Energy transfer between nodal diameters of cyclic symmetric structures exhibiting polynomial nonlinearities: Cyclic condition and analysis

Quaegebeur, Samuel; Chouvion, Benjamin; Thouverez, Fabrice; Berthe, Loic

doi:10.1016/j.ymssp.2019.106604

Cited by 13 publications

(10 citation statements)

References 22 publications

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“…The computational strategy developed hereafter is based on a frequency domain technique, namely the Harmonic Balance Method (HBM). The method has been used by the nonlinear dynamics community for several decades [55] in a wide variety of fields such as bolted structures [23], turbomachinery [49], bladed disks dynamics [12,44], vibro-impact systems [3] and gear dynamics [1,2,62].…”

Section: Numerical Procedures For the Nonlinear Dynamic Analysismentioning

confidence: 99%

Effect of gear topology discontinuities on the nonlinear dynamic response of a multi-degree-of-freedom gear train

Mélot

Benaïcha

Rigaud

et al. 2022

Journal of Sound and Vibration

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Weight reduction is a recurring concern in the design of modern mechanical systems. This search may lead engineers to resort to using gears with holes in order to meet their requirements. This paper presents a methodology to carry out nonlinear dynamic analyses of a gear transmission with holes in the gear blanks subjected to a multiharmonic internal excitation. This work investigates the influence of these holes on the vibration levels, occurence of contact loss and possible bifurcations. The numerical model features two flexible shafts coupled by a spur gear pair with holes. The gear model consists in two lumped masses and inertias and includes the gear backlash as well as the internal excitation sources that are the time-varying stiffness and the static transmission error (STE). The resulting mechanical system is solved in the frequency domain by the Harmonic Balance Method (HBM) coupled with an arc-length continuation algorithm and its stability is evaluated with Hill's method. Results show that adding holes not only impacts the STE but also the mesh stiffness. The interactions of these two quantities has a substantial influence on the bifurcation structure along the main solution branch and leads to a decrease of the span of vibro-impact regions. As the applied static torque is increased, it is found that using holed gear blanks can effectively prevent contact loss and lead to a linear response.

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Section: Numerical Procedures For the Nonlinear Dynamic Analysismentioning

confidence: 99%

Effect of gear topology discontinuities on the nonlinear dynamic response of a multi-degree-of-freedom gear train

Mélot

Benaïcha

Rigaud

et al. 2022

Journal of Sound and Vibration

Self Cite

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“…In practice, the components u k are decomposed into the internal DOFs (subscript i), and the left and right boundary DOFs (subscripts L and R). It respects the following property [2,40]:…”

Section: Cyclic Complex Nonlinear Normal Modementioning

confidence: 99%

“…This leads to fully decoupled equations for linear systems. However, for nonlinear systems, the different nodal diameters interact (the interacting diameters define the interaction space T interact [40,8]) and the system of equations becomes,…”

Section: Cyclic Complex Nonlinear Normal Modementioning

confidence: 99%

“…The vectorsũ k ,f nl,k andf ext,k represent the displacement, the nonlinear forces and the external forces on the k−th nodal diameter. T interact can be taken by default as the whole space 0, K but it might be possible to reduce it depending on the situation [40,8]. Solving (13) with the termf ext,k allows to compute the frequency forced response of the system.…”

Section: Cyclic Complex Nonlinear Normal Modementioning

confidence: 99%

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Nonlinear cyclic reduction for the analysis of mistuned cyclic systems

Quaegebeur

Chouvion

Thouverez

2021

Journal of Sound and Vibration

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Predicting the vibratory response of bladed-disks in turbomachinery is of the utmost importance to design a reliable and optimized engine. Yet, such simulations are challenging mainly due to the large size of the finite-element model used to describe the system, the existence of random mistuning coming from manufacture tolerances, and the nonlinear effects arising from the different components and their coupling. As a consequence, very few reduced-order models handling nonlinear mistuned systems have yet been proposed and the existing ones try to find the best compromise between a computationally efficient simulation and a correct description of the nonlinear phenomena. In this paper, a novel approach is proposed to tackle this challenge. Its key ideas rely on the substructuring concept and the cyclic properties of the structure. A reduction basis composed of cyclic complex nonlinear normal modes is created on each sector of the system leading to a compact nonlinear superelement per sector. The system is then assembled and a synthesis simulation is performed. Due to the main concepts employed, the method is referred to as the Substructuring method based on Nonlinear Cyclic Reduction (SNCR). It is validated on a finite element model of a tuned, a randomly mistuned and an intentionally mistuned bladed-disks. It will be shown to be fast and accurate despite strong nonlinearities. Due to its flexibility and efficiency, the method is expected to have a wide range of possible applications within the community.

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“…These softwares are based on a Petrov-Galerkin method, namely the orthogonal collocation. The HBM has seen a widespread use in fields as diverse as gear dynamics [1,2,48,69], rotordynamics [55], brake squeal [11], bladed disks dynamics [51], nonlinear electrical circuits [26,25], fluid-structure interactions [59,19], micro-electro-mechanical systems (MEMS) [36], nonlinear tuned vibrations absorbers [30,14]. Karkar et al [39] proposed a comparison between the orthogonal collocation and the HBM.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation tracking of geared systems with parameter-dependent internal excitation

2021

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Energy transfer between nodal diameters of cyclic symmetric structures exhibiting polynomial nonlinearities: Cyclic condition and analysis

Cited by 13 publications

References 22 publications

Effect of gear topology discontinuities on the nonlinear dynamic response of a multi-degree-of-freedom gear train

Effect of gear topology discontinuities on the nonlinear dynamic response of a multi-degree-of-freedom gear train

Nonlinear cyclic reduction for the analysis of mistuned cyclic systems

Bifurcation tracking of geared systems with parameter-dependent internal excitation

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