Cutting Tool Engineering
May 2011 / Volume 63 / Issue 5

Maximum speed may be the worst speed

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

A machine’s maximum spindle speed may not be a good one—it may even be one of the worst. That’s the case when the following conditions are present:

A milling spindle’s maximum speed is higher than about 10,000 rpm;

You are applying a short endmill with two teeth;

You are machining a relatively easy-to-machine material like aluminum; and

You are removing a significant amount of material.

Under those conditions, you should reduce the maximum spindle speed by about 25 percent. This month’s column explains why.

Courtesy of S. Smith

Figure 1. The first bending mode of a small-diameter, high-speed spindle.

Courtesy of Dr. Matt Davies, University of North Carolina at Charlotte

Figure 2. Stability lobe diagram measured for a short, 2-flute, solid-carbide endmill in a 20,000-rpm spindle. The vertical axis shows the axial DOC, and the horizontal axis shows the spindle speed. The shaded areas represent chatter, and the red line indicates the maximum spindle speed.

A high-speed spindle usually has a smaller-diameter shaft than a conventional spindle because it is easier to get a small-diameter spindle to rotate at a high speed than a large-diameter spindle. This capability is often expressed as the DN number (a product of the bore diameter of the main bearing in millimeters and the spindle speed in rpm), which is limited to about 2 million for ball bearing spindles.

If the spindle diameter is small and the tool is short, the spindle is often the most flexible element in the system, and the first spindle bending mode is the most flexible mode. Figure 1 shows an idealized spindle, with the shaft supported by two sets of bearings: one in the front and one in the rear. “First bending mode” means the spindle likes to vibrate at a particular frequency (the natural frequency) similar to the red line shown in the lower part of the figure. The bearings appear very stiff for this mode, and there is almost no bearing deflection. The frequency of this mode is determined primarily by the diameter, length and material of the spindle shaft.

No spindle is perfectly balanced. As the spindle rotates, the small amount of unbalance produces a variable force that excites the spindle at the rotational frequency. It’s not good for that force to excite the spindle at the frequency of the flexible mode. In other words, you don’t want the rotational frequency equal to the natural frequency of the first bending mode. Spindle designers call it the “critical speed.” As a rule of thumb, they try to design the spindle so its critical speed is 50 percent higher than its highest operating speed. That way, the user can never choose the critical speed by accident.

For example, if the highest spindle speed is 20,000 rpm, spindle designers try to place the critical speed at 30,000 rpm. That design decision puts the natural frequency of the first mode at 500 Hz.

Machine tool users, especially those cutting materials like aluminum, often select the highest spindle speed as the operating speed. That’s because a high-speed spindle is expensive, and they know the spindle typically has maximum power at maximum speed and believe spindle designers meant for the spindle to operate at that speed.

From a machine dynamics point of view, it is well known that the most stable speed—the biggest stable zone in the stability lobe diagram—occurs at the spindle speed where the tool passing frequency is equal to the natural frequency of the most flexible mode. For the 20,000-rpm spindle with a short, stiff, 2-flute endmill, this most stable speed would be:

05 Machine Technology 3.tif

As noted, 15,000 rpm is not the maximum operating spindle speed. It is less well-known that the minimum part of the stability lobe—the least stable speed—is about a third higher than the best speed. For this example, the speed 33 percent higher than 15,000 rpm is 20,000 rpm. The spindle designers’ rule of thumb and the selection of a short tool with two flutes have placed the worst spindle speed at the maximum spindle speed, the speed many users will select (Figure 2).

What can you do? In the absence of a measurement, make an educated guess. It is likely that the most stable speed for a short, 2-flute endmill in a high-speed spindle is about 75 percent of the maximum operating speed. A 20,000-rpm spindle often “prefers” to run at about 15,000 rpm, and the metal-removal rate is often much higher than at maximum speed. CTE

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
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