Tormek Community Forum

As you know, I am a knife sharpener and not a chisel sharpener.
a few years ago, when I got my T7, I had a customer who asked if I can sharpen chisels. I was at this time proficient with the T7 on knives professionally.  I thought I could add an extra string to my bow by sharpening chisels too. So, I looked at the videos for the Tormek T7 for sharpening a chisel. I thought I did a great job. Until the builder told me that I had not added an extra bevel from the main edge that the Tormek had made.
( Why did the video not do or show this )
Consequently, I have been turning away chisel work. 
The Video shows that you just need to sharpen one angle and not to put a second edge at a slightly higher angle.
I have asked builders and some woodworkers if the chisel should have one angle and one edge or one angle and 2 edges. They all said the chisel should have a one angle and a small bevel on the end of the chisel. 
Can I ask why all the tormek training videos do not tell you this???

Excellent question, Bob.

The second bevel, often called a secondary bevel or micro bevel, is more useful with hand sharpening than with the Tormek. The secondary bevel is added so that the sharpener only has to sharpen (remove steel) from a very small area of the blade, generally around one thirth second of an inch instead of across the entire bevel. When sharpening with bench stones, the labor saved is considerable. When the edge needs to be resharpened, only the secondary bevel touches the sharpening stones. Eventually this tiny bevel becomes larger,, and it is time to regrind the main bevel.

The practice is very ingrained with woodworkers. However, with a Tormek, the grinding is easy enough that the secondary bevel is unnecessary. Tormek has graditionally recommended a single bevel. It is easy enough to add a secondary micro bevel with the Tormek. After the initial bevel is ground, just raise the jig by one turn with the microadjust and use the wheel with the stone grader set to fine. Finish up with the leather honing wheel as usual, and, presto, you have a secondary bevel!

If the customer requests and or expects a secondary bevel, I would just follow his wishes. The ironic thing is that if the customer plans to do minor sharpening between grindings, starting from no secondary bevel will give him a smaller base, which means longer between grinding. So.....give the customer what he wants and collect your fee. With either method you are giving him a superior edge.

Ken

Just to add to what Ken said, let's suppose that a bevel angle of 25° is desired on a chisel. Let's consider three options:

Option A: Grind the entire bevel at 25°, with no secondary bevel.

Option B: Grind a secondary bevel 25°, which would require that the rest of the bevel, that is the primary bevel, be ground at something less than 25°. This will work well for a user who wishes to be able to sharpen the chisel later by hand. As Ken said, he will have an easier time of it as he will have less steel to remove. He will need to grind only the secondary bevel.

Option C: Grind the primary bevel at 25° and the secondary bevel at something more than 25°. This means the chisel will not have a 25° angle where it counts, at the tip. If this is what the user desires then he could request that the chisel be sharpened at that smaller angle, say 20°, and go with Option A or B.

Note that if the user is also a Tormek user, there is no need for a secondary bevel as all sharpening will be done on the Tormek. The Tormek user manual mentions this.
 

Bob,

Just this week I downloaded a new DVD which would be useful for you. Does your sharpening library include Ron Hock's book, The Perfect Edge? (If not, it should.) Ron Hock manufactures plane blades and associated items. He is an expert in the field with decades of experience. He has just done a DVD (90 minutes) related to sharpening. He discusses sharpness in depth, tool steel, heat and cold treating, and then goes into sharpening. The video focuses primarily on woodworking tools rather than knives. However, if a woodworker is willing to pay you to sharpen chisels, this information is valuable to you in real money.

I purchased it, and recommend it highly. It is available in DVD form directly from Hock Tools or as an online download from Popular Woodworking. I did the download. I did not realize that "downloadable" meant that after I logged in, I could watch it as many times as I wanted online. (I had expected to download it directly to my ipad and watch it when no wifi was available.) In spite of this inconvenience, the information is solid, and well worth the price $25 or $30 US.

There is a short free preview on the Hock Tools site. I suggest you make sure the MP4 format is compatable in the UK.

Ken

The VLC media player, available for both PC and Mac, plays just about any video format you can throw at it, including MP4 and DVD's.  It even plays audio files like Wav and CD's.  You have to be trying to play something pretty obscure if VLC won't play it.

I've used it for many years.  It's a great media player and it's free.

http://www.videolan.org/vlc/index.html

Grepper, you're a handy guy to have around. :)

Ken

While sharpening chisels on the Tormek, a micro bevel won't be needed at all. In the opposite a micro bevel will take away one of the biggest benefits the Tormek offers. It's the ability to do the honing work freehanded by using both edges that the hollow grind produces as registration areas on the flat honing medium. The honing work after the Tormek sharpening is absolutely necessary to get the chisels best performance and the best edge durability. Doing this by using the hollow grind is a quick and foolproof freehanded action.

