Hexu Yang

Disk springs are widely used as preload and isolation due to their unique mechanical properties. In the prior research, the effect of linear friction on the disk spring was considered, but contact stiffness, another nonlinear contact factor, is ignored. Accordingly, in this paper, the asymmetric displacements of the contact edges are first derived, and the accurate friction dissipations are obtained, as a way to evaluate the effect of friction on the system. Then the velocity of the edges was obtained to establish a dynamic friction model. Meanwhile, the contact displacement and contact stiffness of the edge are obtained by fractal contact theory. Then the nonlinear static and dynamic models of disk spring with friction and contact stiffness are established by the energy method. The load–deflection relationship, stiffness, and hysteresis of disk spring are studied with different contact states. The results show that the model considering contact stiffness and asymmetric friction dissipation can effectively evaluate the static properties of the disk spring. Friction reinforces the nonlinear behavior of the system, while contact stiffness weakens the nonlinearity of the system. And due to the influence of nonlinear contact factors, the transmissibility curves produce multiple resonance peaks.

According to the working characteristics of a 1.5 MW wind turbine planetary gear system under complex and random wind load, a two-parameter Weibull distribution model is used to describe the distribution of random wind speed, and the time-varying load caused by random wind speed is obtained. The nonlinear dynamic model of planetary gear transmission system is established by using the lumped parameter method, and the relative relations among various components are derived by using Lagrange method. Then, the relative relationship between the components is solved by Runge Kutta method. Considering the influence of random load and stiffness ratio on the planetary gear transmission system, the nonlinear dynamic response of cyclic load and random wind load on the transmission system is analyzed. The analysis results show that the variation of the stiffness ratio makes the planetary gear have abundant nonlinear dynamics behavior and the planetary gear can get rid of chaos and enter into stable periodic motion by changing the stiffness ratio properly on the premise of ensuring transmission efficiency. For the variable pitch wind turbine, the random change of external load increases the instability of the system.

In this paper, the influence of tooth surface wear on dynamic characteristics of the gear-bearing system is discussed. The gear-bearing system considering the factors of tooth surface friction, time-varying meshing stiffness, backlash and et al. is established. Based on the Fractal theory and the Archard theory, the tooth surface wear is calculated, and it is substituted into the calculation of backlash and stiffness to obtain the time-varying backlash and the time-varying meshing stiffness. The Runge–Kutta method is used to solve the dynamic differential equation of the gear system, then the phase diagrams, the Poincare section diagrams and the bifurcation diagrams of the system are obtained. The results show that compared with the constant backlash and normal-distribution backlash under the wear condition, the wear backlash calculated by the Fractal theory and the Archard theory can better show the influence of wear on the system response. With the increasing of the accumulated wear on the tooth surface, the decrement of the time-varying meshing stiffness increases, and the system is more unstable. As the friction coefficient decreases, the regions of periodic and quasi-periodic motion state increase, and the boundaries between the periodic and quasi-periodic motion state become clear. Therefore, friction mainly plays a hysteretic role on the gear-bearing system.