Nauki Techniczne

Archive of Mechanical Engineering


Archive of Mechanical Engineering | 2013 | vol. 60 | No 1 |


Vehicle parameters have a significant impact on handling, stability, and rollover propensity. This study demonstrates two methods that estimate the inertia values of a ground vehicle in real-time.

Through the use of the Generalized Polynomial Chaos (gPC) technique for propagating the uncertainties, the uncertain vehicle model outputs a probability density function for each of the variables. These probability density functions (PDFs) can be used to estimate the values of the parameters through several statistical methods. The method used here is the Maximum A-Posteriori (MAP) estimate. The MAP estimate maximizes the distribution of P(β|z) where β is the vector of the PDFs of the parameters and z is the measurable sensor comparison.

An alternative method is the application of an adaptive filtering method. The Kalman Filter is an example of an adaptive filter. This method, when blended with the gPC theory is capable at each time step of updating the PDFs of the parameter distributions. These PDF’s have their median values shifted by the filter to approximate the actual values.

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Autorzy i Afiliacje

Jeremy Kolansky
Corina Sandu


Despite the ever-increasing computational power of modern processors, the reduction of complex multibody dynamic models remains an important topic of investigation, particularly for design optimization, sensitivity analysis, parameter identification, and controller tuning tasks, which can require hundreds or thousands of simulations. In this work, we first develop a high-fidelity model of a production sports utility vehicle in Adams/Car. Single-link equivalent kinematic quarter-car (SLEKQ, pronounced “sleek”) models for the front and rear suspensions are then developed in MapleSim. To avoid the computational complexity associated with introducing bushings or kinematic loops, all suspension linkages are lumped into a single unsprung mass at each corner of the vehicle. The SLEKQ models are designed to replicate the kinematic behaviour of a full suspension model using lookup tables or polynomial functions, which are obtained from the high-fidelity Adams model in this work. The predictive capability of each SLEKQ model relies on the use of appropriate parameters for the nonlinear spring and damper, which include the stiffness and damping contributions of the bushings, and the unsprung mass. Homotopy optimization is used to identify the parameters that minimize the difference between the responses of the Adams and MapleSim models. Finally, the SLEKQ models are assembled to construct a reduced 10-degree-of-freedom model of the full vehicle, the dynamic performance of which is validated against that of the high-fidelity Adams model using four-post heave and pitch tests.

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Autorzy i Afiliacje

Andrew Hall
Thomas Uchida
Francis Loh
Chad Schmitke
John Mcphee


Active suspension systems ease the conflict between comfort and handling. This requires the use of suitable actuators that in turn need to be efficiently controlled. This paper proposes a model-based control approach for a nonlinear suspension actuator. Firstly the concept is derived in the linear framework in order to simplify the synthesis and analysis phase. There a linear model of the actuator is proposed and discussed. Further, this design phase includes a comparison between model-free PID controllers and a newly proposed two-degree-of-freedom controller which allows one to shape reference and disturbance responses separately. Subsequently, the two-degree-of-freedom controller, which proves to be superior, is adapted to the nonlinear framework by considering a linear parameter varying representation of the nonlinear plant. Finally, the nonlinear controller is implemented in a test car confirming the concept applicability to real hardware.

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Autorzy i Afiliacje

Oussama Ajala
Dieter Bestle
Jochen Rauh


There exist cases where precise simulations of contact forces do not allow modeling the gears as rigid bodies but a fully elastic description is needed. In this paper, a modally reduced elastic multibody system including gear contact based on a floating frame of reference formulation is proposed that allows very precise simulations of fully elastic gears with appropriately meshed gears in reasonable time even for many rotations. One advantage of this approach is that there is no assumption about the geometry of the gears and, therefore, it allows precise investigations of contacts between gears with almost arbitrary non-standard tooth geometries including flank profile corrections.

This study presents simulation results that show how this modal approach can be used to efficiently investigate the interaction between elastic deformations and flank profile corrections as well as their influence on the contact forces. It is shown that the elastic approach is able to describe important phenomena like early addendum contact for insufficiently corrected profiles in dependence of the transmitted load. Furthermore, it is shown how this approach can be used for precise and efficient simulations of beveloid gears.