I'm used to sharpen my chisels for years this way and am rather sure that they perform at their best.

Klaus

I don't think the real issue of this topic is whether or not a micro bevel is necessary. The situation is that the customer expects a micro bevel, and the customer is paying the bill. Right or wrong, the customer wants a micro bevel.

Ken

Basically I agree, Ken.

But if you explain to the customer that in this case a micro bevel is a disadvantage for himself, he possibly will think about it. The customer himself will enjoy the ability to hone the chisel many times until a new sharpening on the Tormek will be needed by taking advantage of the hollow grind. It's so much easier to refresh the edge this way than to refresh a micro bevel freehanded.

Klaus

Klaus,

I am an old chisel sharpener, as I suspect you are, too. I think we are making the presumption that Bob's customer, the builder, would prefer to do the intermittent sharpening himself. This is not always the case. I know several carpenters who do not sharpen chisels. They buy inexpensive new "sharp" chisels and use them until they are "dull". At that point, or sometime later, they discard them and buy new "sharp" chisels. I agree with what you are thinking; this seems sinful.

As a knife sharpener, Bob has another set of skills, sharpening knives. With some study and practice, he can certainly become a proficient chisel (and plane blade) sharpener. At this point, I do not think Bob has acquired the knowledge to explain the situation to the builder. Frankly, I would not encourage the builder to do his own sharpening. I would sharpen his chisels for a fair business price, and offer an ongoing discounted price if he wants regular sharpening.

The builder may use contract labor, and have to provide tools for his workmen. In that case, he might prefer to contract the sharpening to a professional instead of paying his workmen to do a hit or miss job. If I were in Bob's situation, I would quickly become skilled sharpening chisels and plane blades, explain the micro bevel situation to the builder, and offer to sharpen them however he wishes. If Bob can get the follow up work, that's nice work, quickly done, and a nice revenue stream.

I am retired, and have never sharpened professionally. If I had a chance for this kind of work, I might be tempted...... :)

Ken

Thanks Ken and all the guys, I now feel confident, as a result of your dialog, to go ahead and sharpen chisels. I honestly thought I was doing it wrong because of the builder. I now know it was the lack of experience to confidently rebut what he was saying. I now have the knowledge and I expect to add more value to my service now.

Here is a new one Ken.
A friend of mine who is a plasterer, had a couple of bad nicks in his plastering trowel, ( Must have caught a nail or badly used it )  he knows I am a knife sharpener and also has the Tormek T7  as well as other machines, so he asked me if I could sort out the nick.

You know, I tried so hard on the T7 to grind as opposed to sharpen this thing. I actually managed accidentally to put a sharp edge on it. However, he is so happy the edge has gone and he says the plastering is so much smoother because of it.

So, there is a new use for the amazing T7.

Any of you guys had an experience similar with a tool or object you wouldnt have thought possible.??
 
 

That should have said
I also HAVE the T7
Not HAS.
Whoops.

Bob,

Good work with the plastering trowel. It makes me think of an early topic I found on the forum. The poster asked if we can sharpen drill bits with the Tormek. Jeff, the founding moderator replied, "Not yet". I have long thought that the primary constraint with the Tormek is a timidity of imagination.

We now have the DBS-22, which does an amazingly versatile job with drill bits. Compared with the earlier jigs and accessories, Tormek's engineers have done some astounding work. I am convinced that their chief constraint (which forum members do not have) is the discipline imposed by staying afloat in the business world.

One of the primary shifts I have seen in the forum since I joined in 2009 is growth from just using the Tormek well as designed to modifying and adding to both the components and techniques. The really exciting part is the compounding effect added by sharing these ideas with other members.

Dutchman posted his grinding angle booklet several years ago. His inspiration has sparked a whole movement in how we set up bevel angles.

Robin Bailey designed and sells an oversized universal support bar which has expanded the scope of possible work. Robin did this to solve a problem sharpening cleavers and knives.

Herman developed his very versatile small knife platform. This originated from a poster with a problem sharpening small knives. Herman and others have used this jig from everything from very small knives to machetes. One of these homemade jigs should be part of every Tormeker's kit. We are far from achieving its full potential.

The list goes on and on. We are a global team. Ideas bounce around from Australia to the Czech Republic, to France, literally all over the planet, picking up refinements along the way. The latest idea I am presently watching is a you tube from Sandor, a new member (and very experienced and innovative knife sharpener) from Slovakia. His machine for testing edge retention by cutting rope is truly amazing.

Bob, buckle your seat belt; I believe we have only seen the tip of our sharpening innovation iceberg.

