# Aluminum Dice

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This is a good starter project for getting used to working with a vertical mill.
We'll cover how to create a perfect cube, chamfering, and position repeatability.
I made mine at TechShop.

Materials Needed:
Aluminum stock
A small, flat scrap of wood

Tools Needed:
Metal Bandsaw
Vertical Mill
Endmill for machining the faces of the dice
V-mill for chamfering the edges of the dice
Drill bit for drilling the dots
Machinist's square
Clamp to use as a stop on the mill's vice
Parallels
Marker (oil pencil is good, or use a permanent marker if you have a solvent with which to clean it off)

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## Step 1: Rough Cut Then Square Up the Workpiece

Cut your stock slightly larger (say .24") than the desired dimensions of your dice.

Before we can do the more precise milling aspects of this project, we need to square up the rough cut pieces so that each face of the workpiece is perpendicular to the adjacent faces.

You can follow my 'square up stock on a vertical mill' instructable.

Alternately, since we are milling cubes, it is possible to skip some of the steps since the dimensions of this workpiece can be somewhat simplified as follows:

Cut your aluminum stock roughly to size.

Mill side 1 per the instructable

Mill side 2 per the instructable

Instead of milling the side opposite to side 2, turn the cube so side 1 is against the solid jaw of the vise and side 2 is facing to the left. Use a machinists square against side two (the same technique as used when milling side 5 in the instructable).
Mill side 3.

Sides 1, 2, and 3 will share a common corner. This is different than the previously mentioned instructable where sides 2 and 3 are opposite each other.

If you're milling multiple dice, repeat the above steps for each piece, then you can cut them all to the final size at the same time without having to move the 'Z' axis when milling the last three sides.

Put the die in the vise with side 1 against the solid jaw and side 2 face down. Take a skim pass off of the top face.

At this point you can set the proper Z height as the desired height of the cube and machine the remaining unfinished sides using one of the already milled sides against the solid jaw of the vise and a second milled side against the parallel. This lets you machine all three dimensions of your cube without having to make a skim pass on each dimension before cutting the proper depth. Be sure to use the wood scrap whenever you have an unmilled side facing the movable jaw of the chuck.

## Step 2: Calculate Depth of Final Cuts

Right now we have a workpiece that should have faces at 90 degrees from each other, but the size in the X, Y, and Z axes will each be different. We need to bring all of those dimensions to the desired dimension of our finished die.

In my case I was aiming for a 0.65 inch cube. Using digital calipers I measured the distance from the bottom face to the top face. This gives us the distance from the top of the parallels to the bottom of the end mill, assuming we haven't moved the Z axis of the mill since making a skim pass on the top face.

Subtracting our desired dimension from the current dimension of the die gives us the amount of material that needs to be removed.

.740 - 0.650 = 0.09 inches.

## Step 3: Cut the Final Dimensions

Set the z axis dial to zero, then crank the height to the desired cut depth.

If machining to tight tolerances, we would remove that material in two passes, the first pass at .089 inches, then a finishing pass of an additional .001 inches. If you don't really care about being exact, feel free to just make one pass at .090.

You should always try to keep the most precise sides of the die in contact with the fixed jaw and the parallels of the vise as you machine down the rest of the die.

Machine each of the three dimensions of the cube to the proper dimension by milling one side, then rotating the die in the vise without moving the Z axis.

All three sides of our workpiece should now be the same dimension, giving us a perfect cube.

## Step 4: Chamfer the Edges

Remove the end mill from the mill and install a countersink bit.

Position the cutter so that the mill is above the movable jaw of the chuck. The closer you can get to the vise in the 'Z' axis the better, since you will get a larger diameter of the cutting surface in contact with your workpiece. If just the tip of the countersink touches your workpiece, you will get a lousy finish. Lock your 'Z' axis.

Turn on the mill and move the piece in the Y axis until the cutter bites into the workpiece. Move the workpiece in the 'X' axis, removing the sharp edge between two of the machined faces of the die. If you want to create a bigger chamfer, push further into the piece using the 'Y' axis and make another pass. Once you are satisfied with the size of the chamfer, lock your 'Y' axis.

Park the cutting tool to one side of the workpiece, Turn off the mill and unclamp the vise. Rotate the workpiece so that an unchamfered edge is visible above the movable jaw of the vise. Turn the mill back on and make a pass across the workpiece in the 'X' axis.  This should put the exact same chamfer on the new edge that you put on the first edge.

