How To Wheel-grind a straight edge without overgrinding?

[kreisler]

Here the perfect practical example, the Spyderco Yojimbo 2. Its edge length is 75mm, and with this knife model you are forced to start flush on the grinding wheel because the obstructing knife's ricasso/bolster would be in the way otherwise. Let's assume that the edge is 100.0% perfectly mean-straight (because maybe it was factory-ground on a 150mm wide large grinding wheel lol). And let's assume that your grinding wheel width is 45mm, i.e. narrower/shorter than the edge length. Then i am claiming that repeated grinding sessions on this wheel will seriously concave the edge, no matter what you try! In fact, even after the very first wheel grinding session one could see the concaving effect through a 100.0% mean-flat reference surface, with light shining through the concavity. I am not claiming that wheel grinding sessions will not sharpen the entire edge length; they will. All i am claiming is that wheel grinding the Yojimbo edge on a 45mm narrow wheel will instantly ruin the 100.0% perfect straightness of the edge. Solution? If you want to keep the ex-fac perfect straightness, then either grind on a 80mm+ wide wheel or grind the blade on a "wide" 100.0% mean flat benchstone in such a way that each point of the edge gets equal grinding time, i.e. simultaneous grinding contact.

My thoughts on this topic in detail:

I was wondering about the exact maths when you start the wheel-grinding "flush", i.e. the heel is resting on the wheel with the heel being flush with one edge of the wheel, before you start drawing the entire straight blade length along the wheel thickness w1. knifegrinders video shows that grinding on a wheel could lead to a concaving of the (straight) blade section. i agree.

in order to avoid the concaving effect, in the video wootzblade suggests that we "spend more time grinding the heel". i doht fully agree. let's consider the extreme case like the Yojimbo, i.e. a knife blade-handle-geometry which forces the user to start the grinding "flush", and the blade shape has a long straight blade section ending in the heel. so from the very start the wheel width is fully "covered with blade steel" and you leave that blade heel section lying on the grinding wheel. then as soon as you start drawing the blade in the proper direction, the heel point (at x = x0) loses contact with the wheel whereas the "opposite" wheeling point (at x = x0+w1) still gets grinding time T. And the slower you draw the blade, the much more extra dwell time that is. in fact, that point gets the maximum of grinding time of the entire blade length. That point, or the section between the heel point and that point, will eventually develop a recurve. To be crystal clear, after a wheel grinding session, the straight blade section will not be 100.0% straight anymore; this can be easily confirmed by a subsequent honing test on a mean-flat ceramic stone. Never mind the grinding wheel, this phenomenon is equally true for grinding a straight blade heel section on a guided sharpening system (Ruixin, EdgePro, Lansky, KME, etc) or even on the 204MF: whenever the "grinding width" is so much narrower than the blade length, then it becomes impossible to maintain the mean straightness of the (straight) heel section.

Here are the maths and the computational confirmation that my formula is correct:

I don't expect everyone to understand the contents of the above two pics. The conclusion of the graphs/maths is: whatever you try to vary (making t0 shorter or longer or zero, increasing or decreasing v1), there is absolutely no way of grinding each point x for an identical amount of time T(x).

Actually there is. Just take a knife where you're not forced to start "flush", like a Santoku knife or a typical Japanese chef knife. Or check the last pic of my Berndes modding post; before the mod the Berndes geometry would have forced me start wheel-grinding flush, after the mod i could draw the blade across the wheel width in such a way that each point x gets an identical amount of grinding time T(x), so its straight blade section would remain mean-straight even after repeated wheel grinding sessions.

maybe the take home message be: trying to distribute grinding time equally over the entire edge length, i.e.

T(x) = const., for all x​

is h*ll of a challenge! at least in theory.

Do you have similar wheel-grinding experiences or other practical solutions for this "maths problem"?

 

[SOLEIL]

Dude, way overthinking it. If you are not experienced enough to do it hand and eye make yourself a jig to put on the grinding plate and do it that way.