Ken

Elden has posted previously about "sharpening" drywall knives. What you are calling plastering knives. The edge must be straight for the tool to work properly.

As to the issue of the micro bevel, or secondary bevel, on the carpenter's wood chisel. I would think that if the carpenter wishes to be able to sharpen the chisel himself with just a bench stone then he would want the secondary bevel to make that job easier. Once the chisel has been sharpened that way a few times it will become more and more difficult. This is when it will need to be taken back to the Tormek. Repeat business!

Quote from: Waterstone on February 07, 2017, 03:36:49 PM
While sharpening chisels on the Tormek, a micro bevel won't be needed at all. In the opposite a micro bevel will take away one of the biggest benefits the Tormek offers. It's the ability to do the honing work freehanded by using both edges that the hollow grind produces as registration areas on the flat honing medium. The honing work after the Tormek sharpening is absolutely necessary to get the chisels best performance and the best edge durability. Doing this by using the hollow grind is a quick and foolproof freehanded action.

I'm used to sharpen my chisels for years this way and am rather sure that they perform at their best.

Klaus

In fact, by resting the chisel on a fine stone at the two touch points created by a hollow grind (the edge and the other end of the arc described by hollow grinding) you are in fact honing a very fine micro bevel without realising it!  So it's not the opposite benefit as you've stated, it is in fact a benefit of hollow ground tools in general (not specific to the Tormek, rather specific to any wheel based grinding system that yields a hollow grind).  The benefit is simply that a hollow ground bevel creates two touch points, that in turn means the bevel wont rock when you're moving it on a fine hand stone, in fact it positively registers on those two "high points" and that presentation angle certainty allows a uniform micro or secondary bevel to be created at the very tip of the edge.  This may be so small that you don't see light reflecting off it so it doesn't seem like a micro bevel but that's exactly what it is and if you go steady each time you re-hone it, you can go for months without regrinding the primary bevel.

I strongly recommend this rather than Tormek's manual approach which suggests regrinding the primary bevel every time.  The reason is that with some plane blades (eg Lie Nielsen or Veritas tools) they often have super hardened blades and regrinding the entire bevel is not a simple or quick task.  It's a heck of a long time of finger aching grinding whereas if you'd gone with even a small micro bevel you'd get the job done in no time.

Micro bevels are a good thing on many levels and I'm not surprised your customer is asking for one :-)

Interesting point, Rob.

I think we have two different situations: We have the long established Stanley and Record blades, which would have been the norm when Torgny wrote the handbook. They are thinner, and no problem to sharpen using the traditional Tormek method.

We also have the more modern premium planes, which are considerably thicker and made of a more sophisticated alloy. With these "super blades", a micro bevel would be most welcome.

Surprisingly, recent handbook editions have not mentioned this.

Ken

Quote from: Rob on February 12, 2017, 09:41:09 PM
you can go for months without regrinding the primary bevel.

This of course depends on what you're doing with the chisel. A rough carpenter is bound to be tougher on a chisel than a cabinet maker. In cases like this the carpenter may want a primary bevel at an angle a few degrees smaller than the secondary bevel so as to make resharpening on a bench stone faster. He will be making contact at only one point, not two, to take out the nicks that resulted when his apprentice used it on a nail.

Good point, Herman.

In our Walter Mitty idealized lives, we would be using our chisels only for things like dovetailing drawers in Queen Anne highboys. In real life, most of my chisel work has been of a rougher variety. Since purchasing my Tormek,I rarely use micro bevels. If I ever have to revert to using my old waterstones, micro bevels will return.

I have found a chisel edge will last longer with a steeper bevel, 30°, for rough work. I ground a long partial 30° bevel on a chisel before realizing that I only needed to gring a micro bevel.

Talking with the three carpenters who worked on my house over the years, I was surprised to learn that only one of them ever sharpened his chisels, and then only rarely. They are competent carpenters, who work primarily with power tools.

Ken

Quote from: Rob on February 12, 2017, 09:41:09 PM

In fact, by resting the chisel on a fine stone at the two touch points created by a hollow grind (the edge and the other end of the arc described by hollow grinding) you are in fact honing a very fine micro bevel without realising it!  So it's not the opposite benefit as you've stated, it is in fact a benefit of hollow ground tools in general (not specific to the Tormek, rather specific to any wheel based grinding system that yields a hollow grind).  The benefit is simply that a hollow ground bevel creates two touch points, that in turn means the bevel wont rock when you're moving it on a fine hand stone, in fact it positively registers on those two "high points" and that presentation angle certainty allows a uniform micro or secondary bevel to be created at the very tip of the edge. 

