Procedure for Obtaining Cutting Force Coefficient and Process Damping Wavelength (Force Model)
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Generally, cutting force coefficients (Ks) and PD coefficients (λ) are determined experimentally. For a given workpiece in a particular set up, it is possible to make a precise measurement, but there is substantial variability. In this sense, these coefficients are like other material properties such as Young's modulus or fatigue life. The usual procedure is to use a tabulated typical value. If you need a more precise number, you have to measure your workpiece in your set up.
You most likely do not need a more precise number if you are not an academic. If you are a practitioner, you want to stay away from the edges of stability, because at the edges you are sensitive to all of the variables, many of which are not in your robust control. However, in the Dashboard we incorporate uncertainties on the boundary conditions of the stable zones.
While it is possible to carry out finite element simulations of cutting with the proper constitutive material model to determine cutting coefficients, a more common technique is to use the tool and workpiece material in question and measure the force during cutting using a dynamometer. This information can then be used to determine the corresponding cutting force coefficients. See Section 4.7 in the book Machining Dynamics by Schmitz and Smith.
Approximate values are often sufficient to get you the correct process predictions. These are included in the Dashboards. However, if you desire to determine a more precise value for the cutting force coefficients (Ks) and PD coefficients (λ) and measuring the cutting forces during the cut is not possible due to lack of the equipment, we provide a set of cutting tests using a Dashboard to experimentally determine these values.
The following test procedure is useful for determining the proper material (cutting tool) parameters to be used when creating a Dashboard. These values include:
- Cutting Stiffness (Ks)
- Process damping wavelength (λ)
Using the Dashboard
Measure the cutting tool as generally prescribed and generate a Dashboard with MillMax. Using the Dashboard provided with the Dashboard set at full radial immersion (100% Ae). Follow the procedure below and use the accompanying spreadsheet.
Figure 1 - Determine the Process Damping SS transition, PDSS
1. Determine the process damping transition speed, PDSS, and the process damping depth of cut, PDDOC.
As shown in Figure 1, with the Dashboard set at full radial immersion, with the dashboard set at full radial immersion, set the axial depth of cut so that there are clear stable and unstable regions of approximately equal width. Dial the SS to the lowest stable zone, and determine the SS where the Vibration Indicator bar transitions from Stable to Chatter, 753rpm in this example. Record this speed as PDSS in Table 1.
PDSS = 753 rpm
Figure 2 - Determine the Process Damping Depth of cut, PDDOC
1. As shown in Figure 2, Dial the SS to the largest stable pocket. Keep the Width of Cut (Ae) at 100%. Increase the Axial Depth of Cut (Ap) until the stable pocket becomes very narrow. This is the transition depth of cut (Ap) from stable to chatter. Record this value as PDDOC in Table 1.
PDDOC = 0.092"
Figure 3 - Determine Blim the depth of cut where all speeds are stable
1. Determine the Depth of cut value where the entire SS dial goes green (i.e. all speeds are stable). Keep the Width of Cut (Ae) at 100%. As shown in Figure 3, reduce the Axial depth of cut slider bar and determine the depth of cut where all speeds are stable. Record this DOC as Blim in Table 1.
Blim = 0.030"
Figure 4 - Determine a SS for the DOC test, DOCSS
1. 1. Determine a speed which is in between two stable speeds. As shown in Figure 4, with the dashboard set as described in step 1, dial the SS to a speed which is in between two stable speeds. Record this speed as DOCSS in Table 1.
DOCSS = 7900 rpm
Cutting Tests
Two cutting tests will be performed:
1. The Depth-of-cut test: At a DOCSS, the first set of tests will increment depth of cut
from a low depth of cut, below Blim, to higher until chatter is detected using Harmonizer.
2. The Spindle Speed Test: At a pre-selected depth of cut, greater than Blim the second set of tests will increment spindle speed using a constant depth cut starting at some low spindle speed and increasing speed until chatter is detected with Harmonizer.
In both tests utilize the Harmonizer to get a clear detection of chatter conditions.
Depth-of-cut test:
• At the spindle speed DOCSS and a depth of cut that is 1⁄2 blim
• Program successively deeper cuts in an increment equal to 10% of blim
• Using the Harmonizer detect at what depth of cut chatter starts. Go beyond Cut 8 if you must. When chatter occurs use the prior non-chatter cut as the test value (blim-test).
In Material Details, click Show All Fields. Enter the Cutting Stiffness (Ks) in the spreadsheet and select the unit of measure.
Spindle speed test:
• Use 3⁄4 the PDSS of this speed as the starting speed.
• For DOC use a value greater than PDDOC. We suggest use 2 times the limit
value 2*PDDOC.
• Increase spindle speed in 30% increments of PDSS until chatter occurs. Go beyond Cut 8 is you must. When chatter occurs record prior stable speed test as the test limit speed (PDlim-test).
Enter the new Cutting Stiffness (Ks) and Process Damping Wavelength (λ) values into the Material Details and save.