Tormek Community Forum

Elden has mentioned an interest in exploring the effects of hollow or flat grinding. I found this online article:

http://www.amgron.clara.net/page74.html

I don't think the article tells the whole story. One of the most practical solutions I have encountered was from Ernie Conover. Ernie just added three degrees to his bevel angle to compensate for the Tormek's hollow grind. Considering that A2 chisels are routinely ground to at least thirty degrees, this seems a practical solution.

Personally I think the "weakened edge" due to the Tormek's large wheel hollow grinding is more of a theoretical "problem" than a real world deterrent. Looking at ground bevels from the smaller (200mm) T4, I can visually detect a slight bevel, the T7 bevels being less even more slight. I just think the issue goes back to when the standard dry grinders in home shops were six inch wheel diameter, often reduced further from wheel wear. Even then, the hollow grind was valued because it made it easy to place a finer stone on the two high points.

I don't have all the answers on this, and welcome responding posts.

Ken

The edge is not weakened. Rather, it is strengthened. Let me explain.

When the edge angle is measured using the angle master, it's measured at the very tip. As you move away from the tip the angle increases, making the tool stronger, not weaker.

The only way it would be weaker is if the angle at the tip were smaller. And that would occur if the angle were measured incorrectly.

(http://i1291.photobucket.com/albums/b553/htrivilino/bevel%20angles_zpsc7yxvvsw.png) (http://s1291.photobucket.com/user/htrivilino/media/bevel%20angles_zpsc7yxvvsw.png.html)

Herman, your post is most interesting, however I don't fully grasp it. Would you please explain it more fully for me?

Thanks.

Ken

I don't get it either.

Ken, Jeff, the question was discussed last year in Rob's thread "riddle me this".

I fully agree with Herman. The wheel grinding process leaves more steel behind the edge than a straight grinding. This statement is true if angle is measured at the very tip of the bevel.

In the scaled drawings below there is the situation for a grindstone with radius R = 125 mm, chisel blade thickness 4 mm and 25 degree bevel.

(http://img8.rajce.idnes.cz/d0802/10/10887/10887813_70f045b5de254de0d59e05f5324022b7/images/uhel_ostri_2_vrch.jpg?ver=0)

The dimensioned detail below shows the situation at the edge.

(http://img8.rajce.idnes.cz/d0802/10/10887/10887813_70f045b5de254de0d59e05f5324022b7/images/uhel_ostri_2_detail_700.jpg?ver=0)

Sorry, all measures are given in mm.

The drawing is much more clear for larger blade thickness. Let me know if you would like to see the drawings for 8 or even 16 mm chisel blade thickness.
Jan

I must say bullsomething. It is clear from your drawing that there is less metal at some point behind the tip DUE to the hollow grind. If the hollow grind ever touches the leading edge of the grind then the edge becomes so acute as to be useless for wood projects but maybe superb for shaving. I saw the last attempt at explaining this and did not bite then either. Your drawing clearly illustrates the removal of metal behind the cutting edge. Less metal=less strength in general. If I hold a knife edge to the most acute angle with a hollow grind leading up to the cutting edge, you are telling me that it would be stronger than the same edge when flat ground. Measure the edge angle from anywhere you want. There is still a "hollow grind" which means the same as a void of metal. Void means there is nothing there.

   Take it easy there fellows.

   Jan stated that was so if measured at the tip of the bevel. I have kicked this around since reading the "riddle me this post"  and have thought that could be the only way more metal could be left due to a hollow grind.

   I believe the real question is, how does the the Angle Master truly measure an angle? I don't mean theorectically but truly. Has anyone measured an angle with the Angle Master on a hollow grind, then checked that angle with an accurate machinist type protractor measuring device? Have you taken in account there might be a slight deviation from one Angle Master to another one? How accurate is the Angle Master? How accurate is the machinist protractor? How accurately am I reading both devices?

   According to Jan's statements, I believe the machinist protractor then would have to show a higher degree number (be it fractional or greater) than the angle master does. If not, then I believe Jeff's statement would bear truth.

   I have not tried it yet myself. I do have protractor made by General that I plan to check it out with. It is not a Starrett or other high dollar machine shop measuring device, but I beliveve it to be a good quality product. My jury has not issued a verdict yet. :) I think we need to go by actual verified measurements, however realizing the the above mentioned possibilities of error introduction.

As it has been stated before, in essence, does it truly matter? If it does, why do I have a Tormek? I say because it works well!

One of the things I value about the Tormek is its versatility. We are not wedded to any particular "correct" angle. We do have logical parameters. A bevel angle may become so acute that the tool no longer has enough supporting steel for the edge to be durable. At the other extreme, the bevel angle may be too obtuse to be practical for the desired work. Nothing says that chisels must be sharpened with twenty five degree bevels.

The factory bevel angle on Veritas chisels varies with the width of the chisel. 3/8" (10mm) and narrower arrive with thirty degree ground bevels plus two degree micro bevels. Their wider chisels come with twenty five degree bevels plus two degree micro bevels. This seems logical as the cutting force is more concentrated with narrower chisels.

Lie-Nielsen chisels with A2 steel are factory ground with thirty degree bevels at all widths. This is largely due to the structure of the A2 steel. It will hold an edge for a long time, however that edge will never be as keen as a carbon steel edge.

I believe it is valuable to have forum members like Jan who have the mathematical expertise to map out things like this and share the results with the forum. Thanks, Jan.

I also subscribe to the machinist's concept of things not being "exact", but rather "within tolerance". Tolerances may be very narrow depending on the application. The interpretation of the application should guide the craftsman. With wood chisels, I believe we have a fairly wide tolerance range.

Ken

Quote from: jeffs55 on March 31, 2015, 09:52:07 PM
I must say bullsomething. It is clear from your drawing that there is less metal at some point behind the tip DUE to the hollow grind. If the hollow grind ever touches the leading edge of the grind then the edge becomes so acute as to be useless for wood projects but maybe superb for shaving. I saw the last attempt at explaining this and did not bite then either. Your drawing clearly illustrates the removal of metal behind the cutting edge. Less metal=less strength in general. If I hold a knife edge to the most acute angle with a hollow grind leading up to the cutting edge, you are telling me that it would be stronger than the same edge when flat ground. Measure the edge angle from anywhere you want. There is still a "hollow grind" which means the same as a void of metal. Void means there is nothing there.

Jeff, I think you need some more time to digest the surprising statement.  :)

Understanding where we measure the edge angle is of crucial importance for our issue. My statement that "The wheel grinding process leaves more steel behind the edge than a straight grinding" is true, provided we measure the angle at the cutting edge.

You probably consider the edge angle to be the angle of the bevel at the midpoint of the chisel. Then you are right and there is less steel behind the edge due to hollow grind. :)

Jan

I believe Jan and Herman are correct. With the speed and ease of sharpening with the Tormek, it is easy to forget than the cutting only happens at the edge. A good example of this is the clever way Lie-Nielsen has marketed extra blades for its low angle jack planes. One plane can work as low, normal, or high angle just by switching the blades. The user can even quick switch just by regrinding a micro bevel.

While the highly polished full bevel certainly looks pretty, the cutting business only happens at the edge.

