Theoretical modeling and chatter prediction for the whirling process of airfoil blades with consideration of asymmetric FRF and material removal

Invented decades ago, whirling is a machining process primarily employed for producing helical surfaces. In view of its cost-effectiveness, this paper proposes to adapt the whirling process for manufacturing airfoil blades. Considering that chatter often occurs during the whirling process due to the low stiffness of blade workpiece, which impairs the machining quality, theoretical issues in relation to chatter and its prediction for the blade whirling process are investigated. Firstly, the principle of blade whirling is briefly introduced and vibration components in the cutter-workpiece system are analyzed in order to identify the characteristics of blade whirling and establish a reasonable dynamic model. Then, a theoretical model for stability prediction in blade whirling is presented and verified, which fully considers the geometric immersion of the whirling cutter and the dynamic parameters of the workpiece system. In order to ensure accuracy of the prediction results, non-symmetric frequency response function (FRF) matrices are adopted in modeling the system and identifying the modal parameters. After that, the effect of material removal on machining stability is examined. Since a large proportion of material is to be removed, the whirling operation is divided into several steps for exploration. The results show that the material removal changes the natural frequency and modal shape of the system which causes the variation of the limit on cutting depth. Finally, the proposed approach is verified with a scaled propeller blade being machined as a case study.