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Research Papers

Graph-Theoretic Sensitivity Analysis of Multibody Systems

[+] Author and Article Information
Joydeep M. Banerjee

Department of Systems Design Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: jbanerjee83@gmail.com

John J. McPhee

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

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received May 31, 2013; final manuscript received January 24, 2014; published online July 11, 2014. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 9(4), 041009 (Jul 11, 2014) (8 pages) Paper No: CND-13-1115; doi: 10.1115/1.4026646 History: Received May 31, 2013; Revised January 24, 2014

A graph-theoretic formulation to perform sensitivity analysis on multibody systems is presented in this article. In this formulation, linear graphs are used to capture the system topologies from which a graph-theoretic formulation simultaneously generates the system equations and the sensitivity equations. This ensures the automated, accurate, and efficient generation of sensitivity equations. The basic formulation steps are outlined to illustrate the process of the generation of sensitivity equations. The salient aspects of multibody systems are presented along with a brief description of the software platform that has been used to implement the algorithm. A 3D pendulum and a double-wishbone suspension system are analyzed to demonstrate the application of the algorithm. The results are validated by using a finite difference formulation. Finally, the efficiency of the software implementation is assessed by comparing the computational costs associated with the proposed method and that of existing methods.

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References

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Banerjee, J. M. and McPhee, J. J., 2011, “Graph-Theoretic Sensitivity Analysis of Multibody Systems,” Proceedings of the Multibody Dynamics 2011 ECCOMAS Thematic Conference, J.-C.Samin and P.Fisette, eds.
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McPhee, J. J., 2000, Dynamics of Multi-Body Systems: Conventional and Graph-Theoretic Approaches, Department of Systems Design Engineering, University of Waterloo, Waterloo.
Banerjee, J. M., 2013, “Graph-Theoretic Sensitivity Analysis of Dynamic Systems,” Ph.D. thesis, University of Waterloo, Waterloo.

Figures

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Fig. 1

A simple pendulum and its linear graph

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Fig. 2

Three-dimensional pendulum

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Fig. 3

Generation of equations

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Fig. 4

Trajectory of pendulum tip

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Fig. 7

Double wishbone suspension system

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Fig. 8

Schematic of the graph-theoretic model of the suspension

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Fig. 9

Camber angle versus hub height

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Fig. 10

Camber sensitivity versus hub height

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Fig. 11

Validation of camber sensitivity

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