400 % more edge holding - convex vs flat

[EdgePal]

This picture shows the wooden parts of the sharpening tool I talk about above. Study it closly and you can se how they work and that they can hold a wanted angle very exact.

Thomas

 

[EdgePal]

If I change my edge from 10 to 11 degrees I add 10% more material per side of the blade 0,05 millimter behind the tip = 20% more material total - per degree change.

If I have a flat edge in 10 DPS and change the edge to a convex edge with 3 degrees convex sphere per side = 5 degree total change of the edge - and now holds the apex (cutting edge) 16 degrees - and I have add 100% more material to the edge 0,05 mm behind the edge - is that really 400 % stronger edge?
If yes, how is this meassured?

(Notice that I can only meassure (draw) down to 1/1000 part of 1 mm - so I cann not meassure the material on the cutting edge, only 0,05 mm behind the cutting edge).

Thomas

 

[Pteronarcyd]

Nothing in math says you can measure the angle of a convex edge, only the tangents (straight lines) of those edges, and those tangents are not anywhere close to the actual convex edge.

Differential calculus allows one to determine the slope of a curve at a given point. The slope is the angle of the straight line that is tangent to the curve at the point of interest. So, yes, the angle of a convex edge can be determined mathematically, and 42Blades has given a good applied description of how to approximate the angle without imposing the mathematics on us. If you take a first course in calculus you will understand the math and be able to calculate the edge angle once you determine the equations of the two intersecting convex curves that form the edge.

 

[Twindog]

If you look at point D as the apex of a convex blade edge, you might be able to get the gist of the discussion. The convex edge would be the green and reddish lines to northwest of point D.

Lines BD and CD are the two intersecting tangents at the apex of this convex edge. The angle of the tangents at the apex is 90 degrees. That angle is not the angle of the curved edges, it is the angle of the tangents. The tangents are straight lines. You can measure angles of intersecting straight lines. You cannot measure the angles of curved lines, although you can measure the angles of their tangents. But the tangents are not the curves lines. A convex edge has an infinite number of tangents and all have different angles. The angle of the tangents at the apex will be one of those angles.

Of course, you can describe a convex edge mathematically. No one has said you can't.

But the tangents are two straight lines that, in the case of the apex, touch the edge at only one point.

The method you are describing would say that this convex edge is equal to a 90 degree V edge, even though it is perfectly obvious that the convex edge in this diagram is much more acute than a 90 degree V edge. You get to this assumption by saying tangents are the same as curves lines, which is obviously not accurate.

People misuse math to say that convex edges are superior to V edges. They are not. Intersecting curves do not have angles. Their intersecting tangents do, but not the curved lines themselves.

A V edge can be identical, for all practical purposes, to a convex edge. The lines of each would overlap except that the convex edge would curve out by the width of just one atom, making it identical for practical purposes.

A V edge can be more or less acute than a convex edge. It can have more or less metal behind the apex than a convex edge.

The problem is that all convex edges are different, and we have no easy way to know what we're dealing with and no easy way to compare them to V edges. To say that convex edges cut better or hold up better than V edges is nonsense. They may do those things or they may not.

 

[FortyTwoBlades]

If you look at point D as the apex of a convex blade edge, you might be able to get the gist of the discussion. The convex edge would be the green and reddish lines to northwest of point D.

Lines BD and CD are the two intersecting tangents at the apex of this convex edge. The angle of the tangents at the apex is 90 degrees. That angle is not the angle of the curved edges, it is the angle of the tangents. The tangents are straight lines. You can measure angles of intersecting straight lines. You cannot measure the angles of curved lines, although you can measure the angles of their tangents. But the tangents are not the curves lines. A convex edge has an infinite number of tangents and all have different angles. The angle of the tangents at the apex will be one of those angles.

Of course, you can describe a convex edge mathematically. No one has said you can't.

But the tangents are two straight lines that, in the case of the apex, touch the edge at only one point.

The method you are describing would say that this convex edge is equal to a 90 degree V edge, even though it is perfectly obvious that the convex edge in this diagram is much more acute than a 90 degree V edge. You get to this assumption by saying tangents are the same as curves lines, which is obviously not accurate.

