Cutting Tool Engineering
June 2010 / Volume 62 / Issue 6

Fighting chatter with nonproportional spacing

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

Chatter is an expensive and persistent problem when milling. Chatter vibrations can be large enough to damage a tool, cause scrap and even damage a machine. Worse, the risk of chatter may cause machine tool operators to be conservative in their selection of machining parameters, severely underutilizing machine capacity. Machine tools are commonly underused by a factor of two or more.

Chatter is a self-excited vibration, which means a steady input of energy from the spindle motor is transformed through some mechanism into vibration. The primary mechanism in machine tool chatter is “regeneration of waviness.” Essentially, the machining system, including the cutting tool and workpiece, is not dynamically stiff enough. When a tool tooth encounters the workpiece, the contact causes vibration, and the vibrating tooth imparts a wavy surface. The next tooth encounters that wavy surface, and the wavy surface causes a variable chip thickness. The variable chip thickness then causes a variable cutting force, and the variable cutting force causes vibration.

One way to stop this mechanism is to measure the dynamic characteristics of the machining system, use those measurements to calculate the stability lobe diagram and select cutting conditions in the stable region. This previously covered strategy relies on aligning tool vibration with the wavy surface. When the waves are aligned, the chip thickness is no longer variable, and the vibration stops. The stable zones on the stability lobe diagram appear when there is exactly one, two or any integer number of vibration waves between the subsequent teeth. This strategy requires knowing the stable speed, maintaining a stable speed within the acceptable spindle speed range, having evenly spaced teeth and accurately controlling the spindle speed.

An alternative strategy is to disturb the waviness-regeneration mechanism by changing the spacing between the cutter’s teeth. If the teeth have nonproportional, or uneven, spacing, then each tooth encounters the wavy surface left by the preceding teeth with a different alignment, and the vibration is suppressed. A tool with nonproportional spacing can often achieve a higher stable axial DOC than a tool with proportional spacing.

However, the gain needs careful evaluation. Because the feed is constant, a variable tooth pitch leads to a variable feed per tooth. That typically means only one tooth can take the full chip load and the remaining teeth are underutilized. The effective feed per revolution of the tool must be reduced, and the feed reduction must be matched by an increased axial DOC just to break even.

For example, let’s examine a 4-flute endmill with evenly spaced teeth and a maximum stable axial DOC of 10mm. The teeth are 90° apart and oriented at 0°, 90°, 180° and 270°. If the permissible chip load (feed per tooth) was 0.2mm, then the feed per revolution would be 0.8 mm/rev. If only one tooth changed position by 10°, the teeth would be at 0°, 100°, 190° and 280°. Therefore, the space between the teeth is 100° (maximum), 90°, 90° and 80° (minimum).

To keep the feed per tooth at the maximum spacing and acceptable limit, the controlling space is the maximum space. The feed must be reduced from the proportionally spaced case in the ratio of the proportional space to the maximum space (90°/100° in this case). The chip load for each space between the teeth would then be 0.2mm, 0.18mm, 0.18mm and 0.16mm. The feed per revolution would then be 0.72 mm/rev. For such a tool, the permissible stable axial DOC would have to be larger than the ratio of 100/90, meaning 11.1mm just to break even in terms of the metal-removal rate. In general, disturbing waviness regeneration this way must allow the axial DOC to increase by a factor more than the maximum space/proportional space to make the use of a nonproportional spaced tool worth considering.

In a similar way, a variable spindle speed disturbs waviness regeneration, but the spacing can effectively change during more than one revolution. However, because the feed is not variable, the maximum spacing still controls the feed. A variable spindle speed must allow the stable axial DOC to increase by a factor of the maximum space/proportional space before any gain in the mrr is realized. 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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