View Full Version : Forces in X,Y and Z

16-04-2016, 08:49 PM
Do someone her know what forces to expect in the X,Y and Z direction for different materials, feed rates and chip-load? Or if there is equation for it?
I'm especially looking for some general number for aluminium and mild steel (:disturbed: very general question). It's mostly to understand what to expect when doing FEA for stiffness and deflection on a router design. I guess X and Y would be the same.

Robin Hewitt
16-04-2016, 08:54 PM
If you cut downhill, as you should, you don't need much force at all.

Concentrate on speed and rigidity. Nearly everyone fits motors that are way too big, I know I did, cutting force is unlikely to be one of your problems.

16-04-2016, 10:07 PM
Thanks for the response.
Stiffness, rigidity and forces are correlated. If there is no forces there is no need for a big sturdy mill to cut steel for example. Or is there something i'm missing?

Regarding speed, so for example Nema23 3Nm (425oz) motors are strong enough, but too slow? Why do someone use nema34 at all?

Robin Hewitt
16-04-2016, 10:50 PM
If there is no forces there is no need for a big sturdy mill to cut steel for example.

Don't think I am getting at you, but have you actually tried turning the handles on a vertical milling machine? :friendly_wink:

It is very tempting to cut up hill and accept that the tool will bend in to the work piece rather than away, because cutting downhill it can run away with you. You are not so much pushing the tool as trying to stop it.
If there is any backlash everything has gone wrong before you get a chance to compensate.
You can try tightening the Gibb's to get something you can push against but that makes your arms ache. Perhaps that is the force you are thinking about?

16-04-2016, 11:22 PM
I have used vertical milling machines a few times but i'm always using automatic feed. So I guess I have no feeling for it. I do neither know the usual gearing ratio on the handles on a vertical mill.

However in statics, deflection is dependent on torque or force. In both conventional milling and climb milling there will be some forces. There will not be any deflection without it, hesne sources of backlash, rigidity, and stiffness. I'm thinking about designing a machine that potensially can do HS tool-paths, and without knowing the right variables for calculating deflecting it could easily become a overly expensive or a shitty machine.

16-04-2016, 11:39 PM
I found what I was looking for here http://www.mycncuk.com/threads/1524-What-size-stepper-motor-do-I-need?highlight=forces.
Rough estimations
Typical forces in XY
Wood > 5N
Aluminium > 20N
Steel > 75N

17-04-2016, 09:13 AM
Having had my cnc plasma gantry FEA'd this is intersting stuff, but surely those figures are dependant on tool size?

17-04-2016, 09:41 AM
In the past I've used the numbers in post #6 (which came from Irving) for deflection calculations in the absence of anything else. At least you can then start comparing designs with each other.

Recently I found these from Kistler (manufacturer of measurement sensors). For milling they show typical forces (I assume cutting steel with ~8mm tool going by the picture?) of about 160 N?

Also attached turning and drilling for info.






17-04-2016, 09:56 AM
What about the torque reaction from the cutting tool on the Z axis, there must be a twisting motion too there.

HSM Advisor gives tool cutting force and torque etc.

17-04-2016, 11:14 AM
What about the torque reaction from the cutting tool on the Z axis, there must be a twisting motion too there.

HSM Advisor gives tool cutting force and torque etc.

That is your main force that you need to allow for. If you know what torque the cutter needs, you can then calculate the forces required to move the X & Y axis against the cutter, which is the force you'll need for any FEA. However for the axis motion system, you need to add extra to cover any friction/stiction and any inherent losses in the motion system.
It's the Z axis where things get a bit more complicated, but your main force there is going to be while drilling or rotary broaching. Do neither of those, and you're biggest force is going to be from spiral milling cutters continually pulling/pushing the axis down/up.
I've got a couple spreadsheets somewhere for drilling/broaching forces, which I made to work things out for my lathe, however for drilling it won't calculate pull through force, which can potentially pull the Z-axis straight down into the table if the drill grabs as it breaks through the material.

