scholarly journals Model Reduction of the Flexible Rotating Crankshaft of a Motorcycle Engine Cranktrain

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Stefano Ricci ◽  
Marco Troncossi ◽  
Alessandro Rivola
Keyword(s):  
Model Reduction ◽  
Mode Selection ◽  
Normal Modes ◽  
Selection Procedure ◽  
Element Model ◽  
Multibody Model ◽  
Fixed Interface ◽  
Model Reduction Technique ◽  
Rigid Multibody ◽  
Motorcycle Engine

This paper addresses the development of an elastodynamic model of a motorcycle engine cranktrain aimed at accurately evaluating the interactions between the crankshaft and the engine block, thus allowing an improved structural design. A rigid multibody model is first implemented and simulated; only kinematic joints are involved at this stage, leading to a statically determinate assembly of the mechanism. Such a modelling approach prevents the loads at certain interface locations to be evaluated; furthermore, high-frequency dynamic effects cannot be predicted. These drawbacks can be removed by introducing bushing-like elements and/or modelling component flexibility. In this paper, this latter aspect is the objective of the investigation; in particular, a finite element model of the crankshaft is implemented as a replacement for the corresponding rigid member. The well-established Craig-Bampton model reduction technique is used to represent the elastodynamic behaviour of the component with a limited number of coordinates. The mode selection procedure is emphasized here: a measure of modal dynamic importance, namely the effective interface mass fraction, is used to rank fixed-interface normal modes based upon their contribution to loads at the substructure interface; choosing the modal base according to such ranking leads to a minimal yet accurate representation.

scholarly journals Using spectral submanifolds for optimal mode selection in nonlinear model reduction

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200725
Author(s):  
Gergely Buza ◽  
Shobhit Jain ◽  
George Haller
Keyword(s):  
Model Reduction ◽  
Invariant Manifolds ◽  
Mode Selection ◽  
Normal Modes ◽  
Selection Criterion ◽  
Selection Procedure ◽  
Forced Response ◽  
Recent Theory ◽  
Response Curves ◽  
Spectral Submanifolds

Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully selected modes. The criteria to select the modes relevant for reduction are usually problem-specific and heuristic. In this work, we propose a rigorous mode-selection criterion based on the recent theory of spectral submanifolds (SSMs), which facilitates a reliable projection of the governing nonlinear equations onto modal subspaces. SSMs are exact invariant manifolds in the phase space that act as nonlinear continuations of linear normal modes. Our criterion identifies critical linear normal modes whose associated SSMs have locally the largest curvature. These modes should then be included in any projection-based model reduction as they are the most sensitive to nonlinearities. To make this mode selection automatic, we develop explicit formulae for the scalar curvature of an SSM and provide an open-source numerical implementation of our mode-selection procedure. We illustrate the power of this procedure by accurately reproducing the forced-response curves on three examples of varying complexity, including high-dimensional finite-element models.

Modal Selection Through Effective Interface Mass With Application to Flexible Multibody Cranktrain Dynamics

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
S. Ricci ◽  
M. Troncossi ◽  
A. Rivola
Keyword(s):  
High Speed ◽  
Mode Selection ◽  
Selection Procedure ◽  
Connecting Rod ◽  
Nonlinear Simulation ◽  
High Rotational Speed ◽  
Hydrodynamic Bearing ◽  
Multibody Model ◽  
High Speed Engine ◽  
Flexible Component

The development of a multibody model of a motorbike L-twin engine cranktrain is presented in this work. The need for an accurate evaluation of the loads acting on the main engine components at high rotational speed makes it necessary to take element flexibility into account in order to capture elastodynamic effects, which might have a major impact on the dynamics of the system. Starting from finite element descriptions of both the crankshaft and the connecting rod, the classical Craig–Bampton (CB) technique is employed to obtain reduced models, which are suitable for the subsequent multibody analysis. A particular component mode selection procedure is implemented based on the concept of effective interface mass, allowing an assessment of the accuracy of the reduced model prior to the nonlinear simulation phase. Bearing dynamics also plays an important role in such a high-speed engine application: angular contact ball bearings are modeled according to a 5DOF nonlinear scheme in order to grasp the main bearings behavior while an impedance-based hydrodynamic bearing model is implemented providing an enhanced operation prediction at big end locations. The assembled cranktrain model is simulated using a commercial multibody software platform. Numerical results demonstrate the effectiveness of the procedure implemented for the flexible component model reduction. The advantages of this technique over the traditional mode truncation approach are discussed.

Characterization of Nonlinear Coupled Dynamics in Sandwich Structures

2008 ◽  
Author(s):  
Ioannis T. Georgiou
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Geometric Nonlinearity ◽  
Sandwich Structures ◽  
Normal Modes ◽  
Element Model ◽  
Nonlinear Normal Modes ◽  
High Fidelity ◽  
Coupled Dynamics ◽  
Nonlinear Normal

In this work, the nonlinear coupled dynamics of a sandwich structure with hexagonal honeycomb core are characterized in terms of Proper Orthogonal Decomposition modes. A high fidelity nonlinear finite element model is derived to describe geometric nonlinearity and displacement and rotation fields that govern the coupled dynamics. Contrary to equivalent continuum models used to predict vibration properties of lattice and sandwich structures, a high fidelity finite element model allows for a quite detailed description of the distributed complicated geometric nonlinearity of the core. It was found that the free dynamics excited by a blast load and the forced dynamics excited by a harmonic force posses POD modes which are localized in space and time. The processing of the simulated dynamics by the Time Discrete Proper Transform forms a means to study the nonlinear coupled dynamics of sandwich structures in the context of nonlinear normal modes of vibration and reduced order models.

scholarly journals Prediction of Isolated Resonance Curves Using Nonlinear Normal Modes

2015 ◽  
Author(s):  
R. J. Kuether ◽  
L. Renson ◽  
T. Detroux ◽  
C. Grappasonni ◽  
G. Kerschen ◽  
...  
Keyword(s):  
Normal Modes ◽  
Resonance Curve ◽  
Element Model ◽  
Nonlinear Normal Modes ◽  
Initial Guess ◽  
Forced Response ◽  
Numerical Continuation ◽  
Continuation Algorithm ◽  
Resonance Curves ◽  
Nonlinear Normal

Isolated resonance curves are separate from the main nonlinear forced-response branch, so they can easily be missed by a continuation algorithm and the resonant response might be underpredicted. The present work explores the connection between these isolated resonances and the nonlinear normal modes of the system and adapts an energy balance criterion to connect the two. This approach provides new insights into the occurrence of isolated resonances as well as a method to find an initial guess to compute the isolated resonance curve using numerical continuation. The concepts are illustrated on a finite element model of a cantilever beam with a nonlinear spring at its tip. This system presents jumps in both frequency and amplitude in its response to a swept sinusoidal excitation. The jumps are found to be the result of a modal interaction that creates an isolated resonance curve that eventually merges with the main resonance branch as the excitation force increases. Excellent insight into the observed dynamics is provided with the NNM theory, which supports that NNMs can also be a useful tool for predicting isolated resonance curves and other behaviors in the damped, forced response.

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