Planetary gear with clutch. Input/output ratio 1

[soundara]

Hello there,

Please take a look at the attached pic. The sun has 20 teeth,planets(3) have 16 teeth and the ring has 52. The planetary gear ratio(teeth no .ring/sun) is therefore 2.6 . The ring gear is the input of the driveline and the planetary carrier is the output. when the clutch is locked (see figure) The input output gear ratio(ring/planet) is supposed to be 2.6 + 1 . Could you please help me arrive at this formulation.

 

[BrianPetersen]

It isn't.

The ratio is (2.6 + 1) / 2.6 = 1 + (1 / 2.6) = 1.385:1

If you figure out how many times the planets rotate in world co-ordinates during each revolution of the planet carrier, and translate that into the number of teeth that the outer ring has to advance, you can see why this is the case.

 

[tbuelna]

soundara,

Your diagram appears to show the clutch element coupling the sun gear and ring gear. When the sun and ring gears are coupled, you have what is normally called a "shaft". So the input/output ratio is simply 1.0.

When the sun and ring are de-coupled, the sun gear would appear to be free spinning, thus you have an "open" gear system (ie. one that is not capable of transmitting force). So the input/output ratio becomes infinite.

Your schematic seems to be incomplete. Or maybe I'm missing something?

 

[BrianPetersen]

That's true ... my calculation was for sun gear locked stationary. If sun gear is locked to ring gear, the whole thing just spins as a unit. If sun gear is not connected to anything, it's in neutral.

 

[soundara]

well, I will make a few more things clear. The gap that i have mentioned in the figure contains a magnetisable fluid. When the fluid is magnetised, torque is transferred else its a free system with no torque transfer..The magnetisation of the fluid provides the resistance to motion till a threhold value of torque and when the torque above the threshold the sun starts to rotate too (not fixed to the ring anymore). This action is supposed to lead to torque multiplication when it comes out of the output(planet -output drive which is then tranmitted to the rear axle).the input to output ratio is supposed to be 2.6 +1 = 3.6..could you plz suggest me how ths can be reached through formulations...thanks

 

[BrianPetersen]

Unless something in the system is referenced to something stationary, torque multiplication is impossible.

Any gain in torque through the shafts has to be matched by torque applied in the opposite direction to the stationary housing ...

 

[NTROhio]

BrianPetersen and tbuelna are right. The gears have a fixed torque ratio that cannot be changed and is determined by the force balance on the planet gear. Excluding acceleration and gear losses, the contact force between the ring gear and the planet must be equal and in the same direction as the contact force between the sun gear and the planet gear. The force exerted by the planet pin, attaching the planet gear to the planet carrier, on the planet gear will be equal to the sum of the teeth forces and in the opposite direction. This cannot change which means ratio of the net torque cannot change. The ratio between the net torque on the carrier and the net torque on the ring gear will always be 1.385. When the sun gear is locked to the frame the net torque on the ring gear is the input torque and the net torque on the carrier is the output torque so the out:in torque ratio is 1.385. When the sun gear is locked to the ring gear, the input torque is no longer the net torque on the ring gear because some of the torque is pulled off to drive the sun gear. The ratio between the net torque on the ring gear and the carrier remains 1.385 but the input torque is greater than the net torque so the out:in ratio drops to 1. For the out:in torque ratio to be greater than 1.385 the net torque on the ring gear must be greater than the input torque. This requires energy being pulled out of the sun gear and added to the ring gear so there seems to be significant information missing from the system description. The sun gear would be rotating in the wrong direction so any type of drag force directly between the sun and ring gears would pull energy out of the ring gear and reduce the out:in torque ratio to 1. Increasing the torque ratio would require the sun gear being connected to a gear rotating in the opposite direction faster than the ring gear. Any sort of drag coupling will limit the torque gain to the lock-up ratio and the extra energy will be heating the lock-up device.

 

[tbuelna]

soundara,

Don't get too discouraged. Planetary, epicyclic and differential gearing usually confuse me too.

Regards,
Terry