Nauki Techniczne

Archive of Mechanical Engineering


Archive of Mechanical Engineering | 2014 | vol. 61 | No 2 |


In elastic multibody systems, one considers large nonlinear rigid body motion and small elastic deformations. In a rising number of applications, e.g. automotive engineering, turning and milling processes, the position of acting forces on the elastic body varies. The necessary model order reduction to enable efficient simulations requires the determination of ansatz functions, which depend on the moving force position. For a large number of possible interaction points, the size of the reduced system would increase drastically in the classical Component Mode Synthesis framework. If many nodes are potentially loaded, or the contact area is not known a-priori and only a small number of nodes is loaded simultaneously, the system is described in this contribution with the parameter-dependent force position. This enables the application of parametric model order reduction methods. Here, two techniques based on matrix interpolation are described which transform individually reduced systems and allow the interpolation of the reduced system matrices to determine reduced systems for any force position. The online-offline decomposition and description of the force distribution onto the reduced elastic body are presented in this contribution. The proposed framework enables the simulation of elastic multibody systems with moving loads efficiently because it solely depends on the size of the reduced system. Results in frequency and time domain for the simulation of a thin-walled cylinder with a moving load illustrate the applicability of the proposed method.

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Autorzy i Afiliacje

Michael Fischer
Peter Eberhard


This work outlines a unified multi-threaded, multi-scale High Performance Computing (HPC) approach for the direct numerical simulation of Fluid-Solid Interaction (FSI) problems. The simulation algorithm relies on the extended Smoothed Particle Hydrodynamics (XSPH) method, which approaches the fluid flow in a Lagrangian framework consistent with the Lagrangian tracking of the solid phase. A general 3D rigid body dynamics and an Absolute Nodal Coordinate Formulation (ANCF) are implemented to model rigid and flexible multibody dynamics. The twoway coupling of the fluid and solid phases is supported through use of Boundary Condition Enforcing (BCE) markers that capture the fluid-solid coupling forces by enforcing a no-slip boundary condition. The solid-solid short range interaction, which has a crucial impact on the small-scale behavior of fluid-solid mixtures, is resolved via a lubrication force model. The collective system states are integrated in time using an explicit, multi-rate scheme. To alleviate the heavy computational load, the overall algorithm leverages parallel computing on Graphics Processing Unit (GPU) cards. Performance and scaling analysis are provided for simulations scenarios involving one or multiple phases with up to tens of thousands of solid objects. The software implementation of the approach, called Chrono::Fluid, is part of the Chrono project and available as an open-source software.

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Autorzy i Afiliacje

Arman Pazouki
Radu Serban
Dan Negrut


This paper presents the application of a co-simulation approach for the simulation of frictional contact in general-purpose multibody dynamics to a rotorcraft dynamics problem. The proposed approach is based on the co-simulation of a main problem, which is described and solved as a set of differential algebraic equations, with a subproblem that is characterized by nonsmooth dynamics events and solved using a timestepping technique. The implementation and validation of the formulation is presented. The method is applied to the analysis of the droop and anti-flap contacts of helicopter rotor blades. Simulations focusing on the problem of blade sailing are conducted to understand the behavior and assess the validity of the method. For this purpose, the results obtained using a contact model based on Hertzian reaction forces at the interface are compared with those of the proposed approach.

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Autorzy i Afiliacje

Matteo Fancello
Marco Morandini
Pierangelo Masarati


The paper encompasses the overview of hardware architecture and the systems characteristics of the Fraunhofer driving simulator. First, the requirements of the real-time model and the real-time calculation hardware are defined and discussed in detail. Aspects like transport delay and the parallel computation of complex real-time models are presented. In addition, the interfacing of the models with the simulator system is shown. Two simulator driving tests, including a fully interactive rough terrain driving with a wheeled excavator and a test drive with a passenger car, are set to demonstrate system characteristics. Furthermore, the simulator characteristics of practical significance, such as simulator response time delay, simulator acceleration signal bandwidth obtained from artificial excitation and from the simulator driving test, will be presented and discussed.