Ken

OK, OK, OK I finally see the light. If an edge is hollow ground or not it is sharpest at the edge. For the sake of clarity I am going to make up some numbers. Say the edge itself, where it meets the object to be cut is .0001 inches thick. Then, anything behind the edge (behind means closest to or towards the spine) is going to be thicker and grows in thickness the further from the edge you go. The blade grows in thickness as it widens. Widens is from the edge to the spine in this case. A hollow grind allows the edge to become finer, sooner as there is less metal behind the cutting edge. Less metal still makes the blade weaker for hard work but also allows us to put a finer edge on the blade. A flat grind could produce the same edge but the overall thickness of the blade would be so compromised as to make useless at some point except for shaving. That is why razor blades are so thin and is the same concept. I think! It is difficult to shave with an axe but easy to with a razor. I sure agree that the Tormek is a great machine, it is not an "end all" but is a good start towards one. I do not regret buying either one of mine. Once again, I was wrong.

Quote from: kb0rvo on March 31, 2015, 11:20:56 PM
My jury has not issued a verdict yet. :) I think we need to go by actual verified measurements, however realizing the the above mentioned possibilities of error introduction.

As it has been stated before, in essence, does it truly matter? If it does, why do I have a Tormek? I say because it works well!

The hollow shape of the bevel becomes much more important when grinding really thick tools, e.g. heavy duty mortise chisels. In the drawings below there is the situation for 4, 8 and 16 mm (0.16", 0,31" and 0,63") thick tools ground with 25 degrees using grindstone of the  diameter 250 mm (10").

(http://img8.rajce.idnes.cz/d0802/10/10887/10887813_70f045b5de254de0d59e05f5324022b7/images/tvar_ostri_4_8_16_CELEK_580p.jpg?ver=0)

All measures are given in mm.

(http://img8.rajce.idnes.cz/d0802/10/10887/10887813_70f045b5de254de0d59e05f5324022b7/images/tvar_ostri_4_8_16_DETAIL_580p.jpg?ver=0)

The curved wedge circumscribed by the angle 6.9 degrees is the surplus of steel, left behind the cutting edge, due to hollow grind of a 16 mm (0.63") thick tool. This surplus steel disappears when we grind the tool flat with a 25 degree edge angle.
Jan

Isn't this being made more difficult than need be?

Maybe I'm slow, but I don't get it.  :)

By definition a hollow grind is concave.  A inward, curved area "below" a straight line (flat grind) perpendicular to the grind.

Obviously, if the entire face of a chisel for example is concave, more metal is removed than if it were a flat grind.

If the face of a chisel was flat and square and only the first half is hollow ground, then yes, a flat grind would remove more metal because it would "chop off" the top square edge. But that would be a very odd chisel.

Quote from: Ken S on April 01, 2015, 10:19:56 AM
I believe it is valuable to have forum members like Jan who have the mathematical expertise to map out things like this and share the results with the forum. Thanks, Jan.

Thank you Ken for your kind words.  :)
It is a great pleasure for me to be on this forum and share my views with you. Despite of my background in (geo)physics I need your feedback and proofreading to find possible errors and mistakes in my posts.

As I mentioned earlier, the nice drawings shown here, were prepared by my brother, when I was considering how to grind my old heavy duty mortise chisel.


Jan

Quote from: grepper on April 01, 2015, 07:45:03 PM
Isn't this being made more difficult than need be?

Maybe I'm slow, but I don't get it.  :)

By definition a hollow grind is concave.  A inward, curved area "below" a straight line (flat grind) perpendicular to the grind.
Obviously, if the entire face of a chisel for example is concave, more metal is removed than if it were a flat grind.
If the face of a chisel was flat and square and only the first half is hollow ground, then yes, a flat grind would remove more metal because it would "chop off" the top square edge. But that would be a very odd chisel.

Grepper, sorry for my inability to explain it clearly.  :(

Please reconsider it because it is a question of basic importance, paradigm shift.

Referring to my last drawing above, if you hollow  grind the tool with a 25 degree edge angle, measured at the very tip of the cutting edge, you will not remove steel below the straight line 25 degrees. There is no concave curved area below the 25 degree straight line.

Jan,

   When I  stated my jury had not reached a verdict yet and was talking about measuring the angles, I was referring to how the Angle Master measures angles versus a machinists style protractor. I am wanting to verify that the AM measures the tip of the bevel not theoretically but experientially. Obviously the machinist protractor will contact two points, the tip and the heel of the bevel, bridging the the concave. Theoretically (in my thinking anyway) the AM measures the tip of the bevel? My jury is supposed to decide if that is true or false. I am in the process of analyzing that today and am planning on getting a sharp chisel out of the deal!

   While setting up the Tormek, I realized another possibility of error introduction. Wear of the corner of the AM where it contacts the grinding wheel will change the reading of degrees. Looking at mine, that corner is slightly rounded.

Thanks for your explanation Elden.  :)
Jan

Thanks for the extra prod Jan.  You (and Herman) explained it perfectly well... Uhh...Several times.  I had just skimmed and missed the point.  So I re-read the entire post.  Sharpening at a particular angle, the concavity would not exist below the sharpening angle.  What I had not known and even thought about was how a hollow grind bevel angle was measured.  Makes total sense. Very interesting and informative.  Learn something new every week or two!

With a big 250mm wheel, the effect near the edge is minimal, but more so for T4 owners.  But as you say, "The hollow shape of the bevel becomes much more important when grinding really thick tools".  I guess if you were after a wide, thin bevel, a flat grind would be the way to go. I wonder if I could tell the difference on an onion.

Cool info.  Thanks!

My jury has come into the court room before the judge to issue their verdict. Ok, forget the drama.

   After grinding the chisel,  the AM (Angle Master) showed that a 28 degree angle had been formed. The General machinist type protractor showed 30 degrees. As I stated, the corner of the AM pointer that contacts the grinding wheel is slightly rounded. If it was not, the AM  would probably read about 27.5 degrees or a little less. This is fairly thin Stanley chisel as it is 0.125 (1/8) inch or 3.175 mm thick. If the chisel were thicker, the machinist protractor would register a higher number of degrees.

   Thus I believe it can be said experientially, the AM does register degrees at the tip of the bevel. Also that as Jan stated, there is more metal behind the tip of the bevel on a hollow grind than a flat grind it is measured at the tip of the bevel.

   Good job Jan and thanks for pointing it out! I know mathematics and drawings are great, but sometimes the old Missouri mule in me says, "Show me, I am from Missouri!" You proved it on paper, I wanted to see it in steel and more than that, how does the AM register.

   So also, THANKS TORMEK for great products!

Hi Guys,
Interesting subject to follow and good explanations.
I had prepared a long explanation but did not need to press "post"!

I wish you all a happy Easter!

Best Regards,
Stig

Stig, thank you for joining us. Please be so kind and post your explanation. Plurality of views may help to understand this interesting subject even thoroughly.

Happy Easter!  :)  Jan

(http://img5.rajce.idnes.cz/d0505/4/4582/4582843_c9d055dd33a39c30ecd5decf4ea571bc/images/img512.jpg)

Quote from: kb0rvo on April 02, 2015, 12:16:49 AM
My jury has come into the court room before the judge to issue their verdict. Ok, forget the drama.

   After grinding the chisel,  the AM (Angle Master) showed that a 28 degree angle had been formed. The General machinist type protractor showed 30 degrees. As I stated, the corner of the AM pointer that contacts the grinding wheel is slightly rounded. If it was not, the AM  would probably read about 27.5 degrees or a little less. This is fairly thin Stanley chisel as it is 0.125 (1/8) inch or 3.175 mm thick. If the chisel were thicker, the machinist protractor would register a higher number of degrees.

