Question

A compound gear train is composed of four gears, A, B, C, and D. Gear A has 10 teeth and is meshed with gear B. Gear B has 20 teeth and shares a shaft with gear C, which has 16 teeth. Gear C is meshed with gear D, the output gear. Power is supplied at gear A with 100 ft·lb of torque and is traveling at1600 rpm.
1.The necessary torque output for the system is 500 ft·lb. What should the gear ratio of the system be?
2.With a system torque output of 500 ft·lb, how many teeth should gear D have?

Answer 1

@abb0t Ya think you can solve this?

Answer 2

Basically, if the drive gear has lesser teeth it is trying to increase torque. If you can imagine the system it will make more sense. You have a smaller gear rotating a larger one, thus reducing the speed, however, giving off a larger distance for what is being transported, moved, etc. The lb-ft is being increased which is your torque.

output torque, T\(_o\), is 100 lb-ft. We are looking for input torque, T\(_i\)

So first figure out your gear ratios... Gear Ratio= \(\frac{Output}{ Input}\)

Answer 3

erm what's the output and Input ? I remember learning about it but I forget...

Answer 4

output of gear number teeth, and input gear numb.

Answer 5

Gear Ratio= \[\frac{ 100 }{ 500 }\] ?

Answer 6

@abb0t

Answer 7

so 10 -> 20 and 16 -> D?

Answer 8

Can you do me a favor and just show me the formula,how to substitute and Solve, and what my final Answer would be for each question? To get the full picture. I learn better that way?

Answer 9

To solve for 2
use: T\(_1\) w\(/_1\) = T\(_2\)w\(_2\)

Answer 10

solve for w\(_2\)

Answer 11

@abb0t can you plug the numbers in for me?

Answer 12

You're an engineering student! C'mon!

Answer 13

I'm a 10th grader! lol I suck at this stuff.

Answer 14

so... okay wait Torque is 100 so I would divide that by something ? Correct?

Answer 15

Yeah, 100(1600) = 500w\(_2\)

Answer 16

you can use the value of w\(_2\) to see the ratio, it should be clear at that point. and just reduce it to get it in the ones value.

Answer 17

so \[w_{2}\]

Answer 18

would be 320?

Answer 19

yes

Answer 20

Making #1 = 320?

Answer 21

Yes, i should of explained it better. Sorry I am kind of working on something right now at the moment
T\(_1\) is the torque or the first gear, w\(_1\) is the angular velocity of the first gear, T\(_2\) is the torque of the last gear and w\(_2\) is the angular velocity of the last gear.

Answer 22

ohh okay it kind of is clicking now.. Thanks and no it's fine. can you help me with #2 and a couple more too? Or are you busy?

Answer 23

If you notice the ratio of w\(_1\):w\(_2\) = 1:5, yes?

Answer 24

100:500

Answer 25

So that means that w\(_1\) spins 5x faster than w\(_2\)

Answer 26

wait for which question was that for? I'm confused..

Answer 27

therefore, you have 50 teeth

Answer 28

question 2

Answer 29

ohh okay I get it now...