Calculations for Ribbon Blender

You have D (outside flight diameter), d (inside flight diameter), P (pitch of flight).

So consider that b is the result of (D-d)/2.

Now developed the outside diameter, A = square root of [(PI*D)^2+(P)^2]. Then the inside developed diamater, B = square root of [(PI*d)^2+(P)^2]. - Value of PI = 3,1415926...

So the developed inside radius of the flight will be:

r = R-b => b=R-r; b/r=(r-R)/R - 1º step

R/r=A/B; (R-r)/r= (A-B)/B - 2º step

consider that R is the developed outise radius.

so we have:

b/r=(A-B)/B

then...

r=(B*b)/(A-B)

that is valid for cylindrical screw flights made with plates.

enjoy

That screw is called a auger , it is also named the ARCHIMEDES SCREW.It's easy to calc by simple geometry.

First step = get the pipe perimeter

2.875 * pi = 8.7493281 "Think you develope the pipe surface in plain after you mark where the fligth meets the pipe.

So you will have a rectangular triangle whose sides are the pitch = 9" and the developed perimeter = 2.875 * pi = 8.7493281 "and it's hypotenuse is Ih = Square root ( 9^2 + 8.7493281^2)= 12.55192704

This measure is the depeloved perimeter of the internal diameter of the "washer" so Ih/pi = ID in this case is 3.995402467By the same method you can get the outside diameter the 9 in OD is 28.27433388the pitch is the same 9 so the OH =29.67217479and the OD is =9.444946579

so you need to cut a "washer" 9.445" OD and 3.99"cut it and weld one after one and then strech it over the pipe