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Edge retention with different grit finishes on 3Cr13 stainless

Posted by CliffStamp 
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Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 03:59AM
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CliffStamp
I am slowly putting the push cutting measurements together and will add them to the chart shortly by adjusting the order of the stones by that vs the micron size. The reason for this is because some of those results are on worn stones and they are producing finer edges than the grit size would make you expect :

You are then suggesting that that, since push-cutting sharpness and slicing aggression (and therefore ERF) are strongly inversely related (controlling for geometry), that ranking the stones highest to lowest on ERF (which would also be close to lowest to highest on push-cutting sharpness) would be a better reflection of their coarseness or fineness than the grit ratings, yes?

On another note, the strong positive correlation between coarseness of finish and slicing edge-retention suggests that some part of the perceived edge-retention advantages of higher carbide steels for many people may partially be explained by their much lower ease of sharpening, since the time and difficulty required in producing highly polished edges on high-carbide steels may lead users to accidentally leave coarser finishes on them than they think they are, based on the grit ratings of the stones they are using.
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 04:07AM
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CliffStamp
I tried a few experiments to see if I could get there faster or reduce the part which requires any attention. One method was to bring the edge bevel right up to 3000-Henckels and then just micro-bevel with the 8000-henckels. This doesn't reduce the total time, but the edge work is just shaping, I don't really pay attention to it and it can be done (and should be) with a very muddy stone. This is the most efficient from a focused-time perspective but I discovered that if I just micro-bevel with the 8000-henckels and ironically do a really good job then the edge is prone to premature collapse.

Could you explain a little further what you mean by not having to pay attention to the shaping work?
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 02:09PM
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Steel_Drake

Could you explain a little further what you mean by not having to pay attention to the shaping work?

Shaping is very rough stock removal. If you care about aesthetics you have to pay attention as otherwise you will grind grind marks were you don't want them, but if you just want to form a shape it isn't really necessary. For example on the EE Chef, the current and single bevel is 4.5 dps. I can tell that the knife is sitting on the stone on that bevel fairly easily and maintain it during the shaping without even looking at it and doing very high speed passes (multiple passes a second). Now is this perfect - no, absolutely not. There will be some rounding at the shoulder of the edge and some increase in curvature at the apex. But in general, if anything, this will just increase the performance slightly.

But when I move working the apex I have to change, slow down and start doing burr minimization type work. Now if you just want an edge which slices newsprint this isn't necessary. In fact that will usually come right out of the shaping stage. However if you want to move towards very high sharpness then you have to alternate sides, cross scratch patterns, do high angle passes, etc. . Hence at that stage I slow down and if the stone is really soft/muddy I have to really slow down as I want to abrade the steel but not cut into the stone or even form that much of a slurry. But in general unless you are looking for a challenge, there are better ways to sharpen than trying to use a soft/muddy stone to set an apex.
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 02:29PM
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Steel_Drake

[..]

... that ranking the stones highest to lowest on ERF (which would also be close to lowest to highest on push-cutting sharpness) would be a better reflection of their coarseness or fineness than the grit ratings, yes?

It tends to be as the grit rating of a stone is not really a complete indicator of the finish. The grit ratings are generally referring to the particle size, but if you take a diamond plate and a resin bond waterstone of the same particle size, they don't produce the same scratch pattern - the diamond will be much more coarse. What is even more complicated is that some stones tend to see abrasives wear and/or the stone load while some stones are resistant to loading and release fresh abrasives. A soft bond waterstone for example on moderate to grind steels produces a very consistent finish with repeated sharpenings. A hard bond India stone if used on severely hard to grind steels may very well produce a finer and finer finish as the abrasives start to wear.

This is likely why I believe so many people will argue that waterstones cut faster than oil stones. They are using stones like the India abrasives in a very worn condition where the abrasives are all rounded out. If you use them in the as-boxed condition (and maintain them like that) then a coarse India is much faster than a 320 grit Suehiro 'Chemical' which is a very coarse and fast cutting waterstone in general. to get faster cutting than the coarse India you have to do with ultra-fast waterstones which either have severe grit size (Sigma Power 120) or are more friable in abrasive and/or bond and also very coarse (SPS-II 220).