Rob is correct!  :) From the attached drawing it is clear that flat honing of a hollow grind primary bevel (25°) adds a secondary microbevel with an edge angle of 31° (in this case).

For chisel cutting performance the thickness of the microbevel is important as mentioned by Herman. 

Jan

Quote from: Ken S on February 13, 2017, 12:25:16 PM
Talking with the three carpenters who worked on my house over the years, I was surprised to learn that only one of them ever sharpened his chisels, and then only rarely. They are competent carpenters, who work primarily with power tools.

Likely the only hand tool they use on a regular basis is a utility knife. They carry it in their tool belt and replace the blades when they get dull. If they have a chisel it's probably buried in a tool box and not carried in the tool belt. The primary reason they don't use it is because it is dull. And the reason it's dull is because it's so hard to sharpen by hand. Yes, a cabinet maker can sharpen his by hand, but a rough carpenter can't because the chisel gets too much rough use.

Ken, that chisel you mentioned that you sharpen at 30°. If you instead sharpen it at 20° you will find that the edge very quickly crumbles upon heavy use. If you then grind that tip to 30° on a bench stone (a secondary bevel) you're be back in business in a short time.

You make good points about the nature of the use chaps.  I was thinking of cabinetry rather than 1st or 2nd fix carpentry.  And funnily enough, the chippies that did my house could frequently be seen with an upturned belt sander in a vice, roughing a dinged blade back to a useful state.  Those chisels had no idea what a micro bevel looks like!!

I have also done a fair bit of house carpentry myself having built/renovated 3 houses now.  The first time I did this I was kind of apprenticed to a close friend who was at that time a professional carpenter.  He taught me to hone a micro bevel on a stone with one of the old honing guides.  We used to clamp it to the end of a saw horse and then sit with the saw horse between knees (end on) and hone away.  We only ever did that procedure just before we were about to do careful work on either window frames or other finer pieces, often related to kitchens etc.

I know carpenters that use angle grinders to sharpen their chisels!!  Makes me shudder just thinking about it :-)

Quote from: Rob on February 12, 2017, 09:41:09 PM

In fact, by resting the chisel on a fine stone at the two touch points created by a hollow grind (the edge and the other end of the arc described by hollow grinding) you are in fact honing a very fine micro bevel without realising it! 

Good point Rob.

In fact you'll get a small honed area at the very edge that looks like a micro bevel. It's a question of definition after all. To my understanding a micro bevel or secondary bevel is steeper than the primary bevel. If the latter one is ground to 25 deg, the secondary bevel will be 30 deg. or so.

On the Tormek the things are different. If the blade was ground at 30 deg. (what is my most used primary bevel on chisels), the honing will keep this angle. The "micro bevel" will be exactly 30 degrees. Why? The 30 deg. hollow grind that was produced on the Tormek will cause the very bevel tip to be less than 30 deg. due to the hollow geometry. When it will be honed by using both "edges" of the hollow, the edge tip will be "corrected" to be exactly 30 degrees. It's easy to test it.

So while I agree with all of your comments, I doubt that this honed bevel can be called a micro bevel in the usual sense (steeper angle).

Klaus

Quote from: Waterstone on February 14, 2017, 06:51:51 PM

On the Tormek the things are different. If the blade was ground at 30 deg. (what is my most used primary bevel on chisels), the honing will keep this angle. The "micro bevel" will be exactly 30 degrees. Why? The 30 deg. hollow grind that was produced on the Tormek will cause the very bevel tip to be less than 30 deg. due to the hollow geometry. When it will be honed by using both "edges" of the hollow, the edge tip will be "corrected" to be exactly 30 degrees. It's easy to test it.

Klaus

Klaus (Waterstone),

   The content of your comment has been a lengthy hotbed of discussion in the past on this forum!  :) I imagine will continue to be debated from time to time. Notice Jan's comment above.

Addendum:
   Here are a couple of threads in regard to the effects of hollow grinding as ground by the Tormek when the angle is set by the Angle Master

http://forum.tormek.com/index.php?topic=2413.0

http://forum.tormek.com/index.php?topic=3052.0

Thanks a lot, Elden.

It was an interesting read for sure. I completely agree with the conclusion that a hollow ground edge doesn't necessarily has to be weaker than a flat ground bevel. If you compare a 25 deg. flat ground bevel with a hollow ground bevel that has 25 deg. at the very tip, the hollow ground bevel indeed is stronger, no doubt.

However the Tormek angle master doesn't compensate the hollow when adjusting an angle to my experience. If it's adjusted at 30 deg. I get an angle of exactly 30 deg. measured from the edge tip to the 2nd end of the hollow. You easily can test it. If the stone doesn't have the full diameter, it's even easier to see because of the more pronounced hollow it creates. So I don't get 30 deg. at the edge tip where I want to have it.

