Accuracy of angle prediction: experimental results

[Cyrano]

Greetings from a new Tormek user in the USA.

I've had great experiences using the Work Sharp system (with its Blade Grinding Attachment) to get sharp edges on a variety of knives. However, I've learned that for such a system, the resulting angle is affected by blade thickness, in combination with other variables. This poses a challenge in matching an existing edge angle predictably -- hence my interest in the Tormek system.

I was surprised and delighted to see the depth of thought and analysis done by members of this forum in predicting Tormek results using geometric calculation. Kudos and thanks!

To ensure I correctly understood Jan's calculations https://www.dropbox.com/s/ypbtaxgycgoyls0/KENJIG_wheel_support_distance_1.xlsb?dl=1, I performed several sharpening trials using items intended to provide a good variation in apex angles:

• a small rectangular plate of O-1 tool steel
• a narrow strap tie of mild steel
• a Ganzo folding knife of 440C stainless steel
• a RaidOps fixed-blade knife of S30V stainless steel

The results were measured by making impressions of the sharpened profiles in a conforming medium, and measuring cross-sectional slices of that medium by microscopy:



The results showed near-perfect linear correlation between predicted values and measured values:



Of interest is the offset between predicted values and measured values. Does anyone have any ideas on why my results are consistently c. 3 degrees more obtuse than predicted?

[cbwx34]

Greetings from a new Tormek user in the USA.

I've had great experiences using the Work Sharp system (with its Blade Grinding Attachment) to get sharp edges on a variety of knives. However, I've learned that for such a system, the resulting angle is affected by blade thickness, in combination with other variables. This poses a challenge in matching an existing edge angle predictably -- hence my interest in the Tormek system.

I was surprised and delighted to see the depth of thought and analysis done by members of this forum in predicting Tormek results using geometric calculation. Kudos and thanks!

To ensure I correctly understood Jan's calculations https://www.dropbox.com/s/ypbtaxgycgoyls0/KENJIG_wheel_support_distance_1.xlsb?dl=1, I performed several sharpening trials using items intended to provide a good variation in apex angles:

• a small rectangular plate of O-1 tool steel
• a narrow strap tie of mild steel
• a Ganzo folding knife of 440C stainless steel
• a RaidOps fixed-blade knife of S30V stainless steel

The results were measured by making impressions of the sharpened profiles in a conforming medium, and measuring cross-sectional slices of that medium by microscopy:

The results showed near-perfect linear correlation between predicted values and measured values:

Of interest is the offset between predicted values and measured values. Does anyone have any ideas on why my results are consistently c. 3 degrees more obtuse than predicted?

Welcome to the forum.

The fact that you're consistently 3° off on every test, makes me think of the obvious... I'd start by double checking all your measurements/settings.  Are you measuring the:  distance between the top of the USB directly to the stone / the Projection Distance (A) / stone size / etc.  correctly?  The measurements don't need to be "super accurate"... but should be within 1/2 mm or so (obviously they can't all be off)...

I've been messing with a CADD program... here's what the setup should look like for your Ganzo knife...



Blade thickness can also matter... the Tormek clamp is made for knives around 2.2mm thick, and also since one side is fixed it can affect the outcome (but probably not 3° on all your examples).

I am a bit curious how you determined "blade thickness" affects the angle on the WSKO with the Blade Grinding Attachement... I have one, and it's basically holding a knife parallel against an angled belt.  (I ask to help determine what may be going on here).

The geometry calculations are cool... one of my favorite "finds" in the forum.

If none of this helps... wil try again (or maybe someone will see something obvious). 

p.s.  If you found Jan's formula... I'm assuming you found Dutchman's book.   Also, I like your testing!

[Ken S]

Welcome to the forum, Cyrano.

My gut feeling is that your calculations are based on the center point of the universal support bar instead of the top of the bar where the knife jig rests. I recall this kind of a discrepency several years ago. Unfortunately, for some reason I am unable to open the dropbox files. (No doubt my computer inexperience.)

