1. ## Cutting Force Calculations

Hey I'm new to posting on the forums but have obtained a lot of knowledge. I'm on a senior project team for my college that is tasked with designing and building of a CnC machine. We are building it to cut foam for composite molds, with a 8' 4' x 2' work range. We are also looking at having a maximum cutting speed of 200 IPM. One thing that is really stumping us in the analysis is calculating the proper cutting forces. Our advisor wants to know how much force must be applied along the axis to cut the proper material. We have been all over the web and came up with two equations:

HP req = KQ/E
Cutting Force = P/Feed rate (V)

We are trying to apply these equations to our values and we are getting some very large loads to cut "foam". Below is our excel spreadsheet that shows the calculations and motor analysis. I think there is confusion on what force we should analyze, some places call it feed force, tangential force, or radial force. Can these be applied to how we select our motors and to make sure they can supply the right load.
Any insight would be very appreciated.

2. Cutting force is tricky - it would probably be much easier to get a good answer by building a test rig to measure the force directly on your material using whatever cutter / spindle / cutting parameters you plan on using on your machine. You could get this in various ways such as using a force sensor or measuring acceleration or velocity using a known applied force (such a hanging mass). Doing this, you could find the force required to cut your material at various speeds / cutting parameters. Then you could design your motion system to provide that force in addition to the force required to accelerate the moving mass of your machine. I want to do this before I rebuild my current router so I have some real targets to design around.

3. Thank you for the response, that is what we figured it would be. Looking at any of the sites with calculations they had all done testing prior to it. Figured we should ask around before we come to the conclusion of just building it and then testing it.

4. Honestly, if you're just doing foam at 200ipm and aren't using massive bits (say 1/2" diameter or so), you can probably assume a 50lbf cutting force and work from there. That's what a lot of guys have done in the wood router forum in designing their machines, just going on a gut feeling of how hard you push a router to move it through wood.

5. My guess for cutting foam at 200ipm with a 1/2" diameter bit would be a lot closer to 5 lbs than 50.

6. If you size your motors for the cutting force, the force needed topush the cutter through the work, they are probably going to be woefully undersized. During acceleration of the axis up to the programmed feed rate or up the the rapid speed, the force far exceeds even the highest force needed for cutting.

7. Actually your cutting force could easily be higher than acceleration force. It depends on what your acceleration is and what your moving mass is. For example, my router has many times more force for cutting available than it uses for accelerating over the entire range of speeds I run it at (as the available cutting force would vary with the torque curve of the stepper motors). However I've stalled the motors while cutting, meaning I've used all the cutting force available. So cutting forces can definitely be higher than acceleration forces on a real machine.

8. Are you mixing your units by any chance - I see m/s, ft/s, newtons, lbf - all being referred to in the spreadsheet? Should you be considering using sfpm of the cutter not just 'V' = feedrate?

Where did you find the K for foam? I'm hoping the source might have some data on fiberglass or other composites.

Let us know what you find out on your project!

Thx,

9. Just noticed it has been a few months since I posted this. Anyways we were unable to find a K value for foam as it is to hard to determine unless you do tons of testing. We tried to do correlations to K value vs. density and brinell hardness and came up with non-accurate numbers.

All in all we decided that it wasn't a viable option to calculate cutting forces for foam. So we ditched the spreadsheet and did some experiments with our own rotor cutting foam. The most it took to pull a rotor through the foam was no larger than 30 lbs. Hope that helps.