Accuracy of angle prediction: experimental results

[cbwx34]

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.

Or maybe we just need a little better instruction on how to do it.

Edit to add:  BTW... a "consensus" among who?... that this is more accurate?

[Cyrano]

Many thanks to all the contributors in this thread.

Based on the discussion, I now understand the source of my 3-degree discrepancy is as illustrated here, which represents the tool as seen edge-on to the wheel:

   B = my existing measurement, made in a plane parallel to the side wall of the wheel
   C = what I need to measure to get results per Jan's calculation, made in a plane passing through the center of the wheel
   theta = the angle formed by the planes in B and C, above



I understand a difference of c. 4 mm between B and C will account for my c. 3-degree discrepancy ... so let's run the numbers.

For the case where I measured B as 90 mm, I calculate theta as follows:



I use theta to calculate C as follows:



I was expecting to see a difference of c. 4 mm, but I calculate a difference of 0.6 mm. What's wrong with my math? 

[Jan]

Cyrano, your math is OK, you just need a little better instruction how to measure the distance between the top of the USB and the stone surface.

The distance s' is measured in a plane parallel to the side wall of the wheel (perpendicular to the USB). The measurement is done along a line connecting the centre of the wheel and the centre of the USB.

The attached figure shows the situation for typical kenjig with A = 139 mm. In your case R = 125 mm, A = 152 mm and for bevel angle 15° you set the distance s' = 90 mm.

I hope it helps, if not, please do not hesitate to ask again, you are welcome!

Jan

[cbwx34]

Many thanks to all the contributors in this thread.

Based on the discussion, I now understand the source of my 3-degree discrepancy is as illustrated here, which represents the tool as seen edge-on to the wheel:

   B = my existing measurement, made in a plane parallel to the side wall of the wheel
   C = what I need to measure to get results per Jan's calculation, made in a plane passing through the center of the wheel
   theta = the angle formed by the planes in B and C, above


I understand a difference of c. 4 mm between B and C will account for my c. 3-degree discrepancy ... so let's run the numbers.

For the case where I measured B as 90 mm, I calculate theta as follows:


I use theta to calculate C as follows:


I was expecting to see a difference of c. 4 mm, but I calculate a difference of 0.6 mm. What's wrong with my math? 

There's probably nothing wrong with your math... but the width of the wheel has nothing to do with this.

If you look at this diagram...



... the red triangle is the measurement you initially made (only the line straight down actually, I just "connected the dots" to make a (unecessary) triangle)... where the blue line is the measurement needed... (that is measured from the top of the USB directly to the wheel, passing thru the center of the wheel).

Wheel width is not figured into this at all.

Edit to add:

The question I should have asked earlier (to Jan)...

...
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.
...

... is how did you calculate this?  (I know it's right, just curious the route you took, (math/diagram/or something else).

[Ken S]

Cyrano,

A well trained sharpener should be fluent with several methods. In addition to the two being discussed, he should be proficient with the Anglemaster, black marker, substitute target, Herman's platform, and hand held.

For very precise, individually measured work, Wootz' applet has no equal. The sharpener who must sharpen numerous different knives to a standard bevel angle is in the domain of the kenjig group.

I suggest you print out my knife setting article. If you click of the Sharpeneing Handbook with Rich Colvin's forum signature you will find it. Pay particular attention to photo five. It shows a kenjig sitting squarely on both the grinding wheel and the usb. Its thickness gives it stability. There is no paralex error. Your digital caliper may work fine, however, it looks error prone to me.

I think of the kenjig as a single gage block. A one inch gage block may be accurate to millionths on an inch, depending on its grade. By itself, it measures only one distance. By itself, my most used kenjig is designed to set up a 15° bevel with a 250mm grinding wheel and a 139mm projection. It does this very accurately. Different kenjigs can be set up for different variables.

The kenjig is designed for standardization. Wootz' applet is designed for individual set up. I believe there is a place for both.

Ken

[Jan]

CB, I have measured the 4 mm difference in a CAD drawing and then used an inverse algorithm to calculate the bevel angle assuming that R, A and s' are known.

Because my CAD drawing was for A = 139 mm, the results for Cyrano's case are rather indicative.

Jan

[cbwx34]

CB, I have measured the 4 mm difference in a CAD drawing and then used an inverse algorithm to calculate the bevel angle assuming that R, A and s' are known.

Because my CAD drawing was for A = 139 mm, the results for Cyrano's case are rather indicative.

Jan

Cool.  Thanks.

I had actually gone in and checked with the AngleMaster (to make sure what I was thinking made sense)... a distinct "suweeet" was heard when it showed a 3° difference.   (My Cadd diagram also verified it). 

...
I suggest you print out my knife setting article. If you click of the Sharpeneing Handbook with Rich Colvin's forum signature you will find it.
...

Here's a direct link...

http://sharpeninghandbook.info/Tool-Jig-KenJig.pdf

[Cyrano]

As expected, the source of my discrepancy appears to have been inaccuracy in how I was measuring S.

My problem was not in the angle at which I was making the measurement. My problem was the method by which I was judging when my calipers were at the level of the top of the USB.

With this problem corrected, I'm now getting results consistent with Jan's calculator. 

This micrograph illustrates how well I was able to match the factory edge on a Gerber folding knife. The outer profile is the factory edge, and the inner profile is the result of my work using the Tormek:

[cbwx34]

As expected, the source of my discrepancy appears to have been inaccuracy in how I was measuring S.

My problem was not in the angle at which I was making the measurement. My problem was the method by which I was judging when my calipers were at the level of the top of the USB.

With this problem corrected, I'm now getting results consistent with Jan's calculator. 
...

I'm glad you're getting better results... but the line I put in bold tells me, that, unless I'm misinterpreting it, something may still be wrong here.  You shouldn't have to "judge" when the calipers are level with the USB, because the measurement is taken directly from it.

One thing I found in working thru some of this... it's easy to "make the numbers fit the desired results".  Don't get caught in my trap.

With calipers... one end should be on the USB... the other on the stone.  I like to use these two points...



... and when I make the measurement, I "aim" for the stone center...



... to obtain it.  It's no different than using the jig Ken mentioned... (called the Kenjig I believe) ... or a similar method.  Some find it easier to use the bottom of the USB... as you mentioned earlier, just subtract the diameter.  But still measure directly from it.

So... maybe take another look at it?  It might just be a coincidence that it came out right.

[Jan]

Cyrano, I am glad that your results are now consistent with my Excel calculator. 

I have modified the "Starrett square" for easy setting of the USB – grindstone distance.  A 12 mm Al sleeve is attached to the body of the combination square. The sleeve offsets the position of the universal support with respect to the zero on the ruler, but this offset is compensated by the contact block made of two Al plates of trapezoidal shape. In this way the proper function of the ruler is preserved.

Jan

[Ken S]

I like the way CB uses the calipers. It is simple and direct, like the Kenjig. I also like the way Jan has modified his Starrett square.For me the main difference between their methods (including Wootz' applet) and the kenjig is that their set up tools are adjustable and the kenjig is fixed. However, this adjustability comes at a price. The caliper must be reset each time a change is desired. As these worthy sharpeners are skilled, I will concede that their resetting does not introduce error. I will also concede that with their skill, the extra time involved in resetting is minimal.

I like the gage block mentality. A one inch or twenty five millimeter gage block will remain quite accurately that dinension with no resetting. I do not have to be concerned about returning it to a previous setting; it has only one setting.

I do not believe any one method is ideal for all circumstances. I do believe that the kenjig offers the easiest, most repeatable solution for both the new sharpener or the busy rapid fire farmers market sharpener.

Ken