Optimal Design of Lightweight Machines Using Flexible Multibody System Dynamics

2012 ◽  
Author(s):  
Robert Seifried ◽  
Alexander Held
Keyword(s):  
Energy Efficiency ◽  
Multibody Systems ◽  
Multibody System ◽  
Tracking Error ◽  
Dynamic Loads ◽  
Crucial Issue ◽  
Flexible Multibody ◽  
Dynamical Simulations ◽  
Tracking Behavior ◽  
Robotic Applications

In many machine and robotic applications energy efficiency is an increasingly crucial issue. In order to achieve energy efficiency lightweight structural designs are necessary. However, undesired elastic deformations might occur due to the light wight design. In order to achieve good system performance the actual dynamic loads must be taken into account in the design of the system’s components. In this paper optimization approaches for lightweight machine designs are employed to improve the tracking behavior the systems. Thereby, fully dynamical simulations of flexible multibody systems are coupled with both shape or topology optimization for the elastic members of the multibody system. It is shown, that by these approaches the end-effector trajectory tracking error of light wight manipulators can be decreased significantly.

Modeling of Revolute Joints in Topology Optimization of Flexible Multibody Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Ali Moghadasi ◽  
Alexander Held ◽  
Robert Seifried
Keyword(s):  
Topology Optimization ◽  
Multibody Systems ◽  
Multibody System ◽  
Order Reduction ◽  
Flexible Multibody Systems ◽  
Hertzian Contact ◽  
Revolute Joints ◽  
Nonlinear Finite Elements ◽  
Flexible Multibody ◽  
Hertzian Contact Law

In recent years, topology optimization has been used for optimizing members of flexible multibody systems to enhance their performance. Here, an extension to existing topology optimization schemes for flexible multibody systems is presented in which a more accurate model of revolute joints and bearing domains is included. This extension is of special interest since a connection between flexible members in a multibody system using revolute joints is seen in many applications. Moreover, the modeling accuracy of the bearing area is shown to be influential on the shape of the optimized structure. In this work, the flexible bodies are incorporated in the multibody simulation using the floating frame of reference formulation, and their elastic deformation is approximated using global shape functions calculated in the model order reduction analysis. The modeling of revolute joints using Hertzian contact law is incorporated in this framework by introducing a corrector load in the bearing model. Furthermore, an application example of a flexible multibody system with revolute joints is optimized for minimum value of compliance, and a comparative study of the optimization result is performed with an equivalent system which is modeled with nonlinear finite elements.

Approximate End-Effector Tracking Control of Flexible Multibody Systems Using Singular Perturbations

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Thomas Gorius ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Tracking Control ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Feedforward Control ◽  
Flexible Multibody Systems ◽  
Flexible Manipulator ◽  
End Effector ◽  
Nonminimum Phase ◽  
Flexible Multibody

In many cases, the design of a tracking controller can be significantly simplified by the use of a 2-degrees of freedom (DOF) control structure, including a feedforward control (i.e., the inversion of the nominal system dynamics). Unfortunately, the computation of this feedforward control is not easy if the system is nonminimum-phase. Important examples of such systems are flexible multibody systems, such as lightweight manipulators. There are several approaches to the numerical computation of the exact inversion of a flexible multibody system. In this paper, the singularly perturbed form of such mechanical systems is used to give a semianalytic solution to the tracking control design. The control makes the end-effector to even though not exactly, but approximately track a certain trajectory. Thereby, the control signal is computed as a series expansion in terms of an overall flexibility of the bodies of the multibody system. Due to the use of symbolic computations, the main calculations are independent of given parameters (e.g., the desired trajectories), such that the feedforward control can be calculated online. The effectiveness of this approach is shown by the simulation of a two-link flexible manipulator.

Aspects of Symbolic Formulations in Flexible Multibody Systems

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Markus Burkhardt ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Fem Model ◽  
Local Shape ◽  
Flexible Bodies ◽  
Elastic Bodies ◽  
Flexible Multibody

The symbolic modeling of flexible multibody systems is a challenging task. This is especially the case for complex-shaped elastic bodies, which are described by a numerical model, e.g., an FEM model. The kinematic and dynamic properties of the flexible body are in this case numerical and the elastic deformations are described with a certain number of local shape functions, which results in a large amount of data that have to be handled. Both attributes do not suggest the usage of symbolic tools to model a flexible multibody system. Nevertheless, there are several symbolic multibody codes that can treat flexible multibody systems in a very efficient way. In this paper, we present some of the modifications of the symbolic research code Neweul-M2 which are needed to support flexible bodies. On the basis of these modifications, the mentioned restrictions due to the numerical flexible bodies can be eliminated. Furthermore, it is possible to re-establish the symbolic character of the created equations of motion even in the presence of these solely numerical flexible bodies.