 

[Mr.Wizard]

I am just as happy for an excuse to break out the maths but material removal rate isn't determined by time alone but also pressure. You can grind more off the edge near the ricasso by increasing pressure at that point. Of course if you are targeting "100% mean-flat" contact across the full length of the edge is a good idea.

 

[kreisler]

Yes agreed, pressure is another factor which determines the rate of material removal. maybe what we should be looking at is the "rate of blade shape change" upon grinding. A very thin blade section (e.g. near the tip) will change its shape faster because there is less material to maintain the shape, as opposed to the heel section where the blade stock is thicker ("thick behind the edge") and it'd take much more grinding time/pressure to make a change to the blade shape there. Sure, we doht want equal grinding time and equal grinding pressure and speed, if the variation of blade thickness is substantial; our ultimate goal (in this thread) is to keep a straight edge straight. I mean, 100.0% straight.

And my claim stands that this is not possible with an EdgePro/Ruixin/Lansky/etc, 204MF, or a narrow grinding wheel. It's just a claim, i could be wrong though. You guys tell me.

 

[annr]

I agree it is not possible with a narrow grinding wheel (regardless of blade thickness tip to heel).

That is why I use the side of my wheel that has a radius >3”. This still does not solve the problem of blade thickness along the edge. That has to be addressed separately IMO and is a royal pain in the butt with a “pure” straight edge.

 

[SOLEIL]

You guys have a better brains than me. Just looking at the equations makes my brain hurt!

 

[wootzblade]

I agree it is not possible with a narrow grinding wheel (regardless of blade thickness tip to heel).

That is why I use the side of my wheel that has a radius >3”. This still does not solve the problem of blade thickness along the edge. That has to be addressed separately IMO and is a royal pain in the butt with a “pure” straight edge.

"a royal pain in the butt with a “pure” straight edge" - love it, and this exactly is what it is. Illustration:

Before this thread I thought of the grinding time, pressure and the grinding area as contributing factors.
Now Kreisler mentions thickness behind the edge that is varying along the edge due to the blade taper towards the tip - another factor to think about.
I used to think that grinding on a narrow area, like a narrow wheel or with a narrow stone is less predisposed to the middle overgrinding, but Kreisler is right that "thickness behind the edge" factor is not going anywhere no matter how narrow or wide is your wheel or benchstone.

I wrote some about the middle overgrinding on our website http://knifegrinders.com.au/06Procedures_straight.htm
but not to the detail I read in this thread.

 

[kreisler]

Some readers might ask themselves 'what does it matter if the blade develops a recurve, as long as i can grind the edge to perfect sharpness?' That's actually a fair question. Somewhere else i posted (claimed) that Leatherman did not design their Surge main blade to have a recurve, even though it comes with an annoyingly slight recurve OOTB. I had checked several(!) copies of the Surge blade and each copy had the recurve to a different extent. Manufacturing variations. How come?? One logical explanation could be: the designers did not design a recurve to begin with, but during the grinding process the edge developed that slight recurve. Also note that the Surge blade is thicker(!) at the belly nearing the tip, and it is actually very very hard to remove material at that belly with a Ruixin stone. Now have a look for yourself, nobody could make me believe that —if you can see a recurve there— the recurve was designed by the Leatherman designers, just look:

The Surge blade is 'thin behind the edge' nearing the ricasso but(!) 'thick behind the edge' nearing the belly! So it makes perfect sense to me that, if you wheelgrind this blade, it would develop that slight recurve ex-factory. The low-grit grinding marks also point at a robotic mass-machined grinding process without much concern for a designed recurve, imho.

Back to the question 'why does it matter?' Well, it doesn't matter if we use very narrow rods for sharpening, like the 204MF. The 204MF rods will increase the concave blade shape and, more importantly, they get the blade super sharp. A wheel-grinder could cope with the Surge blade too, no problem, because a wheel has rounded edges.