I'm sure this would be anathema to the math people on the forum, however, if the 3° too obtuse error is consistent, The low tech part of me would be tempted just to make a "course correction" and set to 3° too acute.

I can provide some background on the original reason for the kenjig. (I originally named it the Knife Setting Tool-150, the 150 being the length in millimeters.) It was a development of my standardized setting blocks and supported by Dutchman's excellent grinding angle booklet. The original prototypes were made out of cardboard or baltic birch plywood. I still use cardboard for "one off" kenjigs for things like my Chinese cleaver. The idea was to eliminate tedious measurement with the Anglemaster and provide consistent, repeatable bevel angles. It was designed for three groups:
1) New users. It allowed them to automate the jig set up and concentrate on the actual grinding.
2) Occasional users. It allowed them to have consistently sharp knives without a lot of memory tedium.
3) Busy farmers market sharpeners. It allowed them to automate set up for different size knives with almost no adjustment. This led to a considerable improvement is efficiency.

Using Dutchman's tables, I standardized the jig projection at 139mm. The distance from the support bar to the grinding wheel was set from the tables. The distance could be set while setting up for the day, and would rarely need to be changed. If a change was necessary for an unusual knife, the jig could be used to return quickly to the original set up. By using several preset jigs, the projection rarely required adjustment. Again, the jig could quickly return to the original set up.

The concept has grown far beyond its simple beginnings. Auto wheel diameter has been incorporated. Jigs have now been machined from stainless steel in France and made on 3D printers in the Czech Republic. Wootz, in Australia, has developed a computer program to very accurately set angles to 1/10°.

We now have several members highly trained in math and engineering. We will correct your 3° error!

Ken

[Cyrano]

Thanks for the detailed response!

Are you measuring the:  distance between the top of the USB directly to the stone / the Projection Distance (A) / stone size / etc.  correctly? 

I think so, but as you say, this is the most obvious source of error ...

In the following photos, the absolute values shown are not necessarily those corresponding to my experimental cells; rather, they are illustrative of how I made my measurements.

Projection distance:



Stone diameter:



A:



For A, I measured the distance along a perpendicular from the surface of the stone to the centerline of the arm of the USB. Your illustration shows the distance from the stone to the far end of the diameter of the USB bar. If I add 6 mm (half the diameter of the USB bar) to my measurements for A, the expected angles per Jan's algorithm should decrease, not increase. 

I am a bit curious how you determined "blade thickness" affects the angle on the WSKO with the Blade Grinding Attachement... I have one, and it's basically holding a knife parallel against an angled belt.  (I ask to help determine what may be going on here).

The mechanism at work in this phenomenon is that the belt surface is not rigidly planar, but flexibly concave. For a thin blade, the effect is insignificant. For a thicker blade, the belt must remove material at the shoulder of the edge before it can reach the edge apex; this results in enough curvature of the belt to affect the apex angle.

I quantified this mechanism by conducting an experiment using O-1 tool steel bar stock of varying thicknesses, and sharpening each to an apex at a variety of BGA settings. I measured the results using the same cross-sectional imaging method I used in my Tormek experiment described above. The results were self-consistent:



Observations regarding these results:

• At any one blade thickness, there is an excellent linear correlation between angle setting and resulting apex angle. This suggests the combined system of [tool + investigator + experimental process] has good precision (i.e., repeatability.) 
• As blade thickness increases, the offset between angle setting and resulting apex angle increases.
• As blade thickness increases, the slope of the correlation between angle setting and resulting apex angle decreases. I interpret this to mean that as the thickness increases, the curvature of the belt becomes an increasing component of the final apex angle, reducing the effect of the setting angle.

For extremely thin blades, this effect becomes insignificant. For my Shun kitchen knife, with an effective thickness of 0.2 mm, there is no offset between the BGA setting and the resulting apex angle:

[cbwx34]

Thanks for the detailed response!