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Autorzy i Afiliacje

Trong Phu Do
Peter Eberhard
Pascal Ziegler


Complex multi-disciplinary models in system dynamics are typically composed of subsystems. This modular structure of the model reflects the modular structure of complex engineering systems. In industrial applications, the individual subsystems are often modelled separately in different mono-disciplinary simulation tools. The Functional Mock-Up Interface (FMI) provides an interface standard for coupling physical models from different domains and addresses problems like export and import of model components in industrial simulation tools (FMI for Model Exchange) and the standardization of co-simulation interfaces in nonlinear system dynamics (FMI for Co-Simulation), see [10].

The renewed interest in algorithmic and numerical aspects of co-simulation inspired some new investigations on error estimation and stabilization techniques in FMI for Model Exchange and Co-Simulation v2.0 compatible co-simulation environments. In the present paper, we focus on reliable error estimation for communication step size control in this framework.

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Autorzy i Afiliacje

Martin Arnold
Christoph Clauss
Tom Schierz


The present work deals with continuum mechanical considerations for deformable and rigid solids as well as for fluids. A common finite element framework is used to approximate all systems under considerations. In particular, we present a standard displacement based formulation for the deformable solids and make use of this framework for the transition of the solid to a rigid body in the limit of infinite stiffness. At last, we demonstrate how to immerse a discretized solid into a fluid for fluid-structure interaction problems.

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Autorzy i Afiliacje

Christian Hesch
Peter Betsch


The consideration of uncertainties in numerical simulation is generally reasonable and is often indicated in order to provide reliable results, and thus is gaining attraction in various fields of simulation technology. However, in multibody system analysis uncertainties have only been accounted for quite sporadically compared to other areas.

The term uncertainties is frequently associated with those of random nature, i.e. aleatory uncertainties, which are successfully handled by the use of probability theory. Actually, a considerable proportion of uncertainties incorporated into dynamical systems, in general, or multibody systems, in particular, is attributed to so-called epistemic uncertainties, which include, amongst others, uncertainties due to a lack of knowledge, due to subjectivity in numerical implementation, and due to simplification or idealization. Hence, for the modeling of epistemic uncertainties in multibody systems an appropriate theory is required, which still remains a challenging topic. Against this background, a methodology will be presented which allows for the inclusion of epistemic uncertainties in modeling and analysis of multibody systems. This approach is based on fuzzy arithmetic, a special field of fuzzy set theory, where the uncertain values of the model parameters are represented by socalled fuzzy numbers, reflecting in a rather intuitive and plausible way the blurred range of possible parameter values. As a result of this advanced modeling technique, more comprehensive system models can be derived which outperform the conventional, crisp-parameterized models by providing simulation results that reflect both the system dynamics and the effect of the uncertainties.

The methodology is illustrated by an exemplary application of multibody dynamics which reveals that advanced modeling and simulation techniques using some well-thought-out inclusion of the presumably limiting uncertainties can provide significant additional benefit.

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Autorzy i Afiliacje

Nico-Philipp Walz
Michael Hanss


The human environment consists of a large variety of mechanical and biomechanical systems in which different types of contact can occur. In this work, we consider a monopedal jumper modelled as a three-dimensional rigid multibody system with contact and simulate its dynamics using a structure preserving method. The applied mechanical integrator is based on a constrained version of the Lagrange-d’Alembert principle. The resulting variational integrator preserves the symplecticity and momentum maps of the multibody dynamics. To ensure the structure preservation and the geometric correctness, we solve the non-smooth problem including the computation of the contact configuration, time and force instead of relying on a smooth approximation of the contact problem via a penalty potential. In addition to the formulation of non-smooth problems in forward dynamic simulations, we are interested in the optimal control of the monopedal high jump. The optimal control problem is solved using a direct transcription method transforming it into a constrained optimisation problem, see [14].

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Autorzy i Afiliacje

Michael W. Koch
Sigrid Leyendecker


The condition number of the Generalized Inertia Matrix (GIM) of a serial chain can be used to measure its ill-conditioning. However, computation of the condition number is computationally very expensive. Therefore, this paper investigates alternative means to estimate the condition number, in particular, for a very long serial-chain. For this, the diagonal elements of the GIM are examined. It is found that the ratio of the largest and smallest diagonal elements of the GIM, when scaled using an initial estimate of the condition number, closely resembles the condition number. This significantly simplifies the process of detecting ill-conditioning of the GIM, which may help to decide on stability of the system at hand.

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Autorzy i Afiliacje

Suril V. Shah
Subir K. Saha



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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