Tool Rest locking action

[Jan]

Recently I was using the Tool Rest SVD-110 and was surprised by its large locking force. In the handbook I have found the following picture and Tormek statement.



Since then, I wondered how this is possible. Here's my explanation, hopefully it is correct.

To increase the locking force F1 by 250% means to multiply it by a factor 3.5 (100% + 250% = 350%). The knob force F1 can be decomposed into two equal side locking forces F2. 



Because we require that 2 * F2 = 3.5 * F1 we can calculate the angle beta for which the equation is true:
sin (beta) = 0.5 * F1 / F2.

Putting those two equations together we get:  sin (beta) = 1 / 3.5

So, the angle beta = sin^-1 (1 / 3.5). Numerically beta = 16.6 deg.

So really, if the special wedge shaped bore of the Tool Rest touches the round bar of the universal support at an angle of 16.6 degrees, than the locking action is increased by 250%.

Jan

P.S.: Please, if you can, check my calculation.

[Rob]

You're clever Jan!

[Jan]

Thank you, Rob! 

My auxiliary intention was to bridge over the slow new season/cucumber time here and also to provide an hopefully easy topic for Ken's new authority.

Jan

[Ken S]

The new authority is pleased......Good job, Jan.

Ken

[Herman Trivilino]

I think something got garbled in the translation from Swedish to English. The first sentence should be:

"In the patented design, the round bar touches the sides of the tapered bore instead of the bottom."

To increase the locking force F1 by 250% means to multiply it by a factor 3.5 (100% + 250% = 350%).

I agree with that, Jan. The claim is that the torque (or moment for you engineers) is 3.5 times bigger. Bigger, that is, than it would be without the patented design.

Without the design you'd have a force of F₁ applied by the screw, but you'd also have a force of F₁ applied by the bore on the opposite side of the screw. In other words, two equal but opposite forces pushing on the round bar. Of course the bar rubs on the bore in other places, but we'll be gracious and ignore that frictional force. I doubt it makes a significant contribution to the torque. So if you were summing the torques on the round bar you'd have a contribution from each of these forces for a total of 2F₁.

With the patented design we have three forces. F₁ from the screw and two F₂'s from the surfaces of the patented design, so the total is

F₁ + 2F₂.

So the equation is



which reduces to F₂ = 3F₁.

If we look at the three forces applied to the round bar, and apply the condition that the net force in the vertical direction is zero, we see that

F₁ = 2F₂ sin β.

Combining these equations I get sin β = 1/6, or β = 9.6^o.

[Ken S]

Bravo, Herman.

This topic is a fine example of one of the things I enjoy most about this forum. We bring our different backgrounds together. I do believe that the sum of the whole is greater than the sum of the parts.

Jan, if you are ever in Michigan, you should plan to visit Greenfield Village. It is one of my favorite places. Part of the exhibit is a recreation of Thomas Edison's Menlo Park laboratory. Walking around the buildings, you can feel the magic that happens when mathematicians, machinists, chemists, glassblowers, and other tradesmen all work together.

Among the exhibits on display are patent models. Have you been there, Herman? I find the place inspirational. Allow a day to enjoy Greenfield Village and another day to visit the adjacent Henry Ford Museum. They are absolutely must see places to experience for students of all ages.

From my math challenged perspective, I can see how the patented Torlock allows very secure locking strength in a less precice environment. This is very clever. It allows a superior product to be produced more cost efficiently. Like a properly tied knot, it gives both holding strength and easy release.

I have stated this before. When we combine the Torlock with innovations like Herman's HK-50 and build on it like Jan and others have done on this forum, we are on fertile ground.

Keep thinking and keep posting!

Ken

[Jan]

Combining these equations I get sin β = 1/6, or β = 9.6^o.

Excellent analysis, Herman!

Thank you very much for correcting my considerations. You've been more consistent than I was. I think you are correct.

I have enlarged the Tormek drawing of the Tool Rest and added the parallelogram of forces.



The angle beta measured in the drawing is approximately 10 degrees, which is in perfect agreement with your result beta = 9.6 degrees.

Hut off and congrats to you, Herman!