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...since the time and difficulty required in producing highly polished edges on high-carbide steels may lead users to accidentally leave coarser finishes on them than they think they are, based on the grit ratings of the stones they are using.

Exactly, I have made that argument for years but people don't want to hear it. The Mastiff is fond of making this argument on Spyderco's forms (high carbide steels have more "bite" at high polishes). I noted to him awhile ago he was likely seeing simply a higher/more complete polish on the higher grinability steels. I suggested a few simple experiments he could do to verify that. He of course didn't do them and continues to repeat that assertion simply because he likes the thought of it.

You have to keep in mind that a lot of people don't think about knives or abrasives in a rational manner, they have ideas simply because they want them to be true for reasons which are completely irrational. At the end of the day these are small things and don't really do anyone harm. If you want to see the same thing taken to a completely different level then look at the people who promote things like "revitalized water" to cure cancer.

I had a friend stop over and ask me about this recently as they have a relative dying of cancer and treatment isn't working. They wanted to buy one of those water filtration systems which works based on the same principles of homeopathy in that water has memory and that exposure to vitalized, (living) water will get rid of all the problems that we have from drinking dead water. Now in this case you are looking at someone who wants to do something, anything and so they are grasping at any actions. But in many cases people will actually refuse medical treatment (because it also uses dead water) and instead try to cure themselves of cancer with "living water".

Is there such a thing? There is no explanation for how it could work, but that doesn't mean it can't work. However immediately a number of questions were raised to my mind which made the whole thing seem extremely bogus. If I just place a glass of living water next to dead water and the dead water will become alive, and all your very expensive water filtration system does is flow our dead water around living water to make it living water then why can't I just :

-throw a bottle of living water into my well

This will make all dead water in contact with it living water.

-drink a bottle of living water and make all of my internal water living

This will also make any dead water I drink living water. In fact because there is no limit to living water, you can't use it up, the filtration system never gives out and a tiny amount of living water will transform an endless supply of dead water then why don't I just buy a bottle of living water, split it up into tsp amounts and put it into all the wells in my entire town, or just put it in one of the main water supply stations. But no one asks these questions because if you think about them even for a minute then you realize that even if it were true then you don't need an expensive filtration system and thus all the ability for someone to make money is gone.
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 03:41PM
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CliffStamp
Shaping is very rough stock removal. If you care about aesthetics you have to pay attention as otherwise you will grind grind marks were you don't want them, but if you just want to form a shape it isn't really necessary. For example on the EE Chef, the current and single bevel is 4.5 dps. I can tell that the knife is sitting on the stone on that bevel fairly easily and maintain it during the shaping without even looking at it and doing very high speed passes (multiple passes a second). Now is this perfect - no, absolutely not. There will be some rounding at the shoulder of the edge and some increase in curvature at the apex. But in general, if anything, this will just increase the performance slightly.

But when I move working the apex I have to change, slow down and start doing burr minimization type work. Now if you just want an edge which slices newsprint this isn't necessary. In fact that will usually come right out of the shaping stage. However if you want to move towards very high sharpness then you have to alternate sides, cross scratch patterns, do high angle passes, etc. . Hence at that stage I slow down and if the stone is really soft/muddy I have to really slow down as I want to abrade the steel but not cut into the stone or even form that much of a slurry. But in general unless you are looking for a challenge, there are better ways to sharpen than trying to use a soft/muddy stone to set an apex.

For clarification: You use "shaping" to refer to the work you do prior to setting the apex with the micro-bevel, correct? This would be the work done between distressing the edge and the edge no longer reflecting light in your 3 step sharpening video, yes?

This would mean that you are accepting that some rounding and curvature at the apex will occur in the shaping stage in return for being able to go very quickly, and only slowing down and being careful at the apex-setting/micro-beveling stage?

