Template for comparing machines

In earlier columns, I described how to measure the dynamic characteristics of a particular milling tool in a holder and spindle, expressed as a frequency response function. The FRF is then used to produce a stability lobe diagram (Figure 1). The diagram shows which axial DOC and spindle speed combinations will result in chatter-free machining with that tool and holder in that spindle. 

It is also possible to turn the scenario around and start with the desired cut, then produce a template against which the measured FRF can be compared. In principle, the template provides a way to quickly compare competing machine tools to find which ones can perform a planned job.

Figure 1. The shaded cutting conditions in this stability lobe diagram will cause chatter.

Figure 2. An example template for cutting a 10mm-deep slot in 7075 aluminum using a 4-flute tool at 20,000 rpm.

Let’s say the desired cut is a 10mm-deep, full slot in 7075 aluminum using a 4-flute endmill at 20,000 rpm. At least four ways exist to cut without chatter.

1. The combined tool, holder and spindle could be so stiff that a 10mm-deep slot is stable for all available spindle speeds.

2. The 20,000-rpm specified speed could be so fast that cutting a 10mm-deep slot is stable only over the far-right lobe in the stability lobe diagram.

3. The 20,000-rpm specified speed could be so slow that the process damping effect, which involves interference of the flank face with the vibration, stabilizes the cut.

4. The cut at 20,000 rpm and 10mm deep could fall into one of the stable zones between the stability lobes.

Working backward through the mathematics produces a template the measured FRF cannot cross. Figure 2 (see page 22)shows an example template in blue. 

In addition, the measured FRFs for the 4-flute endmill in two competing machines are plotted in black. The flat line of the blue template shows the first stable possibility, a stiff machine and tool. However, these two machines are not stiff enough to cut 10mm-deep slots at any speed as shown by the black lines crossing the blue line. The dips in the template indicate places where the 10mm-deep slot cut at 20,000 rpm would fall into a stable pocket in the stability lobe diagram. The measured FRFs have large peaks at around 2,000 Hz, which do not fit into a stable pocket.

Figure 3. An example template for cutting a 10mm-deep slot in 7075 aluminum using a 4-flute tool at 15,000 rpm.

Figure 4. An example template for cutting a 2mm-deep slot in 7075 aluminum using a 4-flute tool at 22,000 rpm. 

If a template is produced for slightly different cutting conditions, the result will be different. Figure 3 shows the template for a 4-flute tool cutting a 10mm-deep slot in 7075 aluminum at 15,000 rpm. The same measured FRFs shown in Figure 2 are compared against the template. In this case, the large peaks on the measured FRFs fall into a stable pocket, meaning both machines can make this cut if the spindle speed is well controlled.

Figure 4 shows a more extreme case. The template was produced for a 4-flute tool cutting a 2mm-deep slot in 7075 aluminum at 22,000 rpm. A measured FRF, compared against the template, shows the combination of the measured tool and machine can barely make the desired cut, even with the desired cut deep in a stable pocket. This tool in this machine can achieve this cut only if the setup and cutting conditions are well controlled.

If the desired cutting conditions are well known, the template provides a quick way to check which machine/tool combinations can perform the cut. If a number of different cuts are required, the templates for each cut can be superimposed to verify a tool can make them all. 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.