Analytical prediction of chatter stability of end milling process using three-dimensional cutting force model

This article presents the dynamic stability issues in helical-end milling using a three-dimensional cutting force model with flexibility consideration in spindle-tool holder-tool unit. Frequency responses of tool-tip are obtained by finite-element modelling of spindle-tool assembly. Assembly level geometrical variations, such as tapered hole in spindle and holder elements as well as multiple steps in spindle shaft, are properly considered during modelling. These tool-tip frequency responses are validated with 3-D finite-element models, where all component flexibilities are included. The three-dimensional cutting force model is employed to generate the expressions for stable depth-of-cut and operating speeds during machining operation, and these outcomes are compared with those obtained from two-dimensional cutting force model. The 3-D stability model is experimentally verified using the cutting tests at the proposed operational parameters. Later, the work concentrates on the analysis of the cutting forces and the vibrations generated in the helical-end milling process at different depths of radial immersions.