Time-Varying Meshing Stiffness Calculation and Vibration Analysis for a 16DOF Dynamic Model With Linear Crack Growth in a Pinion

Abstract

A modified mathematical model for simulating gear crack from root with linear growth path in a pinion is developed, in which an improved potential energy method is used to calculate the time-varying meshing stiffnesses of the meshing gear pair while we also take the deformation of gear-body into consideration. The formulas for the meshing stiffness are deduced when the crack grows as the linear growth path in the pinion. A 16DOF dynamic model of a one-stage spur gear system is used to study the response from the system considering time-varying meshing stiffnesses and different levels of crack growing in the pinion. As vibration signals induced by the tooth crack are buried in normal vibration signals which are induced by the normal gear pair in meshing at the early stage of crack growth, the algorithm combined autoregressive modeling method and demodulation method is proposed to process the signals to investigate the response characteristics as the crack grows, and the comparison of the relationship between indicators and the crack levels from different simulation methods are given.

Review on dynamics of cracked gear systems

“…13). Considering the effects of the gear tooth root crack which propagates into the gear-body, Zhou et al [46] presented a revised mathematical model based on the assumption of a linear propagation path (see Fig. 14).…”

Fault features analysis of cracked gear considering the effects of the extended tooth contact

“…Conventional methods, such as RMS, kurtosis, and power spectrum, have proved to be effective in fault diagnosis [8,16,17]. However, their main drawback is that they are based on the assumption of stationarity and linearity of the signal generation process [33].…”

“…The key for simulation analysis is to obtain the accurate timevarying mesh stiffness (TVMS), which has a great influence on the gear pair vibration. The finite element (FE) method [1][2][3][4][5][6][7], analytical method (AM) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and analytical-FE approach [23][24][25] have been used to calculate the TVMS of gears. For AM and analytical-FE approach, they can offer a simple and effective way to calculate the TVMS under most conditions.…”

Influences of tooth crack on time-varying mesh stiffness of helical gears

“…In the same year,P.Sainsot and P.Velex [4] deduced the influence of wheel body deformation on tooth deformation. And recently Zhou et al [5] applied this conclusion to the model. The gear was modeled as a cantilever beam from the base circle.…”

“…The gear was modeled as a cantilever beam from the base circle. Also, Zhou et al [5], Tian et al [2], and Pandya and Parey deemed that the gear crack is a linear path starting from the point of intersection of the involute curve and the base circle. Yet in truth the gear tooth starts from the root circle rather than the base circle, which was pointed out by Liang.…”