On the Dynamic Gear Tooth Loading of Planetary Gearing as Affected by Bearing Clearances in High-Speed Machinery

The paper studies the effect of bearing clearances in the dynamic analysis of planetary gear mechanisms in high-speed machinery. For this purpose, an analytical model is developed based on the interdependence between kinematics and kinetic relationships that must be satisfied when contact is maintained between the journal and its bearing. The contact mode is formulated such that the bearing eccentricity vector must align itself with bearing normal force at the point of contact. The analysis mainly relies on determining the direction of the bearing eccentricity vector defined as the clearance angles β_i at the bearing revolutes for each contact mode of the gear teeth. The governing equations of the clearance angles are developed using the geometrical constraints of the contact point location and the velocity ratio. The clearance angles and their derivatives are used to systematically evaluate kinematic and dynamic quantities. A rigid planetary spur gears with two revolute clearances is analyzed to illustrate the procedure.