Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis

Farshidianfar, Anoshirvan; Saghafi, Amin

doi:10.1016/j.physleta.2014.09.060

Cited by 42 publications

(16 citation statements)

References 24 publications

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“…For this reason, the modification of the backlash is possible only to a limited extent. Due to the simplifications related to numerical calculations, the discontinuous characteristics of the gear backlash are sometimes approximated by polynomial functions of degree three [10,11]. An alternative approach to the numerical mapping of the backlash is the approximation with a continuous function, with the equation proposed in the paper [12].…”

Section: Introductionmentioning

confidence: 99%

Modelling of the gear backlash

2019

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In this paper, model tests were carried out, which mainly focused on the numerical mapping of the characteristics of the gear backlash. In particular, the effect of the approximation function on the value of the largest Lyapunov exponent was investigated. The generated multicoloured maps served as a criterion for verifying the results of the model tests. The analysis involved polynomial functions of the third degree, its modified structure, and the logarithmic equation. As a pattern to which the results of model tests were derived, the mathematical model of the gear was used, in which the characteristics of the backlash were modelled with a non-continuous function describing the so-called dead zone. We show that the dependencies described by polynomials imprecisely describe the dynamics of a single-stage gear transmission mechanism. Additionally, the value of the logarithmic coefficient, which approximates the backlash characteristics, for which the Poincare cross section corresponds with its model counterpart, is determined. The coefficient of the logarithmic function was optimized on the basis of

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Section: Introductionmentioning

confidence: 99%

Modelling of the gear backlash

2019

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“…However, spur gears used in SADS have better rigidity than other reducers, so the hysteresis effect is not very obvious. Thus the dead zone model is more tally with the actual situation [5][6][7][8] .…”

Section: B Mathematical Model Of Spur Gear Reducermentioning

confidence: 99%

“…For simplifying analysis, the influences of nonlinear factors in the joints such as backlash and friction have usually been ignored [5][6] . However, in practical engineering, nonlinear factors in the joints have a significant influence on the velocity stability of motor in SADS.…”

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confidence: 99%

Nonlinear modeling of solar array drive system considering backlash and friction

Zhou

Gao

et al. 2015

2015 18th International Conference on Electrical Machines and Systems (ICEMS)

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In this paper, a novel nonlinear dynamic model of the solar array drive system (SADS) with spur gear train transmission is proposed considering backlash and friction, which is composed of servo motor, spur gear reducer, solar arrays and friction. The backlash effect of the spur gear reducer is modeled based on an alternate engagement mechanism, while the transmitted torque is defined via the use of a dead zone function. Friction moment in the SADS is described by the hybrid model including static friction, sliding friction and stribeck effect. Based on the above-mentioned model, the influence of backlash and friction on the velocity stability of motor in the SADS is investigated. This paper can provide a guideline for engineers to follow in the control design of solar array drive system.

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“…In Ref. [21], a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error was established and based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model were predicted. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behavior analysis and time delay feedback control of gear pair system with backlash non-smooth characteristic

Li¹,

Hu²,

Shi³

et al. 2017

J. vibroeng.

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The present work investigates the non-smooth vibration characteristic and time delay feedback control of a gear pair system involving backlash and time-varying mesh stiffness. Firstly, a gear pair model with backlash non-smooth characteristic is established. Then in combination with the discontinuity mapping method, Floquet theory is presented to determine the stability and bifurcation of periodic response, and the period doubling bifurcation has been accurately predicted. Moreover, the maximal Lyapunov exponent is obtained to determine the chaos state in gear pair system which is conform to the bifurcation diagram and Poincare section. Finally, a time delay feedback is introduced to control the dynamic behaviors of the system, and numerical simulation results show that the system can be effectively controlled from chaotic motion into stable periodic motion by increasing the delay feedback gain or delay time.

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Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis

Cited by 42 publications

References 24 publications

Modelling of the gear backlash

Modelling of the gear backlash

Nonlinear modeling of solar array drive system considering backlash and friction

Dynamic behavior analysis and time delay feedback control of gear pair system with backlash non-smooth characteristic

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