Actually, it's totally accurate. That IS a 90° edge, and you'd find that a knife with an edge of that geometry would not cut at any angle under 45° because the edge face on that side would be running dead parallel with the material surface. Think of it as a tiny, tiny 90° flat ground edge with a series of tiny, tiny flat-ground facets behind it, continuously reducing in angle. It's functionally analogous.

People misuse math to say that convex edges are superior to V edges. They are not. Intersecting curves do not have angles. Their intersecting tangents do, but not the curved lines themselves.

Again, math and engineering would disagree with you. The intersection of two arcs DOES have an angle, and it is represented by the intersection of the tangents. The angle of curved lines changes at every given point, but that angle is able to be calculated. Furthermore, there are very simple practical tests that can be used to approximate the angle, and it can be measured using a digital protractor--the apex will not contact the interior angle of the protractor until it is opened to an angle equal to or greater than the angle at the apex.

A V edge can be identical, for all practical purposes, to a convex edge. The lines of each would overlap except that the convex edge would curve out by the width of just one atom, making it identical for practical purposes.

A V edge can be more or less acute than a convex edge. It can have more or less metal behind the apex than a convex edge.

The problem is that all convex edges are different, and we have no easy way to know what we're dealing with and no easy way to compare them to V edges. To say that convex edges cut better or hold up better than V edges is nonsense. They may do those things or they may not.

Specific geometry both at and behind the edge are highly influential on cutting performance. And when holding edge angle consistent, the convex will have a thinner geometry behind the apex. If visual grind height is held consistent, the angle changes and you've just made a thicker edge, including a thickened apex angle.

 

[eKretz]

Geez oh pete. It would probably help to defuse this back and forth if people would use proper terminology. An apex and an edge are the same thing. Anything behind the apex or edge is the bevel (unless it's a full flat ground blade, in which case I'm not sure about the proper terminology). The bevels can be convex, straight or even concave. The apex (or edge) is a line where the bevels meet.

Performance of a blade comes down to way more than the shape of the bevels. Final angle (this would be the angle at the apex, or at the tangent of the curved bevels where the tangents intersect with the apex), radius of the convex or concave bevels, thickness of the blade behind the bevels, apex width, apex deviation from straightness on the micro level (basically what grit you finished with), probably more I'm forgetting.

Then you've got steel alloy, hardness of the blade, whether the blade is being used to push cut or in a sawing motion, speed of the cutting motion, type of material being cut, and so on. Without all the other variables being held the same, this is a silly argument, akin to "what is the best color?"

 

[Kyle363]

Really good read a bit above me in some places but I'm following along

So, no longer avoiding the elephant in the room, Bark River often convexes the entire blade profile. This is considerably different than a convex edge.

There was another video where Mike talks about their "special" convex process. They flat grind the blade (what angle and what thickness i don't know) then they convex the edge then they add additional bevels to convex the entire primary grind then blend the bevels together into one large bevel.

 

[Cobalt]

Really good read a bit above me in some places but I'm following along



There was another video where Mike talks about their "special" convex process. They flat grind the blade (what angle and what thickness i don't know) then they convex the edge then they add additional bevels to convex the entire primary grind then blend the bevels together into one large bevel.

That makes no sense.

So they create a flat grind, then they convex the edge, then they convex the entire grind? WTF? Of course, I know that they make Flat and sabre ground knives. But the few small convex blades I have seen from them looked like one continuous convex from spine to edge.

 

[FortyTwoBlades]

I believe what he's saying is they facet-grind the blade to have more control over the specific curve of the convex, then blend those bevels together. That's really the only way to grind anything resembling a consistent and repeatable convex without some sort of automation involved.

 

[Cobalt]

I believe what he's saying is they facet-grind the blade to have more control over the specific curve of the convex, then blend those bevels together. That's really the only way to grind anything resembling a consistent and repeatable convex without some sort of automation involved.

That makes more sense. I wonder if that is actually being done

 

[FortyTwoBlades]

It probably is. Cut in a series of bevels in progression, then take off the shoulders to "de-polygon-alize" it. To the best of my knowledge this is how most makers do full-height convex grinds.