To get the wanted angle at the edge tip I've to set the angle master at 35 deg. OR I hone the 30 deg. hollow ground bevel in the above mentioned way by using both edges of the hollow.

Klaus

This topic is the forum "How many angels can dance on the head of a pin?" debate. We really should be debating it in Latin. :)

Joking aside, I believe the hollow ground issue is a left over from the 1970s when six inch (150mm) diameter grinders were the standard in most home workshops. (I still have mine.). This diameter produced a very obvious hollow grind. I have compared freshly ground chisels from the T4 and T7. I find it difficult to see a difference by eye. I can see that each is hollow ground, however, the amount of hollowing seems miniscule.

The numbers on the Anglemaster are not sacred. If anyone wants to use a different angle, the Tormek Board of Standards will often grant a variance.  :)  In fact, manufacturers of premium chisels with A2 steel recommend using 30°. Part of the skill of a sophisticated sharpener should be knowing when to alter the standard bevel angle to suit the work. This should be as natural as a baker knowing how to alter the recipe for baking conditions.

We have carving, paring, firmer and mortise chisels. We have chisels made with different amounts of quality standards in alloy and heat treating. We have harder and softer woods. We have different grain directions. Some chisels are pushed by hand, some by wooden mallet or steel hammer. The variable most of us overlook is the width of the chisel. Leonard Lee discussed this in his sharpening book. ( I consider Leonard Lee's book the first and primary book in every sharpener's library.) A wider chisel spreads the stress over a greater area. Therefore narrow chisels should have a somewhat steeper bevel angle.

These factors apply regardless of whether the bevel is flat, hollow or convex.

Ernie Conover, a prominent woodworking writer and teacher from Ohio, US, recommends a useful compromise. He just adds three degrees to the bevel angle to compensate for the hollow grind. Klaus, your thirty degree setting should work just as well and probably extend the sharpness period.

Please forgive my vernacular; my Latin is rusty.

Ken

Quote from: Ken S on February 15, 2017, 12:47:17 PM

I have compared freshly ground chisels from the T4 and T7. I find it difficult to see a difference by eye. I can see that each is hollow ground, however, the amount of hollowing seems miniscule.

Ken,

Jan shows above with his excellent sketch, that the influence of the hollow isn't that miniscule. The difference between the ground angle and the one at the blade tip is about 5 degrees. I don't want to have this kind of deviation. My bench chisels work very well with 30 degrees, with 25 the edge durability will be bad. I've tested it.

You're completely right, that there are many different types of chisels and blade materials. My bench chisels for general purpose work best at 30 deg., the paring chisels are working good with 25 deg. and the mortise chisels want to have 35 deg. at least. But that's not the point to my eyes. Regardless the angle you want to have on the chisel you are grinding, you want to have it as exactly as possible. 5 deg. more or less won't do it.

Klaus

Klaus, the angular difference between the chord and tangent depends on blade thickness.

Jan

Klaus,

I hold Jan's math and technical skills in high regard. I certainly do not doubt his conclusions. I also do not doubt your experience.

How did the 25° become such a sacred cow? How did it become annointed for both chisels and plane blades?

I would guess that a very long time ago, in the era of oilstones, someone chose it as an easy number for students and apprentices to remember. When sharpening was a laborious and frequent chore, long before thinner blades and microbevels, my money would be on the work being delegated to the apprentices.

Twenty five degree bevels have long been a part of our catechism. I vote for following our experience and changing our bevel angles to whatever works best.

Ken

Guys, my drawing posted above is correct but my interpretation of it was not. Sorry for that!  :-[

The angle 31.2° is the heel angle of the chisel blade and not the chord angle. So the actual angular difference between the tangent and the chord is only 3.1° which is the half of the difference between the heel angle and the edge angle (31.2° - 25°) / 2 = 3.1°.

So, flat honing of a hollow grind primary bevel (25°) adds a microbevel with an edge angle of 25° + 3° = 28°.

Jan

Quote from: Waterstone on February 14, 2017, 06:51:51 PM
On the Tormek the things are different. If the blade was ground at 30 deg. (what is my most used primary bevel on chisels), the honing will keep this angle.

Not if you followed the usual procedure of establishing the 30° angle with the Angle Master. The honing on a flat bench stone where both the tip and the heel of the (hollow ground) bevel touch the stone will produce a micro bevel at the tip that's somewhat more than 30°. How much more depends on the radius of the grindstone used to produce the hollow grind and on the thickness of the chisel.

