Neighboring periodic motion in spur gear pair and its identification methods

There exists a kind of complex periodic motion caused by the short-period error such as the pitch deviation, tooth surface crack, and so on, in the gear transmission system. It affects the transmission stationary of the system. This complex periodic motion is defined as the neighboring periodic motion in this paper. Its identification methods are proposed by using the multi-time scale Poincaré mapping sections. The nonlinear dynamics model of spur gear pair considering pitch deviation under multi-state meshing is introduced. The neighboring periodic motion of the system under different parameters is analyzed according to the proposed identification methods. The multi-stable motion of the spur gear pair with short-period error is explored by analysis methods of nonlinear dynamics. Results show that the short-period error leads to the nonstationary transmission of spur gear pair. The periodic motion of the system shows a long-period motion in the micro-time scale due to the effect of the short-period error. The actual periodic number of the system motion is the number of mapping points obtained in the macro-time scale. The number of mapping points in micro-time scale illustrates point clusters. The number of phase trajectory in micro-time scale displays lines clusters. The short-period error affects the range of parameters for multi-stable motion in spur gear pair. These identification and analysis methods provide a theoretical basis for investigation of the neighboring periodic motion in nonlinear systems.