As I mentioned in another thread, my own experience has seemed to indicate that I get better results at the shaping stage by using light pressure and going very quickly rather than by taking my time and being very precise about angle control at the shaping stage as well, hence my curiosity.
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 03:50PM
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CliffStamp
It tends to be as the grit rating of a stone is not really a complete indicator of the finish. The grit ratings are generally referring to the particle size, but if you take a diamond plate and a resin bond waterstone of the same particle size, they don't produce the same scratch pattern - the diamond will be much more coarse. What is even more complicated is that some stones tend to see abrasives wear and/or the stone load while some stones are resistant to loading and release fresh abrasives. A soft bond waterstone for example on moderate to grind steels produces a very consistent finish with repeated sharpenings. A hard bond India stone if used on severely hard to grind steels may very well produce a finer and finer finish as the abrasives start to wear.

That's really interesting in what it implies about the Spyderco stones, my own experiences indicated that the Spyderco medium is actually finer than my DMT XXF. This gives me an idea I need to look into.

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Exactly, I have made that argument for years but people don't want to hear it. The Mastiff is fond of making this argument on Spyderco's forms (high carbide steels have more "bite" at high polishes). I noted to him awhile ago he was likely seeing simply a higher/more complete polish on the higher grinability steels. I suggested a few simple experiments he could do to verify that. He of course didn't do them and continues to repeat that assertion simply because he likes the thought of it.

Not only that, but the low apex-stability of high-carbide steels could reinforce this effect as the typical pattern of apex damage on high-carbide steels would tend to effectively coarsen their apex in use, correct?
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 03:52PM
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Steel_Drake

You use "shaping" to refer to the work you do prior to setting the apex with the micro-bevel, correct? This would be the work done between distressing the edge and the edge no longer reflecting light in your 3 step sharpening video, yes?

Yes, in this stage is where the following are done if necessary :

-thin the primary
-adjust the edge angle
-remove any edge damage/unwanted curvature

and then put the apex in the form ready to take the micro-bevel readily, this depends on the micro-bevel finish. For example if the micro-bevel is going to be very coarse then little to nothing needs to be done specifically. However if the micro-bevel is going to be the MXF DMT then the shaping would end with work on the Naniwa Aotoshi or similar and brought to an apex which either can, or just about push cuts newsprint. If it is less than that then the work on the MXF DMT will simply take so long it is likely to damage the apex more so than set it.

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This would mean that you are accepting that some rounding and curvature at the apex will occur in the shaping stage in return for being able to go very quickly, and only slowing down and being careful at the apex-setting/micro-beveling stage?

Yes. I could grind very carefully and end up with a very strict 4.5 dps bevel but it would gain little to nothing practically and in fact the removal of sharp transitions will increase performance if anything.
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 04:05PM
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Steel_Drake

...
Not only that, but the low apex-stability of high-carbide steels could reinforce this effect as the typical pattern of apex damage on high-carbide steels would tend to effectively coarsen their apex in use, correct?

I believe so yes, depending on what they were cutting.

Years go when I was looking at the edge retention with low edge angles I noticed that the small chips/fractures would allow edges to sustain very low sharpness for basically forever. I called this "self-sharpening", ref : [www.bladeforums.com] . It is one of those things you discover and move on as it is curious but not of practical interest. For me I am not really interested in blades which stay dull a long time, but I do understand others might.

What I do find really curious though is when someone praises something like one of Phil Wilson's knives for high cutting ability due to the geometry (valid point) and then talks about how you can do a massive amount of cutting with them if you will accept very low sharpness cutting (working edges). The part that makes not a lot of sense to me is that if you just sharpened a poor cutting knife then it would cut better than one of Phil's which was dull so what exactly is the point?
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 05:47PM
Wouldn't that 'self-sharpening' edge work well with a steel like D2?
Re: Edge retention with different grit finishes on 3Cr13 stainless
November 28, 2014 06:29PM
Yes, one of the early runs I did was on a D2 custom and I did ~2000 slices into hemp and even getting very sloppy at the end with excessive fast/forceful cuts it became apparent that in no practical sense would such a knife ever dull in that manner. Long before the knife when dull by that kind of slow wear it would corrode, get damaged from accidental impact, etc. .
me2
Re: Edge retention with different grit finishes on 3Cr13 stainless
December 01, 2014 01:00AM
Cliff, you had commented on one of the posts I made on another forum about some cutting I had done with the finish from a Sharpmaker Medium triangle. I made over 700 cuts on 3/8" hemp and the Faberware chef's knife I have would still cleanly slice paper. All you said was something to the effect of "interesting." Would you not expect that level of cutting from such a relatively fine finish?