   Thus I believe it can be said experientially, the AM does register degrees at the tip of the bevel. Also that as Jan stated, there is more metal behind the tip of the bevel on a hollow grind than a flat grind it is measured at the tip of the bevel.

   Good job Jan and thanks for pointing it out! I know mathematics and drawings are great, but sometimes the old Missouri mule in me says, "Show me, I am from Missouri!" You proved it on paper, I wanted to see it in steel and more than that, how does the AM register.

   So also, THANKS TORMEK for great products!

Thank you Elden for posting your results!

Your results are in agreement with the geometrical considerations presented in this thread.
The edge angle measured with Angle Master at the cutting should be smaller than the angle measured with machinist type protractor. This is because the protractor probably measures the mid angle of the bevel.

Keeping in mind the limited accuracy of your measurement,  the angle difference 2 degrees is even numerically OK. Really good job Elden, congrats!  :)

Jan

Stig, would you please post your comments?

As I recall, Tormek holds a patent on the anglemaster. That would indicate the engineering department must have invested a considerable amount of development time. I believe we would all enjoy and benefit from learning about it.

Incidentally, I saw a photo of an earlier version of the andlemaster. (the 100). The current model seems moch more advanced,

Ken

Yesterday I ground two Blue chip chisels to twenty five degree bevels. I ground one with the T7 and the other with the T4. I wanted to see the difference in the amount of hollow grind between the two Tormek grinding wheel sizes. The mathematical part of my brain tells me there is a difference.  If I examine them very closely I think I can see a difference, the T4 grind having more hollow grind. However, I am glad one chisel was ¾" and the other 5/8", because it would be very difficult to tell the difference if both were the same width.

I can easily spot a blade ground hollow with a six inch grinder. The two Tormek grinds hardly looked hollow ground to my eye. I don't pretend to have any expertise in this area. I would not let worries about the amount of hollow grind influence me in deciding between a T7 and a T4.

Incidentally, a Supergrind or T7 with a wheel worn down to eight inches is essentially a slower T4 with a wider wheel. (The T7 has a speed of 90 RPM; the T4 120 RPM.

Ken

Suppose you measure the bevel angle on a chisel with a carpenter's tool, something like this:

http://www.amazon.com/Swanson-Sliding-T-Bevel-Stainless-Fittings/dp/B0008IUWDY/ref=sr_1_14?ie=UTF8&qid=1428028426&sr=8-14&keywords=carpenter%27s+protractor


You have two straight edges that meet and pivot so that the angle between them can be adjusted. One edge is lined up with the back of the chisel, the other with the surface that you grind away when you sharpen the chisel. That edge will indeed not meet that surface and there will be a hollow due to hollow grinding. Since that metal is missing, the chisel is indeed weaker than one that was ground flat.

But using this carpenter's tool in this way to measure the bevel angle is not the way we measure the bevel angle when we use the Angle Master!

What we do is measure the angle at the very tip. If you drew a straight line from that tip it would not meet the heel of the beveled edge in like the carpenter's tool does. Instead it would pass through the steel. There is steel on both sides of that line. Some is on the side closer to the back of the chisel, some is on the opposite side. It's this extra steel on the opposite side that makes the chisel a stronger tool for having been hollow ground. See my drawing in Reply #1 of this thread.

Quote from: kb0rvo on April 02, 2015, 12:16:49 AM
   Thus I believe it can be said experientially, the AM does register degrees at the tip of the bevel.

As you also stated Elden, wear on the plastic tip can effect the accuracy of the measurement. As can many other things. My point was and is that the Angle Master is designed to measure the angle at the tip. I'm glad your measurements confirm that it's working as designed.

My explanation of the material being behind the edge is already covered, Jan´s drawings and the other comments are what I had written so is would only be the same.

The angle master WM-200 is very good and are measuring the tip of the edge. It is compensated for the hollow grind. If you use a regular "angle setter" or a protractor you will fine that the degree will indicate that its not the same as the anglemaster. A protractor are not compensated for a hollow grind but for a flat surface.

Stig

Thanks, all. That is valuable information.

Ken

   Very interesting everyone. Herman, your drawings and explanation makes sense now that it soaked through. Initially I thought your drawing looked like a skew chisel. :)

   When honing a hollow ground chisel  on a bench stone, the bevel angle is being increased if the bevel is contacting the stone at the tip and the heel of the bevel. So honing (which is working to form a flat bevel) a hollow grind causes a more blunt angle. Interestingly, there will be more metal left supporting the tip now than there was supporting the hollow grind you just honed. You have just formed a micro-bevel because the heel of the bevel is holding the angle of the stone at a greater number of degrees than that of the hollow grind. There is a nifty way to micro-bevel your chisel or plane blades if you are so inclined.

Quote from: kb0rvo on April 03, 2015, 08:01:42 PM
   When honing a hollow ground chisel  on a bench stone, the bevel angle is being increased if the bevel is contacting the stone at the tip and the heel of the bevel. So honing (which is working to form a flat bevel) a hollow grind causes a more blunt angle. Interestingly, there will be more metal left supporting the tip now than there was supporting the hollow grind you just honed.

Yes, simply because the bevel angle is larger. We do this all the time. We make the bevel angle larger when we want the chisel to be stronger.

QuoteYou have just formed a micro-bevel because the heel of the bevel is holding the angle of the stone at a greater number of degrees than that of the hollow grind. There is a nifty way to micro-bevel your chisel or plane blades if you are so inclined.

I've been doing it this way for years. It's a quick way to refresh the edge on a dull chisel.

Quote from: kb0rvo on April 03, 2015, 08:01:42 PM
   When honing a hollow ground chisel  on a bench stone, the bevel angle is being increased if the bevel is contacting the stone at the tip and the heel of the bevel. So honing (which is working to form a flat bevel) a hollow grind causes a more blunt angle. Interestingly, there will be more metal left supporting the tip now than there was supporting the hollow grind you just honed. You have just formed a micro-bevel because the heel of the bevel is holding the angle of the stone at a greater number of degrees than that of the hollow grind. There is a nifty way to micro-bevel your chisel or plane blades if you are so inclined.

Yes exactly, Elden!  :)

Assuming we hollow ground a chisel with 25 degrees using grindstone with the diameter 250 mm (10"), then honing on a bench stone will create micro-bevel.

The angle of this micro-bevel depends on the thickness of the blade in the following way:

for tool thickness tt = 4 mm (0.16") the micro-bevel angle will be 25 + 2 = 27 degrees,
for tool thickness tt = 8 mm (0.31") the micro-bevel angle will be 25 + 3.8 = 28.8 degrees,
for tool thickness tt = 16 mm (0.63") the micro-bevel angle will be 25 + 6.9 = 31.9 degrees.

Jan

Hi Folks

Well you've certainly been "riddling this" and no mistake.

Despite the brilliantly documented and geometrically perfect diagrams I think you're all missing one salient point which I cant prove mathematically but just seems intuitively correct to me.

Its that you're not comparing apples with apples when you measure the angles in the way you're discussing.  To my thinking, the angle formed by the hollow grind method should be measured using the chord that would be formed as if it were straight ground (like Hermans theoretical line drawn with the carpenters sliding bevel tool).

