chisel sharpening

[Herman Trivilino]

Herman, the heel angle is the angle of the bevel farthest from the cutting edge. It is given by a tangent to the stone at the heel.

Ahhh... Yes, I see that now.

The angle between the tangent line and the chord is 3.1°, as you've labeled it in your drawing.

I take back what I said about it being 2°. My 1:1 scale drawing isn't precise enough to make that determination. Meanwhile I'm working on an analytical determination, but not getting very far.

I've taken the liberty of modifying one of your drawings, removing the heel angle as I don't see its necessity.

[Jan]

OK, I hope everything was clarified now. I have enjoyed the discussion with you, Herman! 

The heel angle has no role in chisel cutting process but it is the easiest angle to set without sophisticated setting equipment. The heel angel is accurately equal to tool rest angle. Because of this it is good to know the difference between the edge angle and heel angle. 

Jan

[Jan]

Ken, thanks for your patience! You see, that the unique Tormek AngleMaster withstood our discussion without any harm!  On the contrary, possible doubts about its functioning have been dispelled.

I have to admit that, regardless of all my angle setting inventions, I cannot imagine setting the grinder or the tool without the AngleMaster. The only exception is your kenjig and the TTS-100. 

Jan

[Herman Trivilino]

My 1:1 scale drawing isn't precise enough to make that determination. Meanwhile I'm working on an analytical determination, but not getting very far.

I've got it! I fetched the calculations and drawing I'd made when I was designing my platform jig a couple of years ago and they were a big help. I confirm your result, Jan, getting about 3.09° as the angle between the tangent line and the chord line. This is for a grindstone diameter of 250 mm and a chisel thickness of 6.35 mm.

For those looking for a summary, the tangent line angle is the angle you'd set with the Angle Master and the chord angle is the angle you'd measure with a protractor. The difference of 3.09° is due to the hollow grind.

[Herman Trivilino]

The heel angle has no role in chisel cutting process but it is the easiest angle to set without sophisticated setting equipment. The heel angel is accurately equal to tool rest angle. Because of this it is good to know the difference between the edge angle and heel angle. 

Can you help me understand this, Jan? I would think that everything you said above about the heel angle is instead true of the chord angle.

If you lay the chisel down on a flat bench stone as if you're about to grind the bevel, and measure the angle the chisel back makes with the stone, that is the chord angle. I would think that is what you'd call the tool rest angle? What am I missing?

[Jan]

Mentioning the heel angle I have thought the following: imagine you have set your knife platform for an angle of 31.2° before sharpening. When you now sharpen a 6.35 mm thick chisel you will get a cutting edge angle 25° while the heel angle will be 31.2°.

For the same platform setting and a 16 mm thick mortising chisel you will get the same heel angle while the cutting edge angle will be much, much smaller than 25°.   

Jan

[Jan]

I've got it! I fetched the calculations and drawing I'd made when I was designing my platform jig a couple of years ago and they were a big help. I confirm your result, Jan, getting about 3.09° as the angle between the tangent line and the chord line. This is for a grindstone diameter of 250 mm and a chisel thickness of 6.35 mm.

For those looking for a summary, the tangent line angle is the angle you'd set with the Angle Master and the chord angle is the angle you'd measure with a protractor. The difference of 3.09° is due to the hollow grind.

Herman, thanks for your independent analytical confirmation of my angles! Your compliance pleases me.   

Jan

[Herman Trivilino]

Mentioning the heel angle I have thought the following: imagine you have set your knife platform for an angle of 31.2° before sharpening. When you now sharpen a 6.35 mm thick chisel you will get a cutting edge angle 25° while the heel angle will be 31.2°.

Ahhh... yes. Now I see what you mean! I have never used my platform jig to sharpen a chisel. Only knives, and I of course neglect their thickness.

Perhaps I should create a table of platform setting angles. I haven't yet been able to derive a simple expression that relates the chord angle to the bevel angle, grindstone diameter, and tool thickness. I do, however, have a complicated one!



where ß is the bevel angle, r is the grindstone radius, t is the tool thickness, and Θ is the chord angle.

So, in your example we have r=125 mm, t = 6.35 mm, and ß = 25°. Solving for Θ we get (as one of the solutions) about 28.1°.

So this gives us a difference of about 3.1°.

Note: Edited to fix a mistake I made in interpreting the formula. Its results are unchanged.

