Abstract
Due to the change in the number of contact tooth pairs, mesh stiffness is periodically time-varying, which leads to additional time-variant coefficients in the corresponding governing equations of geared dynamic system. Natural frequency of such system differs distinctly from that of the time-invariant system. However, it has not gained enough attentions in geared dynamic analysis, and the natural frequency of geared system is usually assumed to be the average frequency, obtained using the time-average mesh stiffness. Whether it is reasonable for us to obtain the natural frequency of geared system like this should be analyzed seriously. Thus, the natural frequency of parametric vibration for spur-gear-pair system will be researched using Floquet theory in this paper. Influences of the periodically time-varying mesh stiffness parameters (including: mesh frequency and contact ratio) on natural frequency will be discussed respectively in detail. Contrasts between natural frequency and average frequency for the system in stable and unstable regions will be processed and the scope of application for taking the average frequency as a substitution for the natural frequency of geared system will then be presented in the paper.
