[walter]

The4thseal,

BYK A-525 works by pushing air bubbles up. Most dramatic effect is in epoxy/hardener mix, which typically is full of air. With A-525 there will be almost none. To get the result with highly filled mixtures you need to shake it well- I have yet to test it with proper device. But I've seen some void reduction, about 50%- with only modest shaker. Is it worth getting for your machine- definitely. You only need vial or two. For testing? Probably not. Samples are too small to get the vibration and mass effect- you won't see added mechanical strength.
For sample just go to their global website, find product and click 'sample'. Use 0.3-0.5% of total mix including aggregate.

Cheers!

[the4thseal]

thanks I will get some.

[ckelloug]

The models for packing mixtures of grains where individual grains positions in the mixture are random is complicated topic. This is a vague attempt to answer some of John's questions about how the packing models actually work.

In short, you can optimize the packing of aggregate with any roughness or size using de Larrard's complete model. What is described below is the simple Appolonian Model which handles the case where all aggregate are spherical and distributed in size as described. The full Compressible Packing Model which I have implemented in software and been using for my experiments is required to handle the cases where the sizes aren't distributed as described below and the aggregates have different roughness.

The basic results obtained up to now from modeling are that packing density generally goes up with the number of size fractions utilized and the range between the minimum and maximum sizes. If the strength and density of the mixture are not important, don't waste your time with the more complex mixtures: just use pool sand and epoxy noting that you'll probably need between 30% and 40% epoxy for that. Strength goes up as epoxy fraction goes down as long as the epoxy fraction is not so low as to create empty spaces in the mixture.

Practical advice aside, here's packing theory lite:

It must be first emphasized that the theory involves both theoretical and actual packing densities and they are different. The theoretical one is called the virtual packing density and applies in the case where grains are placed individually (as in a computer model); The virtual packing is approximated for spheres by the model in the NISS paper posted here originally by greybeard: http://www.niss.org/technicalreports/tr104.pdf This paper shows that the ideal packing for randomly placed spheres is 71% which is 3% lower than the 74% obtained using a regular face centered or body centered cubic packing (Kepler conjecture).

Recapping, a large box of spheres of a single size will ideally achieve a packing density of 71%. In actuality, the value will likely be lower depending on how the spheres are compacted into the box. De Larrard calls this value Beta. Beta is between .61 and .66 for rough aggregate. Spheres are empirically an excellent approximation for natural sand and materials like Zeeospheres which are intrinsically round.

The next problem that must be addressed is what happens in a mixture of spheres of different sizes. We first notice that the space available in a box of tennis balls to add something tiny like BB's is equal to 29% of the total volume. This follows from the fact that the tennis balls already occupy 71% of the total volume.

While the BB's can theoretically occupy 29% of the space, eventually, the remaining spaces get too small and no more BB's will fit. In this simplified case, the BB's can only occupy 71% of that remaining 29% or about 21% of the total space. Given an infinite number of size fractions where each fraction is much much smaller than the previous one, the theoretical packing density of the mixture will approach 100%.

The actual packing density doesn't approach 100% however. In an actual mixture, particles of different sizes have an effect on one another reducing the overall packing density of the mixture from that predicted by the virtual packing density. There are two effects in the model.

The first is the wall effect where a given size of small particles are pushed up against much larger particles. This generates spaces that are too small to be filled by the given size of small particles and requires smaller particles to fill the spaces.

The second effect is the loosening effect where large amounts of small particles push the larger particles farther apart than they would have been given a mixture with no smaller particles.

Both the wall effect and the loosening effect are minimized when the sizes of the particles are as different as possible. Thus, when each particle is much much larger than the next size down, the packing approaches the virtual packing where each fraction occupies 71% of the space not filled by the larger particles.

In order to keep small particles from forcing the larger particles further apart, we can't add any more of a given size of particles than the volume remaining after adding all of the larger particles. This is similar to the case of adding smaller and smaller particles to a regular packing but since the packing involves random particle locations, it can't really be visualized easily.

De Larrard states in the book that he has used numerical simulation to prove that the form of the optimum aggregate distribution where the aggregate are as widely distributed in size as possible. He states that the form of the solution is the same form as described above for the amount that each size fraction can fill.

Summarizing the form of the optimal size distribution:

If the top aggregate diameter is D, the bottom size is d, and there are n sizes: then the optimal distribution has D as the biggest, D*lambda as the second size, D*lambda^2 as the third size and so forth with d=D*lambda^n-1.

This gives the value of lambda as the (d/D)^-(n-1). <del>In words, the minimum diameter equals the (n-1)th root of (D/d) and each successive size fraction should be D* (D/d)^-(n-2) and so forth up to D*(D/d)^0 which is D. </del> (Thanks go to Greybeard for pointing out that the crossed out statement was wrong.)