Better yet think of two identical triangles where the hypotenuse is the chisel bevel.  One is hollow ground and one is straight ground.  Now overlay one triangle on top of the other.  All the angles remain exactly the same (if we're comparing apples with apples).  All the corners exactly line up.  The only difference between those two triangles is that one still has a straight hypotenuse while the other has a concave one ie the hollow ground one.  If you were to calculate the area inside those two triangles the hollow ground one would have slightly less area than the straight edged one.  And thus, it would have less molecules with which to support the edge, thus it would be weaker.  Even though this is clearly angels dancing on the head of a pin.  But in theory, the edge has less support.

I believe the primary confusing fulcrum in all of this is the notion that each angle must still measure 25 degrees at the tip at the end of the grind.  If that set of variables is true then of course the edge will have more steel because its not "legitimately" a directly comparative test against its rival.

Only when you measure the chord (ie where my theoretical triangles occupy identical footprints) does the discrepancy become clear.

That is exactly what I was screaming all the time. Thank you for saying what I wanted to say.

Quote from: Rob on April 05, 2015, 03:55:42 AM
Hi Folks

Well you've certainly been "riddling this" and no mistake.

Despite the brilliantly documented and geometrically perfect diagrams I think you're all missing one salient point which I cant prove mathematically but just seems intuitively correct to me.

Its that you're not comparing apples with apples when you measure the angles in the way you're discussing.  To my thinking, the angle formed by the hollow grind method should be measured using the chord that would be formed as if it were straight ground (like Hermans theoretical line drawn with the carpenters sliding bevel tool).

Better yet think of two identical triangles where the hypotenuse is the chisel bevel.  One is hollow ground and one is straight ground.  Now overlay one triangle on top of the other.  All the angles remain exactly the same (if we're comparing apples with apples).  All the corners exactly line up.  The only difference between those two triangles is that one still has a straight hypotenuse while the other has a concave one ie the hollow ground one.  If you were not to calculate the area inside those two triangles the hollow ground one would have slightly less area than the straight edged one.  And thus, it would have less molecules with which to support the edge, thus it would be weaker.  Even though this is clearly angels dancing on the head of a pin.  But in theory, the edge has less support.

I believe the primary confusing fulcrum in all of this is the notion that each angle must still measure 25 degrees at the tip at the end of the grind.  If that set of variables is true then of course the edge will have more steel because its not "legitimately" a directly comparative test against its rival.

Only when you measure the chord (ie where my theoretical triangles occupy identical footprints) does the discrepancy become clear.

Rob, it is nice to have you here!  :)
Your thread "riddle me this", started last year, focused my thoughts to this interesting subject.

The most brilliant, for me, is your formulation in reply #13: ,,So if one fixes the angle at the very tip of the edge of both hollow and straight grinds and then compares them, the hollow grind will have more metal BECAUSE the chord will be at a different angle than the straight ground bevel.  If the chord of both are at 25 then the tip of the hollow will actually be less and one might argue that the edge is weaker."

I am a little bit confused by your recent post in this thread.  :o

For chisel properties, to my thinking, mainly the angle at the cutting edge is important, not the angle of the chord, which corresponds to the angle in the mid point of the chisel thickness.

I am really afraid, that Mr. Euclid of Alexandria did not even left here a tiny spot for your dancing angles.


Happy Easter!  Jan

Quote from: Rob on April 05, 2015, 03:55:42 AM
The only difference between those two triangles is that one still has a straight hypotenuse while the other has a concave one ie the hollow ground one.

There's a difference in the way the tools will perform, though. The one that's hollow ground forms a smaller angle at the tip than the one that's ground flat. As Jan has calculated, it's only a couple of degrees, but that's enough to notice in some circumstances, depending on the wood hardness and type of work you're doing. It can also make a difference in the durability of the edge.

On the other hand, if you compare two chisels that are ground to the same angle at the tip, the one that's hollow ground will have more steel remaining on the tool and thus may be stronger, which was the original issue.

What does this Mr. Euclid know? We all know the earth is flat. Why shouldn't our chisel bevels be flat, also? :-X

Back to my original post, why not just add three degrees to the bevel angle for a typical chisel?

Interesting responses, guys.

Stig, this topic has raised an interesting issue. A clarifying sentence or two in the next revision of the handbook would be useful. (what the ang
emaster is actually measuring)

Ken

On a more serious note..... Jan, I have always associated Euclid and his geometry with ancient Greece. I realize the ancient Greeks established trading post cities throughout the Mediterranean world. As I remember, Alexandria was noted for an outstanding library which burned. I did not realize than Euclid lived there. Interesting.

For the record, I do know that the ancient Greeks realized the earth was round, as did well educated persons in Columbus' time. With this knowledge, perhaps they also favored hollow grinding? :)

Ken

Quote from: Herman Trivilino on April 05, 2015, 05:41:31 PM

Quote from: Rob on April 05, 2015, 03:55:42 AM
The only difference between those two triangles is that one still has a straight hypotenuse while the other has a concave one ie the hollow ground one.

There's a difference in the way the tools will perform, though. The one that's hollow ground forms a smaller angle at the tip than the one that's ground flat. As Jan has calculated, it's only a couple of degrees, but that's enough to notice in some circumstances, depending on the wood hardness and type of work you're doing. It can also make a difference in the durability of the edge.

On the other hand, if you compare two chisels that are ground to the same angle at the tip, the one that's hollow ground will have more steel remaining on the tool and thus may be stronger, which was the original issue.

That's JUST IT RIGHT there though Herman :-)  This is such a gossamer thin, subtle difference.  The original issue was an attempt to resolve the assertion that "a hollow ground bevel has a weaker edge than a straight ground bevel"  There was no mention of the tip angles being identical.  The original discussion evolved on a different forum and it was simply an argument where one party asserted hollow ground was weaker and one party asserted the opposite.

It's Mr Euclid and all the other mathematical positions taken that have decided that in order to answer the question then we MUST fix the angle measurement at the tips.  In fact we MUST NOT in order to satisfy the criteria of a fair test in the context of the original question.

Now please remember everyone that this question was never phrased in context of a practical working reality.  It was in theory only, we all know that because the actual hollow ground is so small that it's real difference is negligible. 

To cycle back to the original question:  Is a hollow ground bevel weaker at the edge than a straight ground one?  To my mind (which I fully accept is entirely warped) implicit in that statement is a tacet assumption which states "test must be conducted where conditions are equal for both bevels undergoing the test to remove spurious variables from the conclusion"

In my mind the only test that meets the ciriteria "conditions are identical" is the one where the two triangles are overlapping and identical ie all angles are equal with 25 degrees at the bevel.  Then the grinds take place and the hollow ground triangle now has a crescent moon "nibble" out of it whereas the straight ground one has uniformly less metal across the chord but the tip is still 25 degrees. The hollow ground bevel has a tip that is n degrees less then 25 owing to the metal removed by the arc of the grinder's stone.  n is clearly a very small number indeed but it is still measurable and therefore the ONLY conclusion that can be drawn for the purposes of answering the original question is that in a test where conditions are identical a hollow ground edge will be weaker attributable to the marginally lower mass of metal supporting its edge when compared to a straight grind.

The very MOMENT someone arbitrarily makes the decision that the test has to be conducted with both FINISHED grind tip angles being 25 degrees, the essence of the original question is lost because you're now conducting a different experiment.

Now, the one practical reality it does throw up which Ken alluded to is that the angle master is in essence faulty because the resultant angle you actually grind when you dial in 25 degrees is actually different when you're done.  Does that matter when you're planing?  Not sure, it doesn't to me but then I'm not doing battle with curly maple etc.

