Improved method for determining support bar height constants

[smurfs]

The horizontal and vertical constants used by various calculators to determine the support bar height from a given origin, such as the machine cover or support bar sleeve, are notoriously difficult to measure physically, even for the most skilled. Additionally, if steps are not first taken to ensure the support bar legs are perpendicular to the horizontal running through the wheel axle center prior to measurement, the degree of inaccuracy in calculated bar height will increase the further the support bar is raised from the initial point of measurement.

To overcome these issues I have derived a new method of computing the constants mathematically which is quick and easy and requires no particular skill. As a bonus the math/s used also implicitly caters for any variance from perpendicular of the support bar and mounting at any height, which is particularly useful in home-made bar mountings made from off the shelf components not precision engineered, such as those used in slow-speed honing setups.

The method is machine agnostic and can be applied to any support bar mounting position. It simply requires measurement of the distance between the support bar and wheel axle, and the support bar and sleeve face/mounting/cover, at two different heights. Obviously the accuracy of the constant results will depend on the accuracy of these two sets of measurements, so if necessary check and/or rerun the measurements at different heights should you have any doubts.

The only equipment required are vernier calipers, preferably 300mm.

Here are the steps which would apply to a slow-speed honing setup with both left and right mountings (*):

1. Remove the wheel from the axle.
2. Insert the support bar fully into the mounting sleeve and fasten.
3. Measure and record the outside distance between the axle and support bar (figure 1). Ensure the calipers are parallel to the axle and bar centers.
4. Measure and record the vertical height from the bar top to XB-100 sleeve/housing (figure 1). Ensure the caliper depth gauge is parallel to the threaded bar leg.
5. Raise the support bar by a meaningful distance, say 10 to 15cm, and fasten (figure 2).
6. Repeat steps 3 & 4.

* Actually the procedure is identical for any support bar mounting point. Also note outside measurements are adjusted to center-to-center distances prior to constant calculation.



As depicted in figure 3 the two sets of measurements form a triangle, shown in orange, the sides of which are the distances between the centers of the wheel axle and support bar inserted, the wheel axle and support bar extended, and the difference in support bar heights. The yellow triangle contains the horizontal and vertical constants which historically have been derived through physical measurement.

The math/s is relatively straightforward and is described below for those interested.

For those that glaze over at the thought I have put together a simple DEMO spreadsheet to compute the constants in the above example which you can [download here]. First update the diameter of your slow speed grinder wheel axle, enter your recorded distances and the constants will be displayed. All that remains is to transfer the values to the software that requires it. By the way the spreadsheet as currently designed applies equally to the Tormek vertical mounting and only requires slight modifying for the FVB and horizontal mountings (@jvh, could a utility to determine all constants be included within TormekCalc?).

Now to the math/s.

Using the known three sides of the orange bar-axle triangle (figure 4) we determine angle B, which incidentally is the bit that handles any variability in perpendicular; if the bar leans slightly toward the machine the computed angle is more acute, and if it leans away is more obtuse. This is important as it impacts directly on the constant lengths which are ultimately derived from it.



Next we determine angles D and F in the yellow constants triangle (note that angle E is a right angle and therefore never changes).





We know the length of side e is the same as side c, so the lengths of the two remaining sides from which the vertical and horizontal constant values are derived are computed thus:



and



In this example the vertical constant should be reduced by the height of the previously recorded lower vertical height from the bar top to XB-100 sleeve/housing (step 3 above), plus the support bar diameter. This is because the origin of the height measurement is the face of the XB-100 sleeve/housing, so subtract this distance from the length of side d.

The horizontal constant needs no adjustment so equals the length of side f.

That's it.

If necessary constants may be cross-checked using TormekCalc, viz, for any given bar height you can expect the height of the support bar to bar height origin (sleeve/cover/etc) to correspond to the height of the bar to the wheel surface.

Hopefully this method will put an end to the polarizing discussion around which bar height measurement approach is best as they are now equally valid and accurate 

[Sir Amwell]

This is so helpful to anyone trying to set up a Wootz inspired set up and invested in his software for calculating deburring angles. It eliminates the difficulty of trying to determine those constants by hand and eye with the doubt about perpendicularity of stands. Thank you Smurfs for this innovation. This could be groundbreaking.

[cbwx34]

...

To overcome these issues I have derived a new method of computing the constants mathematically which is quick and easy and requires no particular skill.
...

Thanks for sharing the details (allowing it to be properly vetted).  Looks well thought out.

[Perra]

Good job. I have tested and it fits well with my own measurements. It really makes it easier to find the right distance. Thank you so much for sharing. I intend to copy it and use it in my own program.   

[tgbto]

It indeed makes for measurements that are much easier to make.

Still, I am not sure why one would prefer taking three measurements (both measurements shown here plus the one at sharpening time) compared to only one from USB to top of wheel...

[Ken S]

I would like to preface my thoughts by stating that I mean no disrespect or diminishment to our members who have developed math based bevel angle setting programs.

