So now I don’t know what to make of the o-ring technique. I’m hoping others will do some testing.
I studied the actual sharpened angle with the goniometer after these tests and found something strange. While the Angle Cube was consistently reading a higher angle in the middle of the blade, the goniometer reads a higher angle at the tip of the sharpened blade by nearly a full degree. It’s a pretty accurate device leading me to think that using a cube on the blade isn’t as straight forward as we’ve been believing.
It’s difficult to photograph the goniometer results because you need three hands to do it, or a tripod and the camera set to a timer. I was just using my phone camera, so I’ve got it slightly tilted in the photo showing the belly of the blade which is why it reads slightly differently from side to side. That is truly just my tilting the device while taking the photo. Here is the belly of the blade reading right around 15° per side:
I find the cube to be hard to use for repeatability due to what you say. The goniometer seems more accurate. Based on your clip view at the tip I would have predicted a more obtuse angle at the tip (if I am thinking straight). Did the goniometer verify that ? Can you try it again with a better knife rotation angle vs. the clip ? I do not have a goniometer.
Yes, in both positions I tried, where the stone made a path through the marker that was equidistant from the edge (by eye) through the length of the blade, the tip was about 1° degree more obtuse than the straight portion of the blade. Are you asking that I use the clip method, sharpen the knife and then measure the sharpened angle?
I’m not sure that you can mount the knife using one method, then check it with the ‘O’ ring, to see if it is accurate or not. Just because, they don’t line up, doesn’t mean the ‘O’ ring is not accurate… it may just be another (different) position for sharpening the blade.
So, yes (after seeing your other post), the only way to check if the ‘O’ ring method works, is to set the blade using that method, sharpen it and then measure the angle along the blade.
You can see clearly in the last image that the stone tracks from full bevel to deep into the shoulder as it approaches the tip, which we know would result in a wide bevel and a lower angle.
Yea, I did that (with the marker) and got the same thing. Oh well, fun while it lasted. (It still could be used as a reference to where the blade is positioned?)
What was interesting is how far down I had to tip the knife to get it to clear the marker evenly along the entire length. Angle cube shows it’s tilted at about 39 deg.
I just tried measuring the rotation of the stone on the rod as it travels down the length of the blade with the knife in the same position as the above photos. There is approximately 5° degrees of rotation from the middle of the blade to the belly. The images below aren’t very clear but give some idea as to how much the stones rotate:
Re axial stone rotation, it seems logical that rotating a flat stone against an edge would change the angle because the edges of the stone are farther away from the rod than the center of the stone. Rotating to either lead edge or trailing edge should decrease the bevel angle, as the rod is pushed away from the knife edge.
The curved stone should have less or no effect. I always strive to hold the stone flat against the edge by pressing both thumb and index finger toward the face of the blade. By grasping the block near the bottom, differences in pressure seem to let the stone naturally find flat-against-flat contact.
The difference in the width of the bevels in Clay’s loupe photo may be due to the change in thickness at the shoulder of the bevel. Unless the maker has really tried to uniformly taper the tip, it’s natural for the tip to be thicker than at points lower on the blade.
In my measurements, I too found large apparent differences in 'Cube readings along the tilted blade. They didn’t jive with the measurements I took using the Sharpie method of matching the bevel angle, so I concluded that they weren’t valid.
I have tried the O-ring type method, but concluded that it simply won’t match the curve in most cases (disclosure: I never tried tilting a blade so radically). Generally, I try to imagine a line drawn from and perpendicular to the center of the belly and position the knife to align this with the axis of the rod rotation. Then I use the O-ring method to confirm that the tip will be at a reasonable angle. If not, I will adjust forward or back accordingly, knowing that the belly bevels will be off by a tiny amount.
My customers are friends and family who are getting the service for free, so they don’t dare complain about less than perfect bevels. If someone was paying me to sharpen their $499 chef’s knife, I’d probably rethink my methods.
That difference in bevel width is really small, only about .1 mm or 0.0039". I’d been thinking the same thing about the shoulder thickness. It turns out that difference in thickness is pretty high: 0.008" in the middle of the blade and 0.021" at the tip. So the angle is 1° more obtuse at the tip yet the bevel is 0.004" wider.
