Static load sharing by tooth pairs in contact in internal involute spur gearing with thin rimmed pinion

Involute toothed internal−external standard gear sets are modeled for load-sharing by the teeth pairs in mesh along the line of contact. An analytical solution is proposed. Considering the rigid body in rotation, it is assumed that angular rotation of a gear with respect to the other gear due to deformation along the line of contact is equal. The sum of the normal loads in all tooth pairs in contacts, which equals to the total transmitted load, is considered constant. All possible deformations such as, tooth bending deflection, tooth compressive (contact) deformation, tooth foundation deflection and tooth shearing deflection are considered in analyses. Detailed tooth geometries are incorporated in modeling. Ultimately, the map of load sharing by tooth pairs in contacts, at different angular position, over a cycle of similar contact pattern, is established. Finally, considering thin rimmed gears, the effects of the rim thickness on load sharing, which is the aim of the present investigation are analyzed and the results are presented in terms of backup ratios.