I do not understand "notoriously difficult to measure, even for the most skilled". I have been setting the distance between the grinding wheel and the support bar for over eight years with my humble kenjig.  The kenjig works using the technology of gage blocks. In their most advanced form, precision hardened steel or carbide gage blocks are used in laboratories to measure in millionths of an inch. They are far more precise than calipers.

My shop made Baltic birch plywood kenjigs certainly do not approach this level of accuracy; however, I believe they exceed the needs of knife sharpeners for accuracy and consistency.
Dutchman's grinding tables provided all the math I needed. I designed the kenjig for three groups of users:
1) New Tormek users (to simplify set up)
2) Home users who might sharpen their home knives a couple times per year. (less to remember)
3) Farmers market sharpeners who would need to be able to sharpen a large number of kitchen knives quickly. The kenjig would shorten set up time.

Following Dutchman's method, I made all measurements from the support bar to the grinding wheel. At first, I was very concerned about the effects of wheel diameter wear.
Several factors have lessened that concern:
Dutchman's tables are in ten mm diameter wear increments. Even Jan, one of our most skilled math users, thought making corrections every five mm was adequate.
We are increasingly using constant diameter diamond wheels. Not only would the diameter of an individual wheel remain constant, all of the three diamond wheels share a common diameter.
The 220mm diameter leather honing wheel would remain constant, although it would require a separate kenjig. The cost would be negligible and the extra time involved only a very few minutes. I standardized on 15° bevels. Kenjigs could just as easily be made to other angles. Multiple angles, if desired, would require a separate kenjig.

My workaday kenjig is made out of 12mm bbp. (Heavy cardboard or mat board also work.)
A 25mm width provides a secure footing. Judging by eye, it is easy to see when the grinding wheel sits below the center of the jig. This is not notoriously difficult to measure.
More advanced methods may have their place for top shelf knives. I feel that simpler methods are adequate for most knives.

Ken

[tgbto]

I do not understand "notoriously difficult to measure, even for the most skilled".

I think the OP's point was taht it is difficult to measurz the constants that allow for precise determination of desired top of USB/top of casing distance.

I would tend to agree with you both : the constants mentioned in quite a few calculators are difficult to measure properly. Measuring consistently from top of usb to top of casing is also quite difficult, at least for me. Measuring to the convex surface that is the top of the wheel (with kenjig or calipers) makes it easier to estimate you're measuring from the desired spot with a more-than-adequate accuracy. And does not require said constants.

[smurfs]

Still, I am not sure why one would prefer taking three measurements (both measurements shown here plus the one at sharpening time) compared to only one from USB to top of wheel...

tgbto, the measurements described are performed just once and the constants are stored as configuration settings in the calculators that require them.

I do not understand "notoriously difficult to measure, even for the most skilled".

Ken, with respect you misread my first sentence "The horizontal and vertical constants used by various calculators to determine the support bar height from a given origin, such as the machine cover or support bar sleeve, are notoriously difficult to measure physically, even for the most skilled."

Andrew

[Sir Amwell]

With respect to everyone posting on this subject. Smurf's has offered a solution to those having problems with determining constants to input into software requiring them to get data to find grinding angles. Hence it doesn't matter what technique one uses. I have invested in Knifegrinders software and I want to make it work, for whatever reasons. Bar to stone measurements does not work for me to the level of sharpness I want. It is unhelpful for those who want to make this work to suggest to 'just use bar to stone ' or 'stop getting hung up on accuracy, to the nearest mm is ok and most of my customers can't tell the difference between 110 Bess and 50 Bess so stop worrying'
This is about making information available to users so they can make their own conclusions and implement them as they see fit to their requirements. So I say thank you Smurfs for responding to a cry for help and coming up with a solution. Which is surely what this forum is about?

[Ken S]

Andrew,

You are correct; I did misread your sentence. As a forum, we bring different sharpening needs and expectations.
I have great respect for the advances brought forward by Wootz (Vadim of Knife Grinders). I realize that my knife sharpening needs are simpler than some of our members. Wootz would have described the knives I sharpen (all are mine) as "common knives". I have no problem with that designation. My knives fit both my needs and my budget.
I would feel differently if I was sharpening super steel knives, either for myself or for customers.

I realize some forum members have more math training and interest than I do. I also realize that the products of that interest can benefit all of us. I meant no offense. Nor did I mean to discourage this discussion.

Ken

[tgbto]

Bar to stone measurements does not work for me to the level of sharpness I want.

Sir,

For the sake of the experiment, do you think you could share BESS scores on the same knife sharpened with your old measurements, and the exact ones derived from Andrew's method ?

Cheers,

Nick.

[jvh]

...
To overcome these issues I have derived a new method of computing the constants mathematically which is quick and easy and requires no particular skill. As a bonus the math/s used also implicitly caters for any variance from perpendicular of the support bar and mounting at any height, which is particularly useful in home-made bar mountings made from off the shelf components not precision engineered, such as those used in slow-speed honing setups.
...

Hello Andrew,

nice idea, thanks for sharing. I'll test it later when I have time...

jvh