Search

Considering the effects of the tip-fillet and friction between teeth surfaces, an improved analytical model for time-varying mesh stiffness (TVMS) calculation is further developed based on our previous works (Ma et al. in Mech Mach Theory, 98:64–80, 2016) in which the effects of extended tooth contact, revised fillet-foundation stiffness and nonlinear contact stiffness are taken into account. The proposed model is also verified by comparing the TVMS with that obtained from finite element method. Combined effects of the tip-fillet and friction on the TVMS, loaded transmission error and loaded sharing factor are discussed. The results show that TVMS between double- and single-tooth engagements becomes smooth under the small radii of the tip-fillet, however, an abrupt change of the TVMS from double-tooth contact to single-tooth contact can be observed under the large radii of the tip-fillet. The range of the double-tooth engagement decreases and the single-tooth engagement increases with the increase of the radius of the tip-fillet. In addition, the tooth-surface friction mainly affects the mesh stiffness in single-tooth engagement region due to the change of friction force direction near pitch point, and the extent of variation increases with the increase of friction coefficient. The friction has a larger effect on the TVMS than the tip-fillet for the selected parameters of tip-fillet and friction. This study can provide a basis for the structural design of the spur gears.

Considering the effects of extended tooth contact (ETC), revised fillet-foundation stiffness under double-tooth engagement region, nonlinear contact stiffness and tooth spalling defect, an analytical model for time-varying mesh stiffness (TVMS) calculation of spur gears is established. In addition, the analytical model is also verified by comparing the TVMS under different spalling widths, lengths and locations with that obtained from finite element method. The results show that gear mesh stiffness decreases sharply with the increase of spalling width, especially during the single-tooth engagement; the spalling length only has an effect on the beginning and ending of gear mesh stiffness reduction; the spalling location can affect the range of gear mesh stiffness reduction, and the range will reduce when the spalling location is close to the addendum. This study can provide a theoretical basis for spalling defect diagnosis.

Due to the effects of gear flexibility, the extended tooth contact (ETC) can appear, which is the phenomenon that the incoming tooth pair gets into contact ahead of the theoretical start of contact and the outgoing tooth pair is out of contact later than the theoretical end of contact. A large calculation error for the time-varying mesh stiffness (TVMS) calculation can be caused if the effects of ETC are ignored, especially under the larger torques. In this paper, an improved analytical method (IAM) suitable for gear pairs with tip relief is established to determine time-varying mesh stiffness (TVMS), where the effects of ETC, nonlinear contact stiffness, revised fillet-foundation stiffness, and tooth profile modification are considered. Based on the improved analytical model, TVMS under different torques, lengths, and amounts of profile modification is compared with that obtained from analytical finite element approach [29] and from FE method. The results show that TVMS obtained from the IAM agrees well with that from FE method and from analytical FE approach [29], and the computational efficiency of the IAM is also much higher than that of FE method.

In this paper, a mesh stiffness model is developed for profile shifted gears with addendum modifications and tooth profile modifications (TPMs). The time-varying mesh stiffness (TVMS), load sharing factor (LSF), loaded static transmission error (LSTE) and non-loaded static transmission error (NLSTE) of a profile shifted spur gear pair with TPMs are obtained by the analytical model. The optimum profile modification curve under different amounts of TPM is determined by analyzing the LSTE first. Then, considering the effect of NLSTE, finite element (FE) model of a geared rotor system is established. The system vibration responses under different TPM curves are analyzed and the optimum modification curve is further evaluated by amplitude frequency responses. The results show that the optimum modification curve is related to the amount of TPM and modification coefficients. The comparison of the optimum profile modification curves is evaluated by LSTE and vibration responses, which shows that the optimum modification curve should be determined by evaluating the vibration response of the geared rotor system in the low mesh frequency range.

This paper studies the mesh characteristics and vibration responses of a gear system with crack and spalling faults using different modeling methods. These modeling methods for the time-varying mesh stiffness (TVMS) include Yang's method, Tian's method and Liang's method which can not consider the effect of the fillet foundation stiffness, Zhou's method, Wan's method, two methods proposed by Ma and finite element method which include the effect of the fillet foundation stiffness. The effects of the crack and spalling are introduced into these models to calculate the TVMS for gear pairs with faults, and TVMS are compared based on these methods. By combining the TVMS with a two-dimensional lumped mass model of a gear system, the system vibration responses are compared using these modeling methods. The comparison results show that the fillet foundation stiffness has an important influence on the TVMS and vibration responses of the gear systems. Moreover, the error of repeated calculation of the fillet foundation stiffness must be revised.