However it matters, if we want to sharpen it on a mean-flat benchstone, say a sharply cut 302UF. You cannot really sharpen a recurve blade on a 302UF or a DMT plate. On a flat benchstone you can only sharpen a straight edge or a bellied/convex blade. That's why it matters that we don't want to grow recurves into our blades.

 

[annr]

"a royal pain in the butt with a “pure” straight edge" - love it, and this exactly is what it is. Illustration:

Before this thread I thought of the grinding time, pressure and the grinding area as contributing factors.
Now Kreisler mentions thickness behind the edge that is varying along the edge due to the blade taper towards the tip - another factor to think about.
I used to think that grinding on a narrow area, like a narrow wheel or with a narrow stone is less predisposed to the middle overgrinding, but Kreisler is right that "thickness behind the edge" factor is not going anywhere no matter how narrow or wide is your wheel or benchstone.

I wrote some about the middle overgrinding on our website http://knifegrinders.com.au/06Procedures_straight.htm
but not to the detail I read in this thread.

Yes! And and I can tolerate no daylight between a piece of glass and my edges--not to scientific null--but none to the naked eye when backlit.

 

[annr]

Some readers might ask themselves 'what does it matter if the blade develops a recurve, as long as i can grind the edge to perfect sharpness?'

But can you? if you don't control the edge?

 

[wootzblade]

Before we can counter a problem, we have to recognize the problem. The insight into contributing factors Kreisler and others give here is the best I ever read. I now better understand how to grind to mitigate it.

 

[Mr.Wizard]

And my claim stands that this is not possible with an EdgePro/Ruixin/Lansky/etc, 204MF, or a narrow grinding wheel. It's just a claim, i could be wrong though. You guys tell me.

1. I believe you are overlooking the option to apply pressure unevenly across the Edge Pro stone. By placing my thumb on the corner of the stone holder I can bias pressure to the ricasso side of the stone and intensify grinding there.
2. You may also be overlooking the option of sharpening sections the width of the stone, then blending them. In this scheme every point on a flat blade section gets the same stone contact time before blending.

Theoretically one could correct a recurve by constantly comparing the blade to a flat surface, marking the points that need grinding, spot grinding, and repeating; like scraping.

Practically my standard practice for full sharpening avoids forming a recurve and corrects any existing one: I grind perpendicularly on a bench stone until a flat is formed all along the edge, then sharpen (only) until an apex forms at each point. In the case of a damaged knife like the one wootzblade showed the flat formed will be wide at the heel and belly and narrow at the center of (what was) the depression. I concentrate my grinding/pressure on the points where the flat is wide and use a light touch on the narrow spots. On a blade that requires extensive material removal (as pictured) I will grind perpendicularly again after my coarsest beveling stone to correct any induced error and to remove burr formed in points I over ground.

 

[Mr.Wizard]

I don't expect everyone to understand the contents of the above two pics.

The unit step is not mysterious to me but I still have trouble following your math and you did not label your axes so I am not certain of what you are illustrating. Simulating this myself—possibly with different assumptions—I get a different curve for grinding time at each point on the blade. For a ten unit blade and five unit wheel, starting with the edge of the wheel at the ricasso (x=0) and moving at constant unit velocity, then lifting off at t=8 when the tip is near the middle of the wheel:

 

[kreisler]

—possibly with different assumptions—

You got it all correct, the graph and axises are the same as in my pic! The difference is in the assumptions, i am assuming that the blade is being held for some time t0≠0 at the flush position. Why? To work the heel area longer. Your graph implies a blade which does start flush but is drawn across the grinding wheel width right away, upon blade contact with the wheel.
If i set t0=0 in my graph (or in the equation), then i am getting the same graph as yours.

And once we have sketched the curve, it is just a technicality how we express it ("model it") mathematically, i.e. in form of a function or equation. The most direct way imho is by using the unit step function, an alternative way would be the Piecewise[] function.