Influence of actual static transmission error and contact ratio on gear engagement dynamics

In the literature, many models for depicting the gear mating dynamics are present. In addition, finite element techniques allow to perform highly representative engagement analysis, but with a high computational effort and in particular only after having defined a semi-definitive geometry. When a new gearbox is developed, its geometrical features are not completely defined, and highly refined finite element models cannot be used. On the other hand, performing parametric analysis at the early stages of the design process is mandatory to shorten the lead time. In this direction, an accurate parametric model of gear engagement, which requires a little computational effort, is an enabling technology. In the present paper, the Harmonic Balance Method is used to build a simple engagement model able to predict the dynamic effect in teeth contact and to investigate the contribution to gear dynamics due to actual static transmission error and the contact ratio. A particular emphasis is given to the actual contact ratio estimation and the relationship between the teeth stiffness and the dynamic transmission error. As principal result, the possibility to design teeth stiffness in order to minimize dynamic transmission error is investigated and HBM potential for reaching this goal is evaluated.