# How to calculate the moment of inertia of a worm gear?

Should I consider them as a cylinder to find their inertia? Any tips will be helpful.

• Draw a 3D model and get it to work it out. See OnShape for a superb 3D CAD system that runs in your browser and is free to use if your designs are public. Sep 17 '19 at 17:53

I assume you mean the worm, not the worm gear, but I'll append a note about doing the worm gear at the end.

1. Actually do the integral; if nothing else, it'll justify all those math courses.
2. Do the 3-D route (ick!)
3. Model (on paper) the worm as a stack of disks of alternating diameters; half of them with diameter equal to the worm's minor diameter, and half with diameter equal to the worm's major diameter. Then look up the moment of inertia of each of your modeled disks in a table, then finally multiply by the number of each size of disk. This will slightly overestimate the moment of inertia, which probably isn't a bad thing.

If you really mean worm gear, then model two pieces; one a disk with diameter equal to the minor diameter (i.e. from trough to trough on the gear) with density equal to your worm gear material; the other as a shell with ID equal to the gear minor diameter and OD equal to the gear major diameter, and density equal to half the gear's material density.

Again, it'll overestimate the moment of inertia, but again, that's probably not a bad thing.

The thread's mass is half of the mass of a cylinder with a thickness of the difference between inner and outer. It's CG is 1/3 out from inner circle. 1/3*1/2= 1/6.

If you calculate the I of a cylinder with a radius R = r inner + 1/6 thread depth, you're fine.