# Is cutting depth the square or cube of linear blade speed?

Discussion in 'Physics' started by THE_RB, Jan 1, 2013.

1. ### THE_RB Thread Starter AAC Fanatic!

Feb 11, 2008
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I'm not sure if this is a standard physics concept or not, but I am trying to work out if the depth a blade cuts through a material is based on the square of the linear blade speed or the cube of the speed.

Tests with a kitchen knife and block of cheese looks like it's squared;

speed X, whole blade travel, depth in cheese 2mm
speed 2X, whole blade travel, depth in cheese 7mm

but my test is very unscientific, I'm trying to use gravity to set a constant downforce on the blade and pull it by hand from the tip of the knife handle.

My speed control is pretty sloppy too, but moving the blade faster definitely results in much deeper cut from the same inches of blade travel.

Can anyone tell me if this is a known and understood physics effect of cutting or if it must be worked out somehow?

2. ### Metalmann Active Member

Dec 8, 2012
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There are way too many variables...cheese hardness and temperature.....

If it smells great, I cut faster.

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3. ### strantor AAC Fanatic!

Oct 3, 2010
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different materials respond to different cutting speeds in different ways. Some metals want to be machined at high speed, others at low. Maybe your cheese wants to be cut fast, but your salami wants a slow, firm cut.

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4. ### Wendy Moderator

Mar 24, 2008
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Learning to use a lath and milling machine I learned to listen to the material. A high pitch whine tends to indicate excessive stress, and I backed the feed off a bit. I am no expert, my Dad was, but I never really got to learn under him.

5. ### Metalmann Active Member

Dec 8, 2012
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That's very true, Bill.

On the Net, there are various charts for cutting feeds and speeds...for different ferrous, non-ferrous, plastics, composites; materials.

When it comes to cheese, he may have to create his own charts.

Which would be fun, as long as he adds some Bacon to the mix.

Hard to beat Bacon and Cheese, anything.....

6. ### WBahn Moderator

Mar 31, 2012
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I can almost visualize a very interesting phenomenon going on here. As you draw the knife faster, the high friction causes increase drag on the blade. Nomally, the moment created will have a tendency to rotate the knife up out of the cheese, but I wonder if the stickiness of the cheese might somehow tend to grab the knife and pull it in. Maybe not -- a free body diagram wouldn't seem to support such a notion. But weird things happen when dealing with materials with unusual properties.

7. ### Papabravo Expert

Feb 24, 2006
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I can see "sticktion" or sticky friction really upsetting the model for cheese. The rule of thumb for steel was the "feed" was equal (4*CS/D) where CS was the "cutting speed" and D was the "tool diameter".

8. ### THE_RB Thread Starter AAC Fanatic!

Feb 11, 2008
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Hmm, interesting cheese and lathe anecdotes.

Thanks for the straight answers WBahn and Papabravo, I'm interested in the actual physics of linear cutting speed. The material does not really matter, as known in weapons technology etc things like Samurai swords designed with a curve (or Eastern cutlass type weapons) used in a physical technique to get very high linear blade speeds to cut through a person's entire torso in one swing.

A lot of things in physics are linked to speed squared like force, or speed cubed like wind drag, so I was hoping to get some actual physics discussion on the effect and whether it is squared of cubed.

The same thing happens with a hacksaw blade (if you do a lot of hacksawing you know what I'm saying), if you move the blade slowly from end to end it will cut very little in depth, but moving it very fast over the same distance with the same downforce it removes a lot more material.

It must be removing more material per blade tooth per inch travelled when it moves faster, i'm not sure why, possibly a much greater energy is available at the tooth when moving at higher speed?

(edit) Is there a wear formula for simple bearings or sliding surfaces vs the speed? I think that might equate to a similar thing, ie material removed/cut vs linear speed.

Last edited: Jan 2, 2013
9. ### Papabravo Expert

Feb 24, 2006
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Problem is the physics is neither simple nor straightforward. Material does matter here as well as the material of the tool itself. I think you might be able to develop a set of empirical models where the actual relationship might involve a non-integral exponents, like a 5/2 power. If there is such a theory, I am unaware of it with a degree in Physics and another in EE and a third in finance which has deep connetions to Physics.

Machinig is more art than science and you quickly learn to judge appropriate feeds, speeds, and depth of cut. In fact there is usually a range of such choices that produce good results. A Lablonde and a Bridgeport are actually very forgiving machines in my estimation.

10. ### strantor AAC Fanatic!

Oct 3, 2010
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It doesn't? Right now you're cutting cheese with a knife. What if you were cutting it with a wet piece of paper? Or what if you were cutting the cheese with a slice of the exact same cheese? Do you think that the relationship of speed to depth of cut would remain the same? My talk about machining wasn't meant to sound like an anecdote, but rather a real world practical example.

