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# How would you scale this?

## Question

It is an ice cream machine shaft. How would you make the scaling of this shaft?

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For a very simple analysis,

You need to maintain working stress if you using the same shaft material.

Stress = applied moment x shaft radius / shaft inertia

Applied load (moment, M) are in scale with R^3. (cube of blade radius, could be approximated by the ice cream space)

shaft radius, r define the dimension.

shaft inertia, I defined as pi x r^3 x t for thin hollow cylinder shaft.

t = thickness.

Let's say initially for a 1 m x 1 m x 1 m, you use 100 mm diameter shaft with thickness 5 mm.

If you want to make the ice cream space larger to 2 m x 2 m x 2 m, i.e. 8 times the volume, you need 283 mm diameter shaft, with thickness 5 mm.

You need to consider further whether 5 mm thickness suitable for larger shaft (consider buckling analysis)

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