A Modelling Approach for the Design and Study of Stability Issues in End Milling with Variable Tool Parameters

The development of new spindle designs and their corresponding stability studies provide a guiding technology to reduce the production costs. Prediction of frequency response at the tool tip end is of paramount importance in assessing the machining quality at the design stage. In the present work, a realistic spindle tool unit of a vertical CNC milling machine is considered for the analysis and the spindle-housing system is first analyzed using a finite element modelling. Tool and holder are analyzed as independent systems and the coupled spindle-tool frequency responses at the tool-tip are obtained from receptance coupling method. Unlike the conventional receptance coupling methods, in this work all the component receptances are obtained numerically. Further using the tool tip FRF, stability lobes are plotted analytically at different speeds. In order to obtain the machining stability boundaries, a dynamic milling model is developed with two degrees of freedom spindle tool system with rigid work piece by considering the variable pitch effect and permissible runout effect to carry out the same chip load for each cutting edge.