Making a Cruciform Mandrel

THIS IS A RAW PAGE AND DOESN"T REFLECT CRUCIFORM WORK YET.

For my Experimental Hybrid Rocket Motor work, and my HyperTEK Experimental in particular, I was having trouble casting  the grains because the 1.5" SCH 40 PVC pipe I used as a insulator  / fuel / casting tube when combined with a 1" coring mandrel, only leaves 1/4" web for casting. For any casting formula that isn't runny this isn't much thickness and contributes to a messy cast and also the possibility of air bubbles & voids.

So for these reasons, not for solids loadings, I started thinking about making a finocyl mandrel. The design would allow much more clearance for pouring casting composition into the base.

For you solids guys, this is also applicable, just note that I'm coming at this from a different angle. Note also that Burn Sim will now compute for finocyl cores - but I don't know yet if it'll handle the geometries that I am coming up with. Richard Nakka also has a finocyl calculator spreadsheet that I also haven't tried with my geometry.

Always state your requirements before you start - to ensure that you end up at or close to your goals.

My requirements are

1. (a) Approximate the inital surface area of a 1" core of a 54mm HyperTEK fuel grain.
2. (b) Retain clearance for the GOX fill stem tube. This tube is 3/8" OD, and I'd like to retain 1/2" diameter for clearance

Note that the core cross sectional areas of the circular and our pseudo finocyl equivalent will not be the same even if we succeed in computing a geometry that has the same linear surface area. This will affect the operating pressure of the motor.

I don't have a mill so need to be able to do this with available tools - such as a table saw, router, or router table. My tact is to use hexagonal bar stock such as this from McMaster.com or this from OnlineMetals.com along with a carbide cabinet pilot bit to add the grooves to make it a finocyl.

The stock sizes we'll consider are 1", 7/8", and 3/4" between the flats.

The carbide cabinet pilot bit is a V bit with a 90 degree included angle. Note this won't provide a perfect geometry as the hexagon's 6 triangles have a 60 degree included angle so we may consider another bit if we can find a suitable one.

We will simply set the bit in a router table, adjust the guide for a center across a flat, adjust the depth, and make 6 grooves.

I worked out the formulas myself, but if you want to see the derivation, I found a like for you that is better than any of my notes "The Area Of A Hexagon"

We are starting with a hexagon, and the vendors specify the dimension as "A" above - between the flats. We will be cutting equilateral triangular grooves on each face.

Circumference of a circle = PI * D = 3.142
Circumference of a hexagon (1/2) A = SQRT(3) / 2 * L, so L= 1 / SQRT(3) * A, so Circumference = 6 / SQRT(3) * A = 3.464 * A

Note that we don't actually want that above formula, as we want the same intial surface area which means we want the circumference of the hexagon to match the circumference of the 1" circular core.

Let's look at some basic circumference computations

If we are using a 45 / 90 router bit, then we're cutting equilateral triangle grooves, so for each Groove Width Gw we cut away, we add twice that. So, in effect, for a cut of Gw, we add 2 * G2 to the new circumference.

For the 3/4" Hexagon, we need 3.142 - 2.598 = .544" additional circumference, divided by 6 grooves, yields 0.090666 per groove, or a Groove Width Gw of 0.0453

For the 5/8" Hexagon, we need 3.142 - 2.165 = .977" additional circumference, divided by 6 grooves, yields 0.163 per groove, or a Groove Width Gw of 0.0815"

The 3/4" stock. The groove, is tiny at a hair under 3/64, may be difficult to manageably and accurately cut. It will give us less overall casting room than the 5/8" stock, and with respect to the GOX tube clearance, we have 0.75 - 0.091 = 0.659 This well over our 1/2" core goal and wider actually than the 5/8" stock - we could drop a bar of it right in!.

The 5/8" stock looks tight. The groove, while tiny at a hair under 3/32, is at least manageably large enough to cut. It will give us more overall casting room than the 3/4" stock, and with respect to the GOX tube clearance, we have 0.625 - 0.163 == 0.462. This is a hair under our 1/2" core goal and leave 0.087 or a hair under 3/32" total .

One conclusion we might reach is that a finocyl may not be the best candidate given the relatively large inner core we need to leave with respect to the equivalent diameter we need to maintain.