"At this point the best I've got is "more speed is better" whcih is not real scientific."


You are correct...cutting any type of material, is determined more by actual trial, and/or; error.

All the charts are supposed to do, is to get you in the general area...RPMs, SFPM, etc.

Temperature, hardness, tooth area, friction, angles, etc.; and so many other factors determine actual cutting speed.

The best way to figure out the cheese project, is to write down everything determined by time.

I kind of miss the days when the cutting tool representatives, would come in every week; trying to convince me how THEIR tools were going to make my life easier.

Some of them would leave in frustration, but leaving behind very expensive toys/tools to try out.
If their tooling cut like they said it would, I'd call them back and place an order.
That didn't happen very often, because it was mainly marketing hype.

 

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.

If, in addition to waiting for an answer here, you've been searching elsewhere and haven't turned anything up, then maybe it's time to accept what's been said already. There is no "thumb rule" that you're looking for. These things completely depend on the properties of the material being cut, and the material doing the cutting.

Alternatively, if you have reason to be absolutely sure that some universal relationship between linear speed and cut depth exists, you could devise a repeatable test and uncover this relationship empirically. Make a test jig that holds your knife and cuts at a selectable speed repeatedly. cut several pieces of cheese at one speed, obtain an average, move to a higher speed, repeat. Determine relationship mathematically. I suspect that even this simple goal will prove elusive. I suspect that if your cheese cutting jig were speed adjustable from 0 to infinity, you would notice a point at which increasing speed no longer adds to depth of cut, and may actually start reducing depth of cut as you increase speed.

But let's say you were able to isolate some concrete relationship between speed and depth of cut for your cheese and your knife, I doubt it would be exactly the same if you substituted in my knife and/or my cheese. And it would for sure be right out, if you were to substitute the knife for a hacksaw, and/or the cheese for a steel bar.

As a thought experiment, in the test jig I described, leave your knife in place, but replace the cheese with a diamond. Would the relationship remain the same as the cheese?

 

While not cutting cheese have you seen these? They are about cutting force and soft tissue. There are many more available, hope this helps.

http://www.rams.umd.edu/pdf/MMVR2004.pdf

http://web1.sssup.it/pubblicazioni/ugov_files/200176_MST_Valdastri_Dario.pdf

ftp://ftp-sop.inria.fr/epidaure/Publications/Delingette/ca99.pdf

 

To Strantor; You made a good point about testing might be the only way to really find out for sure. Actually I'm a bit disappointed the relationship is not one of those commonly known facts like "a bullets impacting energy is the square of its speed" or "wind drag is the cube of the wind speed" as they are all based on standard physics concepts of the way speed and force interact.

To Shortbus; Thanks! That first PDF is very interesting, it seems like they actually proved the liver has a much lower "hardness" as the cutting speed increases. That looked linear, so possibly, the cheese or meat gets much "softer" with speed increase so that might compound with the much higher available power at high blade speeds...

Then again maybe what they are measuring is what I said before that due to higher blade speed there is more power to perform a cut, so their force measuing device appears to give the result of the material being "softer". So the two concepts might not stack, they might just be the same concept.

 

I'm not 100% sure, but because KE=(m*v^2)/2 and KE must be conserved when transformed from motion to heat on impact (friction is what slows it), I would deduce that, so long as the cutting material and material to be cut were to remain the same, that a doubling in velocity would translate to a quadrupling in depth.

Now, each different kind of material will have different cut depths if the drop height is the same for all those materials. My inclination would be that ultimately the cut depth is going to be D = (KE_blade) * R, where R is the ratio of how far the cut ends up being to how high the blade started (like 1cm cut for a 20 cm drop).

My equations are not provided in an exact manner, but this is the general flavor I have when looking at this scenario.

EDIT: R is a factor that is able to divide Newtons out of Joules to give you Meters. I assume this blade is being dropped when I say "how high the blade started."

EDIT2: R will change when the angle of the edge changes, the width of the blade changes, etc. This is because, when we divide N out of J, we are dividing out the N that the material will provide against the edges of the blade. Changing the shape of the blade will change that N, therefore your materials ratio table will need to be regenerated if you change your blade. Sharpening/dulling will change this too. I'm sure there are relationships you can explore dealing with frictional coefficients and the angle they are applied at against the sides of the blade edge, but if you're dealing with one unchanging edge then this need not be considered.

EDIT3: If you have no idea what I'm talking about in my analogy above, I'm imagining dropping a chef's knife on uniform blocks of material, like butter, or 3" diameter hot-dogs, or something...

EDIT4 (I swear...): Thermal differences in the material will change the cut depth as well, so assume the same thermal level for all repeated experiments.

 

Thanks for discussing! I thought this had died.

I'm not 100% sure, but because KE=(m*v^2)/2 and KE must be conserved when transformed from motion to heat on impact (friction is what slows it), I would deduce that, so long as the cutting material and material to be cut were to remain the same, that a doubling in velocity would translate to a quadrupling in depth.
...

Yeah first I thought the releationship would be equated to velocity squared too, but that's more for "impact" type events where the kinetic energy is released into the event and the blade comes to a stop.

...
Now, each different kind of material will have different cut depths if the drop height is the same for all those materials. My inclination would be that ultimately the cut depth is going to be D = (KE_blade) * R, where R is the ratio of how far the cut ends up being to how high the blade started (like 1cm cut for a 20 cm drop).

...

EDIT3: If you have no idea what I'm talking about in my analogy above, I'm imagining dropping a chef's knife on uniform blocks of material, like butter, or 3" diameter hot-dogs, or something...
...

It looks again like you are talking about an "impact" type cutting event, ie a blade drop, where the blade comes to a stop in the material as it reaches a depth of cut.

