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BIFURCATION AND CHAOS OF NONLINEAR SYSTEM OF HELICAL BEVEL GEAR WITH CLEARANCE

Fuchun Yang

Open publisher page 1 citations

Abstract

A 7 degrees of freedom dynamic equation of helical bevel gear system with clearance was developed.The evolution of bifurcation and the effects of parameters on bifurcation and chaos of the system were numerically studied by combining bifurcation diagrams and maximal Lyapunov exponent curves.The results indicate that,following the changing of parameters,the global nonlinear characteristics can be revealed from different levels,and the full view of complex evol- ving among period-n,quasi-periodic and chaos vibrations in expounded.The system comes into chaos through three ways: from long periodic shocks to chaos via period-doubling,from quasi-periodic motion after Hopf bifurcation to chaos via chattering shocks,and from quasi-periodic motion to chaos via phase locking.Furthermore,with increasing load and damping coefficient,and decreasing stiffness coefficient,the stable region is expanded,and bifurcation and chaos are slowed and suppressed.

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What this paper is about

A 7 degrees of freedom dynamic equation of helical bevel gear system with clearance was developed.The evolution of bifurcation and the effects of parameters on bifurcation and chaos of the system were numerically studied by combining bifurcation diagrams and maximal Lyapunov exponent curves.The results indicate that,following the changing of parameters,the global nonlinear characteristics can be revealed from different levels,and the full view of complex evol- ving among period-n,quasi-periodic and chaos vibrations in expounded.The system comes into chaos through three ways: from long periodic shocks to chaos via period-doubling,from quasi-periodic motion after Hopf bifurcation to chaos via chattering shocks,and from quasi-periodic motion to chaos via phase locking.Furthermore,with increasing load and damping coefficient,and decreasing stiffness coefficient,the stable region is expanded,and bifurcation and chaos are slowed and suppressed.

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Available abstract

A 7 degrees of freedom dynamic equation of helical bevel gear system with clearance was developed.The evolution of bifurcation and the effects of parameters on bifurcation and chaos of the system were numerically studied by combining bifurcation diagrams and maximal Lyapunov exponent curves.The results indicate that,following the changing of parameters,the global nonlinear characteristics can be revealed from different levels,and the full view of complex evol- ving among period-n,quasi-periodic and chaos vibrations in expounded.The system comes into chaos through three ways: from long periodic shocks to chaos via period-doubling,from quasi-periodic motion after Hopf bifurcation to chaos via chattering shocks,and from quasi-periodic motion to chaos via phase locking.Furthermore,with increasing load and damping coefficient,and decreasing stiffness coefficient,the stable region is expanded,and bifurcation and chaos are slowed and suppressed.

Key concepts: Lyapunov exponent, Period-doubling bifurcation, Bifurcation, Bifurcation diagram, Mathematics, Saddle-node bifurcation, Nonlinear system, Mathematical analysis

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BIFURCATION AND CHAOS OF NONLINEAR SYSTEM OF HELICAL BEVEL GEAR WITH CLEARANCE — Research Paper | ScholarLens