An Original Method for Computing the Response of a Parametrically Excited Forced System

Perret-Liaudet, Joël

doi:10.1006/jsvi.1996.0474

Cited by 36 publications

(19 citation statements)

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“…The use of Fourier space is an interesting alternative for the survey of dynamic behavior of the planetary gear. The method developed by Perret-Liaudet [9], gives the response directly in the frequency domain. A suitable transformation of the equation of motion is made: the response is divided into a DC component x 0 and a dynamic component x d :…”

Section: Resolution Methodsmentioning

confidence: 99%

Influence of manufacturing errors on the dynamic behavior of planetary gears

Chaari

Fakhfakh

Hbaieb

et al. 2005

Int J Adv Manuf Technol

122

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Planetary gears are widely used in the transmissions of helicopters, automobiles, aircraft engines, etc. They have substantial advantages such as compactness and a large torque-to-weight ratio. In this work, a plane model of a planetary gear was investigated. The energetic Lagrange formulation was used to recover the equations of motion of the system. A modal analysis was performed, and the influence of gyroscopic effect in particular was scrutinized. The dynamic response was computed by an iterative spectral method. The excitation is induced by time-varying the gearmesh stiffness. The cases of a healthy planetary gear and one with the presence of eccentricity and profile error were compared. The influence on the transmission ratio was also studied.

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Section: Resolution Methodsmentioning

confidence: 99%

Influence of manufacturing errors on the dynamic behavior of planetary gears

Chaari

Fakhfakh

Hbaieb

et al. 2005

Int J Adv Manuf Technol

122

View full text Add to dashboard Cite

show abstract

“…According to the classical Newmark method, the equivalent stiffness matrices of above systems are break time-varying too so that the inverses of the matrices should be recalculated in each time step which is a tedious job when the DOF of structures becomes large. References [9,10] show us several ways to give approximate results for the structures with time-varying stiffness. But their methods are limited to the systems with periodically varying parameters.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation for dynamic responses of systems with time-varying characteristics

Chen

et al. 2009

Acta Mech Sin

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Based on Neumman series and epsilon-algorithm, an efficient computation for dynamic responses of systems with arbitrary time-varying characteristics is investigated. Avoiding the calculation for the inverses of the equivalent stiffness matrices in each time step, the computation effort of the proposed method is reduced compared with the full analysis of Newmark method. The validity and applications of the proposed method are illustrated by a 4-DOF spring-mass system with periodical time-varying stiffness properties and a truss structure with arbitrary time-varying lumped mass. It shows that good approximate results can be obtained by the proposed method compared with the responses obtained by the full analysis of Newmark method.

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“…Many researchers are concerned about how to establish a suitable method for this kind of forced problem. The existing methods comprise perturbation methods [3][4][5], numerical time integration schemes (like central-difference, Runge-Kutta and Newmark's methods), other numerical schemes treating the parametric system [6][7][8], methods based on Fourier series expansion (requiring the Ritz averaging method [9], Galerkin's procedure [10]), spectral methods (including: iterative spectral method [11] and direct spectral method [12]), modal method [13], etc. As the literature shows, extensive efforts have been devoted to develop specific computing methods for analyzing the response in time domain, while the frequency components containing in the response and their distributing features in frequency domain (named spectral properties in this paper) have not gained sufficient attentions.…”

Section: Introductionmentioning

confidence: 99%

Spectral properties for the vibrational response of parametrically excited system

Han

Wang

2009

Arch Appl Mech

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The response spectra are helpful to understand the vibrational characteristics of linear system, and further could be used as important indications for the failure diagnosis and state detecting of the system. Due to the parametric excitation, the vibrational spectra of linear periodic system differ distinctly from that of the linear time-invariant system. Thus, utilizing the Sylvester's theorem and Fourier series approximations, commonly used in the matrix decomposition, the spectral components for both the free and forced responses of linear parametrically excited system are obtained theoretically in the first part of the paper. The effects of system stability and damping on the response spectra are discussed in detail. Moreover, the external resonant condition for periodic system is found in the analysis. In the following part of the paper, spectral simulations for a spur gear pair under idle load (modeled as the free response) and fluctuating load (modeled as forced response) are done respectively to validate the theoretical results and illustrate the special frequency distributing features of periodic system intuitively.

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An Original Method for Computing the Response of a Parametrically Excited Forced System

Cited by 36 publications

References 0 publications

Influence of manufacturing errors on the dynamic behavior of planetary gears

Influence of manufacturing errors on the dynamic behavior of planetary gears

Efficient computation for dynamic responses of systems with time-varying characteristics

Spectral properties for the vibrational response of parametrically excited system

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