Repeat this process for each edge of the cube.

I found that since the countersink I was using had several flutes, the aluminum chips sometimes got pulled back around to the workpiece instead of being thrown clear, and would gall slightly on the first pass of a chamfer. Simply making a second pass without moving the 'Y' axis removed any galling from the first pass and cleaned up the edge nicely. Using a countersink with fewer flutes would have helped prevent the galling, but I did not have one on hand.

## Step 5: Calculate the Dot Positions

We will need to divide the face of the die into a 3 by 3 grid, leaving a small border around the outside.

In this example I will leave a 5% border.

divide the total length of a side by 10 and subtract that from the length of one side. That leaves us conveniently with 90% to divide by 3, giving 30% for the width and height of each square of the grid.

We really only need to calculate three x,y coordinate pairs. Those three positions can be used to drill all of the dots by repositioning the die below the drill bit.

Top left:
x = border + half of a grid square
= 5% + 15%
= 20%
= 0.13

y = same as x
= 0.13

Top Center:
x = 50%
= 0.325
y = same as top left y
= 0.13

Middle Center:
x = 50%
= 0.325

y = 50%
= 0.325

## Step 6: Rough Mark the Dots

Just to make sure the holes get drilled in the right spots, it is a good idea to mark the faces with a marker before drilling.

One rule you must follow is that opposing sides of a die must add up to 7. That means that 1 is opposite 6, 2 is opposite 5, and 3 is opposite 4.

## Step 7: Drill the Dots

Attach a clamp to the fixed jaw of the vise to use as a repeatable stop in the x axis.

Clamp the die in the vise so that it is butted up against the clamp you just attached to the vise. Be sure that side '1' is facing up.

Use an edge finder to zero the X and Y axes over the top left corner of the die.

Swap a drill bit into the mill. The bit needs to be smaller than the size of the grid squares in order for there to be space between holes drilled in adjacent squares. I ended up drilling with a 0.1 inch bit, which was just about right for the aesthetic I wanted. I did use a long drill bit, and the bit did wander a noticeably due to deflecting. The shorter the bit, the more accurate your holes will be.

Center the drill over the die using the X and Y coordinates from the previous step.

Temporarily lock the quill at the bottom of its travel. Use the knee adjustment to bring the workpiece up to the drill.

Turn on the drill and begin to drill by slowly raising the workpiece. When you are satisfied with the size of your hole, stop raising the the workpiece, unlock the quill, and raise the drill bit away from the workpiece. You can now quickly repeat the depth of that hole by dropping the quill to its bottom position.

Drill out all remaining center holes (we just did side 1, do 3 and 5).

Move to the top middle X/Y position and drill out the two side holes on side 6.

Move to the top left X/Y position and drill out all of the corner holes (sides 2, 3, 4, 5, and 6).

## Step 8: Polish the Dice

Place a 400 grit sandpaper on a flat surface and drag each face of the dice across it firmly until all of the curved lines from the milling process have been removed.

Smoothing down the points of the die just a little bit as well is probably a good idea to help prevent the dice scratching each other when they touch. Some marring is going to be inevitable over time, but this will slow down that process somewhat.

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## 19 Discussions

I present one solution to a perfectly weighted die. This assumes that the holes drilled into the body of the die are flat bottomed, that the cores inserted into the drilled holes are perfectly cylindrical, and sit flush with the bottom of the drilled hole. It also assumes that each face of the die has point symmetry with relation to the center of that face, which is the case with the standard markings of a die.

We can craft an equation that will express how much copper would be
needed at a certain distance from the center of the die in order to
counteract a given amount of aluminum at a second certain distance from
the center of the die, preserving the center of gravity at the geometric
center of the die. This approach allows each and every hole on the die
to be machined to the same depth and filled with the same sized plug, regardless of which face it is on, without disturbing the
balance of the die.

Interestingly, the amount of aluminum
that must be drilled out is based on how large a copper plug must be
accomodated, but the size of the copper plug depends on how much
aluminum will be drilled out. It seems like a catch-22 at first glance, but math is pretty amazing.

We choose the universal depth we want each hole to be after the plug has been inserted. We can then determine, based on the size of the die, how far the copper plug must extend down into the die, starting at the desired depth of the hole after having inserted the plug.

We will use the following designations:

d - the dimension from the middle of the die to any face, or one half the length of a side.

v - the depth of the void of each hole remaining after the plug is inserted.

p - the length of each plug that will be inserted into each hole.