Quote from: Ken S on February 15, 2017, 03:38:09 PM
How did the 25° become such a sacred cow? How did it become annointed for both chisels and plane blades?

I recall experimenting with angles between 20° and 30°. I can tell you for sure that 25° is a good compromise in my experience. 30° is too blunt for work with just the hands using no mallet, 20° is too acute for mallet work as the edge breaks off.

If I have to chisel out a mortise for a door hinge I do some of the chisel work with a mallet and some by hand. But I'm working with pine or the like. If it were oak I'd probably want two chisels, one at 20° for the finer hand work and one at 30° for the rougher work with a mallet.

Quote from: Jan on February 15, 2017, 06:14:36 PM
So the actual angular difference between the tangent and the chord is only 3.1° which is the half of the difference between the heel angle and the edge angle.

You know, when I first saw that it seemed too large a difference and I intended to look over the math and make a drawing to scale to confirm it.Just never got around to it.

Quote from: Waterstone on February 15, 2017, 08:31:05 AM
However the Tormek angle master doesn't compensate the hollow when adjusting an angle to my experience. If it's adjusted at 30 deg. I get an angle of exactly 30 deg. measured from the edge tip to the 2nd end of the hollow.

If you have a measuring method precise enough to reveal the difference, you will notice it. Of course, the precision of the Angle Master is a limiting factor here, too.

Try it with "blade" that's much thicker. For example, a one-inch wide strip of quarter-inch plywood. Scribe a line to simulate the hollow grind and cut it out. Measure the angle with the Angle Master and also with a protractor or speed square. Study Jan's sketch.

There is a simple desk top exercise which can help to understand the angles discussed here. Print an enlarged copy of my sketch and use a plastic school protractor to measure the angles. 

Herman, thank you for your explanatory comments, appreciated.  :)

Jan

I have a hobby interest in machine shop measuring. (This study was instrumental in the development of the kenjig.) A circle contains 360 degrees. Each degree contains 60 minutes. Each minute contains 60 seconds. There are other ways to measure angles, however, they are outside of this conversation.

Like any measuring instrument, the Anglemaster has its measurement tolerance. Any measuring tool with one degree marks as its smallest is probably accurate to plus or minus one degree at best. This is a fact, not a criticism. This tolerance is more than accurate enough for our purpose. After all, many a master Viennese cabinetmaker sharpened his chisels by hand, or had his apprentice do so, and produced very fine furniture.

For more precise measurement, precision blocks are used, for both angles or flat measurement. A hardened and ground steel parallel or angle block may have an accuracy of plus or minus .0001" or only a few minutes or arc. These are adequate for shop floor work. For inspection or laboratory work, accuracy must be considerably tighter, sometimes in millionths of an inch or seconds of arc.

The Tormek TTS-100 uses the principles if exact measurement. Where is excels is in repeatability. The distance of the two holes used to determine the Distance between the universal support and the grinding wheel remain constant. (The two wheels compensate for stone wear.) The three protrusion slots keep the Protrusion of the tool constant. This level of consistency allows us to sharpen with a minimal amount of steel removal.

The kenjig and other similar devices borrow these principles from the TTS-100 and reduce the added error of repeat measuring. In fact, I use the TTS-100 for chisel and plane blade set up. I use a piece of label tape in one of the protrusion slots with marks at several degree positions. I used the Anglemaster for the initial set up, but have rarely used it since. Set up this way is fast and consistent.

Herman makes a good point about bevel angles. Today most woodworkers have few chisels compared to the past. This is unfortunate. We live with compromise bevels instead of having both twenty and thirty degree bevel chisels. As Scotty said in a Star Trek movie, "The right tool for the right job."

Ken

Quote from: Jan on February 16, 2017, 10:10:48 AM
There is a simple desk top exercise which can help to understand the angles discussed here. Print an enlarged copy of my sketch and use a plastic school protractor to measure the angles. 

Yes, but that doesn't involve the Angle Master so it can't convince that the angle ß measured by the Angle Master is indeed the same as the angle you've labeled 25° in your drawing.

QuoteHerman, thank you for your explanatory comments, appreciated.  :)

It is you, Jan, who has brought precision measurements to the forum.

Quote from: Ken S on February 16, 2017, 12:03:47 PM
Like any measuring instrument, the Anglemaster has its measurement tolerance. Any measuring tool with one degree marks as its smallest is probably accurate to plus or minus one degree at best.

The accuracy of the Angle Master is limited by the user's ability to properly align it with the grindstone and the back of the chisel blade. Of course, this also limits the precision. I would estimate its error at ±2° for a typical carpenter's chisel.

QuoteThis tolerance is more than accurate enough for our purpose.

I agree.

