Cliff Stamp
BANNED
- Joined
- Oct 5, 1998
- Messages
- 17,562
Recently I began a series of comparisons of very similar blades on cutting a very abrasive type of cardboard. This was 1/4" double ridged and the cuts made on a slice through 4 cm of blade with the middle 3 cm measured for sharpness slicing light cord. I started off comparing one S30V knife to one ZDP-189 knife with the intention to do a bunch of steels. I then wondered if it would not be more informative to do less steels and more knives. Are all my S30V knives the same? Are all of them less effective slicing cardboard than all of my ZDP-189 knives? So I set off to do a fairly absurd amount of cardboard cutting. Six trials on each knife through a random sampling of cardboard with the force applied and the speed of cuts controlled.
To answer the question of "better" in a significant way I needed a way to model the performance. Forget about splines and power interpolation, I needed a real physical model and ideally a simple one. So it came to me, isn't this a really simple physical situation? Yes - rate of blunting is inversely proportional to the extent of blunting. Isn't there a known solution to that relationship? Yes - y=sqrt(x). Now it isn't going to be ideally that equation for a few reasons which I will mention later on so the model is :
Dullness = (edge retention coefficient) * (amount of media cut)^(law coefficient)
or basically
y=a*x^b
At zero material cut the dullness is zero and thus to model the blunting this initial sharpness is just subtracted off all the measured values of sharpness, or it can be just included as another parameter, but it is the same for every knife and isn't a physical parameter in that sense, though it could be for high polishes at low angles. The law coefficient (b) is between 1 and 0.5. At 0.5 the blunting is a perfect inverse relationship and at 1 it is perfectly linear. The edge retention coefficient (a) is the parameter which measures the resistance to blunting. In this case, I was studing cardboard, so it includes strength, wear resistance, caride stability, fatigue/strength, etc. .
Ok, that is the theory, does it work. The knives were all reground to primaries of 8.0 (5) degrees per side. Yes this is fairly acute, these are knives after all not axes. I experimented to see if it made any difference if I cut the primary with a x-coarse DMT then polished it on 600 DMT and finished with 1200 DMT, or did the first two steps with waterstones. I did three runs each way with each knife. I also did two runs by just resharpening the micro-bevel and not regrinding the primary clean (this is instant, 5 per side on 600, 5 per side on 1200 - done). None of it made any difference. The median performance :
I finally coded the points and the lines the same color in the graphs which makes it easier to tell which data is for which line. The graph includes a 12C27m blade for reference. The work was mainly to look at the S30V blades, I just wanted one external benchmark to give it meaning. Now it is obvious that the model works very well. It is also possible to generate a value for the strength of the coefficients and thus say statistically if one blade actually has better edge retention than another.
I'll post up the gory numerical details later on as I am putting all the details on the web now. But in short, the Rat Trap, Manix and Paramilitary are not statistically different. The Military however is and this obvious if you don't measure anything. At the end the Military is still cutting clean while the others are starting to rip the cardboard. Now the question I have is this, if I run the exact same thing on the three ZDP-189 knives I have will all of them be better, or will the average be better. Will the law coefficient be the same - meaning do they blunt the same way?
The other thing I should mention is that if the law coefficient (b) is the same, then the relationship between the edge retention from one knife to the other is LINEAR. This means if the edge retention coefficient for one blade is 20% more then it directly means it will be 20% more blunt at a given point. This makes it very easy to make definate statements about steels in an easy to understand fashion. I have more to say about this law and how to use/interpret it, which I hereby name the Swaim blunting equation, but that is enough for now. I will note though that it isn't restricted to cardboard, it is a *general* law for blunting on all media - how is that for comprehensive.
The unfortunate thing is that I have in front of me the insane task of looking at all the data I have collected in the last ten years because now I can model it all, or at least attempt to do so. I should check the equation on carpet, ropes, woods, etc. to determine its versatility. This is a good thing but I wish I had thought of doing this in 1998.
-Cliff
To answer the question of "better" in a significant way I needed a way to model the performance. Forget about splines and power interpolation, I needed a real physical model and ideally a simple one. So it came to me, isn't this a really simple physical situation? Yes - rate of blunting is inversely proportional to the extent of blunting. Isn't there a known solution to that relationship? Yes - y=sqrt(x). Now it isn't going to be ideally that equation for a few reasons which I will mention later on so the model is :
Dullness = (edge retention coefficient) * (amount of media cut)^(law coefficient)
or basically
y=a*x^b
At zero material cut the dullness is zero and thus to model the blunting this initial sharpness is just subtracted off all the measured values of sharpness, or it can be just included as another parameter, but it is the same for every knife and isn't a physical parameter in that sense, though it could be for high polishes at low angles. The law coefficient (b) is between 1 and 0.5. At 0.5 the blunting is a perfect inverse relationship and at 1 it is perfectly linear. The edge retention coefficient (a) is the parameter which measures the resistance to blunting. In this case, I was studing cardboard, so it includes strength, wear resistance, caride stability, fatigue/strength, etc. .
Ok, that is the theory, does it work. The knives were all reground to primaries of 8.0 (5) degrees per side. Yes this is fairly acute, these are knives after all not axes. I experimented to see if it made any difference if I cut the primary with a x-coarse DMT then polished it on 600 DMT and finished with 1200 DMT, or did the first two steps with waterstones. I did three runs each way with each knife. I also did two runs by just resharpening the micro-bevel and not regrinding the primary clean (this is instant, 5 per side on 600, 5 per side on 1200 - done). None of it made any difference. The median performance :
I finally coded the points and the lines the same color in the graphs which makes it easier to tell which data is for which line. The graph includes a 12C27m blade for reference. The work was mainly to look at the S30V blades, I just wanted one external benchmark to give it meaning. Now it is obvious that the model works very well. It is also possible to generate a value for the strength of the coefficients and thus say statistically if one blade actually has better edge retention than another.
I'll post up the gory numerical details later on as I am putting all the details on the web now. But in short, the Rat Trap, Manix and Paramilitary are not statistically different. The Military however is and this obvious if you don't measure anything. At the end the Military is still cutting clean while the others are starting to rip the cardboard. Now the question I have is this, if I run the exact same thing on the three ZDP-189 knives I have will all of them be better, or will the average be better. Will the law coefficient be the same - meaning do they blunt the same way?
The other thing I should mention is that if the law coefficient (b) is the same, then the relationship between the edge retention from one knife to the other is LINEAR. This means if the edge retention coefficient for one blade is 20% more then it directly means it will be 20% more blunt at a given point. This makes it very easy to make definate statements about steels in an easy to understand fashion. I have more to say about this law and how to use/interpret it, which I hereby name the Swaim blunting equation, but that is enough for now. I will note though that it isn't restricted to cardboard, it is a *general* law for blunting on all media - how is that for comprehensive.
The unfortunate thing is that I have in front of me the insane task of looking at all the data I have collected in the last ten years because now I can model it all, or at least attempt to do so. I should check the equation on carpet, ropes, woods, etc. to determine its versatility. This is a good thing but I wish I had thought of doing this in 1998.
-Cliff