The prediction of chatter instability in machining steel and thermal-resistant alloys at low cutting speeds has been difficult due to unknown process damping contributed by the contact mechanism between tool flank and wavy surface finish. This thesis presents modeling and measurement of process damping coefficients, and the prediction of chatter stability limits for turning and milling operations at low cutting speeds.

The dynamic cutting forces are separated into regenerative and process damping components. The process damping force is expressed as a product of dynamic cutting force coefficient and the ratio of vibration and cutting velocities. It is demonstrated that the dynamic cutting coefficient itself is strongly affected by flank wear land. In measurement of dynamic cutting forces, the regenerative force is eliminated by keeping the inner and outer waves parallel to each other while the tool is oscillated using a piezo actuator during cutting.

Classical chatter stability laws cannot be used in stability prediction for general turning with tools cutting along non-straight cutting edges;​ where the direction and magnitude of the dynamic forces become dependent on the depth of cut and feed-rate. A new dynamic cutting force model of regeneration of chip area and process damping, which considers tool nose radius, feed–rate, depth of cut, cutting speed and flank wear is presented. The chatter stability is predicted in the frequency domain using Nyquist stability criterion. The process damping is considered in a new dynamic milling model for tools having rotating but asymmetric dynamics. The flexibility of the workpiece is studied in a fixed coordinate system but the flexibility of the tool is studied in a rotating coordinate system. The periodic directional coefficients are averaged, and the stability of the dynamic milling system is determined in the frequency domain using Nyquist stability criterion. The experimentally proven, proposed stability models are able to predict the critical depth of cut at both low and high cutting speeds.