a new angle setting tool

[Jan]

Rick, what I understand under the term "shift of the tangent line" you can see in the drawing attached to my reply no. 30 in his topic. https://forum.tormek.com/index.php?topic=2639.30

The drawing shows the situation for 200 mm stone where the shift is 1.9 mm.

Jan

[RickKrung]

Jan,

Thanks.  That helps me understand what that offset is.  I got the same number, 1.9mm for the 200mm dia. stone from my CAD drawing.  I got 1.54mm shift for the 250mm stone. 

What I still don't get is what the relevance or importance is of that offset. 

I've been using the tangent point, on the OD of the 250mm stone, that is coincident with the center point of the tangent line between the two metal contact discs.  I've been using that 250mm OD tangent point as the point of contact of the apex of the blade being sharpened.  I've been drawing angles out to the projection distance from that reference point and using the 250mm tangent line as the baseline for the angles. 

CB mentioned he thought that tangent point is not the point that you were using.  Could you clarify, please?

BTW, I have been able to confirm a couple other numbers you provided.  The radius of the angle setter holes for the USB is 133.54mm and the offset of the angle is 5.16º (I got 5.156º but rounding makes it 5.16º)

On another issue, I believe closely related, the tangent of the stone is not the angle that a blade gets ground at if the apex is at the tangent point.  The surface of the stone falls away (downward in our drawings) from the tangent line.  The resultant angle of the ground bevel is greater than the tangent line.  That ground angle gets greater the wider the sharpened blade is.  I have been struggling to figure out how that figures into these angles.  It has seemed that the differences in angles is not insignificant. 

Rick

[RickKrung]

...snip...
On another issue, I believe closely related, the tangent of the stone is not the angle that a blade gets ground at if the apex is at the tangent point.  The surface of the stone falls away (downward in our drawings) from the tangent line.  The resultant angle of the ground bevel is greater than the tangent line.  That ground angle gets greater the wider the sharpened blade is.  I have been struggling to figure out how that figures into these angles.  It has seemed that the differences in angles is not insignificant. 

Rick

Here is what I'm referring to.  First a large view of the Hanjig (as confirmed consistent with Jan's drawing), with the Knife Jig and blade, projection distance 139mm, set on the 10º USB hole position.


Close up of the angles at the knife bevel.  10.3º is the angle from the top of the blade (centerline of the knife jig) and the 250mm stone tangent line.  11.7º is the angle from the top of the blade to the actual bevel angle ground by the stone. 


There is a difference of 1.4º, which is a significant difference from the "intended" angle, nominally 10º in this example.  Should not this difference in actual ground angle be corrected for in the design of the jig?  Or maybe I'm missing something else about all this. 

Rick

[Jan]

Rick, I use the same reference point as you. It is the contact point between the apex of the blade and the stone.

The tangent to the stone at this reference point is parallel with a line defined by the two metallic discs contacting the stone surface. Both lines are slightly offset. I admit that your offset estimation is more accurate than mine. I have made small error by measuring the diameter of the contact discs.

The later line defined by the metallic discs was for me the base line for the construction of the setting jig.

The bevel angle is exact only for the apex of the blade provided it is mounted symmetrically with respect to centre line of the knife jig.

Jan

[cbwx34]

Thanks for the replies... so maybe it is being used.   (But at a Farmer's Market?)... 

...
CB mentioned he thought that tangent point is not the point that you were using.  Could you clarify, please?
...

Pay no attention to me... I was going by your drawing vs. Jan's earlier drawing.  Quite frankly, I don't think I'm understanding the differences.

Good luck... if you get it to work out, I'd love to see it in action. 👍

[RickKrung]

Thanks for the replies... so maybe it is being used.   (But at a Farmer's Market?)... 

...
CB mentioned he thought that tangent point is not the point that you were using.  Could you clarify, please?
...

Pay no attention to me... I was going by your drawing vs. Jan's earlier drawing.  Quite frankly, I don't think I'm understanding the differences.

