### Author Topic: Gear ratio problem  (Read 6034 times)

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#### garriwilson

• Supreme Robot
• Posts: 345
##### Gear ratio problem
« on: December 06, 2007, 10:34:56 PM »
Hey guys!
I need to figure out a gear ratio for a small elecic car.
Ok I have 5 gears:10tooth, 20 tooth, 30 tooth, 40 tooth, and 50tooth.
How do I figure out the combination of THREE of those for speed and then for torque?

Thank you and ask if you are confused.

#### bens

• Expert Roboticist
• Supreme Robot
• Posts: 335
##### Re: Gear ratio problem
« Reply #1 on: December 06, 2007, 10:52:40 PM »
Consider a two-gear setup: 10 and 20 tooth.  If you affix the 10-tooth gear directly to your motor and use it to turn the 20-tooth gear, you should be able to intuitively see that the 20-tooth gear will turn half as fast as the motor's output shaft (if the 10-tooth gear is going 1 RPM, the 20-tooth gear will turn at .5 RPM).  What you're doing here is increasing torque at the expense of speed.  Torque is increasing because the 20-tooth gear has a larger radius, so you're applying force farther away from the gear's axis of rotation.  Torque = the cross product of F and r, which in this case has a magnitude of F*r.  If the torque of your motor shaft is T, the 10-tooth gear can deliver a force of T/r10, where r10 is the radius of the 10-tooth gear.  This force, when applied to the 20-tooth gear, generates a torque of F*r20 = T*r20/r10, where r20 is the radius of the 20-tooth gear.  You can expect the 20-tooth gear to have twice the radius of the 10-tooth gear, so using this setup you can effectively double the motor's torque by halving its speed.

If you switch the order of the gears (20-tooth is on the motor's output shaft), you analagously determine that you will double the rotation speed and halve the torque.  Figuring out the three-gear solution is just an extension of this analysis.

#### ed1380

• Supreme Robot
• Posts: 1,478
##### Re: Gear ratio problem
« Reply #2 on: December 06, 2007, 11:02:07 PM »
IIRC you take teh first and last gear and then find out the ratio by deviding # of teach per gear.

yep.
http://www.societyofrobots.com/mechanics_gears.shtml#gearchains
Gear Chains (more than 2 gears together)
Suppose you have 30 gears (holy squirrels!), all in order, like in the image above. How in the monkies do you calculate the gearing ratio of that behemoth? Easy. Ignore all the gears in between the very first and very last gear. If the diameter of the first gear is 2 inches, and the diameter of the last is 1 inch, you have a 2:1 ratio. The gears in between do not matter. Now what direction does the last gear rotate? Easy, you have an even number of gears, so it is counter-rotational of the first gear. What efficiency do you have? Well thats:

effienciency_total = gear_type_efficiency ^ (# of gears - 1) = .9 ^ (29) = 4.7 %

If instead you used 5 gears, you would have:

effienciency_total = .9 ^ (4) = 65.6 %

« Last Edit: December 06, 2007, 11:04:11 PM by ed1380 »
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• Supreme Robot
• Posts: 11,680
##### Re: Gear ratio problem
« Reply #3 on: December 07, 2007, 05:56:06 AM »
are you allowed to do compound gears?

if you have a compound gear, both individual gears (no matter what teeth they have) will have the same velocity and direction. the torque change however will be calculated like normal.

compound gears have 100% efficiency

#### paulstreats

• Supreme Robot
• Posts: 1,381
##### Re: Gear ratio problem
« Reply #4 on: December 07, 2007, 07:22:31 AM »
where does the extra energy come from for the velocity to remain but the torque increase?
A large gear with a gear half the size on the same axle would calculate the same as one normal gear turning a gear half its own size surely? just with a reduction on friction

• Supreme Robot
• Posts: 11,680
##### Re: Gear ratio problem
« Reply #5 on: December 07, 2007, 07:38:51 AM »
man i need to stop replying to posts in the early morning . . . ignore my last post! thanks paulstreats for catching me on that . . .

the correction:
torque and rotational velocity remain the same in compound gears

i was thinking of the force applied by the gear teeth, which does change (because torque remains the same, but gear radius does not)

#### garriwilson

• Supreme Robot
• Posts: 345
##### Re: Gear ratio problem
« Reply #6 on: December 07, 2007, 06:23:57 PM »
By compound gears do you mean gears of the same size and tooths in a row? If yes, then NO I am not allowed to use anything except the gears I have listed.