Also, I'm currently cutting cardboard with the Tojiro petty, sharpened on the 1000 grit King and microbeveled on the Sharpmaker Medium with the 20 dps setting. I'm up to 200' and the edge will still push cut typing paper with no draw. It would treetop arm hair when freshly sharpened. It will also still shave my arm, but takes a little effort, though no irritation. Would you expect a lower degree of edge retention given the steel and finish or is it difficult to predict with changing steel and grit from the ones you're doing now? It still easily slices receipt and notebook paper, which are both lighter than typing/computer paper.
Re: Edge retention with different grit finishes on 3Cr13 stainless
December 01, 2014 01:45AM
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me2

All you said was something to the effect of "interesting." Would you not expect that level of cutting from such a relatively fine finish?

If this was on Spyderco's forum I often quote what you say as a point of reference as Jim has taken to claiming I am simply lying about results now and implying I am the only person getting those kinds of edge retention.

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. it difficult to predict with changing steel and grit from the ones you're doing now?

It is difficult to predict even when I do it because of the effects of random scatter, you can't get any where near to the precision/accuracy most people think/claim. It is reasonable to me but I would not really balk unless the numbers were outside a really wide range.

I will get the exact reference later as I was scanning a bunch of papers last week but I found references in a patent where the same bar of steel was cut into multiple knives and the range in CATRA data from that was from 400 to 600 which is a 50% difference and again this is all mechanical testing done as controlled as it can be in a lab.

In the cardboard runs I am doing now I cut ~500 m with a 3Cr13 blade (x-coarse DMT finish) before the knife loses the ability to scrape shave arm hair. However :

-cardboard is wildly variable, I stock sample from a big pool, if you don't expect 10:1 differences
-speed of cut can easily make 2:1 differences
-sharpening I would not expect to be different between you and me, but in general this is worse than cardboard
-angle/force/control I would expect to be similar as well, but these can be 2:1

This if you look at it I would expect to see a 10x10x2x2x2x2 = 800:1 difference spread, with most of it being spread lower. Hence why it doesn't surprise me with someone cuts a few feet and claims it is very hard on the edge. I normally conclude there it is most likely :

-they can't sharpen
-the cardboard is very abrasive
-they are not cutting with much control or doing it extremely fast

In general the most I would say in regards to steel inferences is relative. I would ask you what would you get with another knife for example.
me2
Re: Edge retention with different grit finishes on 3Cr13 stainless
December 01, 2014 03:05AM
Based on the tests from a couple years ago on the Byrd Cara Cara and Benchmade Griptillian, at the point I am now in the cutting I'd say they would be very close. They would all still shave at or above this level when cutting similar amounts. I'd also say that arm shaving is a poor test of sharpness in terms of repeatability. I need to dig up that annealed 1095 blade and finish it and use it for comparison again. The finish was so rough that it would trap bits of cardboard in the scratches that could only be seen under magnification.
Re: Edge retention with different grit finishes on 3Cr13 stainless
December 04, 2014 10:36PM
I think the person who made this video also thinks he found the self sharpening edgesad smileythis is part 2 of 2)
Cardboard Test Cutting Part 2
Re: Edge retention with different grit finishes on 3Cr13 stainless
December 06, 2014 04:37PM
Norton Crystolon fine and coarse :



See the huge error bar on the coarse (just two runs), this is because of this :

\

+



These are two places on the edge which are only a mm apart. Note how one of them is worn more or less smooth while the other one is much more jagged. As the finishes get more coarse there is more spread in the finish of the edge which means there tends to be much more variability in how it breaks down. It is also really sensitive to the initial sharpness. A very low initial sharpness tends to wear faster into that much smoother edge, a very high one wears into that more jagged edge.

