Jump Phenomena in Gear System to Random Excitation

Dynamics of a Gear System with Faults in Meshing Stiffness

“…Such jumps between different the types of motions, namely chaotic and regular, can be crucial for the system reliability. In this respect our results are consistent with earlier results [14,18,4]. Moreover, the system is more sensitive to errors in the distance between teeth than fluctuations in the stiffness magnitude, although the qualitative effect is similar.…”

“…Also shown is the reverse jump from the regular to the chaotic attractor, but it is clear that the system stays for longer time in the chaotic attractor with intermittent regular motion. This result confirms previous results on stochastic jumps [14,4] in systems with a stochastic force. However, the system modelled here is fully deterministic and the broken teeth act as additional parametric excitation.…”

“…In consequence, under a dynamic load, a typical gear system is a nonlinear oscillator, exhibiting a range of complex behaviour including chaos [4,[7][8][9][10][11][12][13]. In use the geometric parameters of the gears change, and this causes the corresponding nonlinear response to change [4][5][14][15]. Choy et al [16] and Kuang and Lin [17] examined the effect of tooth wear.…”

“…Choy et al [16] and Kuang and Lin [17] examined the effect of tooth wear. Vibrations have also been modelled by including stochastic forces [4,[14][15]18].…”

Methods of nonlinear random vibration analysis

“…Thus the solution of the given random differential equation is converted to a problem in nonlinear transformation of random variables. The method has been used in the study of nonlinear systems under narrow band excitations by several authors (Lennox & Kuak 1976;Sato et al 1985;Richard & Anand 1983;Iyengar 1986). …”