No offense, maybe it's just me, but I don't think anybody answered my question except bens. I don't mean to be rude. Please don't take this the wrong way.

1. I have a motor
2. I can attach a gear to it.
3. I mount the motor on a metal board (flat).
4. Next to the motor gear is an axle where I put another gear.
5. That gear interacts with the gear on the actual axle.
6. So it's three gears in a row. But I don't know I'll ask my leader if I can use only two gears.

Question:

1. If I put the biggest gear on the motor, then the second smallest gear in between the motor and axle, and the very smallest on the drive axle itself, won't the speed increase every time?
2.
Quote
Consider a two-gear setup: 10 and 20 tooth.
by bens. I want to know why this is a good setup. However, I need to figure out the best setup of gears with THREE gears. No more no less.

Thanks so much guys, what would I do without you.

• Supreme Robot
• Posts: 11,680
##### Re: Gear ratio problem
« Reply #7 on: December 07, 2007, 06:44:44 PM »
Quote
No offense, maybe it's just me, but I don't think anybody answered my question except bens. I don't mean to be rude. Please don't take this the wrong way.

Quote
By compound gears do you mean gears of the same size and tooths in a row?
a compound gear is two different sized gears 'glued' together

Quote
If I put the biggest gear on the motor, then the second smallest gear in between the motor and axle, and the very smallest on the drive axle itself, won't the speed increase every time?
The middle gear doesn't do anything useful other than waste efficiency and cause a counter rotation. read my gear tutorial, it will help you a lot. If you do the big gear on your motor, and the 3rd gear is smaller, this is called 'gearing up' - meaning velocity of gear three goes up while torque goes down.

What is the goal for gearing it anyway?

Quote
Thanks so much guys, what would I do without you.
major in english or history

#### ed1380

• Supreme Robot
• Posts: 1,478
##### Re: Gear ratio problem
« Reply #8 on: December 07, 2007, 07:04:45 PM »

Question:

1. If I put the biggest gear on the motor, then the second smallest gear in between the motor and axle, and the very smallest on the drive axle itself, won't the speed increase every time?
2.
Quote
Consider a two-gear setup: 10 and 20 tooth.
by bens. I want to know why this is a good setup. However, I need to figure out the best setup of gears with THREE gears. No more no less.

Thanks so much guys, what would I do without you.
read the purple box in the 3rd post from teh top.
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#### paulstreats

• Supreme Robot
• Posts: 1,381
##### Re: Gear ratio problem
« Reply #9 on: December 07, 2007, 07:33:00 PM »
Quote
1. If I put the biggest gear on the motor, then the second smallest gear in between the motor and axle, and the very smallest on the drive axle itself, won't the speed increase every time?

The speed will increase but the torque(pulling power) will reduce each time.
you will need to find a balance depending on the torque of the motor. You could end up with wheels that spin super fast in mid air but dont have enough power to actually move the car if you gear it up too much.

You usually find that motors spin fast with little torque, so you gear them down to reduce the speed but gain some torque (use the smaller gear on the motor) trying to strike a balance between speed/power. This is generally the case with electric motors
« Last Edit: December 07, 2007, 07:36:55 PM by paulstreats »

#### garriwilson

• Supreme Robot
• Posts: 345
##### Re: Gear ratio problem
« Reply #10 on: December 07, 2007, 07:38:45 PM »
Quote
major in english or history
pshh... yea right!you made me even more grateful lol. never will i major in that i'd rather die

Ok, so more gears means crappy efficiency?

I don't know if we're allowed to break the rules of three gears.

Let me clarify something. This is for a project for my engineering club at school. We're building a small (crappy and cheap) electric auto. I MIGHT draw a CAD. Don't count on it though.

Thanks guys you really helped.
« Last Edit: December 07, 2007, 07:39:20 PM by garriwilson »

#### garriwilson

• Supreme Robot
• Posts: 345
##### Re: Gear ratio problem
« Reply #11 on: December 11, 2007, 11:45:08 PM »
Today, our club met again. I tried to put the 20 tooth and the 10 tooth
I put the 10 tooth on the axle and 20 tooth on the motor because I need speed. However, the 20 tooth gear was unable to reach the 10 tooth, even when I moved the motor as close as I could. So, I decided to use the 30 tooth instead of 20 tooth. Is 30+20tooth combination still better than any three gear combination.