But I think for the purposes of answering the original question it's important we draw the distinction between the test conditions because having re-read all this, it seems to me we've allowed the allure and seductive nature of a binary proposition to sucker us into thinking the tip angles must have perfect mathematical symmetry at the end of the process.  How simple life might be if such things were always possible :-)

Hark.....do I hear dancing angels.......

Quote from: Rob on April 06, 2015, 11:04:58 AM

Quote from: Herman Trivilino on April 05, 2015, 05:41:31 PM

Quote from: Rob on April 05, 2015, 03:55:42 AM
The only difference between those two triangles is that one still has a straight hypotenuse while the other has a concave one ie the hollow ground one.

There's a difference in the way the tools will perform, though. The one that's hollow ground forms a smaller angle at the tip than the one that's ground flat. As Jan has calculated, it's only a couple of degrees, but that's enough to notice in some circumstances, depending on the wood hardness and type of work you're doing. It can also make a difference in the durability of the edge.

On the other hand, if you compare two chisels that are ground to the same angle at the tip, the one that's hollow ground will have more steel remaining on the tool and thus may be stronger, which was the original issue.

That's JUST IT RIGHT there though Herman :-)  This is such a gossamer thin, subtle difference.  The original issue was an attempt to resolve the assertion that "a hollow ground bevel has a weaker edge than a straight ground bevel"  There was no mention of the tip angles being identical.  The original discussion evolved on a different forum and it was simply an argument where one party asserted hollow ground was weaker and one party asserted the opposite.

It's Mr Euclid and all the other mathematical positions taken that have decided that in order to answer the question then we MUST fix the angle measurement at the tips.  In fact we MUST NOT in order to satisfy the criteria of a fair test in the context of the original question.

Now please remember everyone that this question was never phrased in context of a practical working reality.  It was in theory only, we all know that because the actual hollow ground is so small that it's real difference is negligible. 

To cycle back to the original question:  Is a hollow ground bevel weaker at the edge than a straight ground one?  To my mind (which I fully accept is entirely warped) implicit in that statement is a tacet assumption which states "test must be conducted where conditions are equal for both bevels undergoing the test to remove spurious variables from the conclusion"

In my mind the only test that meets the ciriteria "conditions are identical" is the one where the two triangles are overlapping and identical ie all angles are equal with 25 degrees at the bevel.  Then the grinds take place and the hollow ground triangle now has a crescent moon "nibble" out of it whereas the straight ground one has uniformly less metal across the chord but the tip is still 25 degrees. The hollow ground bevel has a tip that is n degrees less then 25 owing to the metal removed by the arc of the grinder's stone.  n is clearly a very small number indeed but it is still measurable and therefore the ONLY conclusion that can be drawn for the purposes of answering the original question is that in a test where conditions are identical a hollow ground edge will be weaker attributable to the marginally lower mass of metal supporting its edge when compared to a straight grind.

The very MOMENT someone arbitrarily makes the decision that the test has to be conducted with both FINISHED grind tip angles being 25 degrees, the essence of the original question is lost because you're now conducting a different experiment.

Now, the one practical reality it does throw up which Ken alluded to is that the angle master is in essence faulty because the resultant angle you actually grind when you dial in 25 degrees is actually different when you're done.  Does that matter when you're planing?  Not sure, it doesn't to me but then I'm not doing battle with curly maple etc.

But I think for the purposes of answering the original question it's important we draw the distinction between the test conditions because having re-read all this, it seems to me we've allowed the allure and seductive nature of a binary proposition to sucker us into thinking the tip angles must have perfect mathematical symmetry at the end of the process.  How simple life might be if such things were always possible :-)

Hark.....do I hear dancing angels.......

Rob, your post reassured me that you understand the subject to the finest details. Without any sophisticated drawings and calculations. Hut off, you have perfect imagination!  :)

All the disputation with you here is about the criteria of a fair test in context of your original question. I am afraid, that your posts may sow seeds of distrust, whether Herman's explanations and my drawings presented here are correct or not. I do not believe it is your intention.

Details are important because "God is in the detail". But also "the devil is in the detail". So, if you hear dancing angels, be careful what kind of angels it is. Good angels function mainly as God's messengers.  ;)

Jan

Quote from: Ken S on April 06, 2015, 03:48:42 AM
On a more serious note..... Jan, I have always associated Euclid and his geometry with ancient Greece. I realize the ancient Greeks established trading post cities throughout the Mediterranean world. As I remember, Alexandria was noted for an outstanding library which burned. I did not realize than Euclid lived there. Interesting.

For the record, I do know that the ancient Greeks realized the earth was round, as did well educated persons in Columbus' time. With this knowledge, perhaps they also favored hollow grinding? :)

Ken

Euclid lived mainly in Alexandria in Egypt. Alexandria was the intellectual and cultural center of the ancient world. The Library of Alexandria had some 700 000 scrolls and books. Euclid is called "Father of geometry". "Our" geometry was fully described in his Elements.
He was surely aware that the Earth is spherical.
I suppose, it would be a pleasure for him to follow our hollow grinding discussion.  :)
Jan

Quote from: Rob on April 06, 2015, 11:04:58 AM
The original issue was an attempt to resolve the assertion that "a hollow ground bevel has a weaker edge than a straight ground bevel"  There was no mention of the tip angles being identical. 

If the angles aren't the same then the comparison makes no sense.

A 10 degree bevel will be weaker than a 45 degree bevel, regardless of whether they're ground flat or hollow ground.

If you want to make a meaningful comparison it has to be done for equal angles. If the angles aren't equal the comparison is meaningless.

I absolutely 100% appreciate the position you've adopted with the statement that the comparison is meaningless unless you fix the bevel tip angles....but.....it's wrong :-) (And you know I love you so don't take that the wrong way).

Actually, that's a bit strong, it's not wrong at all.  It's the inevitable assumption that must be made if mathematical symmetry is to be maintained. And it certainly has a lot going for it doesn't it.  It "feels" right.  To any normal rational mind it is such a seductive assumption to make because you get a nice clean binary solution where the answer is yes or no.  Clean, neat, lovely.  But also wrong unfortunately, at least in the context of the original question and of course in my humble opinion.

If I give you some background maybe you can all click into my wavelength on this, or just tell me I'm an idiot which is infinitely more likely :-)

I was having a debate on another forum ages ago with another chap about this very subject because someone had mentioned it was "common knowledge" that a hollow ground bevel has a weaker edge than a straight ground one.  We then followed pretty much identical lines to what's happened here but it never resolved and normal life resumed.  It's been taken much much further here with the grateful addition of elegantly drawn technical specifications which prove beyond doubt that in the event the angles at the tip remain the same then there is more metal behind the edge of the hollow ground bevel.  Lets be clear, nobody is refuting that conclusion to that set of variables.

But we appear to have gone so far down the channel of the assumption that the tip angles must be fixed that we've either forgotten or ignored the original question.  In order to answer this correctly, it is my view that we need to re-evaluate the original question because we've missed the point.

Herman, you argue that a none fixed angle question is meaningless.  I disagree, it has meaning in the role of attempting to dispel the urban myth about weakness of grind one way or another.  Given that was the original basis for discussion, I think that we should value that meaning appropriately.