Setup knife with o-ring as best as I could see visually
Put 6 marks on knife for cube measurement with bubble level taped on (Bubble Cube)
Reground to burr at 13 DPS bar setting (did not bother verifying the Bar with the cube)
Brought it up thru 600 stone (50 passes each side)
Measured angle with Bubble Cube at 6 marks (tried as best as I could to "not" bias my reading - by taking multiples, etc; most difficult on the curves but the Bubble Cube helped a lot)
Results (pics below):
PT 1 11.7 deg
Pt 2 11.7 deg
Pt 3 11.6 deg
Pt 4 11.3 deg
Pt 5 10.6 deg
Pt 6 10.6 deg
Noticed:
Slop between rod and stone hole changed readings by ~0.5 deg
Twist of stone at a point (especially curves) changed readings by ~0.5 deg
If you carefully sharpen straight up and down with the Bubble Cube fixed to stone (which verifies position) the reading changes very little
While in step 3 if you move take the stone off the knife and come back to the same spot (which Bubble Cube verifies) you get the same readings
Conclusion:
There are enough error sources at work here between the optimal o-ring setup, sharpening and measuring to account for any variation against the ideal case (perfect truncated cone in Yan’s work) (ie. the curved bevel). In my opinion you cannot verify the ideal case with this setup - we need to remove known error sources. It is also my opinion that it is heading in the right direction and does correlate with Yan. A diamond coated magnetic steel rod with an accurate flat (for Bubble Cube) would be my next choice. Do you happen to have one of those from your prototyping phase ?
I just noticed that I must have repositioned the knife after the o-ring setup in search of an even better o-ring sweet spot but no position changes were done between sharpening and measuring.
The curved portion is the correct distance from the center of the bore hole to match up with our flat stones, so the geometry should be similar. The channel on the back could fit a piece of bar steel so that the Angle Cube could easily attach. We could use the PSA diamond films over the curved portion to do actual work.
Interesting, if the radius of the curve is concentric with the rod/hole we might be able to maximize the vector orthogonally to the rod. In other words, the stone point contact to the knife edge will always be perpendicular to the rod for flats and curves. I’m not sure though WDYT. Also, a machinist among us should be able to help with getting a fit of the rod to the hole which would eliminate any slop (at least for testing purposes).
Hey ET, can you work on that part (millionths to you, arc seconds to me) ? No offense intended. We also need an error budget analysis.
Doing it with just the rod might help concept verification but won’t help for actual usage.
BTW, what do you mean “print” this ? Do you have a 3-d printer ?
That’s useful practical information, Clay! Can you give us a photograph of how exactly you got the angle cube plumb? And I’m also curious which loupe you used and how you made a photograph through it (or was it a USB loupe?)
Regarding the alignment guide, I was thinking it would be nice if it used standardized distances between the lines. Say centimeters or – for Americans – parts of inches.
I have to ponder your results from the posts at 1:15 pm and 1:25 pm. But the problem with the O-ring method as well as the calculations I made in my blog post on this subject is that it doesn’t take the “planes” into account. By that I mean it only partially takes the rotation of the stone into account. Anthony’s method does.
I’m reading this subject sequentially – you guys did a lot of work yesterday – and now see more people brought up the axial stone rotation. Redhead, you clearly showed there are multiple sources that make practice deviate from the optimal theoretical situation. That’s good to know.
That would definitely take some variability away. But not all. And how do you make sure the rotation of the stone doesn’t influence the angle reading (that’s similar to a question I also asked in the O-ring topic).
Mark: I think that the purpose of the radial face is to eliminate rocking as a variable. So long as the radius of the stone is constant, the angle will be constant, regardless of stone rotation. Or maybe I’m not understanding your question.
Clay: Can you make a prototype on a 3-D printer? ABS ought to be hard enough to back up film abrasive, and cheap enough to have a limited life (inexpensive replacement).
Maybe the steel plate for the AngleCube attachment needn’t be full length. Use the lower half to add an area for finger placement and protection?
(It still could be used as a reference to where the blade is positioned?)