Are you measuring the:  distance between the top of the USB directly to the stone / the Projection Distance (A) / stone size / etc.  correctly? 

...
A:



For A, I measured the distance along a perpendicular from the surface of the stone to the centerline of the arm of the USB. Your illustration shows the distance from the stone to the far end of the diameter of the USB bar. If I add 6 mm (half the diameter of the USB bar) to my measurements for A, the expected angles per Jan's algorithm should decrease, not increase. 

Projection Distance and the stone look good, but I think you're "mis-measuring" the USB height.  The 90mm is a straight line from the top of the USB to the center of the stone.  The way you're measuring, if I read it right... you're going from the top of the stone straight up to set the USB?  I duplicated this and it sets the USB to high... (in fact, 3° off on a quick test I did).

Remeasure the USB height from the top straight to the stone (like I said aim for the center)... it should lower the USB height... and your angle.

(If this makes no sense, let me know and I'll snap a couple of pictures).

I went ahead and snapped a couple of photos real quick...

I think you're measuring straight down to the stone, like this?



If so, and I set the USB height, then move the calipers to the correct position (top of the USB, aiming for the center of the stone), you see the slight gap...



... lowering the USB  to the correct height should correct the error... it'll lower the angle the knife, etc. is being sharpened at.

p.s.   (I'll look over the WorkSharp info later).

[cbwx34]

...
I'm sure this would be anathema to the math people on the forum, however, if the 3° too obtuse error is consistent, The low tech part of me would be tempted just to make a "course correction" and set to 3° too acute.
...
Ken

Ugh.   

[wootz]

Cyrano, thank you for such a delightful reading.

First, Jan's estimates for the calculated angle tolerances (a quote):
1.0   mm error in stone diameter can change the bevel angle by 0.3°;
1.0   mm error in Jig projection length can change the desired bevel angle by 0.5°;
1.0   mm error in US height setup can change the bevel angle by 0.7°.

I've never tried Dutchman/Jan's method, since in our applet we use vertical distance from the US top to the Tormek housing which is easier to get accurately than the length of a perpendicular to the wheel - the greatest source of error in Jan's estimate.
Moreover so it is interesting to see what actual angles come out when calculated by distance to the wheel.

A slight increase in the resulting angle is expected when you grind on a coarse wheel due to a little shortening of the distance from the knife jig adjustable stop to the edge, when the apex is ground away producing the burr.
I can say for our applet - when we grind on a #1000 wheel, we get an edge angle the same as the calculated target, as checked by the CATRA portable laser protractor, however when we grind on a #220 to #400 wheel, we may get an angle by about +0.5 dps higher than calculated because of that shortening.

Your method of measuring the edge angle is very interesting - when you say "making impressions of the sharpened profiles in a conforming medium" - what is that "medium" please?

[Jan]

Cyrano, welcome to the forum and congrats on your very interesting post. 
Your interest in my geometrical angle setting approach pleases me. 

My formulae embedded in the Excel script is exact, it was derived without any approximations. (https://forum.tormek.com/index.php?topic=3320.msg19878#msg19878)

In my understanding CBWX has correctly identified the probable source of the problem resulting in getting larger bevel angle than desired/calculated.

When you follow the recommendations by CBWX you will shorten the distance between the USB and the stone surface by some 4 mm, which will cause decrease of the bevel angle by some 3 degrees. This will bring your results in compliance with my Excel script calculations. The error in the obtained bevel angle is determined by the accuracy of length measurements and should be only first tenths of a degree.

The beauty of this geometric approach to setting the bevel angle, initially introduced by Dutchman, lies in its accuracy and independence from the Tormek's sharpening machine.