So, lets re-state that rather un-technical, none mathematical, almost entirely free from specification and dimension question:  Is a hollow ground bevel weaker at the edge than a straight ground one?  Can someone point out where in that question we are instructed to fix the tips of the bevel angles please?  Maybe I'm a bit bonkers but I cant see it myself.  To my way of thinking, in order to satisfy the question ie value it's meaning appropriately we must take two theoretical chisels and simply apply the two different grinding techniques and then measure the results.  To be fair to the original question, there is no way we can mess with those chisels in any way.  It's almost like they need to be just fixed in space and the grinding media brought to them with no movement of the chisels at all.  Only then are the test conditions met only then is the test a fair comparison.  Now does anybody dispute that those conditions are reasonable and fair?  So when we do that, inevitably, of course, perfect sense....the chords are what remain the same because the chisels haven't moved at all.  The chords have remained identical at the start of the grind but at the end of the grind, one has slightly less metal all the way down the bevel (straight ground) whereas one has a crescent moon ground away, which undermines the tip and "bingo" weakens the cutting edge.

So now we have two competing methods for testing the theory.  Model one, the above where the chords are fixed, the hollow grind loses.  Model two, the tip angles are fixed, hollow grind wins.

I think what's been troubling me all along is the insistence on model two being the right model for the problem. That doesn't make sense to me.  If we're to satisfy the original question context then what makes sense to me is a test where the chisels are ground in conditions where everything about them is fixed.  In model two we actually rotate the chisel about it's tip when we put it on the hollow grinder to satisfy mathematical symmetry and yet we don't do that for the straight grinder!!!!! When did changing the variables to satisfy a desired outcome become proper science???  On the contrary, we fix all the variables and then change ONLY ONE and measure the results to determine the effect of that variable.  The only variable under test here is the method of grinding, straight or hollow. What model two does is introduce a variable called rotating the tip angle....but only on the hollow grinder!!!  Sorry chaps, that's not science, that's not objective, that's subjective, that's the operator frigging with the test to predetermine the outcome and then justifying it with the word "sense" after the fact!  No no, for the test to be valid, the only variable that can be allowed is the method of grinding, all other things must be fixed (at any angle incidentally....the results would always be the same).

So, I have now exorcised the demon.  I understand both points of view entirely but I believe the fixed chord model is a more appropriate fit to the original question than the fixed angle model.  The fixed chord model is the only truly objective test and ironically (you're going to love this) Mr Euclid would HAVE to agree because being an empiricist, he would have no other rational choice :-)

Quote from: Rob on April 07, 2015, 11:23:30 AM
To be fair to the original question, there is no way we can mess with those chisels in any way.  It's almost like they need to be just fixed in space and the grinding media brought to them with no movement of the chisels at all.  Only then are the test conditions met only then is the test a fair comparison.  Now does anybody dispute that those conditions are reasonable and fair?  So when we do that, inevitably, of course, perfect sense....the chords are what remain the same because the chisels haven't moved at all. 

I dispute that. To be fair to the original question it makes more sense to me that, instead of the angle of the chords being the same, the angle of the tangent lines at the tips are the same. And the reason is simple, the Angle Master jig is the way we measure the angle, and that measures the latter not the former.

Quote from: Herman Trivilino on April 07, 2015, 04:11:53 PM

Quote from: Rob on April 07, 2015, 11:23:30 AM
To be fair to the original question, there is no way we can mess with those chisels in any way.  It's almost like they need to be just fixed in space and the grinding media brought to them with no movement of the chisels at all.  Only then are the test conditions met only then is the test a fair comparison.  Now does anybody dispute that those conditions are reasonable and fair?  So when we do that, inevitably, of course, perfect sense....the chords are what remain the same because the chisels haven't moved at all. 

I dispute that. To be fair to the original question it makes more sense to me that, instead of the angle of the chords being the same, the angle of the tangent lines at the tips are the same. And the reason is simple, the Angle Master jig is the way we measure the angle, and that measures the latter not the former.

Herman you're completely missing the point.  This question was never specific to the Tormek universe. In fact, as I mentioned, it came up on a completely different forum and was an attempt to make some sense out of the urban myth.  The anglemaster is a red herring, it has nothing whatever to do with the wider assertion that's been out there for donkeys years.

If you add in the caveat of how would you use it in a real world, practical sense then I would entirely agree with you and will myself in future use the exact method discussed here ie have the bevel tip ground to 25 degrees, leaving the chord at a blunter angle.  But for the purposes of answering the original question, I maintain that for the test to be reasonable no other conditions can be varied other than the grinding media.  Only then is the test genuinely objective.

For as small the difference you all are talking, I think the real world factor would be the heat (during sharpening) that affected the blades temper at its edge and causing it not to hold the edge as long.

Quote from: Rob on April 07, 2015, 11:23:30 AM

So, I have now exorcised the demon.  I understand both points of view entirely but I believe the fixed chord model is a more appropriate fit to the original question than the fixed angle model.  The fixed chord model is the only truly objective test and ironically (you're going to love this) Mr Euclid would HAVE to agree because being an empiricist, he would have no other rational choice :-)

I am so happy that only the good angels have remained with us!  :)

I understand your point, but I do not believe that the fixed chord model is appropriate to test the original question.
Why?
Having a hollow ground bevel and looking for the position where its angle is equal to the chord angle, we will find that it is roughly in the mid point of the bevel. In the drawing below this point is marked red.

(http://img8.rajce.idnes.cz/d0802/10/10887/10887813_70f045b5de254de0d59e05f5324022b7/images/tvar_ostri_4_8_16_DETAIL_2_580p_2.jpg?ver=0)

The central part of the bevel is far away from the cutting edge, this part of the bevel was hardly ever significantly involved in cutting wood. It is proven, that the tip of the chisel is dominantly important for driving the chisel into the wood.

That is my argument why the fixed chord model may not be appropriate to test your original question.

You mathematicians are struggling to decouple this angle symmetry issue aren't you.  I'll try one more time and then think we'll have to just leave it out there.

Jan....it doesn't matter one jot that the angle of the chord that matches the angle of the tip is in the middle.  It's completely irrelevant to satisfy the logic of the original question. The original question only asks if a hollow ground bevel is weaker or not.  It might reasonably be rephrased as what mass of metal is left behind the edge of hollow versus straight ground.

THE ONLY CONDITION BEING TESTED IS THE GRINDING METHOD.

Thus to satisfy that condition all other variables MUST REMAIN FIXED.  Can we at least agree that to be scientifically valid (objective) that that statement must be true?  We cannot hope to test the result of varying a condition unless all other conditions are fixed....correct?

So the condition we vary is the method of grinding.  Everything else must remain the same, including the position of the chisel with reference to the grinding medium.  So now our theoretical chisel is stuck in space and time (its not a real chisel being setup on a Tormek, we haven't used the angle master to set it up, its just a theoretical chisel that exists in a theoretical laboratory where two different types of grinding media are presented to it).  Next we offer the grinders to it, one straight and one a wheel.  The only means we have of testing those two grinding mediums without varying anything are if the chisel remains fixed.  Thus any theoretical setup must be against the chord because otherwise we would have to tip the edge using a theoretical angle master.  That would be varying more than the grinding medium and would invalidate the result.

Actually, a more useful metaphor might be imagining the grinding medium mounted like the blade of a chopsaw where it's cantilevered down onto a fixed chisel.  The only difference would be in test 1 the chopsaw blade would be circular (hollow ground) whereas in test 2 the chopsaw blade would be straight (like a sanding belt).  Can you see how the only way the test is a fair comparison is if the angle at which the chopsaws are brought down is the same because only if the chisels remain unmoved in any plane can the test be only varying one condition?