[WolfY]

Interesting academic reading.
I often wondered what angle is the WM-200 is referring to and thought it was a straight line from the cutting tip and the heel, letting the hollow be there. I measured the hollow theoretically to be somewhere btw 0.007~0.009 mm with 200~250mm stone dia. which is neglectable.

To make it practical:
Now I can measure WM-200 setting + 1~1.5dgrs to compensate for the difference and have what I thought I had?
To that add 1.5 dgrs for the long bevel in modern kitchen knifes as the WM-200 is intended for measuring chisel edge.
Or, measure on WM-200 14 dgrs will give me about about 16.5dgrs or 33dgrs included.
That would be as close as possible for the "desired" cutting angle. Right?

[Ken S]

I have solved the issue with my Anglemaster. I learned this trick from US precision toolmakers, Starrett and Brown & Sharpe. Once a year, I send my Anglemaster and grinding wheel back to Tormek in Sweden for recalibration. In turn, Tormek AB sends its calibration equipment to the Swedish National Bureau of Standards annually for inspection.

Ken

[Jan]

Ken, it is good to know that you have such an accurate equipment! 

The observed precession of Mercury's orbit was not in agreement with Newton theory. Based on Einstein general relativity the discrepancy was explained. The size of this disagreement was 43 arc seconds per century! You had been able to help them. 

Jan

[Jan]

where ß is the bevel angle, r is the grindstone radius, t is the tool thickness, and Θ is the chord angle.

Thank you for posting the formulae, Herman! 

It shows an important fact: the chord angle depends only on the relative thickness t/r and the bevel angle of the blade. It is good to know. My AutoCAD did not told me that! 

Jan

[Herman Trivilino]

To that add 1.5 dgrs for the long bevel in modern kitchen knifes as the WM-200 is intended for measuring chisel edge.
Or, measure on WM-200 14 dgrs will give me about about 16.5dgrs or 33dgrs included.
That would be as close as possible for the "desired" cutting angle. Right?

Hi WolfY. No, that would not be right. For a typical kitchen knife we grind both sides. Let's say we want a 15° bevel on each side of a knife of thickness 2 mm. In my formula I enter 1 mm for the thickness because I'm sharpening both sides. I get a difference of about 0.8° between the angle you desire and the WM-200 (Angle Master) setting.

This difference is too small for practical use of the WM-200 to detect. For example, if you adjusted the WM-200 with a magnifier and bright light you might be able detect a difference of 1°. More importantly, it's too small to make a difference in the way the knife performs.

Actually, the angle that the two bevels make to form the edge is instead the angle I desire to measure, and this is the angle the WM-200 measures. Well, you do have to double it for a knife with a two-sided bevel. In other words, it's 30° when you set the WM-200 at 15°. When you slice into something this is the angle of the edge that does the slicing!

[Herman Trivilino]

The observed precession of Mercury's orbit was not in agreement with Newton theory. Based on Einstein general relativity the discrepancy was explained. The size of this disagreement was 43 arc seconds per century! You had been able to help them. 

I saw that same drawing when I googled it. It shows the perihelion advancing about 20° per orbit. The actual advance is only about 0.004°.

You might think this is too small to worry about, but the story doesn't end there. Astronomers were able to account for all but about 1% of that advance using newtonian physics. It was this tiny amount that Einstein was able to account for with his 1916 theory. The one that launched him instantly from obscurity to fame when Eddington's eclipse expedition confirmed another of that theory's predictions in 1919. Newspapers in the USA had to report that he was a mathematician because at that time reporters thought that no one in America knew what it meant to be a physicist.     

[Jan]

Now I can measure WM-200 setting + 1~1.5dgrs to compensate for the difference and have what I thought I had?
To that add 1.5 dgrs for the long bevel in modern kitchen knifes as the WM-200 is intended for measuring chisel edge.
Or, measure on WM-200 14 dgrs will give me about about 16.5dgrs or 33dgrs included.
That would be as close as possible for the "desired" cutting angle. Right?

Wolfy, your statement that the AngleMaster works well for setting chisel edge angle is correct. 

If you use the AngleMaster to set a bevel angle for an already hollow grind knife bevel the situation may be different. When the flat lower edge of the angle setter's overbridges the whole hollow grind bevel than the angle you will sharpen will be smaller than the one shown by the angle setter.

For the case discussed by Herman, 2 mm thick knife and 0.8° chord difference,  I would set the angle setter to 2*(15° + 0.8°) = 2*15.8° = 31.6° a expect that I will sharpen a bevel angle of 15° at the very tip.

For the knife mentioned above the chord length is 3.7 mm.

Jan