On transmission errors and profile modifications minimising dynamic tooth loads in multi-mesh gears

A modular three-dimensional model of multi-mesh gears is used to analyse theoretically the link between dynamic mesh excitations and transmission errors. It is demonstrated that dynamic mesh forces are mostly controlled by the local transmission errors associated with each individual mesh. A design criterion is derived which can be used to define the tooth shape modifications minimising dynamic tooth loads. The results from two examples of application on idler and planetary systems prove that the proposed theory is sound and can be applied to a variety of gear geometries. Finally, the interest and limits of using transmission errors from a single pinion-gear pair in the context of multi-mesh gears are discussed.