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alvinlwh

Help me understand how to calculate gear ratio/FDR

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It is easy with Tamiya as the gear ratio chart is usually in the instructions and the choice of pinion (and sometimes spur) are limited. However, I recently built a car with "flexible" gearing where both the pinion and spur can be changed to (almost) any teeth and even pitch.

So, as built, the gears are:

24T pinion > 80T spur (via shaft)> 25T idler > 27T idler > 27T idler > 50T diff (20T & 12T within diff, not sure if matters?) > 55D M chassis tyres.

What are the steps and formula for working out the FDR in this gearbox?

Thanks!

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Internal ratio is output gear/input gear. Idlers don't count (assuming they are really idlers and not some kind of compound gear that is also changing the ratio). Most racing cars will state the internal ratio in the manual somewhere.

FDR is then (spur/pinion)*internal ratio

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1 hour ago, sosidge said:

 Idlers don't count (assuming they are really idlers and not some kind of compound gear that is also changing the ratio). 

Even if the idlers goes 25>27>27?

1 hour ago, sosidge said:

Most racing cars will state the internal ratio in the manual somewhere.

What??? Sorry, don't understand this. Also no internal ratio printed anywhere. The gears goes as I described, in a straight line from the pinion/motor to the diff/driven wheels, one after another. 

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Idler on the right is connected to a shaft driven by a 80T spur which is driven by a 24T pinion. Idler on the left drives the 50T diff. The idlers are, from left to right, 27T, 27T, 25T.

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Your tone is very aggressive. If you don't like the answer I have spent time composing you are welcome to go elsewhere.

There is a reason they are called idlers. One of those is not an idler gear.

If the input is 25T and the output is 50T then the internal ratio is 2:1

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Agree. The right hand gear in the pic is the 25 which is driven by the spur, right? And the left is the 27 that meshes with the 50? If you consider one revolution of the first 25t gear the 27t gears are turning 25/27 of a revolution, but this is irrelevant anyway, because without any compound gearing as @sosidgesays ultimately the 50t (which we can't see in that diagram) is also still moving 25 teeth, so exactly half a revolution, ergo 2:1. 50 out over 25 in. Looks to me the 27t gears are just there to enable the motor to be positioned further from the diff, for whatever reason.

Then multiply 2:1 by 80/24 if that's your spur/pinion combo and that's the ratio of the whole system. 6.67. Right? 

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Hmm unless there is some linguistic nuances I am missing, due to not being a native speaker, I did not read anything here as "very aggressive" - just the usual...

However, back to topic: true idler gears can indeed be ignored (if you calculate ratios step by step they should be canceled out mathematically.)

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58 minutes ago, sosidge said:

Your tone is very aggressive. If you don't like the answer I have spent time composing you are welcome to go elsewhere.

There is a reason they are called idlers. One of those is not an idler gear.

If the input is 25T and the output is 50T then the internal ratio is 2:1

I am not being aggressive, I am confused, the three ?s are to show I am confused, and I even apologised for not understanding.. I posted a picture of the instructions to try make what I was describing clearer. Nothing else.

But anyway, looking at your second answer, I worked it out. The two 27T gears can be ignored.

So thanks for taking your time to compose your answer, I apologise again for being confused and sounding aggressive.

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35 minutes ago, BuggyDad said:

Agree. The right hand gear in the pic is the 25 which is driven by the spur, right? And the left is the 27 that meshes with the 50? If you consider one revolution of the first 25t gear the 27t gears are turning 25/27 of a revolution, but this is irrelevant anyway, because without any compound gearing as @sosidgesays ultimately the 50t (which we can't see in that diagram) is also still moving 25 teeth, so exactly half a revolution, ergo 2:1. 50 out over 25 in. Looks to me the 27t gears are just there to enable the motor to be positioned further from the diff, for whatever reason.

Then multiply 2:1 by 80/24 if that's your spur/pinion combo and that's the ratio of the whole system. 6.67. Right? 

Yah, spur drives shaft which drives 25T, then 27T, 27T then 50T diff.

For the benefit of anyone still interested.

The cause of my confusion and not understanding is the 25T is labelled as idler in the instruction, along with the 27Ts.

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 50T diff goes to the left.

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And 25T driven via a shaft by the spur, 80T in this case.

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Idler gears do not factor into the overall gear ratio at all no matter how big or small they are. Idlers are literally there to change the spin direction or move power farther from the input. 

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9 minutes ago, RichieRich said:

Idler gears do not factor into the overall gear ratio at all no matter how big or small they are. Idlers are literally there to change the spin direction or move power farther from the input. 

Yes, but one of the drive (?) gear is marked as idler in the instructions and that is the cause of my confusion. 

In this case, the two idlers are the same size, so they cancel each other out. But what if they are of different sizes, will there be an effect? 

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Regardless of what the manual says, the 25T is not really an idler gear in this example. And it does not matter how many teeth true idler gears have, be it 27/27 or 27/54 or 27/100 or whatever. It will not change the final gear ratio. Whatever any idler gear "gains" or "loses" from gears before, it will lose or gain to the gear(s) after.