Good luck... if you get it to work out, I'd love to see it in action. 👍

Please, let me try to expound on my newly acquired understanding

There are two tangent lines.  The offset is the distance between them.  One tangent is of the grinding stone, the other is between the two metal contact discs on the jig.  The former is different for each diameter of grinding stone. 

Two tangent lines.


Measured distance between the tangent lines is the offset under discussion.


Rick

[RickKrung]

Rick, I use the same reference point as you. It is the contact point between the apex of the blade and the stone.

The tangent to the stone at this reference point is parallel with a line defined by the two metallic discs contacting the stone surface. Both lines are slightly offset. I admit that your offset estimation is more accurate than mine. I have made small error by measuring the diameter of the contact discs.

The later line defined by the metallic discs was for me the base line for the construction of the setting jig.

The bevel angle is exact only for the apex of the blade provided it is mounted symmetrically with respect to centre line of the knife jig.

Jan

Thanks, Jan.  I did not see your diagram until this morning after I drew what will appear below.  I believe we are in agreement, except I used the 10º USB setting.  Things are much clearer for me now.  I noticed in your diagram, you depict a bevel above the apex but not below. 

In my example, I show the actual angle ground on the bevel in comparison to the angle between the wheel tangent and the jig centerline. 


I wonder if you or any others who have used this jig have measured the resultant bevel angles.  Is there a difference anything like what I have depicted above?  If so, perhaps a difference of a little over one degree is not significant in practical applications, but it is of interest to me and I may adjust for it when I make a jig for myself. 

Rick

[Jan]

Please, let me try to expound on my newly acquired understanding

There are two tangent lines.  The offset is the distance between them.  One tangent is of the grinding stone, the other is between the two metal contact discs on the jig.  The former is different for each diameter of grinding stone. 

Two tangent lines.


Measured distance between the tangent lines is the offset under discussion.


Rick

Yes Rick, your newly acquired understanding is correct. 
Sorry for my inability to explain it in a more simple and compact way.

Jan

[Jan]

Thanks, Jan.  I did not see your diagram until this morning after I drew what will appear below.  I believe we are in agreement, except I used the 10º USB setting.  Things are much clearer for me now.  I noticed in your diagram, you depict a bevel above the apex but not below. 

In my example, I show the actual angle ground on the bevel in comparison to the angle between the wheel tangent and the jig centerline. 

I wonder if you or any others who have used this jig have measured the resultant bevel angles.  Is there a difference anything like what I have depicted above?  If so, perhaps a difference of a little over one degree is not significant in practical applications, but it is of interest to me and I may adjust for it when I make a jig for myself. 

Rick

Rick, the intended bevel angle is exactly equal to 10, 15 or 20⁰, but only at the very apex of the edge and slightly increases towards the heel of the ground.

My understanding of your wondering about the actually ground angle is that you consider chord angle and not tangent angle at the apex. 

Some time ago I have explained the chord vs tangent situation when sharpening a chisel. See the attached figure, please.

Jan

[RickKrung]

Rick, the intended bevel angle is exactly equal to 10, 15 or 20⁰, but only at the very apex of the edge and slightly increases towards the heel of the ground.

My understanding of your wondering about the actually ground angle is that you consider chord angle and not tangent angle at the apex. 

Some time ago I have explained the chord vs tangent situation when sharpening a chisel. See the attached figure, please.

Jan

Jan,

Thanks.  Yes, I was vaguely remembering that someone had described that difference but could not recall who (although I suspected it was you) or in what thread.  I do not recall the conclusions or take aways from it however. 

[Ken S]

Can we make this variation go away once we start using the side of the new diamond wheels to flat grind? Or will the slight hollow effect of the leather honing wheel, although much reduced, still present a problem?

I would suggest that consistency is at least as important as the exact angle reading. If we sharpen ten identical knives in an identical manner, will we not get ten identical angles? If our readings are consistent, but not exact, we can compensate. We can tweak the 139mm Projection very slightly to compensate, if the variance is not within tolerance, providing the variance is consistent. Or, if we prefer, we could accomplish the same goal by tweaking the Distance.