A Recursive Algorithm for Solving the Generalized Velocities From the Momenta of Flexible Multibody Systems

2008 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Numerical Solution ◽  
Multibody Systems ◽  
Multibody System ◽  
Recursive Algorithm ◽  
Mass Matrix ◽  
Direct Methods ◽  
Flexible Multibody Systems ◽  
Hamiltonian Form ◽  
Generalized Coordinates ◽  
Flexible Multibody

The computation of the generalized velocities from the generalized momenta of a multibody system is a part of the numerical solution of the dynamics equations when they are given in the Hamiltonian form. The states of these equations are the generalized coordinates and momenta, (q, p). The generalized velocity, q˙, is defined by q˙ = J−1p, where J is the system mass matrix. The effort in solving q˙ by direct methods is order(N3) where N is the number of bodies in the system. This paper presents an order(N) recursive algorithm to compute q˙ for flexible multibody systems.

Monte Carlo Simulation of Flexible Multibody System with Uncertainties

2011 ◽  
Vol 55-57 ◽  
pp. 1382-1385
Author(s):  
Ting Pi ◽  
Yun Qing Zhang
Keyword(s):  
Monte Carlo ◽  
Multibody Systems ◽  
Multibody System ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Flexible Multibody System ◽  
System Behavior ◽  
Flexible Multibody ◽  
And Performance ◽  
Crank Mechanism

Practical mechanical systems often contain several flexible components and uncertain parameters which makes it hard to predict the system behavior and performance exactly. This research presents the uncertainty analysis of flexible multibody systems with random variables. Absolute nodal coordinate formulation (ANCF), which is different from the traditional finite element method, is employed to model the flexibility here. Monte Carlo method is successfully used to simulate flexible multibody systems of index-3. The method proposed is demonstrated by an example of flexible slider-crank mechanism.

Formulation of Three-Dimensional Rigid-Flexible Multibody Systems

2007 ◽  
Author(s):  
Daniel Garci´a-Vallejo ◽  
Jose´ L. Escalona ◽  
Juana M. Mayo ◽  
Jaime Domi´nguez
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Three Dimensional ◽  
Natural Coordinates ◽  
Flexible Multibody System ◽  
Absolute Nodal Coordinates ◽  
Constraint Equations ◽  
Flexible Multibody ◽  
The Matrix ◽  
Nodal Coordinates

Multibody systems generally contain solids the deformations of which are appreciable and which decisively influence the dynamics of the system. These solids have to be modeled by means of special formulations for flexible solids. At the same time, other solids are of such a high stiffness that they may be considered rigid, which simplifies their modeling. For these reasons, for a rigid-flexible multibody system, two types of formulations co-exist in the equations of the system. Among the different possibilities provided in bibliography on the material, the formulation in natural coordinates and the formulation in absolute nodal coordinates are utilized in this article to model the rigid and flexible solids, respectively. This article contains a mixed formulation based on the possibility of sharing coordinates between a rigid solid and a flexible solid. In addition, the fact that the matrix of the global mass of the system is shown to be constant and that many of the constraint equations obtained upon utilizing these formulations are linear and can be eliminated. In this work, the formulation presented is utilized to simulate a mechanism with both rigid and flexible components.

scholarly journals Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

2019 ◽  
Vol 9 (23) ◽  
pp. 5156 ◽  
Author(s):  
Ilaria Palomba ◽  
Renato Vidoni
Keyword(s):  
Eigenvalue Problem ◽  
Motion Planning ◽  
Modal Analysis ◽  
Multibody Systems ◽  
Multibody System ◽  
Differential Algebraic Equations ◽  
Flexible Multibody Systems ◽  
System Configuration ◽  
Modal Characteristics ◽  
Flexible Multibody

The dynamics of flexible multibody systems (FMBSs) is governed by ordinary differential equations or differential-algebraic equations, depending on the modeling approach chosen. In both the cases, the resulting models are highly nonlinear. Thus, they are not directly suitable for the application of the modal analysis and the development of modal models, which are very useful for several advanced engineering techniques (e.g., motion planning, control, and stability analysis of flexible multibody systems). To define and solve an eigenvalue problem for FMBSs, the system dynamics has to be linearized about a selected configuration. However, as modal parameters vary nonlinearly with the system configuration, they should be recomputed for each change of the operating point. This procedure is computationally demanding. Additionally, it does not provide any numerical or analytical correlation between the eigenpairs computed in the different operating points. This paper discusses a parametric modal analysis approach for FMBSs, which allows to derive an analytical polynomial expression for the eigenpairs as function of the system configuration, by solving a single eigenvalue problem and using only matrix operations. The availability of a similar modal model, which explicitly depends on the system configuration, can be very helpful for, e.g., model-based motion planning and control strategies towards to zero residual vibration employing the system modal characteristics. Moreover, it allows for an easy sensitivity analysis of modal characteristics to parameter uncertainties. After the theoretical development, the method is applied and validated on a flexible multibody system, specifically using the Equivalent Rigid Link System dynamic formulation. Finally, numerical results are presented and discussed.

Active vibration control of spatial flexible multibody systems

2013 ◽  
Vol 30 (1) ◽  
pp. 13-35 ◽  
Author(s):  
Maria Augusta Neto ◽  
Jorge A. C. Ambrósio ◽  
Luis M. Roseiro ◽  
A. Amaro ◽  
C. M. A. Vasques
Keyword(s):  
Vibration Control ◽  
Multibody Systems ◽  
Active Vibration Control ◽  
Flexible Multibody Systems ◽  
Flexible Multibody ◽  
Active Vibration

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

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