Theory of Metal Machining

When it comes to machining metal, I think it would be helpful to be able to predict cutting forces mathematically. I realize that the average machinist may not need to do this precisely, but this matters a lot for the design of cutting tools. I dug up the following diagram, showing how a tool cuts into a work piece. It develops a shear angle, which is some function of the tool geometry and the coefficient of friction between the tool and the work piece.



Much can be read about cutting tool theory. However, almost all the research I have done (from sources outside my own experience) presents a precise mathematical theory only for sharp cutting tools. As for dull or rounded cutting tools, mention may be made of a secondary or tertiary shear zone, but there is no method to calculate the size of this zone, or its effect on the overall force applied to the tool.

My background is mechanical engineering, and I am currently designing band saw blades. With band saw blades, unlike milling cutters or turning inserts, the chip load is very small - in some cases, smaller than the microscopic tool edge radius. In that case, the rake angle is almost meaningless, because the tool is pushing down on the material with a blunt edge, rather than digging down under the material. This causes the tool to act as if it had a negative rake angle. Nevertheless, and perhaps paradoxically, a ductile continuous chip is still formed.

One could imagine that a dull tool has a negative rake angle, which is a function of the tip radius and the Undeformed Chip Thickness. You can measure that negative angle with a good microscope. However, this approach does not match observations predictably. If you take a saw tooth and cut a piece of metal bolted to a force gauge, you'll find forces that don't match up to the calculations resulting from the above diagram (I can explain these in more detail if needed).

My point is that, as far as I can tell, machining theory is lacking when it comes to dull cutting tools. Since most tools are at least somewhat dull for most of their working lives, this is a problem.

In this thread, please present and discuss information you may have found or discovered regarding a theory of metal machining for blunt, dull, or honed cutting tools.

Have you read this book from Sandvik? https://www.amazon.com/Modern-Metal-Cutting-Practical-Handbook/dp/B000ARWOFM

If you have, and it did not provide the answers you are looking for, then I doubt you will find them anywhere short of doing the research yourself.

It's a flaw of many engineers to want to know/control everything about what they are designing.

The reason cutting formulas are based on sharp tools is once a tool is dull it's removed from service. Yes you have to replace/resharpen cutting tools they get dull with use they are a consumable.

That's not to say improvements cannot or should not be made. Better is better.

Much of cutting tool theory goes from sharp to dull enough for sharpening...some times to perhaps a .015 wear land for steel and for cast iron perhaps gong from a sharp corner to a wire out 1/16 radius.
How far to push a cutter before the loss of a good part or cost efficiency of the cutter,
Much the same for grinding wheels from fresh dress to loaded up, going out of round, losing needed smoothness for surface finish.

gregormarwick said:

Have you read this book from Sandvik? https://www.amazon.com/Modern-Metal-Cutting-Practical-Handbook/dp/B000ARWOFM

If you have, and it did not provide the answers you are looking for, then I doubt you will find them anywhere short of doing the research yourself.

Click to expand...

Warning:- It's heavy going!

+ another on the Sandvik book, heavy going but worth it.

Not a deterrent for someone obviously bent on reinventing the wheel...

Taylor’s tool wear formula as a search term will burst the boil of blunt tool research, there’s lots of tool life, wear, tip wear, cratering etc etc
It’s a big field, spc uses it a lot!
Mark

Years ago, an outfit sold an ohm's reciprocator that would measure the current generated by the cutting action and create the equal charge/amount so no electrical caused cratering would happen.
I don’t know if they still exist.

After you read the Sandvik book 4 or 5 times and have it memorized read some of the stuff from Astakhov.
Why the conventional models fail, why the force measurements do not come out right, why almost all FEA systems have to be tweaked along with what happens with a honed tool are explored and theories put forth.
Deeper drilling (pun intended) in the many papers he references.

Your pictured model taught in school is known not accurate and can be wildly off but it is sort of right and it's easy to understand and wrap your head around.
It's more a in the ballpark thing.