I will state below without proof that the ideal virtual packing density for this case is 1- (1-Beta)^n where Beta is defined above and n is the number of size fractions.

The actual density will then be 1- (1 - Beta/(1+n/K))^n where Beta is as defined above, n is the number of size fractions and K is an empirical constant. K has been shown by experiment to be 9 for vibration under 1 psi of external pressure, 4.1 for pouring the mixture into a box and 4.75 for vibration of the mixture without external pressure.

I can probably further explain the models but I would need to study more to do so. I will leave this post as a teaser to see if anyone is interested. I could also write a PDF file that described the equations in more detail if folks are interested.

[greybeard]

Many thanks Cameron, you've managed to bring me out of my darkened room to carry on with my experiments.
The particle separator is nearly finished, bu problems with my car are distracting me somewhat at the moment.

When time allows, and I stress that, I would be interested in the pdf.
But then I expect you might have guessed that anyway.
Thanks again for your contribution.
John

[greybeard]

This posting was one second thought after another, so I've scrubbed it.

Regards
John

[greybeard]

If the top aggregate diameter is D, the bottom size is d, and there are n sizes: then the optimal distribution has D as the biggest, D*lambda as the second size, D*lambda^2 as the third size and so forth with d=D*lambda^n-1.

This gives the value of lambda as the (d/D)^-(n-1). In words, the minimum diameter equals the (n-1)th root of (D/d) and each successive size fraction should be D* (D/d)^-(n-2) and so forth up to D*(D/d)^0 which is D.

.

A typo here I think. The minimum diameter is d .
I'm also a bit confused by the rest of that sentence. I've substituted some simple figures, and it doesn't seem to work.

Regards
John

[ckelloug]

A typo here I think. The minimum diameter is d .
I'm also a bit confused by the rest of that sentence. I've substituted some simple figures, and it doesn't seem to work.

Regards
John

John,

I had almost all of it right except for the line you highlighted. It works like this:

Diameters from biggest to smallest are:
D
D*lambda
D*lambda^2
d=D*lambda^n-1

It can be derived from the last statement that lambda=the (n-1)th root of d/D.

if D= 3mm d =.001mm and n=3 then lambda~.07 and the size distribution is:

3.00mm
0.20mm
0.01mm


If n=10 then

3.00mm
1.23mm
0.51mm
0.21mm
0.085mm
0.035mm
0.014mm
0.0059mm
0.0024mm
0.0010mm

Regards,
--Cameron

[greybeard]

John,
It can be derived from the last statement that lambda=the (n-1)th root of d/D.
--Cameron

I'm happy with everything now.

It was just that you had D/d in a couple of places instead of d/D that threw me.

Back to breakfast.
John

[DaveP]

Hopefully only slightly off subject -Steel City’s new hybrid 10" table saw has a 150-pound black granite top.

http://popularwoodworking.com/awfs#SteelCity

[ckelloug]

Cool Post about the granite top table saw. Interesting that they're not using Epoxy Granite as the tensile and impact strength of E/G are much better than real granite.

While the discussion here is can be a bit technical, it's always good to see new faces and such interesting info.

--Cameron

[greybeard]

Interesting that they're not using Epoxy Granite as the tensile and impact strength of E/G are much better than real granite.
--Cameron

Could it be because they've not yet found this thread ?

John

[Zumba]

Real granite is probably uber cheap compared to E/G. The low prices of granite surface plates confirms this. Enco sells 12x18 "B Grade" surface plates for 25 bucks. Free shipping if you order over $50. So the actual cost of the plate before shipping it overseas is probably about $8.

Those tablesaw tops probably cost the company 15 bucks each.

[walter]

Got my Harbor Freight concrete vibrators. The manual says not to bolt them to a hard surface.

Is there anything else I should know before bolting them to a hard surface?
_

[brunog]

Got my Harbor Freight concrete vibrators. The manual says not to bolt them to a hard surface.

Is there anything else I should know before bolting them to a hard surface?
_

Cool vibrators Walter,

As long as the hard surface is sitting on rubber cushions or springs permiting the hard surface to vibrate, I don't see any!


kkkkkkeeeeeeeeeeppppp oooonnnnn vvvvvvvvvvviiiiiibbbbbbbrrrraaatttttttiiiiiiiinnng ggg!!

Best regards

Bruno

[ckelloug]

Walter,

I agree with brunog that as long as whatever they're bolted to isn't firmly attached to an immovable surface, you should be okay. I assume immovable was mistranslated as hard in the directions.

