Jixie chuandong (Apr 2021)
Research of Gear Meshing Stiffness Identification Algorithm based on Exponential Window Interception Recursive Least Square Method
Abstract
Gear is widely applied in mechanical transmission systems. Gear meshing stiffness is a time varying parameter because of the periodical changing of the numbers of teeth involved in meshing process，the meshing vibration is generated during gear meshing. When the cracks are existed in roots of gear teeth，the meshing stiffness decreased，vibration response of the system due to gear meshing changed as well. Thus，identifying gear meshing stiffness through vibration response is a method monitoring healthy state of gear pairs. For the time-varying character of meshing stiffness，a gear meshing stiffness identification algorithm is proposed based on exponential window recursive least square method（EWRLS） interception and instantaneous frequency of the vibration signal. During the identification of meshing stiffness，EWRLS algorithm takes the speed curves of the input and output gears as the identification input signal and observation signal，respectively. In the algorithm，the exponential window is applied to intercept data，and the recursive least square algorithm is applied to estimate parameters of the system. To calculate speed curve of the input and output gears，the empirical mode decomposition （EMD） method is used to decompose vibration signal into intrinsic mode function （IMF） of different frequency，the IMFs are used to reconstruct character signals of input and output gears basing on the mean frequency of IMFs. The Hilbert transform is applied to calculate the instantaneous frequency curve of the character signals to obtain the speed curves of gears. The simulated signal and measured signal are used to validate the algorithm，results show that the EWRLS algorithm can identify time-varying meshing stiffness of gear pair.
