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Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

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CiteScore 2016: 0.44

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Volume 60, Issue 1 (Mar 2013)

Reduction of a Vehicle Multibody Dynamic Model Using Homotopy Optimization

Andrew Hall
  • Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada
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/ Thomas Uchida
  • Department of Bioengineering, Stanford University, 318 Campus Drive, James H. Clark Center, Stanford, CA 94305-5448, U.S.A.
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/ Francis Loh
  • Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada
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/ Chad Schmitke / John Mcphee
  • Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada
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Published Online: 2013-03-27 | DOI: https://doi.org/10.2478/meceng-2013-0002

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.

Streszczenie

Pomimo stale rosnacej mocy obliczeniowej współczesnych procesorów, redukcja złozonych, wieloczłonowych modeli dynamicznych pozostaje waznym tematem badan, zwłaszcza dla optymalizacji projektowania, analizy wrazliwosci, identyfikacji parametrów i optymalizacji sterowników, które moga wymagac setek lub tysiecy symulacji. W pierwszej czesci pracy autorzy przedstawiaja model o wysokiej wiernosci opracowany dla seryjnie produkowanego samochodu sportowouzytkowego (SUV) przy pomocy oprogramowania Adams/Car (MSC.Software Corporation). Nastepnie w srodowisku MapleSim (Waterloo Maple Inc.) zostały opracowane równowazne cwiartkowe (quarter-car) modele kinematyczne o jednym połaczeniu, typu SLEKQ, dla zawieszenia przedniego i tylnego. By uniknac komplikacji obliczeniowych zwiazanych z wprowadzeniem tulejowania lub petli kinematycznych, wszystkie układy przenoszace zawieszenia zostały zastapione pojedynczymi skupionymi nieresorowanymi masami w kazdym rogu pojazdu. Zaprojektowane modele typu SLEKQ odtwarzaja własciwosci kinematycznych modelu kompletnego zawieszenia wykorzystujac przy tym tablice przegladowe lub funkcje wielomianowe, które zostały wczesniej wyznaczone za pomoca wysokiej wiernosci modelu typu Adams. Zdolnosc predykcyjna kazdego modelu SLEKQ zalezy od uzycia własciwych parametrów opisujacych nieliniowe sprezyny i amortyzatory, które uwzgledniaja sztywnosc i wpływ na tłumienie drgan wnoszony przez tulejowanie i nieresorowane masy. Optymalizacje homotopowa zastosowano w celu identyfikacji tych parametrów, które minimalizuja róznice miedzy odpowiedziami uzyskanymi w modelach typu Adams i SLEKQ. Ostatecznie, z modeli SLEKQ zostaje złozony zredukowany model o dziesieciu stopniach swobody reprezentujacy cały pojazd. Własciwosci dynamiczne tego modelu sa poddane walidacji przez porównanie z własciwosciami wysokiej wiernosci modelu typu Adams w czterokolumnowych testach kołysania i pochylania.

Keywords : Multibody Dynamics; Model Reduction; Vehicle Dynamics; Homotopy Optimization Parameter Identification; Single-link equivalent kinematic quarter-car

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About the article

Published Online: 2013-03-27

Published in Print: 2013-03-01


Citation Information: Archive of Mechanical Engineering, ISSN (Print) 0004-0738, DOI: https://doi.org/10.2478/meceng-2013-0002.

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