I suspect that you have a theory and this is a lead into it so tell us.
Bob

is their a chapter on sudden tool failures, hitting slag hard spots, false cutting edge buildup, tool vibration harmonics ?? part vibration harmonics ?? and obviously vibration can change where tool is on a part it can be hard to predict. same with part material, for example castings have a harder skin and are softer in center of thicker sections. hard to predict exactly when things (parameters)can change every second
.
just saying take what the salesman says and realize they are in business to sell you more tools. i have seen carbide drills not even last 1 minute cause of vibration and chatter

You talk about a sharp tool vs. a dull one. But I suspect, well I know it is not that simple. A tool is sharpened to some degree. Some new tools are "razor sharp" while others come from the factory with a deliberately rounded edge. So even a new tool that is "sharp" is not the same degree of sharpness as another one.

Then, you start using that tool. It does not stay factory sharp for X period of time and then, INSTANTLY become dull. It starts to become duller in the first inch of cutting. Heck, it starts to dull in the first 0.001" of a cut; even in 0.000001" of cutting. Becoming dull is a gradual process that occurs over all of a tool's useful life and the exact point where it is declared to be dull and taken out of service is not the same for the same tool in different shops or machines or even when making different parts. Except for that first instant of contact with it's first cut, we are always using "dull" tools. They are duller than they were when they left the factory that makes them. So it would seem to make little sense to have a theory or a set of equations that only work when the tool is factory sharp.

Looking at the vector diagram in the OP's post, the I do not think that the R vector in the tool seems to be the one that you can measure. It is a combination of a downward force that holds the tool down below the surface of the work and a forward force that is needed to move the tool along the cut. This is how I see that vector being generated. But the drawing instead breaks it down to a F vector which is parallel to the rake Face and a N or normal vector to that rake surface. This breakdown of the actual force vector (R) may be useful for some purposes, but in my mind, it is not the first way that I would choose to represent it. I would start by breaking it down to a vector which is normal to the original face of the work and one that is parallel to that original face.

This component of the overall vector, the one parallel to the original face of the work, represents the amount of force that must be used to push the tool forward in the cut. Not either of the components that are shown in the drawing.

And the other component that I would start with, the one that is normal to the original face of the work, is only the force needed to hold the tool at the desired dept of the cut. This component could be in either the down direction as it would be in that drawing, or in the UPWARD direction if the tool is being drawn down into the work by the action of the cut. This is what happens with a tool with too large of a positive rake angle in a softer material like brass or plastic. We have, at least I have, a special set of drill bits for brass and plastic to fight this force which tries to make the bit dig into the work too fast. Also, this vertical (in that drawing) force is not one that is primarily due to the amount of cutting force. It is, instead, provided by the rigidity of the machine and would only impact the actual cutting force due to friction in the moving parts of the machine that allow the tool to advance in the cut. I also suspect that this vector that is normal to the original face of the work is going to be a LOT smaller than the diagram in post number one would suggest. I further suspect that, to a first approximation, we can probably leave this component of the overall vector analysis out of consideration. At least until we can have a theory and equations that give us a fairly good approximation of the forces involved with the parallel vector.

It is the vector that is parallel to the face of the work that is most likely to be due to the actual work of separating the chip from the bulk of the work piece. And that is the one we should tackle first. Only in trying to reach a reasonable approximation of how this parallel vector will behave should we look at the vectors and other factors that are in action along the rake face of the tool.

One of the first things that I would investigate is the formation of a chip that has alternate ridges and valleys. What is happening there? Is the tool moving in jumps? Is the work being compressed until it undergoes a sudden release? Is there some kind of fluid flow thing? I suspect that you will not understand the forces needed until you can explain this phenomenon. And predict it.

I can see years of research here. Decades even.

carlherrnstein said:

It's a flaw of many engineers to want to know/control everything about what they are designing.

The reason cutting formulas are based on sharp tools is once a tool is dull it's removed from service. Yes you have to replace/resharpen cutting tools they get dull with use they are a consumable.

That's not to say improvements cannot or should not be made. Better is better.

