Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: sub-harmonic motions

Al-Shyyab, Ahmad; Kahraman, Ahmet

doi:10.1016/j.jsv.2003.11.029

Cited by 135 publications

(67 citation statements)

References 20 publications

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“…Also, the quasi-periodic responses show random behaviors, as shown in Figure 14c,d. These results lead to similar trends of quasi-periodic responses to those in the other types of systems [5,18].…”

Section: Investigation Of Quasi-periodic Responses Using Poincaré Mapsupporting

confidence: 78%

“…This phenomenon is associated with the NVH performance (vibration and noise) of the target system and is highly nonlinear behavior, and difficult to analyze. In order to investigate nonlinear dynamic responses in a simple mechanical system, many studies have been conducted using the harmonic balance method (HBM) [4][5][6][7][8][9][10][11][12]. For example, Peng et al [4] suggested nonlinear output frequency response functions using the Duffing oscillator to simulate strong nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Peng et al [4] suggested nonlinear output frequency response functions using the Duffing oscillator to simulate strong nonlinear equations. Al-shyyab and Kahraman [5] investigated sub-harmonics and chaotic motions in a multi-mesh gear train using a nonlinear time-varying dynamic model. Chen et al [6] used the incremental harmonic balance (IHB) method to investigate the limit cycle oscillation of a two-dimensional airfoil with parameter variability in an incompressible flow.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Yoon

Kim

2015

Energies

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Dynamic behaviors in practical driveline systems for wind turbines or vehicles are inherently affected by multiple nonlinearities such as piecewise-type torsional springs. However, various excitation conditions with different levels of magnitudes also show strong relationships to the dynamic behaviors when system responses are examined in both frequency and time domains. This study investigated the nonlinear responses of torsional systems under various excitations by using the harmonic balance method and numerical analysis. In order to understand the effect of piecewise-type nonlinearities on vibrational energy with different excitations, the nonlinear responses were investigated with various comparisons. First, two different jumping phenomena with frequency up-and down-sweeping conditions were determined under severe excitation levels. Second, practical system analysis using the phase plane and Poincaré map was conducted in various ways. When the system responses were composed of quasi-periodic components, Poincaré map analysis clearly revealed the nonlinear dynamic characteristics and thus it is suggested to investigate complicated nonlinear dynamic responses in practical driveline systems.

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Section: Investigation Of Quasi-periodic Responses Using Poincaré Mapsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Yoon

Kim

2015

Energies

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show abstract

“…And the dimensionless governing equations of motion are shown as (10), where is the dimensionless transverse displacement of the th gear ( = 1, 2), 1 is dimensionless difference between the dynamic transmission error and the static transmission error of the two gears, and 2 is the dimensionless dynamic transmission error between gear 2 and the inner ring.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…And the dynamic characteristics of a gear pair are analyzed across a wide range of frequency and torques. Al-Shyyab and Kahraman [10] adopted lumped parameter method to establish a nonlinear time-varying dynamic model for multimesh gear, considering the nonlinear gear gap and gear meshing stiffness. The multiterm harmonic balance method (HBM) was used to gain the steady-state period-1 response, including the Root Mean Square (RMS) and the mean value of the vibration amplitude across a wide range of frequency, taking into account different gear meshing stiffness.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

Liu¹,

Yan²,

Cao³

et al. 2017

Shock and Vibration

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A four-degree-of-freedom nonlinear transverse and torsional vibration model of spur gear transmission system for one-way clutch, two-shaft assembly was developed, in which the one-way clutch was modeled as a piecewise nonlinear spring with discontinuous stiffness, considering the factors such as the time-varying gear mesh stiffness, static transmission error, and nonlinearity backlash. With the help of bifurcation diagrams, time domain response diagrams, phase plane diagrams, and Poincaré maps, the effects of the excitation frequency and the torsional stiffness of one-way clutch on the dynamic behavior of gear transmission system for one-way clutch, two-shaft assembly are investigated in detail by using Runge-Kutta method. Numerical results reveal that the system response involves period-1 motion, multiperiodic motion, bifurcation, and chaotic motion. Large torsional stiffness of one-way clutch can increase the impact and lead to instability in the system. The results can present a useful source of reference for technicians and engineers for dynamic design and vibration control of such system.

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A new approach for non‐Gaussian vibration analysis of hyperbolic tangent package with a critical component

Yang

Wang

et al. 2022

Math Methods in App Sciences

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A new approach is proposed to analyze the non‐Gaussian random vibration of hyperbolic tangent package. Firstly, the non‐Gaussian vibration noise of specified mean, variance, skewness, and kurtosis is developed by Hermite polynomial and verified by Gaussian mixture model theory. Secondly, next to analyzing an analytical and numerical response of the two degrees of freedom linear package, the acceleration response of the two degrees of freedom hyperbolic tangent package system under non‐Gaussian vibration excitation is obtained though the Hermite polynomial and Runge–Kutta method, and the effects of the external excitation and system parameters are investigated. Finally, on the basis of the first‐passage probability of the acceleration response, the reliability analysis method is introduced. The analysis provides a guidance to the vibration reliability analysis and packaging optimization design.

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Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: sub-harmonic motions

Cited by 135 publications

References 20 publications

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

A new approach for non‐Gaussian vibration analysis of hyperbolic tangent package with a critical component

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