What I'm talking about is a "slash" cut with a straight blade.

That means linear blade speed (blade moving at 90 degrees to the cut depth) where the blade speed stays constant and generally does not release the kinetic energy. Think of a hacksaw's motion.

Martial arts guys train to get high linear blade speeds with swords etc, rather than "chop" with a sword like the way people use an axe.

 

Well, I can say that, thinking about it, you're dealing with friction on the *sides* of the blade. This friction goes from (almost) 0 when the edge is just resting/contacting/starting to move on the uncut surface, to a maximum value related to the width of the blade from edge to back and point to point (edge begin to edge end), if the material is thicker than that width but shorter than edge start to end. So to maintain the same cut speed, the wattage of the cutting motor will need to climb as the blade deepens, up to a certain point. Because of friction, thermal events will take place so the longer the blade moves at a given speed, the hotter the material at the cut point will get, and the more frictional force will be generated due to thermal expansion of the material and the blade (slightly). Like with a hacksaw, it depends on the sharpness of the blade and how rough the blade is at the microscopic level (no material is perfectly smooth at the atomic level). You will still need to come up with ratio charts to convert the (horizontal) v of the blade to a d of cutting depth. The amount of force you use on the blade perpendicular to the surface of the material you're cutting will also make a difference.

For exact answers and to calculate a most efficient design, you'll need to turn to multivariable calculus.

 

Thanks, more good info. The stick/slip properties of the material being cut really look to be a major factor.

 

"That means linear blade speed (blade moving at 90 degrees to the cut depth) where the blade speed stays constant and generally does not release the kinetic energy. Think of a hacksaw's motion."




A hacksaw blade cuts in one stroke/direction only.

A bandsaw blade could be considered in linear FPS.

Depending on the texture/hardness,blade type...cheese could lead to massive side friction.
Cutting some rubber materials on a bandsaw also creates a lot of friction, the harder it is, the less friction; normally....because it's easier to clear the chips from the cut path.

With cheese, it more of a shearing cut.

 

Martial arts guys train to get high linear blade speeds with swords etc, rather than "chop" with a sword like the way people use an axe.

There are additional reasons for this behavior. In a steel fight (vs gunfight), the object is NOT to decapitate or puncture vital organs. Attempting such results in the sword getting stuck in bone, costing the wielder a fraction of a second, which results in both fighters being dead due to loss of blood.

The object is to make as many somewhat deep cuts as possible in a very short amount of time to cause massive blood loss. Hollywood ruins actual sword art for the sake of visual effects (same as they do with actual function of firearms, vehicles, gravity, and anything else they can get away with).

Keep in mind that when sword fighting was the only fighting, more died from infections than from a fight itself. Yielding was common once one became disoriented or faint from loss of blood, and it was rare for even the winner to walk away without a few deep slash-wounds of their own.

 

Yeah, swords were meant to make your opponent useless in battle. To make sure he can't fight back. Eliminate him from combat.

There would be a lot less war today, if swords were used.

 

Ever hear of the 100 year war? The mid-evil ages are a good argument against. Those who don't study history are doomed to repeat it.

Dynamite was an ultimate terror weapon that was going to end all wars. Good luck with that.

So far nukes seem to be holding better than poison gas and biological weapons. We can only hope.

I have always wondered how the Asian style of sword fighting would compare against European styles, I suspect given the shear practice of the Europeans I suspect they have much better styles, there are a plenty to choose from.

Hand to hand styles are debatable, and often are.

Sorry about going so far off topic.

 

My understanding is that dynamite was not invented to be a weapon at all, but rather as a safer means of using explosives for productive uses like construction and mining compared to nitro and other contemporary options. It was meant to save lives. That it would become a weapon of war should have been obvious to Nobel, but apparently wasn't.

 

...
The object is to make as many somewhat deep cuts as possible in a very short amount of time to cause massive blood loss. Hollywood ruins actual sword art for the sake of visual effects (same as they do with actual function of firearms, vehicles, gravity, and anything else they can get away with).

Keep in mind that when sword fighting was the only fighting, more died from infections than from a fight itself. Yielding was common once one became disoriented or faint from loss of blood, and it was rare for even the winner to walk away without a few deep slash-wounds of their own.

Sounds like you are talking more about European fencing style swords? They are not a weapon of war, they are more of a sporting weapon or for gentleman's defence.

Samurai trained for 1 strike/1 kill, and actually trained on convicts and corpses to become very competent at removing a head, or even cutting right through a torso in only one strike. That's a weapon of war.

Likewise if you read the Viking sagas there are tons of reports of one strike with a broadsword taking off a head, or severing an arm or leg. Ok, the boradsword is heavier and more strength oriented than a hgihly refined katana, but even the Europeans would train for some linear blade speed in heavy sword strikes (at least the good ones did).

 

Sounds like you are talking more about European fencing style swords? They are not a weapon of war, they are more of a sporting weapon or for gentleman's defence.

Combination of European sword methods and current knife defense methods (should one end up where the only item available is a knife <8" long). No clue who or how it was studied, but many short puncture or slice wounds as possible in a short amount of time is more effective than fewer deep puncture/ high pressure and slower slice attacks.

We are getting into an area that isn't best for this forum, but the science applies to The_RB Cheese Theorem: Faster moving blade is better, both in defense and when making a sandwich.

 

Agreed, the conversation was getting unneccessarily violent. It's mainly the physics of the process that I'm interested in.

As another example even things like guillotines used a slanted blade, to give some linear blade edge speed from a straight downward movement;

Technically there is same energy to "chop" from the same weight falling the same distance whether the blade was slanted or straight, but the slanted blade gets linear edge speed where a straight blade does not.