Error-Controlled Model Reduction in Flexible Multibody Dynamics

Fehr, Jörg; Eberhard, Peter

doi:10.1115/1.4001372

Cited by 38 publications

(33 citation statements)

References 17 publications

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“…The uncertain reduced model quality issue can be solved using Balanced Modal Truncation for the body flexibility model reduction. The use of Balanced Modal Truncation allows to compute an error bound on the approximation error of the reduced model [21]. However, this technique is only computationally feasible for small-scale body flexibility models, such that a two-step approach is required, in which the model is first reduced by another model reduction technique [22], or by performing Balanced Modal Truncation in an approximate manner [21].…”

Section: Body Flexibility Model Reductionmentioning

confidence: 99%

“…The use of Balanced Modal Truncation allows to compute an error bound on the approximation error of the reduced model [21]. However, this technique is only computationally feasible for small-scale body flexibility models, such that a two-step approach is required, in which the model is first reduced by another model reduction technique [22], or by performing Balanced Modal Truncation in an approximate manner [21]. Balanced Modal Truncation defines a mode to contribute significantly to the overall system state if it is easily excited by the system excitation and easily observed in the outputs of interest.…”

Section: Body Flexibility Model Reductionmentioning

confidence: 99%

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Static modes switching for more efficient flexible multibody simulation

Heirman

Tamarozzi

Desmet

2011

Numerical Meth Engineering

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SUMMARYBody flexibility is of ever-increasing importance in multibody simulation. The current state-of-the-art simulation techniques typically have difficulties with systems in which flexible bodies can be loaded in many degrees of freedom (DOFs). However, in many applications, loading is possible in many DOFs but only few are loaded simultaneously at any given moment, such that at any moment only a low-dimensional part of the reduced body flexibility description contributes to the solution. Static Modes Switching, the methodology proposed in this paper, exploits this by judiciously choosing the body flexibility mode set and at any moment only including those modes that contribute to the solution. Static Modes Switching does not improve simulation accuracy; however, it can significantly reduce simulation times. In a numerical experiment, results using Static Modes Switching match results for a conventional model using the same mode set. The approximation errors are negligible compared to the accuracy loss encountered when using a mode set without compensation for the quasi-static response of the high-frequency dynamics, while both simulation results are obtained at a comparable computational cost. Static Modes Switching numerically introduces discontinuities when removing a mode from the mode set. This is overcome by time integration schemes exhibiting high-frequency numerical damping.

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Section: Body Flexibility Model Reductionmentioning

confidence: 99%

Section: Body Flexibility Model Reductionmentioning

confidence: 99%

Static modes switching for more efficient flexible multibody simulation

Heirman

Tamarozzi

Desmet

2011

Numerical Meth Engineering

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“…However, the transformation to modal coordinates is not the only possibility. In Fehr and Eberhard [3] more powerful methods for transformation are presented. By using such methods, the number of ansatz functions can be decreased.…”

Section: Multibody Model With Elastic Plate and Hertzian Contactmentioning

confidence: 99%

Investigation and design of an impact actuated micro shift valve

et al. 2013

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New concepts for an impact actuated micro shift valve are presented which are useful e.g. as implant for the hydrocephalus disease. Such an implant must fulfil requirements, such as using biocompatible materials, a separation of the actuator from the fluid, MRT safety and low energy consumption in order to allow a battery powered system. The concepts are based on impacts that transmit an impulse into the interior of the valve through the casing, switching the valve. In order to predict the energy transmitted into the valve, an elastic multibody model is created, verified with full finite element simulations and experiments on scaled-up models. Using this model, the most important effects and parameters are discussed. Also, fluid effects are included into the elastic multibody model for a qualitative assessment of its influence on the efficiency. The simulations are compared to experiments performed with a scaled model for two different cases. Two designs of a shift valve based on impact actuation are built as prototypes and tested.

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“…The balanced truncation reduction method for first order systems has some additional advantages like an immediately available error bound (29), see [20], [32], [2], [1]. This error bound is lost for balanced truncation for second order systems.…”

Section: ) Advantages and Disadvantagesmentioning

confidence: 99%

Model reduction of an elastic crankshaft for elastic multibody simulations

et al. 2012

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System analysis and optimization of combustion engines and engine components are increasingly supported by digital simulations. In the simulation process of combustion engines multi physics simulations are used. As an example, in the simulation of a crank drive the mechanical subsystem is coupled to a hydrodynamic subsystem. As far as the modeling of the mechanical subsystems is concerned, elastic multibody systems are frequently used. During the simulation many equations must be solved simultaneously, the hydrodynamic equations as well as the equations of motion of each body in the elastic multibody system. Since the discretization of the elastic bodies, e.g with the help of the finite element method, introduces a large number of elastic degrees of freedom, an efficient simulation of the system becomes difficult. The linear model reduction of the elastic degrees of freedom is a key step for using flexible bodies in multibody systems and turning simulations more efficient from a computational point of view. In recent years a variety of new reduction methods alongside the traditional techniques were developed in applied mathematics. Some of these methods are introduced and compared for reducing the equations of motion of an elastic multibody system. The special focus of this work is on balanced truncation model order reduction which is a singular value based reduction technique using the Gramian matrices of the system. We investigate a version of this method that is adapted to the structure of a special class of second order dynamical systems which is important for the particular application discussed here. The main computational task in balanced truncation is the solution or large-scale Lyapunov equations for which we apply a modified variant of the low-rank ADI method. The simulation of a crank drive with a flexible crankshaft is taken as technically relevant example. The results are compared to other methods like Krylov approaches or modal reduction.

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Error-Controlled Model Reduction in Flexible Multibody Dynamics

Cited by 38 publications

References 17 publications

Static modes switching for more efficient flexible multibody simulation

Static modes switching for more efficient flexible multibody simulation

Investigation and design of an impact actuated micro shift valve

Model reduction of an elastic crankshaft for elastic multibody simulations

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