Cutting Tool Engineering
October 2011 / Volume 63 / Issue 10

Finding stability with 'super diagram'

By Dr. Scott Smith, University of North Carolina at Charlotte

For a given radial DOC when milling, the stability lobe diagram shows the combinations of axial DOC and spindle speed that will result in either chatter or stable milling. Slot milling is the least stable case, and NC programming based on stability for slotting automatically means that other radial DOC operations are also stable.

However, besides the stability issue when slotting, there are other constraints that have an impact on the choice of toolpath. For example, the geometry of the finished part is affected by the surface location error (SLE). Typical NC programming software only accounts for the kinematic motion of the tool, assuming the tool is a rigid cylinder and the workpiece is a rigid prism. However, the tool is a collection of cutting edges bound together, and the tool and the workpiece deflect in response to the cutting force. It is the combination of the deflections and the position of the cutting edges that imparts the finished surface (see the Machine Technology column in the August 2010 issue).

The finished surface is often mislocated, and the SLE is not intuitive. The surface location depends on the frequency of the teeth passing, dynamic characteristics of the system, helix angle, workpiece material and chip load.

To describe the effect of milling dynamics on the finished workpiece, Dr. Tony Schmitz at UNC Charlotte has produced a modified stability lobe diagram, including restrictions on SLE. He calls it the “super diagram” (Figures 1, 2 and 3).

All images courtesy of R. Zapata and T. Schmitz

Figure 1. Milling super diagram with the maximum SLE specified to be no more than 30µm and a chip load of 0.15mm per tooth.

The SLE in Figure 1 is specified to be no more than 30µm, and the chip load is set at 0.15mm per tooth. Black regions indicate the conditions where chatter would occur. White regions indicate where the machining would be stable and the SLE specification would be met. Gray regions indicate where the machining would be stable but the SLE specification would not be met. Figure 1 shows the SLE specification is not met in a large portion of the stable machining zone. The feasible machining conditions to satisfy stability and SLE criterea are mostly located around 40,000 rpm and less than a 2mm axial DOC or around 25,000 rpm and less than a 1mm axial DOC.

Interestingly, there are some regions where a larger axial DOC results in a better SLE than in regions with a smaller axial DOC. The super diagram only considers the maximum absolute SLE and does not, for instance, indicate surface roughness.

Relaxing the specification by allowing the SLE to be as large as 70µm results in the super diagram shown in Figure 2. In that case, a substantially larger feasible machining zone is available.


Figure 2. Milling super diagram with the maximum SLE specified to be no more than 70µm and a chip load of 0.15mm per tooth.

In a similar way, reducing the chip load opens up more feasible machining zones until, with a chip load of 0.075mm per tooth and a permissible SLE of 70µm, all stable cuts satisfy the SLE condition (Figure 3).

Figure 3.tif

Figure 3. Milling super diagram with the maximum SLE specified to be no more than 70µm and a chip load of 0.075mm per tooth.

The milling super diagram can be created for any radial DOC. It is particularly useful in the process planning stage, where it serves as a guide to the NC programmer for selecting appropriate cutting conditions. CTE

Parameters used in the super diagram examples
Parameter Value



Damping percentage


Natural frequency

2,400 Hz

Tool diameter


Helix angle


Number of teeth


Tangential cutting


700 N/mm2

Normal cutting coefficient

210 N/mm2

Feed per tooth

0.15 mm/tooth (Figures 1, 2)

0.075 mm/tooth (Figure 3)

Radial DOC


Scott Smith 8_09.tif About the Author: Dr. Scott Smith is a professor and chair of the Department of Mechanical Engineering at the William States Lee College of Engineering, University of North Carolina at Charlotte, specializing in machine tool structural dynamics. Contact him via e-mail at For more information about the milling super diagram, see R. Zapata and T. Schmitz, 2009, “A New ‘Super Diagram’ for Describing Milling Dynamics,” Transactions of NAMRI/SME, 36: 245-252.
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