Ma - specific gravity of aluminum, or 2.7 according to user RayJN

Mc - specific gravity of copper, or 8.94 according to user RayJN

The equation I came up with is based on generic equations to determine the rotational force (torque or moment) exerted by a mass at a given distance from a fulcrum, and is as follows:

Ma * (v+p) * (d - ((v + p)/2)) = Mc * p * (d - (v + p) + (p/2))

d-((v+p)/2) is the center of the total aluminum that will be removed

d-(v+p)+(p/2) is the center of the copper plug that will be inserted into the hole.

Since the crafter of the die chooses how large the die is, as well as how deep the finished holes should be, and the specific gravity of the materials we've chosen doesn't change, that only leaves one variable 'p' for which we can solve.

If d=.5 (representing a one inch die) and v=.05 (or 5% of the length of a side), that gives us:

2.7 * (p + .05) * (.5-((p+.05)/2)) = 8.95 * p * (.5 - (p + .05) + (p/2))

which winds up making p = 0.0234 (rounded to the nearest ten-thousandths of an inch). So, that is the height of your copper plug, and the hole you would drill into the aluminum would be that plus 'v' (depth of the void above the core, or .05), giving 0.0734 as the depth of the hole to be drilled in the aluminum.

1 reply

The easiest way to balance the die is to use an end mill to make the pips. Just go six times deeper on the "one" side when machining the holes than you do on the "six" side, five times deeper on the "two" side, four times deeper on the "three" side... you get the picture. If you follow this pattern you have removed the same amount of material from each side.

so what exactly is techshop?? Is it just a shop that people can go and use whenever they want for a certain price?

And great ible I am doing some machining to make a metal ring so this helped a lot

YESH. I love aluminum for having a lower melting point than lots of other metals and it seems whenever I'm playing a board game we need more dice.

You could cut out the same pattern on each die, like you suggested below, then color one side of aluminum plugs however you like, and add the plugs to each side so that you have 1,2,3,4,5,6. That way the only unbalancing would come from the negligible amount of ink/dye you use on the aluminum plugs.

I'm really happy to see I wasn't the only one thinking of the balance when I saw this! Not neurotic, just detail oriented.

just drill the same number of holes on each side, in the same pattern, say 6mm deep, and put a 5mm plug of copper and a 1 mm plug of aluminum in each hole, put the aluminum plug in first for dots you want to see, and the copper plug in first for the dots you want to hide. then every side will be the same.

1 reply

Your die would still be considered unbalanced. If you cut your die in half, each half would weigh the same, but your center of gravity would still be further towards side 6 than side 1 due to the fact that more copper plugs are further towards the outside of the die on the six side than on the 1 side.

copper has a specific gravity of 8.94 aluminum 2.70

the opposite side of the die are supposed to add up to 7

1-6 2-5 3-4 which would make the 6 the heaviest unless you varied the depth of the holes to compensate.

TechShop is practically a necessity in modern society, but we are turning into a nation of haves and have-nots. Accordingly, I'm calling for enactment of legislation for Comprehensive Techshop Availability Reform (The C-TAR Act of 2014).mandating that Techshops be set up within 46 minutes driving time (at legal speed limits) of every population cluster of 5000 people. As an interim measure, until TechShops can be deployed across this great land of ours, the legislation will direct all military maintenance depots, repair ships, refit facilities, government agency maintenance shops, etc. in an area underserved by TechShops to open their facilities after normal working hours to their owners, the American Public, so that we all can have access to advanced (and basic) tool and machinery. To ensure adequate funding of this vital program, all American will be required to buy a membership at a qualified tech shop such as a TechShop brand tech shop., or pay a penalty each year until compliance with C-TAR is achieved. Of course, if you like your current TechShop, you can keep your current TechShop. Another "of course" is that we will need to achieve enrollment by a certain critical mass of a key demographic... people with "skilz". If the only people who sign up during open enrollment are fumble-fingered people who can't follow instructions...well, the cost of machinery repair and emergency room visits will make the whole shebang non-viable.,

You'd have to venture even deeper into the math zone than that. Ignoring the weights of the other faces and focusing just on the one and the six, filled as you described, the center of gravity would be slightly towards the six side, since the center of the mass of copper on that side would be further from the physical center of the die. Beyond that, I'm not motivated enough to bother with calculations unless someone is offering grant money. ;)