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RESEARCH PAPERS

# Comparison of the Classical Formulation With the Reference Conditions Formulation for Dynamic Flexible Multibody Systems

[+] Author and Article Information
C. B. Drab, J. R. Haslinger

Math Consult, Altenberger Strasse 69, A-4040 Linz, Austria

R. U. Pfau1

Math Consult, Altenberger Strasse 69, A-4040 Linz, Austriapfau@mathconsult.co.at

G. Offner

AVL LIST GmbH, Hans-List-Platz 1, A-8020 Graz, Austria

1

Corresponding author.

J. Comput. Nonlinear Dynam 2(4), 337-343 (Mar 20, 2007) (7 pages) doi:10.1115/1.2756066 History: Received September 29, 2006; Revised March 20, 2007

## Abstract

Within the framework of the “floating frame of reference” formulation for dynamic flexible multibody systems, the separation of local and global motion is important. We compare the new approach with reference conditions as algebraic constraints with the classical one leading to a system of ordinary differential equations. The approach using reference conditions is motivated either from the need of keeping the error introduced when linearizing the elastic forces as small as possible (Buckens frame) or from minimizing the relative kinetic energy contained in the elastic deformations (Tisserand frame). The reference conditions impose algebraic constraints on the body level leading to a differential-algebraic equation (DAE) to be solved. The equivalence and the differences of the two approaches are shown. The index of the DAE system with reference conditions is shown to be either 2 or 1.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic representation of the floating frame of reference approach. ΣI is the inertial coordinate system, and ΣB is the reference coordinate system.

Figure 2

Schematic representation of the multibody model of the four-cylinder diesel engine test example

Figure 3

Angular velocity in the direction of the main rotation (Ω1) of the crankshaft for the two sets of reference conditions (rc1, rc2), calculated with accuracy 1×10−4

Figure 4

Difference between the two sets in the angular velocity in the direction of the main rotational (Ω1) of the crankshaft for two accuracies (1×10−3, 1×10−4)

Figure 5

Difference in the angular acceleration of the crankshaft in direction of main rotation for accuracy 1×10−4

Figure 6

Difference in the velocity vB,2 of the crankshaft for the accuracies (1×10−3, 1×10−4)

Figure 7

Difference in the rotational velocity ω90150, DOF 4 and 5, for node 90150 of the crankshaft for the accuracy 1×10−4

## Errata

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