 

Just imagine, instead of the 25/27/27/50 your example has, the same setup with 10/25/25/100 and calculate what happens if you turn the first gear 10 times:

The second will turn 4 times, the third also turn 4 times and the last will turn 1 time.

If you change that to 10/25/50/100 and turn the first gear 10 times:

The second will turn 4 times, the third will turn 2 times and the last will again only turn 1 time.

Or with 10/50/25/100: 

second will turn 2 times, third 4 times and last again just 1 time.

See, it doesn't matter.

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@hIghQ thanks, helpful exploration. So just for my knowledge and to clarify, idlers only comes in pair right? So they actually cancel each other out. Just trying to learn here. 

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You can have just one. It would change the direction of the next gear vs not having an idler, but not the ratio. You can have multiple and they can be different sizes. Each one you add will just change direction and alter positioning. 

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Just now, BuggyDad said:

You can have just one. It would change the direction of the next gear vs not having an idler, but not the ratio. You can have multiple and they can be different sizes. Each one you add will just change direction and alter positioning. 

So in other words, take the first and last gears and ignore any middle ones? 

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1 minute ago, alvinlwh said:

So in other words, take the first and last gears and ignore any middle ones? 

Yes. Also, you can figure this out the long way using math. The input is 25 teeth and the diff is 50 teeth. So you have 50/25 = 2. If you want to include the idlers, again which you don't need to do, you have this:

27/25 x 27/27 x 50/27 = 1.08 x 1 x 1.852 = 2

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20 minutes ago, RichieRich said:

Yes. Also, you can figure this out the long way using math. The input is 25 teeth and the diff is 50 teeth. So you have 50/25 = 2. If you want to include the idlers, again which you don't need to do, you have this:

27/25 x 27/27 x 50/27 = 1.08 x 1 x 1.852 = 2

Got it, thanks! 

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So, your ratio is like 6.65, I guess?  

You can calculate only when there is a step-down.  Same tooth gears lined up like Konghead, they are 1:1, so they should be excluded. 

Two laterally connected gears (with a shaft or molded together) don't count either, because they turn at the same rate.  

 

In your case, Pinion to Spur:  24:80 = 1: 3.33 

(shaft connection of 80:25 is ignored, they are attached and turn at the same rate)

The smaller gear attached to the spur by shaft--- turning the middle idler:  25:27= 1:1.08

(ignoring one 27t counter gear)

Counter gear to diff. 27:50= 1:1.85

If you multiply all;   3.33 x 1.08 x 1.85 =  FDR 6.65.

 

You can replace one set of calculation by changing pinion, etc.  For example, if you have an option to change the pinion to 22, and spur to 85, the first gear ratio would be 3.86.  Replace that in instead of 3.33.  Then you get FDR 7.71.  If you just change the pinion to 20, that's 20:80 = 1:4.  That means, 4 x 1.08 x 1.85= 7.99.  If you change just the pinion to 25t then 25:80= 1:3.2.  So 3.2 x 1.08 x 1.85 = FDR 6.39.  

 

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@Juggular after looking at some examples/calculations/answers above, I did work it out to 6.66. But as usual, your calculations is really useful in illustrating the answer in detail. Actually, I am surprised you didn't put up some pictures as well. Perhaps I should throw some bearings into the equation?

(just kidding) 🙃

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Hey hey. Can you please cunfirm my calculations? There is gearbox ratio (only internal gears) and overall ratio (so called ORA) including spur gear and motor pinion, right?

Now internals are:

28t (gear on mainshaft)
27t (middle gear)
52t (diff gear)

Gives a internal ratio of 1.86, right?

Using a 96t spur and 21t motorpinion makes ratio 4.57 gives ORA=8,5

Thanks.

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46 minutes ago, Collin said:

Hey hey. Can you please cunfirm my calculations? There is gearbox ratio (only internal gears) and overall ratio (so called ORA) including spur gear and motor pinion, right?

Now internals are:

28t (gear on mainshaft)
27t (middle gear)
52t (diff gear)

Gives a internal ratio of 1.86, right?

Using a 96t spur and 21t motorpinion makes ratio 4.57 gives ORA=8,5

Thanks.

I had worked out the formula for Internal ratio. You do not even need to care about the intermediate gears to work it out 

It is: SI/P = FDR. 

So if you know your spur (S), pinion (P) and FDR (published in manual usually), you can work it out. 

To work it out on your example (I am assuming you got your 8.5 FDR from somewhere and it is correct). 

96I/21 = 8.5

96I = 8.5 x 21 = 178.5

I = 178.5/96 = 1.86

You are correct. 

However since you already got the teeth of other gears, we can double check:

52/28 is also 1.86.

EDIT: further note, the SI is useful if you are working on a chassis where only pinions are changeable and spur is fixed. Just work out the SI and record it. Divide it by your intended pinion and you get your FDR! Here is an example of my gearing notes. 

ZqCiSQm.jpg

 

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