 

[Kyle363]

That makes more sense. I wonder if that is actually being done

I'm sure it is but to what level of accuracy is a different question. I've noticed a a lot of variation in their grinds, which I think comes down to who grinds it. They're producing a lot of knives so naturally they have several people grinding with different levels of experience. I've had far better convex edges from some other makers where its only one or two people convexing every blade.

FortyTwoBlades thank you for all your insight on sharpening and edge angles. Also thank you for being able to clarify things.

 

[HeavyHanded]

I'd be astonished if they weren't mostly done by hand/eye on a slack belt.

 

[Cobalt]

I'd be astonished if they weren't mostly done by hand/eye on a slack belt.

That is what I thought they were doing. I still have a hard time believing that they will facet a profile then round it off.

 

[FortyTwoBlades]

That is what I thought they were doing. I still have a hard time believing that they will facet a profile then round it off.

...Why? If you just use a slack belt for your shaping work you'll have a tendency to create blades that are thicker in the middle than they are at the spine. Faceting then blending allows you to create a true continuous and full-height convex without that issue.

 

[Cobalt]

Because faceting is time consuming. Many more steps to grind out the blade. When you are making thousands of blades that time matters. Also, I looked on youtube and found a video that explains that they are using a slackbelt and grinding spine to edge in one process. starts at 2:15 min in

 

[FortyTwoBlades]

Because faceting is time consuming. Many more steps to grind out the blade. When you are making thousands of blades that time matters. Also, I looked on youtube and found a video that explains that they are using a slackbelt and grinding spine to edge in one process. starts at 2:15 min in

It's in no way more time consuming. You're still removing the same amount of metal...

Also, you don't really think they're showing the entire process of grinding the blade in that few seconds of film, do you? While it's possible that they do full-height grinds in one step, I find it extremely unlikely and kind of a sloppy practice because you'll have a much greater degree of variability in doing that than faceting and blending, which--due to human error alone--is already going to have a fair amount of variation piece to piece. In fact, slack-belt grinding is slower than faceting because a backing surface allows the abrasive to bite deeper instead of the belt deflecting under the pressure.

 

[Cobalt]

It's in no way more time consuming. You're still removing the same amount of metal...

Also, you don't really think they're showing the entire process of grinding the blade in that few seconds of film, do you? While it's possible that they do full-height grinds in one step, I find it extremely unlikely and kind of a sloppy practice because you'll have a much greater degree of variability in doing that than faceting and blending, which--due to human error alone--is already going to have a fair amount of variation piece to piece. In fact, slack-belt grinding is slower than faceting because a backing surface allows the abrasive to bite deeper instead of the belt deflecting under the pressure.

Explain to me how it is not more time consuming? You are grinding flat facets first then going back and rounding it off. Two different grinder setups. No way that is not more time consuming. You grind facets, then you go back and round off. There is no way it takes the same time to do as just grinding a convex profile. NO way.

I have met several knife makers who do full height convex grinds and love it and do it all the time. Not a big deal on a slack belt.

 

[FortyTwoBlades]

I did. And it's not necessarily two different grinder setups. I flat and slack belt grind on the same machine without any adjustments needed. I have a slack belt portion both above and below the platen on my grinder. At any rate, it's pretty common practice to do full height convex grinds by faceting and blending because of how much more control it gives you over the shape of the convex produced. The resulting geometry is no less of a convex at the end of it, but the result is more consistent side to side and piece to piece than if not doing it.

 

[Cobalt]

I did. And it's not necessarily two different grinder setups. I flat and slack belt grind on the same machine without any adjustments needed. I have a slack belt portion both above and below the platen on my grinder. At any rate, it's pretty common practice to do full height convex grinds by faceting and blending because of how much more control it gives you over the shape of the convex produced. The resulting geometry is no less of a convex at the end of it, but the result is more consistent side to side and piece to piece than if not doing it.

who knows, maybe the guys I met do it as well. I never knew that facet grinds were even part of the process, so I never asked. I thought slack belt full height was normal. Very interesting stuff.