Rotationless formulation for large deformations in flexible multibody dynamics

Especially for specific applications, such as contact problems, computer methods for flexible multibody dynamics that are able to treat large deformation phenomena are important. Classical formalisms for multibody dynamics are based on rigid bodies. Their extension to flexible multibody systems is typically restricted to linear elastic material behavior whereas large deformation phenomena are formulated in the framework of the nonlinear finite element method. In the talk we address computer methods that can handle large deformations in the context of multibody systems. In particular, the link between nonlinear continuum mechanics and multibody systems is facilitated by a specific formulation of rigid body dynamics [1]. It makes possible the incorporation of state-of-the-art computer methods for large deformation problems. In the talk we focus on the treatment of large deformation contact whithin flexible multibody dynamics [2]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology Optimization of Members of Elastic Multibody Systems

Lightweight techniques are applied increasingly often for modern machine designs in order to reduce the moving masses and therewith the energy consumption. However, as a result the stiffness of the system decreases causing undesired elastic deformations and therewith end-effector deviations. In this work a topology optimization procedure for elastic multibody systems based on the solid isotropic material with penalization approach is presented to lower end-effector tracking errors. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation and feed-forward control of a flexible parallel manipulator

The importance of lightweight constructions are steady increasing since they promise a low energy consumption together with higher movement speeds. However these demand modern, model-based feed-forward control designs. Especially the undesired vibrations due to the reduced overall stiffness of such manipulators have to be taken into account. A convenient way to model the dynamical behavior of systems that perform large, nonlinear motions superposed with small, elastic deformations is the floating frame of reference approach in a flexible multibody system. The application of the Newton-Euler-Formalism together with D'Alembert's principle to parallel manipulators results in a set of differential-algebraic equations. Therefore, the consideration of the trajectory tracking problem with so-called servo constraints appears to be promising. In case of a non-flat system, the arising set of differential-algebraic equations, which consists of the system dynamics, the holonomic loop closing constraint equations and the servo constraints embodies nontrivial dynamics. With an oblique projection, the embedded set of ordinary differential equations describing the internal dynamics can be obtained. The stability properties of these dynamics determines the complexity of the feed-forward control design, as two-point boundary value problems might have to be solved. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contact Modeling in Multibody Systems with Elastic Bodies in High-Frequency Applications

This paper discusses the refinement of multibody models by integration of flexible bodies and by considering nonlinearities from contacts. It presents common approaches for contact modeling in multibody simulations and strategies to include flexible bodies. A contact model is implemented in the elastic multibody model. Experimental results show that significant effects of system dynamics can be modeled by use of a multibody model including elastic bodies and contacts. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Various Feedforward Schemes and a Passivity Based Backstepping Feedback Control of an Elastic Robot

Lightweight constructions in industry plants lead to elastic deflections causing vibrations and a loss in tracking precision. In order to keep the tracking error for these elastic multibody systems low, the proposed control strategies are combinations of feedforward and feedback schemes. In this work various implemented strategies for computing a feedforward control are proposed and compared, which can be calculated with some simplifications from the mathematical model of the elastic multibody system. Some of these are considering the elastic deflections. The stabilization of the error dynamics is achieved by a simple PD-joint control or passivity based backstepping. In this algorithm the system is split into subsystems and for these subsystems simple control concepts can be applied. The feedback control law of the total system is obtained by means of backstepping theory, considering the internal energy flows in the system. Experimental results are presented to verify the control strategies. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of model reduction techniques on the impact force calculation of two flexible bodies

One important issue for the simulation of flexible multibody systems is the reduction of the flexible body's degrees of freedom. For the reduction process finite element data and user inputs are necessary. The model reduction program for elastic multibody systems MOREMBS, which is developed at the ITM, has an easy-to-use interface and the data can be gained from the programs ABAQUS or ANSYS. In this work, the simulation of a fuel injection process is investigated with MOREMBS. We focus on the interaction between valve and armature. These two bodies impact in every injection circle. The impacting bodies are modeled as flexible and the contact force is calculated by a penalty approach. One essential part of this work is the investigation of the influence of different model reduction techniques on the impact force calculation of the flexible multibody system. The main reduction techniques modal reduction, Krylov-subspace based and Gramian matrix based techniques are compared. The results achieved with modal reduction, the state of the art reduction method, are not acceptable here. Krylov-subspace based techniques are especially well-suited for large sparse systems but are not error controlled. However, by choosing appropriate moment-matching properties the impact force calculation is nearly as good as with a full finite element model. The Gramian matrix based reduction techniques can be fully automated and are error controlled but require high computational effort. Hence, appropriate approximation schemes have to be used for them. With Gramian matrix based methods we can even further reduce the size of the subsystems compared to Krylov-subspace based methods and still have an impact force calculation nearly as good as with finite element results, but we gain a simulation speedup by the factor 4000. In addition, a parameter study of the parameters involved in the model reduction process is presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Approach to Feed-Forward Controller Design for Underactuated Multibody Systems in the Presence of Uncertainty

