Matching grinding wheels of different diameter

[wootz]

When you use several progressively finer grinding wheels to sharpen a knife, and these wheels are not of the same diameter, as you move to the next wheel you have to adjust height of the Universal Support to maintain the same grinding angle.
For example, to sharpen a knife I may use 3 grindwheels: Tormek 220 grit SG or SB, aftermarket 800 grit, and 4000 grit SJ or aftermarket.
My T7 wheels diameter at the moment is anywhere between 235 and 250 mm, and aftermarket between 252 and 254 mm.
(If you use Tormek wheels only, this happens as you move between SG or SB and SJ.)

I used to have a funny procedure to adjust the US height as I change wheels, till Jan pointed out inaccuracies in my approach.
Jan started me thinking, and since then I have changed grindwheels matching to calulated absolute values for the US height.

Universal Support height for a given grinding angle can be calculated by Pithagorean theorem, where hypotenuse is calculated by Ton Nillesen's (Dutchman) formula F0, and the other right triangle side is a constant horizontal from the US centreline to the shaft centreline (51 mm in my T7).

I borrowed a sketch from the Ton Nillesen's work to illustrate the right-angled triangle used in the calculations - in red.



Universal Support height from its base to the top of the support bar = the calulated value for the vertical cathetus - constant vertical from the shaft centreline to the US base (i.e. the Tormek's housing top - 29.3 mm in my T7).

Theoretically, I should get exact angle match when I change grindwheels.
Practically, as measured by AngleCube and AngleMaster where applicable, a nice match.
To eliminate the blade width variable, I checked with a knife that is 2.5mm thick at the spine where I clamp it, so its edge is exactly at the jig centreline.
The US height was set with the help of a calipers depth probe.
E.g. having changed a 244mm stone to 253mm, AngleCube relative reading of the bevel angle was 0.1 degree (the AngleCube accuracy is 0.2 degree). A knife sharpened at 15 degrees grinding angle on three stones 244mm (#220), 253mm (#800) and 243mm (#4000), showed exactly 30 degrees on laser goniometer.

When I sharpen a batch of knives at the same angle, and keep the distance between the adjustable stop and knife edge constant as I change knives, I recalculate the US height for a given stone only after truing.
If for whatever reason I change that distance, or have to sharpen at a different angle, I recalculate the US height.

Time-wise it is quick, since I put the formulas in a simple script.

[wootz]

Generally speaking, the above script is just another application of the cosine rule to Tormek that we have been watching on this forum in the succession of:
- Dutchman's tables;
- Kenjig designed to set the grinding angle by distance from US to the stone;
- and this script for setting the grinding angle through US height over the Tormek case.

[Ken S]

Wootz,

Your work is awesome! Using theory you, Jan, and Dutchman (plus Herman) understand and I accept of faith, I think we can interject some low tech kenjigs here.

If we simplify things by using a fixed projection length (the well known by now "139mm" distance). we can calculate kenjigs for different wheel diameters. For example: Start with one for the 600 grit wheel, say 252mm. 250mm would be a logical next jig. Then go down in five mm intervals. Make up a series of kenjigs with the groove cut for the various diameters. Label the jigs, for example, "fifteen degree bevel with 252 mm diameter wheel".

The total length of each of the jigs could match the diameter of its calculations, or, if longer, pencil marks could notate that length.

Doing the calculations for these jigs and the simple woodworking involved in constructing should require very little time. The kenjigs will become part of your permanent Tormek kit.


One of the things I appreciate about this forum is being able to piggyback my simple ideas with high powered math which is beyond my training. Thanks.

Ken

ps We are not limited to any one projection distance. It just simplifies both the math and the set up. In fact, a second projection distance for paring knives with just the regular knife jig or for a Chinese cleaver using Robin's extended universal support would be very useful.

[Jan]

Wootz, thank you for posting your new method for matching grinding wheels of different diameter. 

Your new matching method is based on generally valid geometrical rules and so can be used for grindstones of arbitrary diameters.

From the context it is clear, that your method was developed for the US in vertical sleeve, nevertheless it would not be difficult to modify it for the horizontal sleeve. 

Your basic script for US height calculation works fine. The only difficulty I faced was the decimal marker. In this country we use comma as symbol for decimal marker. I had to change "." for "," in the script and everything was OK. This gave me opportunity to see how nicely your script is written and admire sophisticated string commands.

I have checked your matching method on my T7 for wheels with diameters 240 and 220 mm and can confirm that it works correctly.

Congratulations to the invention of a new procedure for setting the US. Great job.

Jan

[wootz]

Ken, Jan, thank you for kind words, but you are giving me too much of credit.
The maths is not mind-bending, and the script is nothing fancy.

What really deserves credit, is the constructive criticism, and inspiring atmosphere of this forum.
If not for everything that has been said here before, I wouldn't even look in this direction.

[Ken S]

Wootz,

I think of the forum as a pulling boat (a term from my Outward Bound days, more commonly known as a life boat.) The oarsman on the port side does a better job if there is an oarsman on the starboard side. Both do better with someone minding the tiller and a navigator. I think we are a great team!

Ken

[Jan]

Wootz, you are a very humble person. 