--

As an aside, I don't think I have done this extent of edge retention comparisons at this level of frequency before and it is becoming apparent that while they do produce some interesting results they are not overly practical. I can easily for example take this knife and a very basic stone like this one, put a finish on a $1 knife which can slice ~1000 pieces of 1/2" hemp, it is at < 1.5% or optimal sharpness but can still slice newsprint and then make a sandwich cutting up various fruits and vegetables including a tomato with no crushing/tearing or slipping.

However from a practical point of view :

-what are the odds I would ever cut this much clean material and not damage the edge

-why would I use a knife at < 1.5% of optimal sharpness anyway

The knife starts off cutting the hemp at ~4-5 lbs, at the end it is approaching 20 lbs which is hugely inefficient. In reality I would sharpen it when it exceeded 10 lbs which would still only require sharpening every few hundred cuts and would require a few passes on a coarse stone.

The more of this kind of work I do, the more it becomes obvious that Roman's view on steels for knives, which I once regarded as far too simplistic and over generalized makes the only kind of practical sense.
Re: Edge retention with different grit finishes on 3Cr13 stainless
December 08, 2014 03:07PM
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CliffStamp

The more of this kind of work I do, the more it becomes obvious that Roman's view on steels for knives, which I once regarded as far too simplistic and over generalized makes the only kind of practical sense.
Hi Cliff, mind elaborating on this a bit? What was that view? I lack context for understanding, but love overgeneralizations winking smiley.
Re: Edge retention with different grit finishes on 3Cr13 stainless
December 08, 2014 03:18PM
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Bogdan M.

[...]

What was that view?

Knife steels should be chosen to produce maximum cutting ability :

-enough toughness to prevent impact fracture
-maximum strength and apex stability to allow minimal cross sections

He has very little value in wear resistance for reasons I will note in a response here : [www.cliffstamp.com] .
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 17, 2015 05:37PM
Summarized : [www.cliffstamp.com] .
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 17, 2015 08:51PM
Fascinating. Is iSharpness initial slicing sharpness or initial push-cut sharpness, or some mathematical average? If it's slicing sharpness, I'm confused about why the higher grit edges pretty consistently have higher slicing sharpness -- I would think that would be close to the same or slightly worse than the lower grit edges. Given the wide variability in sharpness, I'm also a little confused about why the sharpness doesn't have a stronger influence than the grit finish on the edge retention. I thought you had established in other work that starting with a sharper knife buys more edge retention if you're cutting to a fixed % from optimal (simply because there's "more" sharpness to begin with).

Two other questions:

1. How different would the graph look if the ranking on the x-axis was in terms of push-cutting sharpness rather than manufacturer's listed grit rating?
2. Any plans to add some really high (sub-micron) grit finishes?
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 17, 2015 08:56PM
I think the question I numbered 1 above is interesting because with a little effort, I achieved a hair-whittling edge off a 325 grit stone yesterday. I've only just started measuring push-cutting sharpness quantitatively so don't have a baseline for this, but I assume that hair-whittling requires a much higher-level of push-cutting ability than you standardly get at 325 grit. Does this mean that the slicing edge retention I'll get from this sharpening will be closer to what you normally see off, say, a Spyderco Medium? Or will I get the 325 grit edge retention (in a slice) combined with high push-cutting ability (best of both worlds)?
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 17, 2015 09:58PM
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ianevans
I achieved a hair-whittling edge off a 325 grit stone yesterday. I've only just started measuring push-cutting sharpness quantitatively so don't have a baseline for this, but I assume that hair-whittling requires a much higher-level of push-cutting ability than you standardly get at 325 grit.

That term, while helpful is a bit broad, I don't think it is impossible even off of much more coarse stone as hairs in general vary quite a lot and how you make that cut is a strong influence.

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Or will I get the 325 grit edge retention (in a slice) combined with high push-cutting ability (best of both worlds)?

This is a good question, and the problem with the results which I didn't really talk about is actually noted in your question. To be really specific, an x-coarse DMT edge will have a low push cutting sharpness even when sharpened ideally, an x-fine DMT edge will have a low push cutting sharpness when sharpened poorly. However with the x-coarse DMT it indicates a high slicing edge retention, with the x-fine it just indicates poor performance in general.

