chisel sharpening

[Herman Trivilino]

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.

I wasn't aware that anyone used the WM-200 that way. I always set it on the flat part of the knife, not on the bevel, so I would set it at 15° in this case. The bevel is far too narrow, it seems, to be used accurately in the way shown in your picture. In the example we're looking at, the bevel width would be only 3.5 mm. The base of the Angle Setter on the WM-200 has a width of about 12 mm. You'd be using only about 30% of that base, causing the accuracy to really suffer it seems. We're talking about a 0.8° discrepancy here!

[WolfY]

Jan,
Just as Herman stated the WM-200 is not constructed to measure the cutting bevel but the flat side of the chisel. E.g for knifes it's the secondary bevel. Cause it is not straight I add about 1~1.5 dgrs to compensate. Actually measuring with the WM-200 giving us the angle on the other side. The side with the contact to the stone.

As for adding for the "real" angle, whether it is given for the cutting edge or the heel I did not care till now, and will not care in the future as I get good results and don't want to complicate a simple process.
So. For ex. measuring 15 dgrs gives me about 32dgrs edge that works very well for kitchen knifes.
That with the reservations for my added experience and knowledge of what the customer wants

[Jan]

I wasn't aware that anyone used the WM-200 that way. I always set it on the flat part of the knife, not on the bevel, so I would set it at 15° in this case.

It is the basic handbook method for setting a new edge angle on knives. The other method is recommended for thin knives.   

We're talking about a 0.8° discrepancy here!

Yes, it is within specifications because Tormek mentions VM-200 accuracy of 1°. 

Jan

[Ken S]

The Anglemaster on the small bevel surface is more easily seen, in my opinion, in the handbook than on the knife itself. That is why I have pursued alternative methods, such as the kenjig and the substitute target. The substitute target allows the Anglemaster to be placed on a large flat surface, such as it is when measuring a chisel or plane blade.

Ken

[Jan]

You are correct, Ken. The AngleMaster is quite often a stumbling block.

Your substitute target is a perfect idea how to use the AngleMaster for knives setting in a more convenient and accurate way.  The ideal thickness of the substitute target is 1.25 mm.

Your kenjig (139 mm) concept is my favourite method to set an edge angle for knives.    Currently I am considering a kenjig for smaller knives with protrusion 132 mm. Kenjig concept works well also for tapering blades and I consider it as the most accurate method.

As you know I have modified the TTS-100 to work in conjunction with knife jig for selected bevel angles (10°, 15° and 20°). This setter operates for all stone diameters. Sharpeners on the knife.cz forum were impressed by this possibility and are testing this setter for additional bevel angles (12.5° and 17.5°).

Nevertheless all three methods require that the blade is correctly mounted in the knife jig. But to verify the symmetrical mounting we need the AngleMaster again. 

Jan

[Herman Trivilino]

The Anglemaster on the small bevel surface is more easily seen, in my opinion, in the handbook than on the knife itself.

Ken, your comment prompted me to do some calculations. I reckon the blade thickness in that handbook drawing is 4 mm. At a 25° edge angle that would give a bevel width of about 8 mm, taking up about two-thirds of the base of the Angle Setter on the WM-200. This can be verified by looking at the figure.

By the way, a 25° edge angle on a 4 mm wide kitchen knife is quite extraordinary. The bevel angle would be 12.5°, which is quite small. And a thickness of 4 mm is quite large. The edge on such a knife would not last long, in my experience. Moreover, it would take a great deal of skill to produce it uniformly on a Tormek. I therefore am of the opinion that it's not a realistic example.

I measure the bevel width on my heaviest kitchen knife to be only about 1 mm. I measure the thickness to be also about 1 mm. These measurement were taken with a hand-held steel ruler under a good light with a magnifier, and they are (roughly) confirmed with my formula, using a bevel angle of 20°.

[Ken S]

Well stated, Jan.

My first substitute was made out of steel approximately 1.5 mm thick. I ground it down to close to 1.25 mm. Two thichnesses of a standard gift card work well, also.

I used the standard 139 mm with the Tormek small blade tool to make only one kenjig necessary for most kitchen knives. With a basic understanding of the theory behind the kenjig, a second kenjig for smaller knives is more convenient.  Switching the Distance back and forth between the two kenjigs is quick, accurate, and requires no measurement. Separate kenjigs can also be made for different bevel angles.