I think that programming scripts still does not belong to ordinary skill of a knife sharpener. The Cosine and the Pythagorean theorems are certainly not astonishing, but thank God if their proper application leads to the desired goals.

Writing scripts requires some skill also, because "the devil is in the detail". I saw it with my decimal comma problem, until fixing it, the script was delivering meaningless figures.

So congratulations are definitely in place. 

Jan

[wootz]

... The only difficulty I faced was the decimal marker. In this country we use comma as symbol for decimal marker. I had to change "." for "," in the script and everything was OK.

... "the devil is in the detail". I saw it with my decimal comma problem, until fixing it, the script was delivering meaningless figures.

Thanks for drawing my attention to this, Jan.
I think I could reproduce what you are saying on my PC, and modified the script to make it work for both comma "," and "." as the decimal.
The above script has been updated.

Could you do me a favour, try the updated version on your computer and tell me if it works right?

[Jan]

Wootz, I have tested the updated version of your script and it works fine also with comma as decimal marker. 

It provides slightly different figures compared with the initial script, because you have changed the ConstantHorizontal from 51.4 to 51 mm.

I have again admired your programing skill in overcoming this issue. Thank you in the name of potential "decimal comma" users. 

I was wondering if suitable format specifier could do the job as well?

Jan

[wootz]

Hi Jan,
Thank you for testing the script, it is finished, as Ken joked elsewhere, for both hemispheres now.

As to the ConstantHorizontal, I went to my local dealer with a caliper, and asked his permission to measure the display Tormek T7, and two more T7s he had in for repairs - they all showed 51mm.
I thought this value is better suited for general use.

I cannot do without this script because AngleMaster does not work for aftermarket oversized wheels, including the paper wheel of 254mm.
(Obviously for the script to work for my paper wheel setup, I had to edit the constants ConstantHorizontal and ConstantVertical.)

[Ken S]

Wootz,

You need to leave the comfortable world of high tech and Mr. Euclid and venture into the depths of low tech!

Just because Tormek ends the diameter correction scale at 250mm does not mean that we cannot add a few millimeters with a sharpie. Just eyeball it or use a rule for layout. At this point, we may have three choices:

1) Remove the locking screw. Move the arrow to your new 254 mm mark and tape it in place. You are good to go!

2) Use your calipers and measure the change in the diameter compensator. Make a shim that thickness and place it under the diameter compensator when you measure.

3) (the nuclear option ) File the groove enough to allow the arrow to point to your 254 mm line. If this totally fails, a replacement part is available for $3.73 US.

Regards from the low tech land,

Ken

[Jan]

Hi Jan,
Thank you for testing the script, it is finished, as Ken joked elsewhere, for both hemispheres now.

As to the ConstantHorizontal, I went to my local dealer with a caliper, and asked his permission to measure the display Tormek T7, and two more T7s he had in for repairs - they all showed 51mm.
I thought this value is better suited for general use.

I cannot do without this script because AngleMaster does not work for aftermarket oversized wheels, including the paper wheel of 254mm.
(Obviously for the script to work for my paper wheel setup, I had to edit the constants ConstantHorizontal and ConstantVertical.)

Wootz, you have internationalized your scrip. 

Bellow there is a map from Wikipedia showing where the comma and point are used.  https://en.wikipedia.org/wiki/Decimal_mark



For us in countries with decimal comma, the decimal point is not a problem, because we take it as the common "international" notation used in computers. The problem occurs only when programs do not ask the operating system for the decimal mark selection. Some commands than can generate incorrect results. Wootz has overcome this issue in an original way.

Wootz, more accurate value for the ConstantHorizontal* is fine with me. It has minimal impact on the US height, only 0.1 mm for the default input values. But just that little difference 0.10 mm alerted me, because the devil is in the detail, however after a while I heard the angels sing.   

I will correct the ConstantHorizontal in my Autocad model where I am using approx. value 52 mm.

Jan

P.S.: * Explanation. Wootz uses the ConstantHorizontal = 51 mm to tell the script what is the horizontal offset of the vertical sleeve from the shaft.

[Ken S]

Jan,

Fascinating post!

Ken

[wootz]

Wootz,

You need to leave the comfortable world of high tech and Mr. Euclid and venture into the depths of low tech!

Just because Tormek ends the diameter correction scale at 250mm does not mean that we cannot add a few millimeters with a sharpie. Just eyeball it or use a rule for layout. At this point, we may have three choices:

1) Remove the locking screw. Move the arrow to your new 254 mm mark and tape it in place. You are good to go!

2) Use your calipers and measure the change in the diameter compensator. Make a shim that thickness and place it under the diameter compensator when you measure.

3) (the nuclear option ) File the groove enough to allow the arrow to point to your 254 mm line. If this totally fails, a replacement part is available for $3.73 US.

Regards from the low tech land,

Ken

OMG
... and only when I went to the 'nuclear option', I realized the AngleMaster lower scale has a 10" mark. Shame on me, I should better know my instruments.

[Jan]

Ken, I was delighted to read your advice for oversize wheels. 

You showed almost the same inventiveness as Wootz by internationalization of its script. 

Jan