QuoteAfter all, many a master Viennese cabinetmaker sharpened his chisels by hand, or had his apprentice do so, and produced very fine furniture.

It would be interesting to see how precise and accurate they were at this skill. An archaeology project!

 Herman,

Many years ago I saw Duncan Phyfe's tool chest on display in Williamsburg. It was behind glass. I would have enjoyed examining his bevel edges. I suspect many of them would not pass our rigorous inspection, although he did make acceptable furniture. :)

Ken

In the topic "hollow vs flat grinding thoughts" you can find the following statement:

Quote from: Stickan on April 03, 2015, 03:50:10 PM
The angle master WM-200 is very good and are measuring the tip of the edge. It is compensated for the hollow grind. If you use a regular "angle setter" or a protractor you will fine that the degree will indicate that its not the same as the anglemaster. A protractor are not compensated for a hollow grind but for a flat surface.

I am wondering how to understand that the AngleMaster is compensated for hollow grind.

In the first picture the flat lower edge of the angle setter touches hollow grind bevel. In this situation some compensation is imaginable, because the chord angle can be slightly lowered to get the intended edge (tangent) angle.

But in the second picture the flat lower edge of the angle setter touches a flat back of a plane iron and there is no need for a compensation as it was in the previous case.

What is your opinion?  ;)

Jan

Herman and Jan,

I agree with what you are saying, even the plus or minus two degrees with the Anglemaster. My concern is that many of our members and guests may read this topic and wrongly conclude that the Anglemaster is an inaccurate tool. It is not; it is well within the accuracy needs for its function.

Leftover from my darkroom, I have an Eastman laboratory thermometer. It is mercury and guaranteed to be accurate within a quarter degree Fahrenheit from 66 to 75°. It was a laboratory  essential. For deciding which coat to put on the children before school, it is essentially worthless. Sharpening a chisel is not a job requiring the skill of a tool and die maker.

The Anglemaster is not a fixed tool. It can be easily adjusted to suit the user's needs. It is leagues ahead of the Anglemaster-100, which it replaced (and is still standard equipment on some of the clones.) I have stated before that the Anglemaster is much easier to use in very good light. This recommendation has been in the handbook for many years.

Ken

Quote from: Jan on February 15, 2017, 06:14:36 PM
Guys, my drawing posted above is correct but my interpretation of it was not. Sorry for that!  :-[

The angle 31.2° is the heel angle of the chisel blade and not the chord angle. So the actual angular difference between the tangent and the chord is only 3.1° which is the half of the difference between the heel angle and the edge angle (31.2° - 25°) / 2 = 3.1°.

I've gone over this, Jan, and tried to replicate what you've done. I can't seem to get it to work out. I don't know how you got the 31.2° and I don't understand why you think you have to divide the difference by two. It seems to me that the difference is what we're interested in. I understand the tangent angle, I understand the chord angle. I don't understand the heel angle.

Quote from: Jan on February 16, 2017, 04:16:31 PM
I am wondering how to understand that the AngleMaster is compensated for hollow grind.

I wouldn't say it that way. I would say that there is no compensation. Rather, I'd say that the Angle Master measures the angle at the tip, and the fact that there's a hollow grind means that if you measure the angle with a protractor you won't get the same value as you do when you measure with the Angle Master.

QuoteIn the first picture the flat lower edge of the angle setter touches hollow grind bevel. In this situation some compensation is imaginable, because the chord angle can be slightly lowered to get the intended edge (tangent) angle.

But in the second picture the flat lower edge of the angle setter touches a flat back of a plane iron and there is no need for a compensation as it was in the previous case.

The only reason the it touches a hollow grind bevel in the first picture is because it's touching a knife whose upper side was sharpened with a hollow grind. The illustration is intended to show the difference between a single bevel tool and a double bevel knife. The issue of the difference between a hollow grind and a flat grind is being entirely ignored here. It is, after all, negligible for something as thin as a knife.

Quote from: Ken S on February 16, 2017, 07:57:02 PM
I agree with what you are saying, even the plus or minus two degrees with the Anglemaster. My concern is that many of our members and guests may read this topic and wrongly conclude that the Anglemaster is an inaccurate tool. It is not; it is well within the accuracy needs for its function.

Hopefully, Ken, everyone will realize that every measuring instrument is an inaccurate tool because there is no such thing as perfect accuracy.

I do agree that its precision is well within what's needed. In fact, most of these discussions we have about angle measurements are largely academic and have no practical significance. For example, the difference between a hollow grind and flat grind is insignificant for a 250-mm diameter and most tools. When I tried to duplicate Jan's drawing I drew it using a 1:1 scale and measured a difference of 2° for a 6-mm wide tool and a 250-mm diameter grindstone. As mentioned before, I doubt the Angle Master can be used with this precision. And even if it can, I doubt that anyone is careful enough to achieve it. We just don't care about a 2° difference for anything that we do!

