Stability of a machining process depends on a series of events which happen consecutively in a loop. Firstly, as a result of the machining process, cutting forces result. Then, depending on the flexibilities of tool and workpiece, tool and/or workpiece experience displacements due to the cutting forces. The relative displacements of the tool with respect to the workpiece are important in terms of stability. Difference between the current relative displacements and the relative displacements at the previous period results in dynamic chip thickness. Then dynamic chip thickness acts as a feedback loop and affects the uncut chip thickness. The block diagram explaining this process is presented in Figure 1.


Figure 1. Block diagram for self-excited vibrations

The stability of the system depends on the phase angle between the current relative displacement values and the values one period before. If they are in phase, uncut chip thickness stays bounded. If they are not in phase, dynamic chip thickness shows variation as presented in Figure 2 and the process results in instability. The resulting vibrations are called self-excited vibrations or chatter vibrations. They are among the most important problems in machining. They deteriorate the surface quality by leaving chatter marks on the surface.

Using stability diagrams is an efficient way to avoid chatter vibrations. The stability diagrams separate the stable and unstable regions and help the process planner select process parameters that result in stable cuts. A representative stability diagram is presented in Figure 3. The region below the curve is the stable region, whereas the region above the curve is the unstable region. For a given cutting process, resulting surfaces for two different combinations of cutting depth and spindle speed are shown in Figure 3 to be representative. As can be seen from the figure, the one above the stability diagram curve has clear chatter marks whereas there are no chatter marks on the one below the curve.

Aerospace materials like Titanium and Inconel alloys are machined at low cutting speeds where process damping affects are observed. Process damping effects need to be included in the stability diagram predictions for such processes.


Figure 2. Current displacements and the ones that are one tooth period before in a milling process which cause dynamic chip thickness variation


Figure 3. A representative stability diagram