Finding harmony in stable cutting

Experienced end users can tell when a machine tool sounds right and when it doesn’t. Stable, chatter-free milling produces a clear tone—a single, dominant frequency. Chatter, on the other hand, produces a harsh tone, often with different frequencies mixed together. But machinists may not know that the frequency of the sound—its pitch—tells how to change the spindle speed to find a stable zone.

Let’s start by considering the cutting sounds that are a normal part of milling. Often there is the sound of the tool’s teeth hitting the workpiece. That hitting causes a force at the tooth passing frequency, and that force causes the tool to vibrate, creating the sound. A tool with two teeth rotating at 15,000 rpm will have a tooth passing frequency of 500 Hz. 

15,000 rpm × 2 teeth/rotation × min./60 sec. = 500 teeth/sec. 

If a slot is being cut, the force is close to sinusoidal, and the resulting sound is almost purely 500 Hz. Musicians know that the frequency of the note A above middle C is 440 Hz, which is often used as the basis for tuning instruments with a pitch pipe. The note B above middle C is 494 Hz, so stable milling at 15,000 rpm with a two-toothed tool sounds like B above middle C, especially when milling a slot. 

Other frequencies may also be present in the sound. For example, tool runout causes a once-per-revolution force, or 250 Hz for the previously listed case. The runout frequency is exactly half of the tooth passing frequency. If the radial DOC is small, then the force is a series of sharp spikes appearing at the tooth passing frequency. This kind of force leads to other sound components at exact multiples of the tooth passing frequency, and these are called “harmonics.” 

When milling with a two-toothed tool at 15,000 rpm and a small radial DOC, there will be sound frequency components at 250 Hz (runout), 500 Hz (teeth passing) and multiples of those (750 Hz, 1,000 Hz, 1,250 Hz and so on). Because the resulting sound waves line up exactly, the combination sound will still be clear and dominated by the tooth passing frequency.

What if the cut is not stable (chattering)? All assemblies of tool, toolholder and spindle have one or several frequencies at which they would like to vibrate, and these are called “natural frequencies.” When chatter occurs in milling, a new frequency appears in the sound that is not the runout frequency or the tooth passing frequency, and not harmonics (integer multiples) of those two. It is the chatter frequency. The chatter frequency is close to, but not equal to, one of the natural frequencies, and it is not connected to the tooth passing frequency. The chatter frequency sound mixes with the pure sounds of the tooth passing and the runout frequencies, and the resulting sound is harsh because the frequencies are not aligned. 

Interestingly, the chatter frequency also is an indicator of what spindle speed change should be made to stop the chatter. In previous columns, I have described the stability lobe diagram and discussed that there are spindle speed ranges where milling is more stable than in other ranges. If there is a spindle speed range where the milling will be stable at the current axial and radial DOC, the chatter frequency will guide you to it. 

To get from chatter to stable milling, choose a new spindle speed so the new tooth passing frequency matches the old chatter frequency, and adjust the feed to keep the chip load constant. For example, when milling at 15,000 rpm with a two-toothed tool, if the chatter frequency is 427 Hz, then the new speed to try would be 12,810 rpm.

427 teeth/sec. × 60 sec./min. × rev./2 teeth = 12,810 rpm

It is unlikely you would choose this spindle speed by chance. So how do you know what the chatter frequency is, and how can you choose a stable speed? You need a microphone to record the sound and a Fourier Analyzer device to extract the component frequencies from the time-based sound signal. The microphone should be directional so stray environmental sounds don’t interfere with the measurement. The microphone can be inside or outside of the enclosure as long as it can effectively capture the cutting sound. 

You need to know the spindle speed to identify the tooth passing and runout frequencies and separate them from the chatter frequency. The commanded spindle speed does not always match the running spindle speed. 

Software is available to quickly identify the frequencies and calculate the new spindle speeds and feeds. A product called Harmonizer from BlueSwarf MLI is available, and the Web-based tool (NET-Harmonizer) is also suitable. 

When the spindle speed that creates stable, chatter-free machining is found, it is music to a machinist’s ears. CTE

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 kssmith@uncc.edu.