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Autorzy i Afiliacje

Michael Kleer
Andrey Gizatullin
Klaus Dreßler
Steffen Müller


This work deals with the effectiveness of a multi-body approach for the study of the dynamic behavior of a fixed landing gear, especially the research project concerns the drop tests of the AP.68 TP-300 aircraft. First, the Digital Mock-up of the of landing gear system in a C.A.D. software has been created, then the experimental structural stiffness of the leaf spring has been validated using the FEM tools MSC.Patran/Nastran. Finally, the entire model has been imported in MSC.ADAMS environment and, according to the certifying regulations, several multi-body simulations have been performed varying the heights of fall and the weights of the system. The results have shown a good correlation between numerical and experimental tests, thus demonstrating the potential of a multi-body approach. Future development of the present activity will probably be an application of the methodology, herein validated, to other cases for a more extensive validation of its predictive power and development of virtual certification procedures.

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Autorzy i Afiliacje

Romeo Di Leo
Angelo De Fenza
Marco Barile
Leonardo Lecce


Recently, the authors proposed a geometrically exact beam finite element formulation on the Lie group SE(3). Some important numerical and theoretical aspects leading to a computationally efficient strategy were obtained. For instance, the formulation leads to invariant equilibrium equations under rigid body motions and a locking free element. In this paper we discuss some important aspects of this formulation. The invariance property of the equilibrium equations under rigid body motions is discussed and brought out in simple analytical examples. The discretization method based on the exponential map is recalled and a geometric interpretation is given. Special attention is also dedicated to the consistent interpolation of the velocities.

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Autorzy i Afiliacje

Valentin Sonneville
Alberto Cardona
Olivier Brüls


This paper presents a control concept for a single-axle mobile robot moving on the horizontal plane. A mathematical model of the nonholonomic mechanical system is derived using Hamel’s equations of motion. Subsequently, a concept for a tracking controller is described in detail. This controller keeps the mobile robot on a given reference trajectory while maintaining it in an upright position. The control objective is reached by a cascade control structure. By an appropriate input transformation, we are able to utilize an input-output linearization of a subsystem. For the remaining dynamics a linear set-point control law is presented. Finally, the performance of the implemented control law is illustrated by simulation results.

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Autorzy i Afiliacje

Tobias Zaiczek
Matthias Franke


In modelling flexure based mechanisms, generally flexures are modelled perfectly aligned and nominal values are assumed for the dimensions. To test the validity of these assumptions for a two Degrees Of Freedom (DOF) large stroke compliant mechanism, eigenfrequency and mode shape measurements are compared to results obtained with a flexible multibody model. The mechanism consists of eleven cross flexures and seven interconnecting bodies. From the measurements 30% lower eigenfrequencies are observed than those obtained with the model. With a simplified model, it is demonstrated that these differences can be attributed to wrongly assumed leaf spring thickness and misalignment of the leaf springs in the cross flexures. These manufacturing tolerances thus significantly affect the behaviour of the two DOF mechanism, even though it was designed using the exact constraint design principle. This design principle avoids overconstraints to limit internal stresses due to manufacturing tolerances, yet this paper shows clearly that manufacturing imperfections can still result in significantly different dynamic behaviour.

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Autorzy i Afiliacje

w. Wijma
S.E. Boer
R.G.K.M. Aarts
D.M. Brouwer
W.B.J. Hakvoort


Redundant constraints in MBS models severely deteriorate the computational performance and accuracy of any numerical MBS dynamics simulation method. Classically this problem has been addressed by means of numerical decompositions of the constraint Jacobian within numerical integration steps. Such decompositions are computationally expensive. In this paper an elimination method is discussed that only requires a single numerical decomposition within the model preprocessing step rather than during the time integration. It is based on the determination of motion spaces making use of Lie group concepts. The method is able to reduce the set of loop constraints for a large class of technical systems. In any case it always retains a sufficient number of constraints. It is derived for single kinematic loops.