The performance of a model-based tracking controller depends on the quality of the underlying model. Especially for flexible multibody systems, the derivation of a suitable model and the subsequent controller design are challenging tasks. In the paper, it is shown how in a straightforward approach a feed-forward controller for a flexible multibody system is designed based on a simplified model which approximates an elastic beam by a combination of rigid beams and force elements. Furthermore, the modelling error due to this harsh simplification is included as uncertainty in the simplified model and considered in the model-based feed-forward controller design using fuzzy arithmetic. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics of variable-length tethers with application to tethered satellite deployment

The dynamics of variable-length tethers are studied using a flexible multibody dynamics method. The governing equations of the tethers are derived using a new, hybrid Eulerian and Lagrangian framework, by which the mass flow at a boundary of a tether and the length variation of a tether element are accounted for. The variable-length tether element based on the absolute nodal coordinate formulation is developed to simulate the deployment of satellite tethers. The coupled dynamic equations of tethers and satellites are obtained using the Lagrangian multiplier method. Several tethered satellite systems involving large displacements, rotations, and deformations are numerically simulated, where the tethers are released from several meters to about 1 km. A control strategy is proposed to avoid slackness of the tethers during deployment. The accuracy of the modeling and solution procedures was validated on an elevator model.     

Forced oscillations with a sliding regime range of a two-mass system interacting with a fixed stop : PMM vol. 37, n6, 1973, pp. 999–1006

We investigate, by the method developed in [1]. the forced oscillations with a sliding regime range of a two-mass system with elastic connection between the elements, impacting a fixed stop. The system being considered is a dynamic model for a number of vibrational mechanisms. Forced oscillations with a sliding regime range of a system with shock interactions are periodic motions accompanied by a period of an infinite succession of instantaneous collisions of two fixed elements of the model [2]. Within the framework of conditions of roughness of the parameter space [3], in this paper we study by the method of [1] periodic motions with a sliding regime range of a two-mass system with a stop. This problem was posed because in real systems the velocity recovery factor R changes from shock to shock, mainly taking small values (0, 0.2). At the same time, the regions of realizability of one-impact oscillations, in practice the most essential ones among motions with a finite number of interactions over a period, narrow down sharply as R decreases and becomes very small even for R < 0.6 [4]. Thus, the stability of the given operation can be ensured by a law of motion which is independent or weakly dependent on R (^*) (see footnote on the next page). By virtue of what has been said above, finite-impact periodic modes are little suitable for this purpose. Regions, delineated in the parameter space of the model being considered, of existence of stable periodic motions with a sliding regime range have proved to be sufficiently broad. By virtue of the adopted approximation of the sliding regime, the dynamic characteristics of these motions do not depend upon R. The circumstances mentioned confirm the practical value of motions with a sliding regime range in dynamic systems with impact interactions.     

A flexible approach to the simulation of hybrid multibody systems

The present works deals with the incorporation of both flexible beam and shell structures into the realm of flexible multibody dynamics. Geometrically exact beam formulations based on classical Simo-Reissner kinematics are suitable for modelling beam-type flexible components in the context of finite-deformation multibody dynamics. So geometrically exact shell formulations are based on Reissner-Mindlin kinematics. In [2], a flexible framework for dealing with flexible structural elements in a multibody context is described. A specific isoparametric finite element discretization of a shell formulation leads to semi-discrete equations of motions assuming the form of differential-algebraic equations (DAEs). A compatible isoparametric formulation of beams has already been developed in [1]. The uniform DAE framework makes possible the incorporation of alternative finite element formulations. In addition to that, various time-stepping schemes such as energy-momentum methods or variational integrators can be applied. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some generalized pseudo-plane deformations for the neo-Hookean material

We consider deformations and motions that correspond to a non-uniformaxial stretch superimposed to a general pseudoplane deformationof the first kind. We provide the general determining equationfor this kind of solution when the constitutive equation forthe stress tensor is derived from the elastic neo-Hookean strain-energydensity. Then we provide some explicit solutions which are generalizationsof the non-symmetric torsion of a slab and some finite-amplitudepseudo-planar elliptical motions.     

