Gears

[numbcrunch]

I have a motor that turns at an rpm of s1 and a driven wheel with a cog with t2 teeth that needs to turn at s2 rpm, how can I work out a formula to allow me to calculate what number of teeth the motor cog needs (t1) and any intermediate cogs required.

I can work out the ratio required from this information but that only allows me to find the number of teeth on the motor cog which does not come out as a whole number, which to me means that I need more than one cog.

Thanks in advance.

 

[numbcrunch]

OK, lets put some numbers to this.

The motor turns at 0.86 rpm (s1) and does not yet have a cog or gear train (t1). How can I calculate what cogs are required to allow the motor to turn a 48 tooth cog (t2) at 0.125 rpm (s2).

Rearranging the conservation formula

s1 x t1 = s2 x t2

to give

s2 x t2 / s1 = t1

and punching in the numbers

0.125 x 48 / 0.86 = about 6.97 teeth or precisely 6 and 42/43 teeth = 300/43 teeth

So the motor needs a 6.97 tooth cog which is impossible, so how would I re-calculate this to find what cogs I need in the gear train?

I think I may need a different method.

Can anyone help please?

 

[Deleted member 4993]

OK, lets put some numbers to this.

The motor turns at 0.86 rpm (s1) and does not yet have a cog or gear train (t1). How can I calculate what cogs are required to allow the motor to turn a 48 tooth cog (t2) at 0.125 rpm (s2).

Rearranging the conservation formula

s1 x t1 = s2 x t2

to give

s2 x t2 / s1 = t1

and punching in the numbers

0.125 x 48 / 0.86 = about 6.97 teeth or precisely 6 and 42/43 teeth = 300/43 teeth

So the motor needs a 6.97 tooth cog which is impossible, so how would I re-calculate this to find what cogs I need in the gear train?

I think I may need a different method.

Can anyone help please?

Now you have to compromise!

Nearest "nice" number of teeth is 8.

So your out rpm would be 0.1075 rpm - can you live with that.

If not you need to increase input rpm to 1 rpm.

This is what "design" is all about!!

 

[numbcrunch]

Thanks for that Subhotosh. I do understand the need for compromise in the real world of design.

However, is there a method to calculate this to perfect accuracy using exactly the given values and two or more cogs. Imagine this as a type of clock mechanism that needs to be extremely accurate. The actual application of this is the building of an equatorial mount to allow a telescope to track the the stars with high precision for long periods for photography. Obviously it would be easier to purchase a ready made accurate motor drive complete with gearbox ready built for the purpose.

I am sure there must be a way to calculate an accurate solution, even if that solution proves mechanically impractical and is just a mathematical exercise. Maybe that solution involves an iterative algorithm rather that a formula.

Any ideas on this would be of interest, since I have pondered this for a few hours now without enlightenment