11. ### WBahn Moderator

Mar 31, 2012
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I don't think my experience supports this. It's hard to say because I doubt it is very easy for a person to truly put the same down force on the blade at different speeds. But I've done quite a bit of slow sawing and filing at times and the pile of filings per stoke seems comparable to faster strokes. A good way to measure the effect would be to use a band cutoff saw (there's a specific name for this saw and it escapes me just now) but it uses its own weight for the down force (in the simple ones) and normally the band speed is pretty low, but it is adjustable. I don't have access to one any more, but it would make an interesting experiment.

12. ### WBahn Moderator

Mar 31, 2012
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I know that how I machined brass and aluminum was quite different from how I machined mild steel and that form stainless steel. And more different yet were how I machined G-10, copper, teflon, plexiglass, and titanium.

13. ### Metalmann Active Member

Dec 8, 2012
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Are you thinking of my horizontal bandsaw?:

http://www.northerntool.com/shop/tools/product_200419821_200419821

Or a horizontal hacksaw?:

http://www.alibaba.com/product-gs/350038960/Hack_Saw_Machine_G7016_G7025.html

14. ### WBahn Moderator

Mar 31, 2012
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The horizontal bandsaw, though I'm pretty sure I know it by another name.

15. ### Metalmann Active Member

Dec 8, 2012
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Another common name was horizontal cutoff saw.

16. ### THE_RB Thread Starter AAC Fanatic!

Feb 11, 2008
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Thanks Papabravo, i'm very interested in your input.

Maybe if we can move away from machining and talk about linear blade speed of a smooth edged blade. The phenomenon is very easy to observe if you get a piece of cheese (which I chose because it has a fairly constant consistency and no hard skin, not because the material matters that much) and a sharp long knife .

If you rest the knife blade on the cheese with just the weight of the blade with no movement, no velocity, it cuts about zero depth. It just sits on top of the cheese.

Move the blade slowly from end to end and it cuts a shallow cut. Move the blade very fast from end to end and it cuts quite deep. All tests have the same weight on the blade and same length of blade travel.

It's not just something I made up, this is a standard concept in martial arts weapons technology etc and the difference between an "axe like" hack with a sword that cuts 2 inches depth and a high linear blade velocity slash with a sword that cuts very deep or right through.

Maybe we can nut out some of the physics of movement? Moving the blade at double the speed would require double the power correct? (assuming the work remains the same). What about the amount of energy available in something that moves twice as fast?

(edit) I had a quick google for linear wear vs speed and found this;

I'm not sure how well it applies but it does show some exponential effect of linear speed on wear.

Last edited: Jan 3, 2013
17. ### THE_RB Thread Starter AAC Fanatic!

Feb 11, 2008
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I'm still stuck with this, the best I can find is the energy of a moving object is related to the square of it's speed, so when the blade is moving twice the speed there is 4 times as much energy available, but that would only be of consequence if the blade is decelerated during cutting and the speed reduces (releasing the energy to perform cutting).

I didn't find a lot on that "exponential" speed to wear ratio, and suspect that is mainly a heat related factor of sliding surfaces, and may not apply to blade cutting?

So at this point it looks like power is the thing, being linear to speed. Assuming it is a fixed amount of work to push the blade through the substance, a fast moving blade has a lot more power available per inch of blade travel, so it pushes deeper in cutting per inch of blade travel.

If that is the case cut depth is not exponential to blade speed, but linear to blade speed.

There's also another factor of friction, with slow blade speed a lot of work is lost on friction of the blade sides pressed against the material, but as speed increases it gets past the stick-slip point so the blade sides are slipping and now all the available work is at the cutting edge, so the power from movement is now almost totally available for cutting and not lost on friction on the sides of the blade.

That would appear to give an exponential effect, at least at lower speeds.

Please argue if any of that is wrong, or if I have missed something!

18. ### thatoneguy AAC Fanatic!

Feb 19, 2009
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Take your example to extremes to get an idea.

Assuming a non-serrated blade, which is perfectly smooth:

cutting edge and blade is 1 iron molecule thin, how does it cut?

cutting edge is a 1cm² piece of bar iron, how does it cut? (It WILL, given enough force and speed)

The answer is somewhere between those two extremes, e.g. friction vs. separation.

Why do cheese cutting devices use a round wire rather than a flat blade?

19. ### Papabravo Expert

Feb 24, 2006
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I think I know that one.

Minimize the surface area and the shear force of the cut cheese on the sides of the blade

20. ### THE_RB Thread Starter AAC Fanatic!

Feb 11, 2008
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Yeah that's because those devices don't have the benefit of having any linear blade speed, they just push downwards so they need to minimise all losses like the side friction.

But the point still stands, that same wire would cut many times better if it had linear speed.

I'm kind of disappointed here, it would have been nice to get some general physics "rule" for cutting factors like the linear blade speed. At this point the best I've got is "more speed is better" whcih is not real scientific.