You need to stop making the angle at the tip of the blade the focus of the variable since its irrelevant for the purpose of the discussion.  It's not comparing apples with apples.  You either set BOTH tests up using the chord to define the angle or set BOTH tests up with the grinding tip as the angle by which they're setup.  But you cant set one up using the chord and the other using the "resultant" ground tip angle because it's an illegal test condition.

You're using the tip angle as the deciding factor when it's actually the consequence of using a hollow grind.  We're testing the effect of hollow grinding, not the effect of fixing the tip angle at 25 degrees.  Do you see the difference.  It's a funny one this and no mistake :-)

I do appreciate the mental somersaults of this, it's quite outwardly innocuous but actually its a bit of a conundrum.

I am absolutely certain of the rational conclusion to this by the way.  100% :-)  And Euclid would back me all the way.

Thank you for repeated detailed explanation, Rob. I believe I understand you fully.

You have formulated the original question and so you are also the person to perform the exegesis.  :)

I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.

The discussion in this thread, before you have joint us, was focused on the chisel tip cutting edge. The situation at the tip was not well understood before. Herman explained it here, I have added the drawings and Stig agreed with us. Then it was described how to use the chord of a hollow ground for micro bevel. I think it is quite fruitful and useful thread.

Jan

I agree, this has been a fruitful topic. I look forward to studying it; the non math people on the forum, like me, have a slower absorption rate. Thanks for the info, guys.

Ken

Ok, Rob. First you told us that having identical angles didn't matter:

Quote from: Rob on April 06, 2015, 11:04:58 AM
The original issue was an attempt to resolve the assertion that "a hollow ground bevel has a weaker edge than a straight ground bevel"  There was no mention of the tip angles being identical. 

Then you told us that it does matter ...

Quote from: Rob on April 06, 2015, 11:04:58 AM
In my mind the only test that meets the ciriteria "conditions are identical" is the one where the two triangles are overlapping and identical ie all angles are equal with 25 degrees at the bevel. 

... but apparently only under the conditions that you specify. You are saying we should be measuring the angle of the chord (the angle of the secant line) and I am saying that we should be measuring the angle at the tip (the angle of the tangent line).

For the mathematically inclined, the larger the radius of the grindstone, the closer we get to the two lines being the same.

So, if we all agree to do it Rob's way and measure the angle of the secant line the hollow ground chisel may be weaker because it contains less steel.

If instead we retain the freedom to measure the angle of the tangent line then the hollow ground chisel may be stronger because it contains more steel.

My choice is to retain the freedom to measure the angle of the tangent line for two reasons:

1. That's the angle at which the two steel surfaces meet when they form the edge on the tool.

2. That's the angle we measure with the Tormek Angle Master.

I would argue that the Tormek Angle Master method is the better way to do it because it measures the angle at which the two steel surfaces meet when they form the edge. If you were dealing with a small enough radius that it made a difference, you find that two tools sharpened this way, one flat and the other hollow, would perform more like each other if you matched the edge angle at the place where the two surfaces meet rather than some other angle such as the one that Rob tells us we must use.

I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.

How many times did I say that?

Jan
[/quote]

Quote from: jeffs55 on April 08, 2015, 05:32:58 AM
I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.

How many times did I say that?

Jan

[/quote]

Quote from: Jan on April 07, 2015, 09:26:43 PM
It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.

Eureka :-)
It's been obvious to me from the start (& Jeffs55)...but I've never been able to tear you guys away from the belief that the resultant tip angle is where all the action is.  I'll say for the last time chaps that we all need to recall this was a theoretical question only, in a vacuum if you like.  It wasn't ever related to the Tormek or how one might achieve the necessary angles on the Tormek with the anglemaster.  Somewhere along the journey, I guess because I posted it on the Tormek forum, it picked up an energy all of its own and became related to how it might get done with Tormek actual accessories (the angle master in particular).  It was originally a teasing type statement that came out of chatroom internet ether, what I call urban myth that stated simply "a hollow ground bevel has a weaker edge than a straight ground one"  There were no qualifying statements really.  We invented everything else, like, the tip angles must be the same or the chord angles must be etc etc.....all our own assumptions after the fact. 

So what I think this thread has ended up doing is shine some very thoughtfully considered light, with some excellent technical drawing and maths to prove the discussion about the tip angles.  It's also evolved the dialogue about the angle masters capabilities and has possibly set peoples minds at rest about whether or not they need be concerned about whether an edge is hollow or otherwise ground.  I have really enjoyed everybody's superb input so I thank you for that.

One final point from me. Despite the assertion that the chord angle is the only fair and true method by which I believe you can compare straight versus hollow, I actually agree the tip angle discussion is by far the more useful one for a practical application, with a real Tormek in the real world :-)

Thanks Rob for your kind summarizing words. I really appreciate it!  :)

Jan

P.S.: Today I hear dancing angels too. May be they had been waiting for the outcome of our discussion and they are now happy we have found consensus. As spiritual beings, messengers and guardians, they may have some access to our forum. More likely through our minds then through an IP address, I guess. Having said that, do knife sharpeners have some special patron saint? It may be Saint Catherine of Alexandria, also known as Saint Catherine of the Wheel.

Quote from: jeffs55 on April 08, 2015, 05:33:41 AM

Quote from: jeffs55 on April 08, 2015, 05:32:58 AM
I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.
Jan

How many times did I say that?

Sorry, Jeff(55) for not responded sooner to the reservations expressed in your posts.  :(

For me it is quite challenging to express my thoughts and fully understand some posts here because English is foreign language for me. I am doing my best, but you know, you can not teach an old dog new tricks. So, mea culpa!

You are resonating with Rob's way, Herman and I prefer to measure the tangent line angle at the tip. The most comfortable attitude is to understand both ways and in specific situation to use the more appropriate approach.  :)

In my thinking, Rob's way is more a thought experiment, while Herman's way is better linked to everyday sharpeners practice and sheds light on topic, which had not yet been understood well.

Jan

I must confess that when I was doing comparison chisel grinding between the T4 and T7, I used different width chisels. If I examine the two chisels very carefully with a straightedge and good light, I believe I may be able to perceive a slight difference. I do not doubt that there is a difference. I have misplaced my angel measuring tool.

I also believe the weakness aspect to the edge, however I also believe that how an individual chisel is heat treated is a more noticeable factor. With some specialized tools, such as Jan's grandfather's large mortising chisel, I might opt for a flat grind with water stones. However, I would certainly do the hard grinding with the Tormek and do only the final flattening of the hollow grind by hand.

Ken

Quote from: Jan on April 08, 2015, 11:46:39 AM

Quote from: jeffs55 on April 08, 2015, 05:33:41 AM

Quote from: jeffs55 on April 08, 2015, 05:32:58 AM
I want to ask if there were any doubts about the outcome of the thought experiment you have described?  It seems obvious to me, that if you hollow ground a flat chisel against the chord, you will weaken the bevel, simply because you will remove material.
Jan

How many times did I say that?

Sorry, Jeff(55) for not responded sooner to the reservations expressed in your posts.  :(

For me it is quite challenging to express my thoughts and fully understand some posts here because English is foreign language for me. I am doing my best, but you know, you can not teach an old dog new tricks. So, mea culpa!