On the topic of post curing, I have not been able to get hold of the reichhold apps engineer. The 37-127 data sheet does say however on page 3 that 24 hours at 77F plus 2 hours at 250F was the cure schedule used for the strength tests that they performed.

The high temperature cure at the end increases the cross link density which impacts high temperature strength the most and general strength some. The high temperature used however would indicate to me that it may be difficult to get maximum strength without really cranking the temps. Even with Cobalt Acetyl Acetonate, the nanoresins paper I read in one of the books I cited earlier had them scurrying around increasing the temperature they were post curing at trying to get the epoxy to fully cure in their tests.

I wouldn't sweat the post curing too much if you can't do it but if you happen to still have a couple of heat lamps, placing the cured beam under them for post curing the following day could not hurt. I think it's probably important to not intentionally heat the mixture until the main cure has been achieved.

--Cameron

[Geof]

Got my Harbor Freight concrete vibrators. The manual says not to bolt them to a hard surface.

Is there anything else I should know before bolting them to a hard surface?
_

I think it will depend on how big your hard, or immovable surface, is. If you bolted them direcly to a massive structure then the flanges on the motor are experiencing much more force than if they were resiliently mounted to the same structure. However, I don't think the vibration transmitted to the structure would be reduced so much that it would be ineffective.

Bolted to a small structure which is itself resiliently supported as brunog says would probably be fine. But I think small in this context is no heavier than the vibrator itself.

[walter]

Great info. Thank you all!

[lazlo]

Got my Harbor Freight concrete vibrators. The manual says not to bolt them to a hard surface.

Hi Walter, Cameron,

This thread is up to 154 pages, and close to 2,000 posts -- could you summarize where you're at? It looks like Walter has a "simplified" mix that he posted around 1769 or so that he's going to pour and mix with these Harbor Freight vibrators?

What epoxy did you guys settle on?

In other words, could you summarize the simple recipe that Walter's about to pour (sources for the materials would be great!), while Cameron continues to perfect the aggregate packing density?

Thanks!

Robert

[walter]

Hi Robert, we are working on multiple solutions.


1. E/G as a filler- existing machine base/frame damping.

Already done, with great results- check out Davo's work (post #606). Material suitable: various Epoxy/Granite mixtures, Sand-only solutions, Portland-Cement-in-Rubber-Bag solution, etc. Cost from extremely cheap for sand and cement solutions to $0.80/lb for various E/G mixtures. Equal performance- your budget should be your guide.


2. E/G for mineral casting- Simplified 1ksi mix; limited strength/toughness- internal bracings recommended.

Designed by Cameron, at $0.90/lb with Shopmaninc 635 Thin Epoxy System, BYK A-525 air release additive and food wrapper as mold release agent. Mixture sourced at Agsco Inc (quartz, aluminum oxide) and The Cary Co. (zeeospheres):

1 part #6 Agsco Brown Aluminum Oxide
1 part #4 Agsco Quartz
1 part #2 Agsco Quartz
1 part #2/0 Agsco Quartz
1 part G850 Zeeospheres
2 parts G800 Zeeospheres

Originally designed with G200 zeeospheres (check out post #1705). I'm using what I have in stock.


3. High performance E/G for mineral casting- Cameron's 2-4 ksi solution with commercial strength; For small and large stand-alone machine bases/frames.

High density system- possibly with 635 Epoxy, air release agent, silica fume, nanosand, coupling agents, surfactants and various other additives. Vacuum/press compaction recommended.



I'm getting ready to pour solution #2 using simple wooden mold (see pic) and 2 vibrating motors.

Cheers!
_

[ckelloug]

Lazlo,

I'm up to my eyeballs in electrical conduit for my shop, my day job and rain storms here. I'll try to post something vaguely useful tomorrow. The aggregate sizing theory posted a couple posts back is optimal according to the research I've done. Unfortunately a rather balky and extensive math model is used to determine the likely performance of mixtures and I'm a ways behind into coding my implementation of that model into something anybody else would be able to use successfully. Of course if you want to help code up the packing density model from De Larrard in a generically useful form, I won't reject help

BYK A525 de-airing additive, DOW Z6040 epoxy active silane bonding agent, and a mixture with a 85-95% intrinsic packing density with about 8% epoxy is what I'm aiming for in what Walter described as mixture number 3. I have done no experiments yet so I don't know the ultimate success to be achieved here but I'm hoping for a flexural strength of better than 2ksi and hopefully the 4 ksi achieved by commerical mixtures or perhaps more if I'm lucky. Until I get my shop running and either make or acquire reliable flexural strength measuring instruments, all I have is theoretical results and some calculations made from some of Walter's tests.

--Cameron