While writing this, I had a new thought about the Anglemaster. With tapered body knives, like my German style Henckels, the measuring surface of the Anglemaster could be placed on the taper of the knife. With the jig flipped over, measuring the same tapered part of the knife, once the measurements agree, the knife is properly set in the jig.

I applaud the efforts of our friends and fellow Tormekers in the Czech Republic and Slovakia. Please keep us posted!

Ken

Ken

[Ken S]

Herman

Your post came in as I was writing. In my opinion, the Anglemaster works best with larger surfaces like the back of chisels. I freely admit that my constraint with the small surface mating with a standard knife bevel is my eyesight.

I prefer to avoid the limitation by using Dutchman's or Jan's math tables and simple devices like the kenjig or higher tech versions of it.

I suspect the drawing in the handbook is designed to clearly illustrate the idea, rather than be an exact replica. As such, it is effective.

Ken

[Jan]

While writing this, I had a new thought about the Anglemaster. With tapered body knives, like my German style Henckels, the measuring surface of the Anglemaster could be placed on the taper of the knife. With the jig flipped over, measuring the same tapered part of the knife, once the measurements agree, the knife is properly set in the jig.

Yes Ken, you are correct. Recent Sandor's topic "My way of mounting knife in SVM-45 jig" advices how to mount the blade symmetrically with respect to flipping the jig over. I have tested it, it works, but requires some practice to do it in a short time. 

My advice for your Henckels would be: mount it symmetrically in the jig and then set the edge angle using your kenjig. Other vice you will have to measure the angle of the tapered body and correct the AngleMaster setting for it.

Jan

[Herman Trivilino]

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.

Here's a simpler formula:

r cos(2θ-β) + t = r cos β.

Consider the angle between a tangent line (that is, a line tangent to the rim of the grindstone) and a line parallel to the upper surface of the tool. At the point on the rim touched by the upper surface of the tool this angle equals β (by definition). As we move along the rim towards the lower surface of the tool this angle increases. Its value halfway along is θ (because there the tangent line is parallel to the chord that cuts across the hollow grind). Thus it increased by θ - β. And therefore by symmetry its value must again increase by θ - β as we proceed the remaining half to the point on the rim touched by the lower surface of the tool. Thus its value at that point is 2θ - β.

Note that β is the angle you measure with the WM-200 whereas θ is the angle you'd measure with a protractor.

[Jan]

Thanks for the simpler formula, Herman. The quantity 2θ – β is called a heel angle. 

The attached graph shows that the difference between protractor measurement and WM-200 setting (θ – β) is almost linearly increasing with tool thickness. The graph was constructed for stone radius 125 mm and bevel angle 25°.

Jan

[Jan]

Herman's simplified formula inspired me to wonder if it is possible to calculate the bevel angle β when we measure the chord length L and the tool thickness t. I assume we know the stone diameter D.

It turned out that it is possible and the bevel angle is given by the following expression:

β = arcsin(t/L) – acrsin(L/D)

Example: Using grindstone with a diameter D = 240 mm a 3 mm thick chisel was sharpened. The measured chord length of the grind was 6.5 mm.

Question: What is the bevel angle? 
Answer: The bevel angle is 25.9°. 

Jan

[Herman Trivilino]

Thanks for the simpler formula, Herman. The quantity 2θ – β is called a heel angle. 

Ah, yes, so it is. ;-)

The attached graph shows that the difference between protractor measurement and WM-200 setting (θ – β) is almost linearly increasing with tool thickness. The graph was constructed for stone radius 125 mm and bevel angle 25°.

I think this is the so-called small angle approximation, Jan. When the angle θ – β is small the chord length and the arc length are nearly the same. The value of the angle in radians is approximately equal to both its sine and its tangent.

Here's another approximation:

cos θ ≈ cos β - t/D.

Try using that to make your graph and I bet it will come out exactly linear.

By the way, the angle subtended at the center of the grindstone is 2(θ – β). If you bisect this angle it's easy to see that its value is θ – β. It's another way to show that the heel angle is 2θ – β.

[Herman Trivilino]

β = arcsin(t/L) – acrsin(L/D)

Note that arcsin(t/L) is θ, and acrsin(L/D) is θ – β.

[Herman Trivilino]

Here's another approximation:

cos θ ≈ cos β - t/D.

Try using that to make your graph and I bet it will come out exactly linear.

That's a bet I would have lost!