If you have a high push cutting sharpness and a high slicing sharpness and the grit rating of the stone is very coarse, then the first thing I would check is if the stone simply isn't loaded/worn because it could be simply acting like a very fine stone as it basically is one.
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 17, 2015 10:05PM
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ianevans
Is iSharpness initial slicing sharpness or initial push-cut sharpness, or some mathematical average?

It is slicing.

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I'm confused about why the higher grit edges pretty consistently have higher slicing sharpness -- I would think that would be close to the same or slightly worse than the lower grit edges.

This is sensitive to load. The sharpness is measured under a very low load, 35 grams, so the very coarse finishes can't actually cut as well under that load. It is like taking a very coarse saw and using it lightly, it won't cut as well as a much finer saw with a low force. This adds a layer of complication because to be specific when you measure slicing sharpness you have to specify the force you are applying, it is also dependent on the material. I didn't get into this because right now I would be satisfied if people would realize the difference between cutting ability and sharpness and then split sharpness into push vs slice.

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I'm also a little confused about why the sharpness doesn't have a stronger influence than the grit finish on the edge retention. I thought you had established in other work that starting with a sharper knife buys more edge retention if you're cutting to a fixed % from optimal (simply because there's "more" sharpness to begin with).

I didn't address this very well in the write up, I will add it now. What happens is that the very coarse finishes have a multi-stage series of blunting where they have to have the tips worn, the inside of the scallops wear, then they tend to break/chip and form new ones and it all starts over, until finally they are worn smooth. A much finer finish doesn't really go through that and just blunts smooth much quicker.

This is all on a slice, if you do the whole thing on a push it reverses and the graph runs the other way. The performance of the coarse edges on a push is so bad they can collapse immediately as in within the first few cuts. The really coarse ones can't even make a few cuts at all.



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1. How different would the graph look if the ranking on the x-axis was in terms of push-cutting sharpness rather than manufacturer's listed grit rating?

It resolves a number of the odd points such as the Sharpmaker Medium rods.

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2. Any plans to add some really high (sub-micron) grit finishes?

Possibly, I ran out of hemp again, it takes a lot to do that kind of work due to the number of trials involved.
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 18, 2015 07:24AM
Nice write-up. I appreciate you putting it together.

Is there a reason you don't specify the stopping point for the cutting? I was looking for it, but o only see it referenced in the graph.

_______________________________________________________________________________________________

Always in search of a good choppa'
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 18, 2015 03:37PM
Oversight, I just added it.
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 18, 2015 04:58PM
Would it be pratical for you to do an additional run to narrow the error bar on the initial sharpness from the Sigma Power 120? I believe you said the spread was due to improving techinque. Can you demonstrate consistent ability in the upper end of that bar, and will the TCE be unaffected?
Re: Edge retention with different grit finishes on 3Cr13 stainless
January 18, 2015 07:36PM
The noise goes as root (n) so I would have to do four times the amount of runs to cut the error bars in half. Now in this case that is a bit of an exaggeration because the early runs had a higher amount of noise due to me just figuring out how to sharpen with x-coarse abrasives and the influence of wear. To get really consistent runs with the Sigma Power 120 I would need to either not use it for anything but the micro-beveling -or- make sure it was recut before each run. I may in the future add to this with more stones or do some runs to bring down the error bars. When I get some really coarse diamond/cbn or hang out with a tile installer I am going to recut the surface of the dressing stone and see how that works freshly cut to test out the idea that it is grinding as it does due to worn abrasives.
Re: Edge retention with different grit finishes on 3Cr13 stainless
March 19, 2015 04:52PM
If only I had seen this topic on time - I'd save me a few dozen hours sharpening my kitchen victorinox knives with various stones and diamond plates over the last few months.
All is not in vain - at least I found that my conclusions are correct and once again confirmed the truth of how little I understand of sharpening knives at least with regard to what happens invisible to the human eye.

Thanks for the great info.

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Edited 1 time(s). Last edit at 03/19/2015 06:10PM by stefan_wolf.