Good luck!
Jan

[Ken S]

Thank you for posting the link to the related forum topic. I found a very perceptive quote there from Dutchman:

"The distance is measured NOT to the top NOR the center of the support. It is part of the triangle thorough the knife in the jig. So it should be measured to the heart of the jig just above the center of the support. Measuring the distance to the top of the support however will give a negligible error.
Please keep in mind that this subject is not an academic item, but a proposal to simplify the jig-setting  Thank you "

While I appreciate the very high level of precision being used in this process, for me, Dutchman's last sentence captures the process for me.

This all reminds me of the three phase problem solving process I became aware of twenty years ago. At the time, I had a photographic side business which included mounting prints and cutting overmats. Phase one was six months of great frustration. I like "floating mats", where there is a thin uniform border between the edge of the photograph and the overmat. This is the method Ansel Adams described in his technical books. It is very difficult to do properly, but unmatched if done right. Most people take the expedient path and just cover up part of the image.

I purchased a top of the line C&H professional mat cutter. At the time, it cost at least twice the price of a Tormek. This was an Ansel Adams level cutter. It got me closer to what I wanted, but I was still frustrated. The frustration prepared me for phase two.

Coincidentally, I have a hobby interest in machine shop layout and technology, which has included collecting an irrational amount of machinist tools. I started aligning the forty inch long round bar on which the cutter slid. My alignment tool was a dial indicator mounted on a surface gage. I could align the bar within .001" on the dial indicator. (I realize there was an error factor, however, my accuracy was close to that.)

Using my method, my wife cut her first rectangular mat. It involved two set ups. We realized her one cut with the first set up was too short. Normally this would have meant discarding the mat and starting over. Using my method, she was able to return to the first set up with enough precision to finish the cut with the blade exactly in the kerf, no mean trick for a mat cutter.

My mounting and matting tool kit resembled a machinist tool box.

Phase two is very exciting. The brain is well tuned into the process. The results are astounding. A by product of this level of concentration is a surprisingly rapid fire pace in solving related problems. In addition to precise cutting of regular mats, I could cut fancier corner mats using the same thought process. I believe many of you have reached phase two. Reaching it was a struggle for me. My formal mathematics education ended in high school fifty years ago. My computer knowledge is essentially word processing. Sadly, I do not believe most people ever have the satisfaction of reaching phase two, or are even aware of it.

I believe many of you have reached this rare level of understanding. So many of the posts on this forum have gone so far beyond the level of how much honing compound to use. I find these developments truly amazing and satisfying.

Phase three? Dutchman has reached phase three. He developed the math solution which made this whole ball of wax possible (phase two). He also realized that this was a practical solution to a jig setting problem, not an academic exercise. The mathematical foundation is still there, and very solid, however, Dutchman has kept his focus on the practical elements.

Likewise my print mounting and mat cutting technique evolved into a much more practical level. The precision was still there, but it was in the background.

A kenjig (or a janjig, the double ended version) is easily made at essentially no cost in very little time with very little required skill. I make the standard fifteen and twenty degree angles from baltic birch plywood on my bandsaw. I often cut the basic rectangular shape on my table saw. For occasional use, cardboard cut with scissors works just as well. Are these as accurate as laboratory grade ground hardened steel or carbide Starrett inspection tools? Certainly not. I am not trying to achieve accuracy in minutes or seconds. Frankly (please, knife/math members, no fainting), I do not care if my 15° is actually a consistent 14° or 16°. I can set up a knife in a jig in almost no time. In fact, my goal is to be able to be able to sharpen an assortment of knives using a kenjig and Tormek knife jigs in a time which closely aporoximates hand held sharpening.

I do value the high level of mathematics shown by other forum members. I also value the very high level of precision Wootz has incorporated into his applet. I have it loaded on my computer. I find it invaluable for precise work. I use the applet differently than Wootz. Wootz has developed a very commendable high end sharpening business. His customers expect top notch sharpening with very neat, accurate bevels. My knife sharpening is essentially garden variety kitchen knives for my own kitchen. What is everyday high precision for Wootz is the heavy artillery I can bring in if needed for me. I am grateful to have that artillery in reserve.

