An analytical method to determine the addendum modification parameters of involute helical gears

Due to the simplified tooth profile and the complicated load distribution along the contact line, the traditional analytic method cannot satisfy the accuracy requirement while carrying out addendum modification of the helical gears. To overcome this disadvantage, a new way based on cross-section method is presented to calculate the deformation of helical tooth tip. First, the tooth is divided into copies of cross-section along face width and the moment of inertia for each section is calculated. Also, the load is distributed according to length of the contact line, and the effect of deflected load is taken into account as well. Based on these works, a general formula of helical tooth tip deformation is deduced. Then, this formula is applied to calculate the addendum modification width a(c). In addition, considering that tooth tip modification will shorten the meshing line, three models used to control length of the remaining meshing line are proposed and addendum modification height h(c) is defined accordingly. Finally, an instance is given to verify the good agreement between results of this study and those of a finite element model. Apart from this, engineering application of this method is provided.