NEIGHBORING PERIODIC MOTION AND ITS IDENTIFICATION FOR SPUR GEAR PAIR WITH SHORT-PERIOD ERRORS

The pitch deviation and other errors as the short-period error in spur gear pair lead to complex periodic motion which affects the transmission stationarity of gear systems. The complex periodic motion is defined as the neighboring periodic motion. It is identified by using the multi-time scale Poincaré mapping sections. A nonlinear dynamics model of the spur gear pair with pitch deviation is introduced in order to study the neighboring periodic motion of the gear pair. Backlash, time-varying contact ratio and other parameters are considered. The dynamics model is numerically calculated by the variable step 4-order Runge-Kutta method. The proposed identification method is used to analyze the neighboring periodic motion of the system under different parameters. The information of attractors and the basin of attraction in the state plane can be obtained by the improved cell mapping theory. The multi-stable neighboring periodic motions of the system under the variation of torque and meshing frequency are investigated by typical nonlinear dynamics analysis methods, such as multi-initial values bifurcation diagrams, phase diagrams, Poincaré maps, basin of attraction and bifurcation dendrogram. Results show that the short-period error in the spur gear pair leads to the complex periodic motion of the system. In the micro time scale, Poincaré mapping points of the system show the form of point clusters. The number of point clusters and actual motion period of the system are the number of Poincaré mapping points in the macro time scale. The short-period error leads to the increase of the number of attractors in the micro time scale which makes the motion transition process of the system more complex. The reasonable range of parameters and initial values can improve the transmission stationarity of the gear pair. The identification and analysis methods provide a theoretical basis for the study of the neighboring periodic motion in nonlinear systems.