## Feb 24, 2017

### [2.70] Kinematic Coupling Round 2 (plus bonus annealing fun!)

Last time I made a kinematic coupling for a Slocum class,  the result was a tiny magnetic coupling for a pen. Well, time to make another 6-contact-point mechanism to constrain 6 degrees of freedom!

This time, I'm revisiting some material science fun - material properties of tempered and annealed aluminum. Last time I did this, I took 7075-O aluminum and heat treated it to approximately T6 temper. This time, I'm starting with a block of 6061-T6 and seeing how far I can anneal it.

I filled in two estimation spreadsheets for the kinematic coupling. This one assumes the grooved half is made of 6061-T6, and the second one assumes the grooved half was softened to T0. In both cases, I'm using pine spheres for the ball half.

For this spreadsheet, I assume that there's a 20N preload pressing the halves together but at an imperfect angle (5deg, so modeling a weight slightly cantilevered off the center). I also assume that I will be measuring Abbe-error at a distance of 10ft.

 pine balls on 6061-T6 grooves

 pine balls on 6061-O grooves

An interesting observation that emerges from these two spreadsheets is that annealing the aluminum is expected to yield no difference in kinematic coupling errors. Of course, that does make sense, since pine has a both a substantially lower yield strength and lower stiffness than even soft aluminum.

I ran the spreadsheet again, using ball values for steel, and found that actually my problem is that the yield strength differences between T6 temper and T0 are too small to see much difference in error... and given that 6061 will have the same elastic modulus at any hardness, I'm not really sure what I expected in the first place. Anyway, moving on.

This KC used a much less involved method of construction than the previous one. I grabbed leftover wooden drawer knobs and drilled 1/4"-diameter blind holes to accept steel dowel pins. Then, I drew a circle on some scrap aluminum (this isn't the one that will be baked) and marked and punched locations spaced 120 degrees apart. These punched spots were drilled through with a 1/4" bit and again with a 19/32" reamer (I couldn't find a 1/4" one!)

19/32" holes ended up being too much of a slip fit, so I shimmed the dowels with some tape.

 Completed upper half of the KC
The lower half of the coupling was made of a 1/4" chunk of 6061-T6, and used the same method as KinematicCouplingPen to form the grooves - indexing head for 120 deg rotation, preliminary cuts used a flat endmill followed by a chamfered bit (this one was a bit big for a countersink). I also drilled some 5/8" clearance holes for attachment to future tensile-tester fasteners.

Tensile testing ended up not happening, for reasons I'll get into later in the post :)

A note on machining - this go around I learned from my previous mistakes and locked the spindle when machining the grooves, instead using the much more rigid knee to control z-axis height.

 Completed kinematic coupling
For testing, I relied on good old Abbe Error. Magnify your errors by projecting them really far away!

 Abbe Error diagram from last time
This KC has coupling radius "r" = 19.6mm, and my projection distance was 6.33m.

$d = \frac{rD} {L} = \frac{D} {322.96}$

$\frac{d}{D} = 3.096 \times 10^{-3}$

For these repeatability experiments, a projected deviation of 1mm indicates a coupling error of 3 microns. The experiment consisted of taking the KC top off and setting it down again, then marking the new location of the laser dot. I repeated this process 10 times.
 KC was clamped to the table and a laser strapped to the upper half pointed at a paper on the wall
 Actual piece of paper taped to the wall
So how did I do? For the just-laser-pointer trial (self-weight provides a 2N preload), my max radius across the entire spread was 6.06mm. Maximum distance between consecutive trials was 8.64mm, and maximum distance from the origin (laser location before I started the repeatability test) was 12.3mm in the negative x direction.

I added some weight on the center of the KC and tried this experiment again with a 10N preload. Here, max spread radius was 5.50mm, max distance between consecutive trials was 8.48mm, and maximum distance from the origin happened from origin to location1 was 10.99mm

An interesting observation for both cases was that the origin itself - before I started messing around with the KC - is on the extreme edge of the spread (the origin location is marked with a sunburst pattern). I wonder whether the KC settles to a new favored position over time, versus when I quickly pick it up and set it down during the experiment.

Translating these results to errors in the coupling, I get this:
So this kinematic coupling is repeatable to approximately 15 microns. This happens to be 5x worse than the first one I made, but definitely took less than 1/5 the time to make.

Going back to the kinematic coupling spreadsheet and updating values to better reflect real life, I found that I should expect a displacement error of 12.7 microns (10N preload, where the added 8 N was assumed to be 1deg off center, because nothing's perfect). Pretty close to real life!

Alright alright, what happened to the material science part?
Well, the internet suggests that a good way to soften 6061-T6 is to coat your piece with a layer of sharpie or bar soap and then torch it with an acetylene torch until the soot burns off. If you let it air cool, it should be somewhere between T3 and T0.

So I did that, then remembered I had an evening lab class in the metallurgy lab and the forge would still be hot when we finish with classwork! This was convenient, because the kinematic coupling piece is rather thick and torching it would only superficially soften the outer faces.

 Ooh, fire
Unfortunately aluminum is less forgiving than copper and is more difficult to judge temperature by eye. It also happens to be that aluminum's forging temperature is only approx. 300 or so degF lower than its melting temperature... which is to say I spent too much time taking pictures and accidentally let my workpiece partially melt.

If you create deep grooves in a block of aluminum, the thinner bits heat up faster. Womp womp.

 #hubris #stoptakingpictures #startpayingattention
So no stiffness testing between kinematic couplings this time. Luckily for me, I already did the assignment part.

What else can you do with a melty piece of aluminum? Nominally it should be T0, but in this state it's difficult to stick in an Instron.

I decided to try a very handwavey version of the Rockwell/Brinell hardness test methodologies to finish off this fun experience. I got a 18-oz ballpeen hammer and a metal punch, and struck each material with vaguely the same amount of force. Then I measured the depth of the indentation.

 Indent on melty-aluminum vs indent on your standard 6061-T6
Melty-aluminum's punch was 1.2mm deep, and T6's punch was 0.25mm deep. If we assume (dubious) that I actually used the same amount of force striking each piece, melty-aluminum is 4 or 5 times softer than 6061-T6.

6061-O aluminum has a Brinell hardness of 30, compared to T6's hardness of 95. Between like-materials and this close together on the scale, we can assume the hardnesses and scale values to be linear and say 6061-O is 3 times softer than 6061-T6. So my melty-aluminum is either at T0 or softer. I'm leaning 'softer', since it... melted. I guess this doesn't actually count as "annealed".

(Kinematic Coupling spreadsheet says I wouldn't have noticed a significant difference in error, anyway. Hrmph)

#### 1 comment:

1. the KC spreadsheet will oly tell you if it actually yields... but not how much
you sure do really excellent experimentation and documenting of you work. I am really impressed
and I believe that a hit over (450 D F max) : Full annealing of 6xxx and 7xxx series alloys to the -O temper is typically done by heating to 415 C, holding for 2-3 hours, followed by slow cooling (30 C/hour) to a temperature of 260 C, then air cooling. Refer to ASM HANDBOOK Volume 4, ASTM B 918, or similar documents for more information.