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Autorzy i Afiliacje

Andreas Müller



Prof. Marek Wojtyra, Warsaw University of Technology, Poland


Editorial Board

Prof. Krzysztof Arczewski, Warsaw University of Technology, Poland

Prof. Janusz T. Cieśliński, Gdańsk University of Technology, Poland

Prof. Antonio Delgado, LSTM University of Erlangen-Nuremberg, Germany

Prof. Peter Eberhard, University of Stuttgart, Germany

Prof. Jerzy Maciej Floryan, The University of Western Ontario, Canada

Prof. Janusz Frączek, Warsaw University of Technology, Poland

Prof. Zbigniew Kowalewski, Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland

Prof. Zenon Mróz, Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland

Prof. Andrzej J. Nowak, Silesian University of Technology, Poland

Dr. Andrzej F. Nowakowski, The University of Sheffield, United Kingdom

Prof. Jerzy Sąsiadek, Carleton University, Canada

Prof. Jacek Szumbarski, Warsaw University of Technology, Poland

Prof. Tomasz Wiśniewski, Warsaw University of Technology, Poland

Prof. Günter Wozniak, Chemnitz University of Technology, Germany


Assistant to the Editor

Małgorzata Broszkiewicz, Warsaw University of Technology, Poland


Editorial Advisory Board

Prof. Alberto Carpinteri, Politecnico di Torino, Italy

Prof. Fernand Ellyin, University of Alberta, Canada

Prof. Feng Gao, Shanghai Jiao Tong University, P.R. China

Prof. Emmanuel E. Gdoutos, Democritus University of Thrace, Greece

Prof. Gregory Glinka, University of Waterloo, Ontario, Canada

Prof. Andrius Marcinkevicius, Vilnius Gedeminas Technical University, Lithuania

Prof. Manuel José Moreira De Freitas, Instituto Superior Tecnico, Portugal

Prof. Andrzej Neimitz, Kielce University of Technology, Poland

Prof. Thierry Palin-Luc, Arts et Métiers ParisTech, Institut Carnot Arts, France

Prof. Andre Pineau, Centre des Matériaux, Ecole des Mines de Paris, France

Prof. Narayanaswami Ranganathan, LMR, Ecole Polytechnique de l'Université de Tours, France

Prof. Jan Ryś, Cracow University of Technology, Poland

Prof. Adelia Sequeira, Technical University of Lisbon, Portugal,

Prof. Józef Szala, University of Technology and Life Sciences in Bydgoszcz, Poland

Prof. Edmund Wittbrodt, Gdańsk University of Technology, Poland

Prof. Jens Wittenburg, Karlsruhe Institute of Technology, Germany

Prof. Stanisław Wojciech, University of Bielsko-Biała, Poland


Language Editor

Lech Śliwa, Institute of Physiology and Pathology of Hearing, Warsaw, Poland




Editorial Office:

Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology

Nowowiejska 24, Room 132, 00-665 Warsaw, Poland

Phone:  (+48) 22 234 7448, fax: (+48) 22 628 25 87,


Instrukcje dla autorów

About the Journal
Archive of Mechanical Engineering is an international journal publishing works of wide significance, originality and relevance in most branches of mechanical engineering. The journal is peer-reviewed and is published both in electronic and printed form. Archive of Mechanical Engineering publishes original papers which have not been previously published in other journal, and are not being prepared for publication elsewhere. The publisher will not be held legally responsible should there be any claims for compensation. The journal accepts papers in English.

Archive of Mechanical Engineering is an Open Access journal. The journal does not have article processing charges (APCs) nor article submission charges.

Original high quality papers on the following topics are preferred:

  • Mechanics of Solids and Structures,
  • Fluid Dynamics,
  • Thermodynamics, Heat Transfer and Combustion,
  • Machine Design,
  • Computational Methods in Mechanical Engineering,
  • Robotics, Automation and Control,
  • Mechatronics and Micro-mechanical Systems,
  • Aeronautics and Aerospace Engineering,
  • Heat and Power Engineering.

All submissions to the AME should be made electronically via Editorial System - an online submission and peer review system at:

More detailed instructions for Authors can be found there.

Polityka Open Access

Archive of Mechanical Engineering jest czasopismem wydawanym w wolnym dostępie na licencji CC BY-NC-ND 4.0.

Archive of Mechanical Engineering is an open access journal with all content available with no charge in full text version. The journal content is available under the licencse CC BY-NC-ND 4.0

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