Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems

“…Numerical integration for the nonlinear parts is processed, the numerical integration error is controlled and this strategy is validated in our analysis by comparing with the exact results with Runge-Kutta method. In addition, in the nonlinear problem, it cannot be avoided that the unstable dynamic response or unstable periodic solution such as snapback phenomena [24][25][26] or jump phenomena [27,28] in gear dynamics. A common way is to introduce the continuation method, which can overcome this problem and is adopted by many researchers to solve the nonlinear problem recently, such as Grolet and Thouverez [29], Dou and Jensen [30].…”

Section: Ihbm and Continuationmentioning

confidence: 99%

Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method

Chen

2015

Nonlinear Dyn

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A compressed air generator hang under vehicle is simplified as a suspension mass connected to a vertical spring and two horizontal springs. It is configured generally as a geometrical negative stiffness to reduce dynamic stiffness. The periodic motion, chaotic motion and bifurcation of the compressed air generator model are investigated using the incremental harmonic balance method in combination with arc length continuation technique. The stability and bifurcation route are also distinguished with Floquet theory. The system exhibits a period doubling bifurcation route to chaos in different regions of excitation frequency. The stiffness ratio of the vertical spring and the horizontal spring has a significant influence on the dynamic response. When the vertical stiffness is close to the stiffness at horizontal direction, resonance occurs with the emergence of the chaotic motion. The dynamic response of the vibration system can be improved by reducing the stiffness in the horizontal direction to increase the stiffness ratio. L. Yuanping Key Lab of Disaster Forecast and Control in Engineering, Ministry of Education of the People'

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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.…”

mentioning

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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Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems

Cited by 121 publications

References 26 publications

Generalised non-dimensional multi-parametric involute spur gear design model considering manufacturability and geometrical compatibility

Generalised non-dimensional multi-parametric involute spur gear design model considering manufacturability and geometrical compatibility

Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method

Nonlinear modeling of solar array drive system considering backlash and friction

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