Cutting Tool Engineering
March 2010 / Volume 62 / Issue 3

Setting tool length

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

It’s common sense that to get the highest possible metal-removal rate when milling, the user should simply select the shortest tool that is geometrically capable of making the desired part feature. The tool should be as short as possible so that it is as stiff as possible. That’s because a stiff tool deflects and chatters less.

There is just one problem with that line of thought: it’s wrong. The reason is the highest achievable mrr depends not just on the stiffness, but also on the maximum spindle speed, damping and natural frequency of the toolholder-and-spindle system.
Courtesy of All Figures: Dr. Matt Davies, University of North Carolina at Charlotte

Figure 1: Stability lobe diagram for an 11.8mm-dia., 104mm-long, 2-flute, solid-carbide endmill in a 20,000-rpm spindle.

Figure 2: Stability lobe diagram for an 11.8mm-dia., 118mm-long, 2-flute, solid-carbide endmill in the same spindle and toolholder as Figure 1.

For most tools, the phenomenon that limits mrr is not available spindle power or the tool’s strength or wear rate, but rather the onset of chatter. For a given tool, toolholder and spindle, some spindle speeds are more stable against chatter and some less so. This is often expressed in a stability lobe diagram.

Figure 1 shows a stability lobe diagram for a long, slender endmill. It extends 104mm from the end of the holder for a length-to-diameter ratio of about 8.8:1. The shaded parts of the diagram represent chatter, and the white portions represent stable milling. While the spindle has a 20,000-rpm maximum speed, the stability lobe diagram was calculated to 30,000 rpm. At the 20,000-rpm top speed, the tool can only take an axial DOC of less than 0.1mm in a slot without experiencing chatter. This represents a low-power cut.

However, Figure 1 also shows a large stable zone at around 25,000 rpm. If it was possible to move that stable gap to a lower speed or even 20,000 rpm, then the mrr could be improved. The tool system’s natural frequency controls the locations of the stable gaps in a stability lobe diagram.


Figure 3: A 7000 series aluminum workpiece made with the tool described in Figure 2.

Lowering the natural frequency moves a stable gap to a lower spindle speed. One way to lower the natural frequency is to make a tool more flexible by extending it. Figure 2 shows the stability lobe diagram for the same tool in the same spindle, but adjusted so the tool extends 118mm from the nose of the holder for a length-to-diameter ratio of 10:1. In this case, the stable gap is almost exactly at the spindle’s top speed, a concept called “tool tuning.” At that speed, a stable axial DOC greater than 0.5mm is possible.

Counterintuitively, lengthening the tool from 104mm to 118mm improved the mrr more than fivefold at the top spindle speed. Figure 3 shows a workpiece that was machined with the longer tool. It could not have been successfully machined with the shorter tool.

Of course, a longer tool is not always better. If the spindle in this example had a maximum speed of 12,000 rpm, the shorter tool would have been preferable because the stable gap would have lined up better at that speed. Generally, the mrr decreases as a tool gets longer. However, considering the alignment between the maximum spindle speed and the stable zones, there will be particular lengths that are more favorable and allow the use of longer tools to achieve higher removal rates than possible with shorter tools.

For a given spindle, it is possible to use stability lobe diagrams to create a set of tuned tools in different diameters. These tools could have their lengths adjusted to maximize mrr at the spindle’s top speed. CTE

About the Author: Dr. Scott Smith is a professor and chairman of the Department of Mechanical Engineering at the William States Lee College of Engineering, University of North Carolina at Charlotte. He specializes in machine tool structural dynamics. Contact him via e-mail at

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