cutting force

Hi All,
The following email is a reply I received after my inquiry "How to
calulate the force required to rout a piece of wood".
The example is the force applied to a spindle when a 12.7 mm dia
cutter is feed into a piece of wood 20 mm deep and 75 mm per sec.



HI,

Sorry for being so late in my answer.
Here are some basics of cutting mechanics. I hope it will help you.
In order to find the force applied on the spindle, you need to know
the chip
thickess (or feed per tooth): it's the most important parameter. A
good
approach is to consider the force (F) as a linear function of the
chip area
(bh) with:

b=depth of cut (mm)
h=feed per tooth (i.e. the chip thickness)

In routing or slotting, b is choosen by the operator while h can be
written
as a function of feed speed (Vf,mm/min), rotation rate (N,RPM) and
number of
teeth (Z) as:

h= Vf/(N.Z)
with h in mm.

Thus, this results in:
F=k.b.h
with k=specific force coefficient (in N/mm2).

k will mostly depend on:
- the wood specie (especially its density)
- the tool geometry

So, as for tool geometry, you have also to take in consideration:
-the rake angle of the tool.
-the sharpness of the edge.
For these latest parmeters there is no mathematical model; only
experimentation and measurements with the tool you want to use can
yield the
actual forces.

From my experience in MDF board machining, with a sharp 10 degrees
rake face
tool, I found:
k= 16 N/mm2

Applying the previous rule, for a 20 mm depth of cut, N=10.000 RPM,
Vf=75
mm/sec and Z=3 teeth:

h=75.60/(10.000.3)=0.15 mm/tooth.

THus, the force applied can be approached by:

F= 16.20.0.15= 48 N

The better is to pratice some basic cutting tests with the tool and
the
specie you will use with 4 or 5 chip thickness. Then, you will be
able to
predict the foce for any process conditions (N, Vf, Z and b)

I hope this will help you to solve your problem

Regards.

Jean-philippe Costes, Dr.
National Reaserch Council, Innovation Center
3250 East Mall V6T 1W5
tel : 604-221-3000, (5576)
fax: 604-221-3088
Vancouver, Canada