17-04-2016, 02:01 PM
I believe what the graph shows is the total measured force between the tool and the table (Fx, Fy, Fz) when using a sensor between the part and the bed, so includes the all cutting forces resolved into x,y,z:
Feed force - in direction of cut
Feed normal force - 90 degrees from direction of cut
Feed passive force - feed up/down due to helix)
all of which include any moments caused by cutting

They do talk about another sensor which goes into spindle (RCM) and so torque can be measured directly and extracted out separately.

But in terms of machine design I would have thought you want to know the total force Fx, Fy, Fz on the tool and a target stiffness to aim for. Then use FEA, or hand calcs to work out if you meet the required stiffness when applying the force at the tool tip.

For stiffness targets I've seen figures quoted for commercial machines in the region of 10 - 25 N/um (10,000 - 25,000 N/mm). I think one of my DIY machines was between 1000 - 2400 N/mm and was ~OK but I would aim higher for a good machine and I think it is easily possible.

17-04-2016, 06:12 PM
10-25 N/μm seems reasonable, and a good number to aim for. I searched around for CNC N/μm and found a good preview on work-piece precision https://books.google.no/books?id=0zFMCFlANNAC&pg=PA234&lpg=PA234&dq=n/%CE%BCm+cnc&source=bl&ots=ZSvrgXQ8w1&sig=6FLySUCuqydG0L1Eg1PJQdYmMSE&hl=en&sa=X&ved=0ahUKEwjNivvWgZbMAhWCJ5oKHfPMB_oQ6AEIODAG#v=on epage&q=n%2F%CE%BCm%20cnc&f=false .

Seems like the "hardcore" machine centers have a stiffness around;
X axis: 30-62 N/μm
Y axis: 30-40 N/μm
Z axis: 67-95 N/μm
Radial: 25 N/μm (5000rpm), 20 N/μm (25000rpm)
This is for vertical CNC mill setup. So for a router it would be a bitt less.

According to the link above it seems like the tools are the weakest and the least stiff part of the machine. Where they use the usual deflection calculation for a circular cross section and match it to some real measurements. 0.15 N/μm for 6mm tool.

10-07-2016, 11:48 AM
If anyone is interested in prediction of cutting forces in aluminum milling I would recommend to read the article:
"A comparison of analytical cutting force models" published by WIAS
There you can find very simple models to compute cutting forces for aluminum end milling as a function of chip thickness and axial depth of cut.
Here I try to resume Kinzle-Victor model for predicting forces for end milling Aluminum
The Kinzle-Victor model predicts Fi(Fr,Ft) tangential Ft and radial Fr milling cutting forces
Fi, according Kinzle-Victor model, can be predicted through this formula:

Fi(Fr,Ft)=Ki(Kr,Kt)*a*h^(1-mi(mr,mt)) where

Fi is force in N,
a is the load per tooth in (mm) ,
h is the depht of cut in (mm) and
Ki and mi are constants that depend of h values

For end milling aluminum the values of constants Ki(Kr,kt) and mi(mr,mt) are:

Kr=39 for (0.001 < h <0.01) ;
Kr=99 for (0.01 <= h <0.1) ;
Kr=298 for (0.1 <= h <1)

Kt=336 for (.001 < h <.01)
Kt=493 for (0.01 <= h <0.1) ;
Kt=667 for (0.1 <= h <1)

mr= 1 for (0.001 < h <0.01);
mr=0.8 for (0.01 <= h <0.1);
mr=0.32 for (0.1 <= h <1)

mt=0.53 for (0.001 < h <0.01) ;
mt=0.45 for (0.01 <= h <0.1);
mt=0.32 for 0.1<= h <1

For example for a cutting depht of 0.5 mm and a load per tooth of 0.1 mm the forces for aluminum are:
Ft=Kt*a*h^(1-mt)=493*0.5*0.1^1-0.45=69 N
F=Kr*a*h^(1-mr)=99*0.5*0.1^1-0.8=31 N

Model computes tangential and radial forces located at xy plane but doesnt compute axial force at z axis and I dont know if are average or peak forces