For my simple requirements, I am not concerned if my supposedly 15° bevels are acrually 14° or 16°. While more precise angles may be required for some very high end work, I believe the average farmers market customer will be delighted with a sharp knife with reasonably accurate bevel angles.

Ken

[Dutchman]

...
For my simple requirements, I am not concerned if my supposedly 15° bevels are acrually 14° or 16°. ...

Yes Ken, I completely agree with you. In this thread, however, it is about the fun of mathematics 

... While more precise angles may be required for some very high end work, ...

I doubt that. I do not know an application in which the accuracy of the sharpening angle would be so crucial.

[Jan]

Rick, you are welcome! 

Ken, you are correct, the new diamond wheels with constant diameters reduce the need for such a special setting jigs like the one discussed here. At T8 or T7 machines it can be used for setting the USB height for honing. In combination with the mounting set BGM-100 it can be used for setting the angles for grinding at bench grinders.

In my understanding, the diamond wheels with constant diameters may revive the use of your kenjig. My double ended kenjig will enable to sharpen and hone majority of kitchen knives for a desired bevel angle.

I think, I will not surprise you, when I tell you that I am already inventing a tool for smoothly setting of arbitrary bevel angle on machines with diamond wheels. It will be simple and suitable for 3D printing! 

Jan

[Ken S]

Dutchman,

You are quite correct; this topic is really about the fun of mathematics. I would add the value of mathematics in a most positive way. While my mathematics is limited, I appreciate that errors are cumulative and appreciate how mathematics can lower our degree of errors. We have not stated it, however, using mathematics and precision drawings has allowed us to move far beyond the limitations of the Anglemaster. I do not mean to be critical of the Anglemaster. It is accurate enough for its intended purpose, however, it is limited by its thick lines. Even a much more expensive tool like a Starrett protractor with engine cut lines has limitations. The more we can incorporate mathematics into our set up tools, the more we can raise the standards of both our critical work and the general work. Your calculations, begun with a handheld calculator, have certainly sparked a whole area of development in angle setting.

Jan,

I look forward to all of your ideas, especially those related to 3D printing. I believe in the value of being a novice, like me, in mew areas to sharpen the mind.

The new diamond wheels have many advantages. However, we have much to learn about sharpening with them. The sharper cutting grains of diamonds may not always be advantageous. We have often used slurry to help sharpen. The possibility of controlled flat grinding with the side of the wheel will present many new possibilities. The old flat vs hollow grinding debate will take on new dimensions. I believe most of this discussion will be generated on the forum; Tormek has not said much oabout any new wheels, including the SB and SJ.

I look forward to interesting discussions.

Kn

[RickKrung]

Thanks to all who contributed.

I didn't do any math, just precision drawings, but it was fun gaining a better understanding.  I will make one of these, using the tangent, to find out whether it serves my purpose.  I've collected the bearings, fasteners and need to dig out some aluminum plate.  I will build it using inch dimensions and have redrawn it based on 5/8" bearings, etc. 

I do have a fabrication question, regarding the overlap in the USB holes.  It appears nice to have that as it allows more angles to be included, but I have a machining question.  What drill/reamer/counterbore was used?  My question concerns the flutes catching the sharp corners of the adjacent holes, pulling the tool off-center or just ruining the cut.  I have a 12mm reamer (with a long shank) which would make nice precision holes, but I if fear will do just, grab the corners.  If it had a pilot, it could not wander.  I have some piloted metric counterbores but they typically are oversized, which I do not want.  I have a boring head, which would work, but takes a bit more work to use.  I could make these where the holes do not overlap, but that means making three for all the angles that I want, which would be nice to avoid by having overlapped holes. 

I have not tried using the reamer yet, so do not know if my fears are real.  What have any of you who have made this (machined) used? 

Thanks,

Rick