Click to expand...

many a finishing mill needs to cut 3 or 4 feet before its stable. that is it needs to wear in a bit. have seen over .0005" height differences in finished surfaces before.
.
as tool dulls and part material sticks to cutting edge that can result in over a .0006" lower height cause false cutting edge buildup.
.
also some newer mills have a burnishing action. rubbing and smoothing surface to mirror like finish. this can result in bump .0006" where cut begins as mill needs to warmup, hard to describe

What you forget is the material. Steels are sheared into chips differently from bronze, brass, aluminium, titanium or plastics. Great differences also among steels and then hardened ones to round it off. I want to say that tool geometry is first of all a function of a material[FONT=&quot]’s properties. How much you want to machine off in a given time is secondary. As tool materials we have hardened carbon steels, alloyed high speed steels, metal carbides, metal oxides, ceramic metal compositions, and diamond.[/FONT]

So many factors determine tool cutter life that each too need be considered for its material, geometry, edge condition and each environment of machine and fixture rigidity and then also the material to be machined and the time frame to determine feed rates. With so many variables often the machining operation is initially planned from past history and then changes made to make best use of cutter and machine.
One example is the sharp edge. With luck a particular cutting tool will start and run x number pieces 7 out of ten starts. But 3 out of ten starts it will get an edge fracture and only run one eighth of the x number.
So, to avoid the possible edge fracture one finds that a small rub on a wire brush will break in the edge and avoid the early use fracture. The edge changed cutter now only produces 85% of the original X number but with expected use of all 10 cutters the operation is improved.
Each cutter and job have its own variables and often tool cutter breakage is the major cost variable to avoid to achieve best cost efficiency.

I must say I'm surprised at the volume of responses to this in one day's time. I won't reply to all of them individually, but I'll try to generally address the key points.

First, why is it necessary to delve into a theory for a rounded edge? The comment has been made multiple times that, essentially, when there's no point, there's no point. In other words, when the tool no longer has a sharp point, it's time to throw it away, so there's no point in analyzing it anymore. My rebuttal is this: most tools start off with a rounded edge due to an edge hone. The shape of the hone matters, and the ideal geometry can vary based on the material and cutting conditions. If a model can be developed, based on material properties, chip load, friction coefficient, etc... then one could develop a specification for which edge shape goes with which product, and what the tolerances must be.

As for the resources mentioned: I will seek out a copy of the Sandvik book. In the meantime, I looked at a paper by Astakhov, which points out many of the flaws with the "single shear plane model" which I referenced in the OP. He mentions a "slip line model". That lead me to a paper by Ozturk and Altan, entitled "Slip-Line Metal Cutting Model with Negative Rake Angle". A diagram of this is here:



As for the comment about over-engineering: it wouldn't be engineering if it weren't overdone! That said, I would much prefer not to over-complicate the matter. Instead, I would simply like to make a useful prediction, not an exact prediction. But the single shear plane model, as I have found experimentally, is neither exact nor useful. It's not even close.

Do I have a theory to propose? You had to ask. The answer is "sort of". More, I have several ideas, and have tried many of them only to find that these models also fail to make useful predictions. I want to get other opinions. Here is what I have tried so far:

1. Single Shear Plane Model, using the Nominal Rake Angle. In this, the shear angle is simply 45 + (Rake Angle - Friction Angle)/2. If I have a rake of 10 degrees (measured from the vertical axis), and a friction angle of 10 to 20, then the shear angle is 40 to 45 degrees. For a material with a shear strength of 100ksi, and a tool of width .034" (remember, it's a saw blade), and an undeformed chip thickness (UCT) of .0004", the force should come out to 2 or 3 lbs, mostly in the cutting direction. (R = shear * width * UCT / sin^2(phi), and the direction of force on the tooth comes out to 2*phi from the vertical, where phi is the shear angle). This is completely off. Time and time again, experiments show something like 20 to 30 lbs, directed at about 40 to 50 degrees from the horizontal.

2. Single Shear Plane Model, using an Effective Rake Angle. Carbide teeth aren't so sharp, even if you leave them un-honed. So we should have some sort of "effective rake", which is severely negative. Say you have a tool with a .001" radius, and your undeformed chip is also .0004". Then my approximation is that the "effective rake" is a line from the tip of the tooth at maximum depth, to where the surface of the workpiece touches the tooth. In this case, that's about -63 degrees from the vertical. Now plug that into the Single Shear Plane model, with the same numbers as above. Roughly, phi = 6, and R = 124 lbs, directed up at 78 degrees from the horizontal. Now that's overkill.

