Modeling of variable-pitch/helix milling system considering axially varying dynamics with cutter runout offset and tilt effects

• A variable-pitch/helix milling dynamic model with axially varying dynamics is established. • An updated cross-axis and cross-point modal testing method is proposed for long cutters. • Cutter runout including radial offset and axial tilt is considered and its influence on stability is investigated. • The model is validated by a series of milling experiments with large axial depths of cut. In order to meet the growing industrial demand of high quality and high efficiency machining, long cutters with larger axial depth of cut are extensively implemented in peripheral milling of deep pockets, grooves, and thin-wall parts. However, due to their high flexibilities, chatter easily occurs during the machining process. It has been demonstrated that milling cutters with variable pitch and/or variable helix angles can mitigate the chatter, which are gaining increasingly important applications. Although this kind of cutters have been studied in some detail in previous research, few studies have focused on the interaction dynamics complicated by actual cutter runout in long tool-part contact zone. This paper systematically studies the dynamics and stability of variable-pitch/helix milling system with long end cutters. The cutters are divided into a series of axial disks, and each axial disk includes several cutting elements which are equal to the number of teeth. Variations of pitch and helix angles, cutter run-outs including radial offset and axial tilt, and mode shapes with the cross terms in the orthogonal direction, are assigned to these cutting elements. The system, involving multiple regenerative delays as well as the axially varying dynamics, is formulated as a matrix form of time-periodic delay differential equation with multi-modal dynamic parameters. An updated cross-axis and cross-point modal testing method is then proposed to obtain the dynamic parameters, which can effectively avoid multiple hits when impacting the cutter with hammer. The stability lobes are predicted in state space by developing an improved semi-discretization method, by which the pitch variations and actual runout effects on stability are investigated. It is shown that the stability lobes differ significantly when the combined effects of cross-axis and cross-point FRFs and actual cutter runout are considered. A series of cutting experiments is conducted to demonstrate the proposed model and method. Results show that these lobes well agree with the experimental results.