Nonlinear dynamic characteristic of gear system with the eccentricity

In this paper, the dynamic behavior of a spur gear system was studied with external and internal dynamic incentive. The vibration differential equations for spur gear system were expressed in equivalent discrete models of mass, damping, and spring elements using the Lagrange equation considering the effect of lateral-torsional vibration coupling on the dynamics of gears, which was solved by the Newmark method. The investigation was carried out with multi-degree of freedom system for spur gear model, which took into account gravity, gear eccentricity, backlash, dynamic transmission error and external dynamic incentive. The lateral and torsional response characteristics of geared system were analyzed by changing the value of the rotational speed, backlash and eccentricity. It was shown from the research that the jump discontinuous phenomenon occurred at lower backlash value with increasing rotational speed and the frequency amplitudes also increased, and the regions of continuous frequency became winder when the rotational speed difference was greater. Moreover, complicated combination frequency components followed a rule of increasing firstly and then decreasing with the different backlash and eccentricity. The study may contribute to a further understanding of the dynamic characteristics of such a gear rotor-bearing system

The Dynamics Analysis of Two Delayed Epidemic Spreading Models with Latent Period on Heterogeneous Network

Two novel delayed epidemic spreading models with latent period on scale-free network are presented. The formula of the basic reproductive number and the analysis of dynamical behaviors for the models are presented. Meanwhile, numerical simulations are given to verify the main results