3. Single Shear Plane Model, using an Effective Rake Angle and reversing the friction component. Here, I reason that, if you ever got up to such high forces directed mostly in the feed direction, you wouldn't be able to feed at all. Then, the material would slip under the tool instead of going up the face. So the direction of friction is now backwards: reverse the negative sign of the friction angle, and you get phi = 21 degrees, R = ll lbs, directed at 41 degrees from the horizontal. Here, the force is low, but at least the angle is close to accurate. Problem: this assumes that the chip is flowing the wrong way.

4. Dual Shear Plane Model. Here, I split the undeformed chip into 2 layers. The bottom layer starts at the maximum tool depth, and ends at the point where the round edge makes a 45-degree angle; this layer slips under the tool. The upper layer continues from there up to the surface - and beyond! From a video I found (Zerspanen von Stahl X 2 CrNi 18 9 - Schnittvorgang im Feingefuge; Variation des Schneidenradius), it looks like the material actually bulges up (plastic strain) before it shears. (That is, whenever the built-up-edge goes away). This makes sense - if there's too much down force and not enough forward force, the material wouldn't shear - but it would deform. Furthermore, this matches the study above by Ozturk and Altan (which I didn't discover until just now). So, in my model, each layer has its own separate shear plane, separate UCT, and separate effective rake angle. If the UCT is really small, I roughly assume that the material will bulge up until it gets past the round part of the tool. In that case, I get R = 20 lbs, directed at 38 degrees from the horizontal. Again, my experiments show something like 20-30 lbs, directed at 40 to 50 degrees.

Now I'm in the right ballpark at least, but there are still some issues. If I set the UCT at .0004, I get the same force as if I set it at .0015. That's very unrealistic: otherwise we could just plunge the tool in and enjoy some drastic savings on cycle time. No, if you quadruple the chip load, you're probably going to overload the tool. However, I have done an experiment where I saw only a slight increase in force even while doubling the chip load, if the change was enough to get past the round part of the tool.

Input is welcome. The point of this is not to create a super-complicated theory, but rather to explore a lot of information that will later be pruned down to a few simple, fruitful truths, which make useful predictions about small chip loads with rounded-edge tools.

Thanks for your time!

I would add that high-quality cermets like Kyocera has produced for 40 years are in a different category of chip formation entirely. It would take quite some fancy camera to show that. Turning 1" Ø steel at 6000 RPM dry without the part getting hot obviously involves practically vaporizing the chip rather than simply fracturing it. Same for milling: We routinely take .200" off a Stressproof bar with a face mill at 1800 RPM dry and the part is still cool to the touch. How that is possible with an insert with a 20° edge chamfer and a wiper? There is quite obviously more to that than appears in the textbooks, most of which were written when K&T horizontals were the backbone of machining. Given the value of the proprietary knowledge it may never appear in textbooks (kind of like the thread on swaging, just try to find a textbook on that).

There is quite obviously more to any machining or grinding operation than can ever exist/appear in any textbook.

I went to Carboy tech school back in the 60s. They had figured that a good carbide operation would provide 31 minutes of machining per insert on average. Sure, enough many of our milling and lathe operations provided that on average ..and some did not..

Just the thickness of the insert can absorb more heat and so last longer on some operations...A very thin insert might be lower cost and last just as long on another operation.


I got all these books about how to plant a tomato plant but the methods were not any help.

Why not?

A darn rattle snake would just not go away.

Not true just an example that a surprize can fudge op the plan.

The dual shear model is interesting. When the tooth enters the work will it take a full "bite" as in a single shear model then transition to a dual shear model? How does that transition effect the point radius?

What happens when the tooth exits the work?

Is it possible to polish and etch a cut specimen to determine if there is in fact a zone of deformation?

The video I posted above has a section at the end showing what happens when a rounded tool first enters the work. I looks like it rubs without taking much of a chip until it gets down to a certain depth. However, the Built-Up Edge is so prevalent in these videos that it's hard to tell what would happen without it.

I think most of my proposed plastic deformation would be one step towards eventual shear - what I mean is, instead of shearing as soon as the tooth arrives, the tooth pushes the material plastically for a bit before it finally shears it. In that case, I doubt the work piece would show any signs of this deformation, though the finish would be bad. So I'm not sure if it would be possible to find that out with a sample.