This high tech work benefits the entire forum. The new user, frustrated by trying to use the Anglemaster with his knife, can make a kenjig following simple instructions in a matter of minutes out of cardboard. The only required tools are household ruler and scissors and a pencil. This will allow him to grind consistent bevels repeatably at a level of accuracy far exceeding his need. This simple tool, like the Borg collective on Star Trek, is the product of the collective, not just one mind. It began in Holland and has grown in stages all over the world.

Cyrano, I hope you will become an active member of this group.

Ken

[cbwx34]

Cyrano, thank you for such a delightful reading.

First, Jan's estimates for the calculated angle tolerances (a quote):
1.0   mm error in stone diameter can change the bevel angle by 0.3°;
1.0   mm error in Jig projection length can change the desired bevel angle by 0.5°;
1.0   mm error in US height setup can change the bevel angle by 0.7°.

I've never tried Dutchman/Jan's method, since in our applet we use vertical distance from the US top to the Tormek housing which is easier to get accurately than the length of a perpendicular to the wheel - the greatest source of error in Jan's estimate.
Moreover so it is interesting to see what actual angles come out when calculated by Jan's method.

A slight increase in the resulting angle is expected when you grind on a coarse wheel due to a little shortening of the distance from the knife jig adjustable stop to the edge, when the apex is ground away producing the burr.
I can say for our applet - when we grind on a #1000 wheel, we get an edge angle the same as the calculated target, as checked by the CATRA portable laser protractor, however when we grind on a #220 to #400 wheel, we may get an angle by about +0.5 dps higher than calculated because of that shortening.

Your method of measuring the edge angle is very interesting - when you say "making impressions of the sharpened profiles in a conforming medium" - what is that "medium" please?

I'd like to expand on this a bit.

First, the US height being "the greatest source of error" is the same no matter how one gets there.  (I'm not sure if you're saying that the way it is measured is the source of the error, or just that your way is more accurate so the chance is reduced... I can interpret it both ways). 

2nd, your technique uses Dutchman's/Jan's main formula... but it then makes a 2nd calculation to determine the height based on the Tormek casing.  So you have, (both in theory and in actual use) introduced a couple more sources of error... you add an additional calculation, plus it requires specific measurements of the Tormek to achieve it.  So, for example, if I needed an exact amount of water... I pour it into a measuring device, then decide to check it by pouring it into a 2nd measuring device, but also decide I'll convert it from metric to "imperial"... they both may show the same amount, but I've left an ever so slight amount behind... and may have an ever so slight change when the calculation is done.

But, like the water example, in the end, I'll probably have the right measurement for the job... the differences are inconsequential.

While the main theory is relatively simple... it took me a while to "wrap my head around it", for a couple of reasons.  One... everybody involved in this seems to have a slightly different take on it, and come up with slightly different answers, and the other is... none of them are "exact".    (Even a CATRA protactor test has a range of accuracy... +-1° in your case?).

Don't get me wrong... I love how this procedure sets the angle... I do believe it is more accurate than using the AngleMaster, for example... if for no other reason than it doesn't have to "deal" with the angle grinds of the knife.  Whether one measures "to the wheel" or "to the Tormek"... you'll certainly get an answer that is very accurate... (probably more than what is needed, given all that is going on).    In your procedures... I do think it acheives a higher level of "relative accuracy"... by that I mean you may not be sharpening at the "exact" angle, but since some of your steps require slight changes in the angle... that is in all likelihood being achieved.

...
When you follow the recommendations by CBWX you will shorten the distance between the USB and the stone surface by some 4 mm, which will cause decrease of the bevel angle by some 3 degrees. This will bring your results in compliance with my Excel script calculations. The error in the obtained bevel angle is determined by the accuracy of length measurements and should be only first tenths of a degree.

