The spur planetary gear torsional stiffness and its crack sensitivity under quasi-static conditions

• A detailed calculation procedure for estimating the overall and subsystem torsional mesh stiffnesses of a planetary gearbox
• Verification of the speed ratio squared relationship between the overall torsional stiffness and the subsystem stiffness
• The crack within the sun-planet mesh component gave the highest sensitivity within the overall stiffness
• The increase of the carrier arm stiffness can help enhance the gear crack sensitivity detection

The sun–planet and ring–planet tooth mesh stiffness variations and the resulting transmission errors are the main internal vibration generation mechanisms for planetary gear systems. This paper presents the results of torsional stiffness analysis of involute spur planetary gear systems in mesh using finite element methods. A planetary gear model with three planet gears and fixed ring gear and its subsystem models have been developed to study the subsystem and overall torsional stiffnesses. Based on the analysis of torsional mesh stiffness, predictive models for single branch sun–planet–ring and overall planetary gear torsional stiffnesses have been proposed. A crack coefficient was introduced to the sun–planet and ring–planet meshes to predict the effect and sensitivity of changes to the overall torsional mesh stiffness. The resulting mesh stiffness crack sensitivity of the overall gear system was analysed under quasi-static conditions. It was found that the carrier arm stiffness has great influence on the crack sensitivity while the overall stiffness was most sensitive to the crack on the sun–planet mesh.