Math on pulley to platter calcs?

[AVWERK]

I'm getting out my old TT project after 15 years in a box, and can't find the motor.

My question is the air bearing platter from a (Mapleknoll Athena) measures 7.875" DIA. (pulley surface dia)

I need to machine a new motor pulley for 33 1/3 rpm (Not interested in 45)

I'll most likely use a 300 or 600 rpm motor. AC sync.

What would be the motor pulley dia. at 300 or 600 rpm turning 7.875" to get 33 1/3rd rpm?

This is a suspended design and will use a rubber belt, what 3/32nd in dia. maybe?

Appreciate any information

Regards
David

[Steerpike]

Its a simple ratio calculation:
You want to reduce 300rpm down to 33.333333 rpm,
i.e., by a factor of 9.000

Your pulley diameter must be 9x smaller than the platter diameter.

There are fine tweaks to this figure based on the 'roundness' of the pulley face (you need a somewhat sounded pulley to make the belt run centrally) but without going into too much detail, the calculated value of pulley diameter should be around the average of the largest (central) diameter and the smallest (the two edges).

[Mark Kelly]

It's more complex than that.

If the belt is rubber then add one belt thickness to each diameter. The correct equation is then: motor speed x (Dpulley + Tbelt) = platter speed x (Dplatter + T belt)

which simplifies to: D pulley = [platter speed x (Dplatter + Tbelt)/motor speed] - T belt

You nominate a belt of 3/32" which is 2.38mm so for 300 rpm motor you end up with [33.333 x 302.38/300] - 2.38 which is 31.22 mm rather than the 33.333 mm pulley from the incorrect equation above.

This ignores the effect of belt creep but belt creep is small and varies with torque so it's hard to include accurate compensation. If you cut the pulley at 31.2 mm you'd be close.

If you use a material other than rubber the equation must be further modified. Multiply the belt thickness by twice the Poisson's ratio of the material before substituting it into the equation. Rubber has a Poisson's ratio of 0.5 (eg it is completely incompressible) so for rubber the simplified version works.

[Nanook]

most folks don't consider the need to compensate for thickness and material of the belt.

The simple equation works very well for materials such as Mylar or video tape. (although they both can stretch), that are very thin. And of course small adjustments can be made via a controller.

stew