Modeling dynamics and stability of variable pitch and helix milling tools for development of a design method to maximize chatter stability

- Chatter stability of variable pitch and helix tools is formulated.
- Stability of variable pitch and helix tools is solved using frequency domain and semi-discretization methods with experimental verification.
- Effect of pitch and helix variations on stability limits is demonstrated.
- A practical and accurate method for optimal selection of pitch angles to maximize stability limits is presented.

Chatter is one of the major limitations in milling operations causing poor quality and reduced productivity. Stability diagrams can be used to identify deep stable pockets which usually occur at high spindle speeds. However, the required high cutting speeds may not be applied in some cases due to machinability or machine tool limitations. It is known that variable pitch and helix tools help suppressing chatter even at low cutting speeds. These tools may offer high productivity if they are properly designed. The literature on variable geometry milling tools is mainly limited to modelling and simulation whereas for industrial applications design guidelines are needed for selection of variation pattern and amount which is the focus of this paper. Dynamics and stability of variable pitch and helix tools are modelled and solved in frequency domain as well as using Semi-Discretization Method employing multiple delays. A practical but accurate design method is presented for selection of the best variation combination to maximize chatter free material removal rate without using time consuming computer simulations. Increased stability with the tools designed using the proposed method is demonstrated by several examples which are verified experimentally.