First, we will have a competition for speed, then hill climbing. So, for hill climbing, I just need to switch the gears right? Or will a three gear combination work better for torque?

Sorry if my questions are dumb, thanks a lot!

• Supreme Robot
• Posts: 11,680
##### Re: Gear ratio problem
« Reply #12 on: December 12, 2007, 05:35:06 AM »
Quote
Is 30+20tooth combination still better than any three gear combination.
There is no such thing as the 'better' gear ratio, it depends entirely on your application.

A 30:20 ratio is 1.5 < 30:10 ratio is 3. This ratio will give you half the speed but twice the torque as your previous choice.

Quote
First, we will have a competition for speed, then hill climbing. So, for hill climbing, I just need to switch the gears right? Or will a three gear combination work better for torque?
So if you have a really fast output, with no torque, it won't be able to climb a hill.

This is a RMF problem, actually . . . plug in the numbers to determine the RMF need to climb the hill.

Then you need to calculate if the torque can lift your robot up the hill. Here is a hint:

(if you can't get it, Ill give you some more hints)

#### garriwilson

• Supreme Robot
• Posts: 345
##### Re: Gear ratio problem
« Reply #13 on: December 14, 2007, 08:02:28 PM »
I'm so sorry, I meant to say 30 tooth with 10 tooth combination. Sorry I got mixed up.

I have a question: If the torque of my car is sacrificed as much as possible to the increase of speed, won't my car like not move at all because there's not sufficient torque. Or maybe it will be slower because it's torque is weak?

What I'd like to know is (if you haven't already told me and it passed by me) how to figure out the torque and speed of my car by just knowing the gear ratio and the mass. I don't need to figure out how much I need for it to climb or go fastest, but to calculate the speed for each one and get the fastest one.

Thanks

#### ed1380

• Supreme Robot
• Posts: 1,478
##### Re: Gear ratio problem
« Reply #14 on: December 14, 2007, 08:16:46 PM »
it also depends on rpm.

Quote
If the torque of my car is sacrificed as much as possible to the increase of speed, won't my car like not move at all because there's not sufficient torque. Or maybe it will be slower because it's torque is weak?

it'll move slower and slower until it can't move at all, and teh motor will get bogged down more and more

lol trust me since I'm learning to drive stick right now and this town has a few hills
« Last Edit: December 14, 2007, 08:18:16 PM by ed1380 »
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#### nottoooily

• Full Member
• Posts: 91
##### Re: Gear ratio problem
« Reply #15 on: December 15, 2007, 04:23:20 PM »
Hi

Quote
What I'd like to know is (if you haven't already told me and it passed by me) how to figure out the torque and speed of my car by just knowing the gear ratio and the mass. I don't need to figure out how much I need for it to climb or go fastest, but to calculate the speed for each one and get the fastest one.

Everyone wants to know this, but unfortunately it's not possible to find the speed driving horizontally based on only that information. With a perfectly efficeint drivetrain you could achieve arbitrarily high speed just by gearing it up as high as you like. The actual speed at a particular torque is limited by rolling resistance, etc, which is usually easiest to find by experiment with the same wheels, bearings, surface, weight you're going to use - pull the car along with a forcemeter.

In selecting the gear ratio you should also design it to run the motor at the speed it provides maximum power. I think this is usually about 70% of no-load speed, but check the data sheets. If you bog it down you're losing power you might have had. Equally, if it spins too freely you're losing power you might have had.

#### robonoob

• Robot Overlord
• Posts: 149
##### Re: Gear ratio problem
« Reply #16 on: January 14, 2008, 08:02:30 AM »
if i were you i would probably build the whole car... then i would get the mass of it... then i would calculate the minimum torque needed for the motor to move your car(no actually i would get a little bigger torque) then i would get the gears that  offer you that torque(prefferably a little bigger torque) and then test it if it runs on the surfage you need it to run...
if u use the minimum torque needed then  in theory it would run pretty fast if the car is lightweighted and you have a fast motor

just calculate the torque you will need and then use the fastest motor and gear it down( towards more torque) untill you have this torque and if your motor was fast enaugh that you still remained speed aswell as torque then you will have the car run as fast as it could

if you need to make your robot hill climbing and if it doesn't need to be fast then gear it down as much as you can so it has  very much torque but very little velocity