Dynamics of a Gear System with Faults in Meshing Stiffness

Gear box dynamics is characterised by a periodically changing stiffness. In real gear systems, a backlash also exists that can lead to a loss in contact between the teeth. Due to this loss of contact the gear has piecewise linear stiffness characteristics, and the gears can vibrate regularly and chaotically. In this paper we examine the effect of tooth shape imperfections and defects. Using standard methods for nonlinear systems we examine the dynamics of gear systems with various faults in meshing stiffness.Comment: 10 pages, 8 figure

A boundary integral formalism for stochastic ray tracing in billiards

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain

Analysis of nonlinear oscillators in the frequency domain using volterra series Part II : identifying and modelling jump Phenomenon

In this the second part of the paper, a common and severe nonlinear phenomenon called jump, a behaviour associated with the Duffing oscillator and the multi-valued properties of the response solution, is investigated. The new frequency domain criterion of establishing the upper limits of the nonlinear oscillators, developed in Part I of this paper, is applied to predict the onset point of the jump, and the Volterra time and frequency domain analysis of this phenomenon are carried out based on graphical and numerical techniques

Global dynamics of a harmonically excited oscillator with a play : Numerical studies

This work was supported by the National Secretariat of Science, Technology and Innovation of Ecuador (SENESCYT); the Escuela Superior Politécnica del Litoral of Ecuador (ESPOL); the National Natural Science Foundation of China (11272268, 11572263) and Scholarship of China. A.S.E. Chong and Y. Yue acknowledge the hospitality of the Centre of Applied Dynamics Research at the University of Aberdeen.Peer reviewedPostprin

Resonances of the SD oscillator due to the discontinuous phase

Resonance phenomena of a harmonically excited system with mul-tiple potential well play an important role in nonlinear dynamics research.In this paper, we investigate the resonant behaviours of a discontinuous dynamical system with double well potential derived from the SD oscillator to gain better understanding of the transition of resonance mechanism. Firstly,the time dependent Hamiltonian is obtained for a Duffing type discontinuous system modelling snap-through buckling. This system comprises two subsystems connected at x = 0, for which the system is discontinuous. We constructa series of generating functions and canonical transformations to obtain the canonical form of the system to investigate the complex resonant behavioursof the system. Furthermore, we introduce a composed winding number to explore complex resonant phenomena. The formulation for resonant phenomena given in this paper generalizes the formulation of n Omega0 = m Omega used in the regular perturbation theory, where n and m are relative prime integers, Omega 0 and Omega are the natural frequency and external frequencies respectively. Understanding the resonant behaviour of the SD oscillator at the discontinuousphase enables us to further reveal the vibrational energy transfer mechanism between smooth and discontinuous nonlinear dynamical system

Piecewise Volterra modelling of the Duffing oscillator in the frequency domain

When analysing the nonlinear Duffing oscillator, the weak nonlinearity is basically dependent on the amplitude range of the input excitation. The nonlinear differential equation models of such nonlinear oscillators, which can be transformed into the frequency domain, can generally only provide Volterra modelling and analysis in the frequency-domain over a fraction of the entire framework of weak nonlinearity. This paper discusses the problem of using a new non-parametric routine to extend the capability of Volterra analysis, in the frequency domain, to weakly nonlinear Duffing systems at a wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address