Can anyone help help me with a Gear Ratio?

[LazyBoy]

Hi,

I have 2 solid spinning rods:

Rod 1 has a diameter of 4mm at one end and 34mm at the other end.
Rod 2 has a diameter of 12mm at one end and 34mm at the other end.

Can anyone explain or tell me the gearing ratio for each rod?

Very much appreciated.
LazyBoy

 

[Minder]

What are you looking for exactly? Obviously with a solid rod there is no 'gear ratio'!
The rpm is identical for both ends.
The ratio comes when you interact with another rotating object.
M.

 

[LazyBoy]

Errr but if the 4mm outside diameter end of the rod is spinning at say 1,000 rpm then the 34mm outside diameter other end of the same rod must be spinning slower, yes/no?

4mm to 34mm = 1,000rpm / 30 = 33.3 ratio?
12mm to 34mm = 1,000rpm / 22 = 45.4 ratio?

 

[Minder]

You are talking surface feet/min not rpm or gear ratio.
This is just a direct ratio of the circumference of each end x rpm. They both have the same rpm,
It would be identical to a solid shaft that has a small dia pulley on one end and a larger one the other end, no gearing or change of ratio takes place until another secondary driven member is introduced to one end or the other.
M.

 

[LazyBoy]

I think that I am not explaining myself very well here, sorry M.

Am I talking about rotational speed ratios?

So if the rotation speed of the 4mm diameter rod is 1,000rpm the 34mm diameter rod would be 33.3rpm?

 

[Minder]

You would need to describe the driving method for each and how each rod relates to the other?
I must be missing something?
M.

 

[Alec_t]

Am I talking about rotational speed ratios?

You seem to be talking about the circumferential linear speed, not the angular rotational speed.
If you have two stepped/tapered shafts interacting (e.g. linked by a belt) as Minder says, then you can establish a 'gear ratio', like this.

 

[Minder]

That would be like describing apples and oranges, they have no relationship to each other.
The only difference as stated is the SF/M or circumferential rate.
Which is easy to calculate based on rpm.
M.

 

[LazyBoy]

That would be like describing apples and oranges, they have no relationship to each other.
The only difference as stated is the SF/M or circumferential rate.
Which is easy to calculate based on rpm.
M.

So how could I explain the advantage or disadvantage of having a smaller diameter spindle over having a larger diameter spindle?

Is this correct:
4mm to 34mm = 1,000rpm / 30 = 33.3 circumferential rate ?
12mm to 34mm = 1,000rpm / 22 = 45.4 circumferential rate ?

 

[Old Grey]

Imaging the are Vee pulleys.

Rod 1 - the 4mm rod turns 1 rev, 4 x 3.14159 = 12.57mm belt travel, but the other end also does 1 rev, so it's 34 x 3.14159 = 106.8mm belt travel.

You will have to work out the rest because I'm not exactly sure what you need.

 

[Merlin3189]

Perhaps it would help if you explained what you really need to know? And what these rods are?

I was very confused at first. I thought you had two fishing rods (for spinning) and wanted to know the best sort of reel to use with each! I think I was mistaken - though I'm still not sure, because I still can't think what two rotating tapered rods in isolation are.

It seems you have two metal, plastic, wood or something tapered rods which are actually rotating rather than standing in your garage. How are they supported? What is making them rotate? Why are you making them rotate? Why do you want to know how fast they are rotating? Are the two rods connected in any way? Why do you ask about gearing?

I think if you just told us plainly what your real problem is, people would be much more able to help.

how could I explain the advantage or disadvantage of having a smaller diameter spindle over having a larger diameter spindle?]

Smaller spindles are lighter. large spindles are stronger.

 

[LazyBoy]

So sorry guys.

I am trying to work out the advantage or disadvantage of having two identical toy spinning tops (like inception tops) except one top has a 4mm diameter spindle and the other has a 12mm diameter spindle?

I am guessing the gearing from along the users finger/thumb is the answer...?

Please note that the flywheel diameter is 34mm on both tops

 

[Alec_t]

If you're talking tops, then the same amount of finger movement in a given time would make the 4mm diameter one rotate faster, but would require greater force to do so.

 

[Old Grey]

Like he said.

If your thumb moves 12.57mm the 4mm top will spin 1 rev, but the 12mm (12 x 3.14159 = 37.69mm per rev) moving 12.57 is about a third of a rev.

It will also take maybe 3 times the force for the 4mm, but you will get more revs per spin

 

[LazyBoy]

So could you call this difference between the 4mm and 12mm spindle and the users fingers a gearing ratio?

 

[Alec_t]

I wouldn't. That would be stretching the meaning of 'gearing ratio' somewhat, since the normal definition of 'gear' is a toothed wheel.

 

[Minder]

Not always, gearing is applied to any increase/decrease in ratio of a drive system, in this case the ratio element is used on its own which is meaningless without acting in conjunction with any other drive element.
M.

 

[LazyBoy]

Not always, gearing is applied to any increase/decrease in ratio of a drive system, in this case the ratio element is used on its own which is meaningless without acting in conjunction with any other drive element.
M.

So if the users fingers are the drive element how would you describe the drive system's different ratios/gearing?

 

[Merlin3189]

Thanks for the clarification. It's so much easier when people know the real situation.

Like other people, I haven't really thought about this one before and am not sure how to describe it.
It's like a rack and pinion, which is sometimes called a gear.

I'm not sure you can talk about a gear ratio, because a ratio mathematically is fraction derived from a comparison of two similar quantities - like two diameters, two numbers of teeth, two lengths, etc.
But in more general parlance we do talk about mixed comparisons, such as power to weight ratio of an engine.(*)

A R&P is converting a linear movement (length) to rotation (angle), so while mathematically not a pure ratio, we could say the 4mm spinner did 80 turns per m and the 12mm spinner did 27 turns per m and call these turns per m ratios. That would help you make a comparison of the force required to give both the same acceleration. (Though the calculation of achievable speed is rather more complex.)

The big problem with such mixed comparisons is that we have to be very careful to state and remember the units attached to this number and you can't easily compare, say, 80 turns per metre with 29 degrees per mm.
For real ratios the number is the same whatever units we use (which, of course, must be the same for both devices.)

So could you call this difference between the 4mm and 12mm spindle and the users fingers a gearing ratio?

IMO you can call it what you like! But I'd just stick to calling it, the ratio of diameters or ratio of circumferences. That tells people what they need to know about the spindles.

What would you gain by calling it a gear(ing) ratio? You would confuse and mystify many people.(**) I don't think any of the text book material on gear ratios would apply or help you calculate the speeds, forces, etc.

(*)By which is actually meant, the power to mass ratio.
And there is a more acceptable technical term, the specific power.

(**) As witness the confusion during the first 11 posts of this thread.