Quote from: Herman Trivilino on February 17, 2017, 04:16:02 AM

Quote from: Jan on February 15, 2017, 06:14:36 PM

The angle 31.2° is the heel angle of the chisel blade and not the chord angle. So the actual angular difference between the tangent and the chord is only 3.1° which is the half of the difference between the heel angle and the edge angle (31.2° - 25°) / 2 = 3.1°.

I've gone over this, Jan, and tried to replicate what you've done. I can't seem to get it to work out. I don't know how you got the 31.2° and I don't understand why you think you have to divide the difference by two. It seems to me that the difference is what we're interested in. I understand the tangent angle, I understand the chord angle. I don't understand the heel angle.

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. The heel angle is always larger than the cutting edge angle.

The reason why I am taking only half of the difference between the heel angle and the edge angle is given by the inscribed angle theorem. Its applicability was numerically proven in my AutoCad drawings.
(http://www.mathopenref.com/arccentralangletheorem.html or https://en.wikipedia.org/wiki/Inscribed_angle#Theorem)

Jan

Quote from: Herman Trivilino on February 17, 2017, 04:29:25 AM

Quote from: Jan on February 16, 2017, 04:16:31 PM
I am wondering how to understand that the AngleMaster is compensated for hollow grind.

I wouldn't say it that way. I would say that there is no compensation. Rather, I'd say that the Angle Master measures the angle at the tip, and the fact that there's a hollow grind means that if you measure the angle with a protractor you won't get the same value as you do when you measure with the Angle Master.

Herman, thank you very much for your responses.  :)

I totally agree with you! The AngleMaster is not compensated for hollow grind. The AngleMaster is compensated for changes in stone diameter.  ;)

Jan

Quote from: Jan on February 17, 2017, 10:11:04 AM
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.

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

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

Quote from: Herman Trivilino on February 17, 2017, 03:38:17 PM
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.

Quote from: Jan on February 17, 2017, 03:57:50 PM
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?

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

Quote from: Herman Trivilino on February 17, 2017, 05:21:36 PM

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

Quote from: Jan on February 17, 2017, 06:21:09 PM
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!

(http://i1291.photobucket.com/albums/b553/htrivilino/Chord%20Angle_zpsy1hnecdg.gif) (http://s1291.photobucket.com/user/htrivilino/media/Chord%20Angle_zpsy1hnecdg.gif.html)

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.

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?

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 :)

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

Quote from: Herman Trivilino on February 17, 2017, 09:56:17 PM

(http://i1291.photobucket.com/albums/b553/htrivilino/Chord%20Angle_zpsy1hnecdg.gif) (http://s1291.photobucket.com/user/htrivilino/media/Chord%20Angle_zpsy1hnecdg.gif.html)

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

Quote from: WolfY on February 18, 2017, 05:34:27 AM
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!

Quote from: Jan on February 18, 2017, 04:41:17 PM
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.  >:(   

Quote from: WolfY on February 18, 2017, 05:34:27 AM

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

Quote from: Jan on February 18, 2017, 06:56:49 PM
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!

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 :)

Quote from: Herman Trivilino on February 18, 2017, 10:04:25 PM

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.   ;)

Quote from: Herman Trivilino on February 18, 2017, 10:04:25 PM

We're talking about a 0.8° discrepancy here!

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

Jan

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

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

Quote from: Ken S on February 19, 2017, 02:26:08 PM
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°.

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

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

Quote from: Ken S on February 19, 2017, 06:44:43 PM

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

Quote from: Herman Trivilino on February 17, 2017, 09:56:17 PMI 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!

(http://i1291.photobucket.com/albums/b553/htrivilino/Chord%20Angle_zpsy1hnecdg.gif) (http://s1291.photobucket.com/user/htrivilino/media/Chord%20Angle_zpsy1hnecdg.gif.html)

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.

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

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

Quote from: Jan on February 26, 2017, 12:44:59 PM
Thanks for the simpler formula, Herman. The quantity 2θ – β is called a heel angle.  :)

Ah, yes, so it is. ;-)

QuoteThe 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.

Quote from: Jan on February 26, 2017, 08:25:16 PM

β = arcsin(t/L) – acrsin(L/D)

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

Quote from: Herman Trivilino on February 26, 2017, 10:46:27 PM
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!

Thank you Herman for the discussion of the results, appreciated!  :)

It is nice to have on hand the important formulas describing grinding on a wheel.

Jan