You are resonating with Rob's way, Herman and I prefer to measure the tangent line angle at the tip. The most comfortable attitude is to understand both ways and in specific situation to use the more appropriate approach.  :)

In my thinking, Rob's way is more a thought experiment, while Herman's way is better linked to everyday sharpeners practice and sheds light on topic, which had not yet been understood well.

Jan

I think given English isn't your first language Jan you put us all to shame my friend :-)  Your command of English is doubtless a lot better than my command of your native language :-)

I also agree that my scenario was entirely "thought" only and that Herman's is much more real world and practical.  I appreciated all the points of view and perspectives, a most interesting debate :-)

Ok theory set aside, let's assume someone brings me a chisel that is flat ground at a 25° bevel. After it is sharpened they want it to be just as "strong" as it is now. I plan to use the Tormek to form a hollow grind that covers the whole face of the chisel. It is also desired that no more pressure will be required to make the resharpened chisel to cut than when it it was fully sharp with the flat bevel. Without trial and error methods and minimal steel removal, where should the Tormek wheel first come into contact with the flat ground bevel assuming the flat bevel is truly and squarely flat?

Quote from: kb0rvo on April 09, 2015, 01:12:32 AM
Ok theory set aside, let's assume someone brings me a chisel that is flat ground at a 25° bevel. After it is sharpened they want it to be just as "strong" as it is now. I plan to use the Tormek to form a hollow grind that covers the whole face of the chisel. Without trial and error methods and minimal steel removal, where should the Tormek wheel first come into contact with the flat ground bevel assuming the flat bevel is truly and squarely flat?

If you set the Angle Master to 25^o you will end up with a chisel that has more steel on the heel relative to the tip than it had when it was flat ground at 25^o. The angle at the tip will be 25^o when you're done. The angle at the tip was 25^o when it was flat ground. Theoretically that extra steel will make the chisel stronger and it should perform the same at the tip. It will not perform the same at the heel, though, as that extra steel on the hollow ground chisel may be a bother when paring.

But, to answer your question, you would have to set the Tormek Angle Master at a smaller angle. How much smaller? It depends on the thickness of the chisel. See the chart Jan posted earlier in this thread.

We really should be debating this in Latin wearing our Oxford Don attire. :)

Two images come to mind:

The first image is a skate board park, with concave ramps to build up speed. That seems to fit one idea of hollow grinding, where there is not much steel behind the blade.

The second image is the truck emergency ramps on very hilly highways. I seem to recall seeing these on the West Virginia Turnpike as part of very long and steep downgrades. The theory is that if a big truck looses its brakes on a downgrade, the driver can pull onto the ramp. the ramp goes up gradually and causes gravity to stop the truck (assisted by softer paving). This images better fits my idea of a hollow grind starting with the designated angle. It is more substantial.

I think we should consider grinds in three categories. The first is flat grinding. The second is the traditional hollow grinding of the home and small workshop equipped with a six inch dry grinder. This is the obvious hollow grind.

I would suggest a third category. This is the mild hollow grind of a larger grinding wheel. The spiritual ancestor of this group is the large, hand turned wet grinding wheel. By definition and Mr. Euclid of Alexandria, this kind of grinder also produces a hollow grind. For lack of a more scientific term, I would call this a "barely hollow grind". I would classify both Tormek models in this category, the T7 being further in the category.

Ken

Quote from: Ken S on April 09, 2015, 04:00:06 PM

I would suggest a third category. This is the mild hollow grind of a larger grinding wheel. The spiritual ancestor of this group is the large, hand turned wet grinding wheel. By definition and Mr. Euclid of Alexandria, this kind of grinder also produces a hollow grind. For lack of a more scientific term, I would call this a "barely hollow grind".

Ken

Does this grinding wheel correspond with your understanding of a "barely hollow grind"?  :)

(http://www.heritageofindustry.co.uk/Longer%20Tours/PreviousLongerTours/2009_Asturias/Grinding.jpg)

Jan

Great, post, Jan. :)

That's it!

Ken

Now that's a real water wheel!

Jan,

Your last post reminds me of something I remember from being a student in the Leica School thirty years ago. The topic was Leica filters. We presumed they were ground flat. The instructor corrected us. They were ground to a radius. I remember the radius as forty five kilometers, although it may have been forty five meters. Either way, it seemed flat to me.

Ken

My shop floor appears flat, but it's actually hollow ground to a radius of 6000 km.  ;D

Is that to keep the ball bearing parts you drop in the center?

Ones I was looking up the meaning of the phrase "nose to the grindstone" and have found the following explanation:

(http://upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Finch_Foundry%2C_grindstone.jpg/640px-Finch_Foundry%2C_grindstone.jpg)

A large waterwheel powered grindstone. The user would lie on the plank above the grindstone while grinding metal items, giving rise to the phrase nose to the grindstone. (http://en.wikipedia.org/wiki/Grinds)

Jan

Another very iinteresting post, Jan.

Ken

Congrats, Ken, on exceeding 1500 posts this week!  :)
Keep us posted!

Jan

Thanks, Jan. I remember when the first forum member passed the fifty post mark. (I was the second.)

Ken

Quote from: Ken S on April 11, 2015, 03:53:59 AM
Is that to keep the ball bearing parts you drop in the center?

It's not a dip, Ken. It's a crown. A ball bearing stays anywhere you put it!

Herman, I think the same mason got carried away with the crown in my garage floor. Instead of logically flowing toward a drain in the center, the crown diverts all the water melting off the car toward the side, which is used for misc. (junk) storage.

Ken

Quote from: Herman Trivilino on April 09, 2015, 01:32:04 AM

Quote from: kb0rvo on April 09, 2015, 01:12:32 AM
Ok theory set aside, let's assume someone brings me a chisel that is flat ground at a 25° bevel. After it is sharpened they want it to be just as "strong" as it is now. I plan to use the Tormek to form a hollow grind that covers the whole face of the chisel. Without trial and error methods and minimal steel removal, where should the Tormek wheel first come into contact with the flat ground bevel assuming the flat bevel is truly and squarely flat?

If you set the Angle Master to 25^o you will end up with a chisel that has more steel on the heel relative to the tip than it had when it was flat ground at 25^o. The angle at the tip will be 25^o when you're done. The angle at the tip was 25^o when it was flat ground. Theoretically that extra steel will make the chisel stronger and it should perform the same at the tip. It will not perform the same at the heel, though, as that extra steel on the hollow ground chisel may be a bother when paring.

But, to answer your question, you would have to set the Tormek Angle Master at a smaller angle. How much smaller? It depends on the thickness of the chisel. See the chart Jan posted earlier in this thread.

Elden's question was already answered by Herman. My belated remark concerns the second paragraph of his answer.

If you plan to form a micro bevel, by the way nicely described in reply #28, and you wish to have the angle of this micro-bevel 25 degrees, than you have to set the Angle Master at a smaller angle.

Assuming you are using grindstone with the diameter 10", then
for chisel thickness t = 1/8" you set the Angle Master at 23.5 degrees,
for chisel thickness t = 1/4" you set the Angle Master at 22.0 degrees,
for chisel thickness t = 3/8" you set the Angle Master at 20.5 degrees.

Assuming you are using grindstone with the diameter 8", then
for chisel thickness t = 1/8" you set the Angle Master at 23.0 degrees,
for chisel thickness t = 1/4" you set the Angle Master at 21.0 degrees,
for chisel thickness t = 3/8" you set the Angle Master at 19.5 degrees.

Jan