Sincerely
Jan

[Jan]

Jan, if you are ever in Michigan, you should plan to visit Greenfield Village. It is one of my favorite places. Part of the exhibit is a recreation of Thomas Edison's Menlo Park laboratory. Walking around the buildings, you can feel the magic that happens when mathematicians, machinists, chemists, glassblowers, and other tradesmen all work together.

Thanks for your response, Ken.
I am sure, I would enjoy it! 

Like a properly tied knot, it gives both holding strength and easy release.

Fully agreed, it is a very apt comparison for Torlock.

Jan

[Herman Trivilino]

Ken, I have not been but it sounds like something I need to add to my bucket list.

Jan, that's awesome to know that the result of my calculations matches the Tormek drawing. Thanks for bringing up this topic. It was a fun exercise in what engineers call Statics. I taught that course once, a long long time ago, despite being out of my element I had a good time. My students knew no better!

In your diagrams, Jan, note that the direction of F₁ needs to be reversed for consistency.


Edit: Please ignore my comment about reversing the direction of F₁. I see now that you are adding forces (hence your reference to the paralleogram.)

[Ken S]

Jan and Herman,

Speaking as one whose high school math was in the 1960s, I am very glad you two are on the forum.

To put in more of a plug for Greenfield Village, the other exhibits include many significant nineteenth century technological places. The Wright Brothers Bicycle Shop; the first Ford factory; a working vintage machine shop (which is also used to maintain the place!); an amazing carousel; and the Thomas Edison, a working steam locomotive. The locomotive was especially enjoyable for me because I was able to get close enough to see how it worked, including the sanders for placing sand on wet tracks for better traction. The place really brought out the inner child in me.

Ken

[Herman Trivilino]

Is there a large exhibit displaying machines with gears and wheels? I remember seeing videos of such a thing taken by a physics instructor. He used the videos, along with video analysis software, to study gear ratios and the like with his students.

[Ken S]

I don't remember a gear exhibit, although that seems a likely candidate for the (next door and affiliated) Henry Ford Museum.
I did find this link which looked fascinating:
http://www.dbusiness.com/daily-news/Annual-2015/Henry-Ford-Museum-Will-Add-Historic-Math-Exhibit-in-2016/

The Henry Ford Museum has been described as "America's Attic". I think it's a magic place.

Ken

[Jan]

Jan, that's awesome to know that the result of my calculations matches the Tormek drawing. Thanks for bringing up this topic. It was a fun exercise in what engineers call Statics. I taught that course once, a long long time ago, despite being out of my element I had a good time. My students knew no better!

Herman, it is surely a deeply satisfying feeling. Please enjoy it. I rejoice over it with you! 

Having once taught Statics, you are definitively better disposed for this topic than me.

Once, I also passed a course of general physics but not technical one. That time we all were eager to hear about quantum mechanics rather than the classical one.

Jan

[Jan]

Jan and Herman,

Speaking as one whose high school math was in the 1960s, I am very glad you two are on the forum.

So it was a time when we were multiplying numbers using a slide rule or logarithmic tables, is not it true? 
From my point of view, the applied mathematics itself did not changed so much, since that time. Computers mainly allow us to solve problems, to which we previously did not dare to think of.

Jan

P.S.: This pocket slide rule I inherited from my grandfather, who before the WWII worked for the company AEG, where he got it as working tool.

[Herman Trivilino]

My freshman year of college started in 1973. I was a math major taking calculus-based physics. We spent the first week learning how to use a slide rule. We had a small CRC reference book with tables of log and trig function values. Two years later I bought my first calculator, the HP-25, and never looked back.

I wasn't the only one. Demand fell off so fast that companies like K&E were stuck with warehouses full of them.  Thousands were destroyed and are now considered valuable collector items. The really nice precision ones are works of art.

My professor kept using his despite the laughs it got from his students. When I became a professor I kept using my HP-25 despite the laughs it got from my students. Apparently the newfangled LCD displays with battery lives of a few months are preferred to the LED displays with battery lives of a few hours.

My favorite calculator now is the RealCalc app on my Android phone.