Elastic Wave Propagation in Soft Microstructured Composites Undergoing Finite Deformations

We consider the propagation of elastic waves in soft composite materials undergoing large deformations. The analysis is performed in terms of small amplitude motions superimposed on a deformed state. By consideration of 2D periodic laminates and 3D fiber composites, we find that an applied deformation influences the elastic waves through the change in the microstructure, and through the change in the local material properties. These effects can be significantly amplified by the deformation induced elastic instability phenomenon leading to microstructure transformations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

昆虫翼拍动中受载变形的粘弹性本构模型

昆虫翼拍动受载时发生被动变形,被看作为有助于改善飞行性能的机制之一．决定这种被动变形大小的一个关键因素是昆虫翼的材料本构关系,至今缺乏研究．基于蜻蜓翼(离体)的应力松弛实验和模型翼拍动时受载变形的有限元数值分析,揭示了粘弹性本构关系是昆虫翼材料性能的合理描述,并研究了粘弹性参数对被动变形的影响．     

The discrete null space method for constrained mechanical systems in nonlinear structural and multibody dynamics

Corresponding to d'Alemberts principle in classical mechanics, the discrete null space method developed in [1] provides an energy-momentum conserving time stepping scheme for conservative finite-dimensional dynamical systems subject to constraints. The elimination of the Lagrange multipliers from the temporal discrete system leads to a reduced number of unknowns and to an improved condition number during the iterative solution of the nonlinear system. External and internal constraints are fulfilled likewise at the time nodes, wherefore the discrete null space method is particularly suited for the treatment of elastic multibody systems in structural dynamics. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Maxwell-Contact

In multibody systems, two alternative approaches exist to compute contact forces between bodies. The unilateral constraint contact and the unilateral regularized contact do not take into account the influence of the deformation due to other contacts on a body using rigid body dynamics. In this paper, a third alternative, i.e. the Maxwell-Contact, is derived coupling the deformations of different contacts on one body quasi-statically. An academic example validates the fundamental properties of the contact model and the application in a simulation of a pushbelt CVT shows improved results. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Closed-form control oriented model of highly flexible manipulators

This paper first presents a highly flexible 3D manipulator with links of arbitrary shape, then develops a closed-form dynamic model that best describes it. The model is based on a Newton–Euler formulation and the substructuring method is used to account for large deformations. The formulation of the motion equations starts from a data set which can be either analytically or numerically computed by finite elements(FE) codes. Simulation has been used to validate the model and compare the results with those of two different multibody software and one experimental, which was obtained from the Multi-Elastic-Link Robot Identification Dataset (MERIt), developed by the TU Dortmund. Then, thanks to the approach here adopted, an integral manifold model is derived, suitable for advanced control system design.     

Thermodynamically consistent nonlinear model of elastoplastic Maxwell medium

The paper is devoted to new applications of the ideas underlying Godunov’s method that was developed as early as in the 1950s for solving fluid dynamics problems. This paper deals with elastoplastic problems. Based on an elastic model and its modification obtained by introducing the Maxwell viscosity, a method for modeling plastic deformations is proposed.     

刚柔耦合系统动力学建模及分析

准确预测经历大范围刚体运动和弹性变形的柔性体的行为,是当前柔性多体系统动力学领域关注的主要课题.基于线性理论的传统方法由于无法计及动力刚化效应,导致在许多实际应用中得到错误的结果.本文从离心力势场的概念出发,应用Hamilton原理建立了具有动力刚化效应的刚柔耦合系统的运动方程,证明了该方程解的周期性,并采用了Frobenius方法给出了其精确解的一般形式.通过算例分析了刚体运动对弹性运动的模态和频率的影响.     

Active damping control for an underactuated multibody system

Light-weight robots and manipulators stand out due to their very good weight-to-load ratio and a low energy consumption. Unfortunately, the light-weight design yields a lower stiffness, which results in undesired elastic deformations, especially during high-speed working motion. One way to limit these unwanted oscillations can be implemented with modifications of the command signals, e.g. by input shaping or pre-computed feed-forward control. However, a feedback control-concept has the ability to provide a fast compensation of elastic deformations due to high-speed working motions or in case of unwanted environment contact as well as in the presence of other external disturbances. In this contribution, an active damping control (ADC) for fast moving manipulators with significant structural elasticities is presented. This approach does not require additional actuators and it is suitable for a large variety of manipulators that exhibit structural vibrations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)