0
Research Papers

Reduction of Multibody Dynamic Models in Automotive Systems Using the Proper Orthogonal Decomposition

[+] Author and Article Information
Ramin Masoudi

Department of Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1,Canada
e‐mail: rmasoudi@uwaterloo.ca

Thomas Uchida

Department of Bioengineering,
Stanford University,
Stanford, CA 94305-5448
e-mail: tkuchida@stanford.edu

John McPhee

Professor
Department of Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: mcphee@uwaterloo.ca

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 2, 2014; final manuscript received December 12, 2014; published online February 11, 2015. Assoc. Editor: Rudranarayan Mukherjee.

J. Comput. Nonlinear Dynam 10(3), 031007 (May 01, 2015) (8 pages) Paper No: CND-14-1116; doi: 10.1115/1.4029390 History: Received May 02, 2014; Revised December 12, 2014; Online February 11, 2015

The proper orthogonal decomposition (POD) is employed to reduce the order of small-scale automotive multibody systems. The reduction procedure is demonstrated using three models of increasing complexity: a simplified dynamic vehicle model with a fully independent suspension, a kinematic model of a single double-wishbone suspension, and a high-fidelity dynamic vehicle model with double-wishbone and trailing-arm suspensions. These three models were chosen to evaluate the effectiveness of the POD given systems of ordinary differential equations (ODEs), algebraic equations (AEs), and differential-algebraic equations (DAEs), respectively. These models are also components of more complicated full vehicle models used for design, control, and optimization purposes, which often involve real-time simulation. The governing kinematic and dynamic equations are generated symbolically and solved numerically. Snapshot data to construct the reduced subspace are obtained from simulations of the original nonlinear systems. The performance of the reduction scheme is evaluated based on both accuracy and computational efficiency. Good agreement is observed between the simulation results from the original models and reduced-order models, but the latter simulate substantially faster. Finally, a robustness study is conducted to explore the behavior of a reduced-order system as its input signal deviates from the reference input that was used to construct the reduced subspace.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Vehicle model with a fully independent suspension. The dynamics of this 14DOF system are governed by a set of pure ODEs.

Grahic Jump Location
Fig. 2

Simulated trajectory of the independent-suspension vehicle using original and reduced-order models

Grahic Jump Location
Fig. 3

Simulated pitch and yaw angles for the independent-suspension vehicle using original and reduced-order models

Grahic Jump Location
Fig. 4

Errors between the original and reduced-order models for pitch and yaw angles in the independent-suspension vehicle

Grahic Jump Location
Fig. 5

Schematic of the single double-wishbone suspension system (a) and its corresponding topological graph (b). The kinematics of this single-degree-of-freedom suspension system are described by a set of nonlinear AEs.

Grahic Jump Location
Fig. 6

Simulated time histories of the spindle (wheel carrier) translational displacement (a) and second Euler angle (b) for the double-wishbone suspension system using original and reduced-order models

Grahic Jump Location
Fig. 7

Errors between the original and reduced-order models for spindle translational displacement and second Euler angle in the double-wishbone suspension system

Grahic Jump Location
Fig. 8

High-fidelity vehicle model with double-wishbone and trailing-arm suspension systems. The dynamics of this 14DOF freedom system are governed by a set of DAEs.

Grahic Jump Location
Fig. 9

Simulated trajectory of the high-fidelity vehicle model using original and reduced-order models

Grahic Jump Location
Fig. 10

Simulated time histories of lateral speed (top) and vertical oscillation speed (bottom) of the chassis, along with the corresponding errors, in the high-fidelity vehicle model using original and reduced-order models

Grahic Jump Location
Fig. 11

Simulated time histories of spindle translational displacement (top) and second Euler angle (bottom) for the double-wishbone suspension system using original and reduced-order models, where a perturbed input (increased frequency) is applied to the lower-dimensional model

Grahic Jump Location
Fig. 12

Simulated time histories of spindle translational displacement (top) and second Euler angle (bottom) for the double-wishbone suspension system using original and reduced-order models, where a perturbed input (increased amplitude) is applied to the lower-dimensional model

Grahic Jump Location
Fig. 13

Root-mean-square errors for spindle translational displacement and second Euler angle of the double-wishbone suspension in terms of various perturbations in frequency (top) and amplitude (bottom) of the input

Grahic Jump Location
Fig. 14

Simulated time histories of the second Euler angle for the double-wishbone suspension system using original and reduced-order models, where a perturbed input is applied to the lower-dimensional model with three states (top) and six states (bottom)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In