Analyses of Spur and Helical Gears

Abstract: The thesis contains three papers that comprise studies of the dynamic behaviour of involute spur and helical gears, and one paper that describes a method to determine the influence of misalignment on the static helical gear tooth stress. In the first study, the influence of the contact ratio on the dynamic response of a spur gear was examined. The spur gear pair was modelled using a single degree of freedom model with a piecewise constant gear mesh stiffness. By adopting this gear mesh stiffness variation, the dynamic response can be solved analytically. Based on a stability analysis of the resulting dynamic transmission error, the proper contact ratio to use in order to avoid tooth separation near a specific critical rotational speed was determined. In the other two studies of the dynamic behaviour of a gear set, the contact and the load between the gear teeth were more thoroughly investigated. The position of the contact and the distance that the gear teeth must deform were determined for every time increment in the dynamic simulation. This method ensures that the load is properly modelled, even at the beginning and at the end of the meshing cycle. The technique was applied to a helical gear, which requires a 3D-analysis when calculating the load distribution along the line of contact. Furthermore, this technique was applied to a spur gear set to study the influence of the elasticity of the bearings and the significance of the gear mesh friction on the dynamic response. In addition, a method to determine how a misalignment of the gear axes will affect the static gear tooth stress of a helical gear pair is presented. Due to the misalignment, the load distribution along the line of contact will be shifted and the maximum contact pressure and the maximum fillet stress will be affected. A tooth contact analysis to find the contact between two helical gear teeth and the distance that the gears have to deform is included in the thesis.