Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash

Walha, Lassâad; Fakhfakh, Tahar; Haddar, Mohamed

doi:10.1016/j.mechmachtheory.2008.05.008

Cited by 172 publications

(109 citation statements)

References 15 publications

(33 reference statements)

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“…Figure 3 shows a schematic illustration of the dynamic model of one-way clutch, two-shaft assembly considered in the present analysis. In this model, 1 is the base circle radius of gear 1, 2 is the base circle radius of gear 2, 1 is the mass moments of inertia of gear 1, 2 is the mass moments of inertia of gear 2, is the mass moment of inertia of inner ring, 1 is the mass of gear 1, 2 is the mass of gear 2, ℎ is the damping coefficient of the gear mesh, ℎ ( ) is the time-varying stiffness coefficient of the gear mesh, which can be obtained by assuming a rectangular wave as shown in (2) [8,18], where ℎ is the average mesh stiffness value, ℎ and are the th Fourier coefficient and phase angle of ℎ ( ), respectively, and…”

Section: Working Principle Of One-way Clutchmentioning

confidence: 99%

“…And to analyze the nonlinear dynamic behaviors of gear transmission system, the different excitation of static transmission error, dynamic meshing stiffness, bearing contact stiffness, prime mover, clearance nonlinearity, and load fluctuation are added [1][2][3][4][5][6][7]. Walha et al [8] investigated the dynamics of a twostage gear system with mesh stiffness and backlash. Parker et al [9] used a finite element/contact mechanic model to investigate the dynamic response of a spur gear pair.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Working Principle Of One-way Clutchmentioning

confidence: 99%

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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show abstract

“…2). The gear mesh stiffness variation can be decomposed in two elements: an average component denoted by kc, and a time variant one noted by kv(t) (Walha et al, 2009).…”

Section: Modelling Of a One-stage Gear Systemmentioning

confidence: 99%

Dynamic response of a spur gear system with uncertain parameters

Guerine¹,

Hami

Walha

et al. 2016

jtam

Self Cite

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In this paper, we propose a new approach for taking into account uncertainties based on the projection on polynomial chaos. The new approach is used to determine the dynamic response of a spur gear system with uncertainty associated to gear system parameters. The simulation results are obtained by the polynomial chaos approach for dynamic analysis under uncertainty. The proposed approach is an efficient probabilistic tool for uncertainty propagation. It has been found to be an interesting alternative to the parametric studies. The polynomial chaos results are compared with Monte Carlo simulations.

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“…Walha [9] investigated the dynamics of a two-stage gear system involving backlash and time dependent mesh stiffness, which found phenomenon of loss of teeth contact because of the discontinuity of the kinematic movement. Byrtus [10] established a gear system dynamics model using modal synthesis method, in which the time-varying mesh stiffness, side gear clearance, non-linear bearing forces were considered, but impact of flexible shaft was not studied.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics Analysis of a Gear-Shaft-Bearing System with Breathing Crack and Tooth Wear Faults

Cui¹

2015

TOMEJ

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Considering backlash, time-varying mesh stiffness and radial clearance of bearing, nonlinear dynamic model of gear bearing flexible shaft system is established taking into account breathing crack in shaft and tooth wear. Nonlinear dynamic equations are solved by Runge-Kutta method. Effect of backlash, crack in shaft and tooth wear faults on the nonlinear dynamic behavior of gear-shaft-bearing system is studied. The results show that gear-shaft-bearing system may change from periodic motion to non-periodic motion as backlash increases, and gear pair change from normal mesh to tooth separation, double-sided impact fault. If crack fault appears, quasi-periodic and chaos motion region increases, and gentle crack fault can result in instantaneous tooth separation and double-sided impact faults. Serious tooth wear fault will also induce tooth separation and double-sided impact faults. If both shaft crack and tooth wear faults exist, tooth wear fault will be intensified by double-sided impact fault from shaft crack, which will result in early failure of the gear system.

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Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash

Cited by 172 publications

References 15 publications

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

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

Dynamic response of a spur gear system with uncertain parameters

Nonlinear Dynamics Analysis of a Gear-Shaft-Bearing System with Breathing Crack and Tooth Wear Faults

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