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Technical Brief

On the Projection of a Flexible Bodies Modal Coordinates Onto Another Finite Element Model With Local Modifications

[+] Author and Article Information
Wolfgang Witteveen

Mechanical Engineering Degree Program,
Upper Austria University of Applied Sciences,
Wels 4600, Austria
e-mail: wolfgang.witteveen@fh-wels.at

Pöchacker Stefan, Florian Pichler

Mechanical Engineering Degree Program,
Upper Austria University of Applied Sciences,
Wels 4600, Austria

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 7, 2018; final manuscript received April 10, 2019; published online May 13, 2019. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 14(7), 074501 (May 13, 2019) (7 pages) Paper No: CND-18-1500; doi: 10.1115/1.4043524 History: Received November 07, 2018; Revised April 10, 2019

The time integration of a complex multibody system is a time consuming part of the entire evaluation process of a flexible component. A multibody simulation of a flexible crankshaft, for instance, interacting with pistons, con rods, fly wheel, hydrodynamic bearings and further takes several hours of central processing unit (CPU) time and may dominate the entire simulation chain. Small, local changes in the involved finite element (FE) models, for example, another notch radius, normally require a new time integration of the entire multibody system. In this publication, a remarkably simple method is presented, so that the multibody simulation of such a variant can be skipped entirely. Instead, a simple and cheap projection of the original results to the modified FE model is proposed. One simple and one elaborate example demonstrate the extraordinary resulting quality for minor design changes like notch radius variations.

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References

Shabana, A. A. , 2013, Dynamics of Multibody Systems, Cambridge University Press, Cambridge, UK.
Witteveen, W. , 2012, “ On the Modal and Non-Modal Model Reduction of Metallic Structures With Variable Boundary Conditions,” World J. Mech., 2(6), pp. 311–324. [CrossRef]
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Callahan, J. , Avitabile, P. , and Riemer, R. , 1989, “ System Equivalent Reduction Expansion Process (SEREP),” Seventh International Modal Analysis Conference, Las Vegas, NV, pp. 29–37.
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Figures

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Fig. 1

Circular cantilever beam

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Fig. 2

Representative modal coordinates (numbers 1 and 10)

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Fig. 3

Von Mises stress distribution around time t = 0.107 s when the critical node has its stress maximum

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Fig. 4

Time history of von Mises stress at node 101,661 (SimBx) and node 100,393 (SimA)

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Fig. 5

Spatial distribution for 1587, 92, 21, and 5 coincident FE nodes

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Fig. 6

Relative error of the von Mises stress with respect to the number of coincident FE nodes

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Fig. 7

Variant with a large radius. Von Mises stresses at a certain time instant due to a full time integration and due to a projection based on SimA.

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Fig. 8

Portion of time history of projection error, e, according to Eq. (12)

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Fig. 9

Relative deviation of the eigenfrequencies

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Fig. 10

Representative modal coordinates (mode numbers 1 and 24)

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Fig. 11

Safety factor against fatigue failure

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Fig. 12

Portion of time history of von Mises stress of node 13,478,114

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Fig. 13

Portion of time history of projection e error according to Eq. (12)

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Fig. 14

Relative deviation of the eigenfrequencies

Tables

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