The beauty of this geometric approach to setting the bevel angle, initially introduced by Dutchman, lies in its accuracy and independence from the Tormek's sharpening machine.

Good luck!
Jan

Thanks for the verification of the angle change... (and the part about the accuracy was in part, what I meant above).

[cbwx34]

Thank you for posting the link to the related forum topic. I found a very perceptive quote there from Dutchman:

"The distance is measured NOT to the top NOR the center of the support. It is part of the triangle thorough the knife in the jig. So it should be measured to the heart of the jig just above the center of the support. Measuring the distance to the top of the support however will give a negligible error.
Please keep in mind that this subject is not an academic item, but a proposal to simplify the jig-setting  Thank you "

While I appreciate the very high level of precision being used in this process, for me, Dutchman's last sentence captures the process for me.
....
Ken

  Good point... (and a point worth highlighting)...

[Ken S]

"First, Jan's estimates for the calculated angle tolerances (a quote):
1.0   mm error in stone diameter can change the bevel angle by 0.3°;
1.0   mm error in Jig projection length can change the desired bevel angle by 0.5°;
1.0   mm error in US height setup can change the bevel angle by 0.7°.

I've never tried Dutchman/Jan's method, since in our applet we use vertical distance from the US top to the Tormek housing which is easier to get accurately than the length of a perpendicular to the wheel - the greatest source of error in Jan's estimate."


First, I believe we need to establish our "in tolerance" ranges for angles. These should vary depending upon the intended use. If I took a prized knife to a high end sharpener like Wootz, my expectations and tolerance would be much more demanding that taking my kitchen knives to the busy farmers market sharpener.

Lookng at Jan's three sources of errors, we can measure the diameter of the grinding wheel with calipers or a rule. We can make minor course corrections if necessary. The average user will not wear down the grinding wheel sharpening flat knives overnight.

I set my projection using a pencil line on my kenjig. The line marks 139 mm, which is my standard projection. A knife line would be more precise, however, a millimeter error would surprise me.

I set the distance between the bar and the grinding wheel using the notch in the kenjig. It isn't inspection grade, however it is reasonably consistent. While doubtless not "dead nuts" accurate, I can't imagine the notch being a full millimeter off. I can see minor errors compounding, however, I think it is possible that some of the errors might cancel each other out, at least partially.

I have used the kenjig for several years. Setting the distance has become second nature for me as no doubt using your applet is to you. I think "easier to use" can be learned.

I have no doubt that using the applet is more accurate than using my humble jig. I suppose things get back to our tolerance range.

Ken

[Jan]

Ken, you are vise and very humble man.  What concerns your kenjig (or my janjig) I envisage a new dawn rising over this simple setting tool. The recently introduced Tormek diamond wheels with fixed diameter will significantly reduce the number of kenjigs necessary for knife grinder's everyday life.

Jan

[Ken S]

Jan,

It must be true that great minds think alike. The constant, matching diameters of the three diamond wheels eliminates the need for compensation with the ken and jan jigs.

Speaking of the janjig, I have an idea which might help with the leather honing wheel. (The idea is based on an idea by woodworking teacher, Ernie Conover. Ernie liked the Tormek, but thought he could work just as well freehand instead of using the jigs. If anyone could, it would be Ernie. Ernie used a flat very fine ceramic stone instead of the leather honing wheel.

My idea would be to use the janjig to set the leather honing wheel for the bevel side onle. Then, with the chisel still in the jig, use the fine ceramic stone on the back of the chisel.

Oops, I'm back in my chisel mode again........

Ken

[wootz]

Curtis, you miss the point I am afraid.
Maths are fine whether it is Dutchman, Jan or me.
Method of taking measurements is different, and we've got a chance to compare them thanks to Cyrano.
There've always been a consensus that measuring the vertical from the US top to the Tormek housing as we do is more accurate compared to the wheel.
Here comes a man with a truly scientific mind, but new to the method, tries by distance to the wheel, and gets a 3 degree discrepancy.