Managing surface location error: General Industry Coverage

An endmill with six straight teeth is shown in Figure 1 in three different radial immersions. The desired surface, marked “S,” is not generated continuously but in a series of instants when a tooth is in the position marked “A.” A tooth in position A imprints the tool deflection on surface S. The tool deflection in response to the cutting force at that moment matters but the deflection of the tool at other times does not because the other deflections are imprinted on material that is later removed.

In the first case (left), the radial DOC is small enough that only one tooth is in contact with the workpiece when a tooth is in position A. The chip thickness at A is close to zero, so the force on the tool is close to zero, and, therefore, the surface is almost perfectly located.

If the radial DOC increases, the picture at the instants in time when the desired surface is generated does not change until the second tooth becomes involved in the cut (center). Now, there are two teeth cutting simultaneously, and the force on the second tooth (Ft2) causes deflection of the tool. The error in surface location undergoes a sudden step change when the second tooth begins to cut. If the radial DOC increases still further, a third tooth becomes involved in the cut, and the surface location error changes in another discrete step.

For slow-speed milling, applying a tool with six straight teeth, where the radial DOC is gradually increasing, the surface location error does not gradually increase. It arises in two discrete steps.

In reality, the situation is usually more complicated. The teeth are generally not straight but aligned in a helix. The contact point between tool and desired surface rises along the tool axis as the tool rotates. If tool deflection changes with time, the surface location error changes from the bottom to the top of a wall created by the endmill. In addition, if the tooth passing frequency is high enough, the tool behaves dynamically—it vibrates. In that case, timing is what counts: the key is the location of the tool in its cycle of motion when a tooth is in position to generate the surface of interest. While the surface location error is not intuitive, it is predictable. 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. A more detailed account of this topic is in his book “Machining Dynamics—Frequency Response to Improved Productivity,” co-authored by Tony Schmitz.