How to find torque on planet carrier

[csiddharthn]

I have the following data in an epicyclic gear train:

Angular speed on ring = 1500 rpm, teeth on ring = 30
Angular speed on sun = 3200 rpm, teeth on sun = 10
Angular speed on carrier = 1925 rpm, teeth on planets = 10

(The ratios of teeth are for simple calculation assumed 3: 1: 1 among ring, sun and carrier.)

Now,

torque on ring = 190 Nm
torque on sun = 50 Nm

How do I find the torque on the planet carrier?

 

[moogull]

Hi Csidd,

A question for you; when you mention that there are torques on the ring and sun gears, does this mean that they are the two inputs to the system and that the carrier is the output? If so I think you can use a power balance. Ideally, power out = power in. Not ideally, power out = efficiency*power in. Also, can you specify the directions of the rotations?

 

[moogull]

In addition, this is a nice article that may help you out without having to wait for a response from anyone: http://www.me.unm.edu/~starr/teaching/me314/planetary.pdf

 

[Baluncore]

I have not checked your gear ratios and relative RPMs.
Analyse the energy flow per minute.
power = rpm * torque

Wsun = 3200 * 50 = 160 k
Wring = 1500 * 190 = 285 k

The problem is that we do not know the direction of the torque.

There are two possible solutions.
The sum = 445 k
445 k / 1925 = 231. 169 Nm

The difference = 125 k
125 k / 1925 = 64.93 Nm

 

[alphy]

To find the torque on the planet carrier, we can use the formula for torque in a gear system:

Torque = Force x Radius

In this case, the force is the tangential force applied to the teeth on the ring, sun, and carrier, and the radius is the distance from the center of the gear to the point where the force is applied.

First, we need to calculate the tangential force on the ring and sun gears. This can be done using the formula:

Force = (Angular speed x Number of teeth x Gear ratio) / (2 x π)

Using the given data, we can calculate the tangential force on the ring and sun gears as follows:

For the ring gear:
Force = (1500 rpm x 30 teeth x 3) / (2 x π) = 713.5 N

For the sun gear:
Force = (3200 rpm x 10 teeth x 1) / (2 x π) = 508.6 N

Next, we need to calculate the radius for each gear. The radius is the distance from the center of the gear to the point where the force is applied. In this case, we can assume that the radius for all three gears is the same, as they are all part of the same gear system.

Now, we can use the formula for torque to calculate the torque on the planet carrier:

Torque on carrier = (Force on ring x Radius on ring) - (Force on sun x Radius on sun)

Substituting the values we calculated earlier, we get:

Torque on carrier = (713.5 N x r) - (508.6 N x r)

Since the radius is the same for both gears, it can be factored out:

Torque on carrier = r x (713.5 N - 508.6 N)

Finally, we can substitute the given torque values for the ring and sun gears to find the torque on the planet carrier:

Torque on carrier = r x (190 Nm - 50 Nm)

Therefore, the torque on the planet carrier is equal to r x 140 Nm, where r is the radius of the gears. To find the exact value, we would need to know the specific radius of the gears in the epicyclic gear train.