all details of our numerical examples.
Journal Article