Question about torque through a differential. 4

[sean7457]

I've currently got a gearbox that is driven by two electric motors. Each motor is ran through the same differential such that if one motor were to fail, the other motor could still drive the system.

My question is: Will the differential act as a torque multiplier?

I tend to think of it like a traditional differential in a car, only backwards -- replace each tire with a motor, and use the driveshaft as the output for the system. Assume the gear ratio between the motor and diff are 1:1.

The argument I've been having is that one of my co-workers seems to think that in this setup, the diff will add a 2:1 gear reduction, and thus double the torque output. In other words, if both my motors are putting out 10 ft*lb of torque, and they are tied directly to the differential at 1:1 and the differential is tied directly to my output at 1:1, I will still have a total of 20 ft*lb of torque coming out of my gearbox.

I understand that if you lose one motor, the speed will be halved, but the total torque out should remain constant? The load would just shift from one motor to the other?

...I hope I haven't confused anybody. Thanks in advance for any and all help.

 

[Compositepro]

I assume there is a mechanism to prevent back-spinning the failed motor. The torque on the two motor (wheel) shafts of the differential must always be equal, whether or not they are turning. All the differential does is to allow them to turn at different speeds. So, no it will not change the torque if one or two motors are running. Only the speed will change.

 

[sean7457]

Yes, both motors have brakes to prevent any back spinning.

That is exactly what I was always taught. I just wanted to verify that I hadn't forget any fundamentals of differential design.

Thanks!

 

[Tmoose]

But, if one motor become effectively locked, so the output rpm doubles, the ratio between still-driving motor and the output is now 2-1. I'd wonder what the power requirement of the load is when running at 2X rpm, and what the gearbox and other down stream components think of running so fast.

 

[sean7457]

Actually, if one motor locks up, the output speed would be cut in half -- not doubled.

As far as the torque goes, the output torque would remain constant, however, the load on the motor that is still operational would double. Which would also be true for any portion of the gearbox that is tied to that motor.

 

[LionelHutz]

I don't think the load on the operational motor increasing is true. The load on the operating motor and that side of the gearbox should remain constant. Assume the required output torque remains constant when one motor is stopped. Then, then the output shaft speed will drop to half and the output shaft power will drop to half. So, the operating motor must still produce the same input shaft power and since it's speed did not change it's still running at the same torque.

Of course, the above is assuming these electric motors are constant speed (they're likely squirrel cage induction motors) and that the load requires a constant torque at all speeds. In reality, the output torque will be whatever torque the load requires and the most likely case is that the required load torque will fall when the speed is reduced.

I've been thinking about this differential type gearbox and it's a very clever way to couple two motors to one load. This type of gearbox could be considered a constant torque unit which more or less adds the HP and speed of the motors together.
You can start one motor and accelerate the load to half speed then start the second motor to get the load to full speed. The motors will automatically share the load even if they are not identical. Heck, you could have an odd ratio 2-speed arrangement using different speed motors ( with matched or similar rated torque).

 

[Compositepro]

Differential gearboxes have been used for a very long time on machines like printing presses where precise registration between rotating shafts is needed. For example you can drive multiple printing drums (for different colors) with one line shaft driven by a 100 hp motor. A hand-wheel on a differential gear box can change the registration between drums while the machine is running. Or a one hp gear motor can be used so that a 0-100% change in the in the speed of this motor results in a 1% change in the speed of the differential output shaft. This has become somewhat obsolete with the development of very sophisticated electronic drives for motors.

 

[Warpspeed]

Running two motors through a differential will certainly double the effective torque, just as if the two motors were hard coupled would double the torque.

If one motor fails, going into this differential, you still get the torque doubling effect, but the output speed will now be half. Thus half the power too.

As already stated you will need a sprague clutch, or something to prevent reverse rotation of the no functioning motor for this to work.

 

[Compositepro]

Warpspeed, it sounds like you are disagreeing with what has been said but I don't think you mean to. A differential is designed to multiply torque between engine and wheels, as you say. This ratio is fixed by design, and is often greater than 2.0. When you say doubling the effective torque, you seem to be saying that this is due to having two motors rather than one.

In this case, where two motors are coupled to differential, and one motor stops, then the torque ratio of the differential will not change, but the speed ratio will change.

 

[Warpspeed]

A differential just splits torque two ways in a normal vehicle application, but this is something very different.
The torque multiplication in a car comes from the crown wheel and pinion ratio, not from the actual differential.

You said:

"In this case, where two motors are coupled to differential, and one motor stops, then the torque ratio of the differential will not change, but the speed ratio will change".

And I said:

"If one motor fails, going into this differential, you still get the torque doubling effect, but the output speed will now be half. Thus half the power too".

Which is exactly the same thing.
One motor stops, the differential's output torque remains the same, but the output shaft speed will be reduced to half the motor speed.

 

[Compositepro]

Except that in most cases "doubling" would be wrong. The true ratio might be 3.0 or 1/3 or something else.The change in speed ratio will always be exactly 2.0. The torque ratio and the change in speed ratio are not related to each other as your wording implies.

 

[Warpspeed]

Yes they most certainly are related.

The speed and torque relationship of a standard differential will always be exactly 2:1

Forget about the crown wheel and pinion ratio, they are quite independent of the actual differential, and not relevant to this discussion.

 

[patprimmer]

Warpspeed is correct.

Regards
Pat
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[patprimmer]

Lionel is also correct

Regards
Pat
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[Compositepro]

You will have to explain the usefulness of a two shaft differential since, as you say, the the ring gear and pinion are not part of a differential.

A differential in the real world has three shafts. Torque on two of these shafts will always be equal, or 1:1 ratio. The torque ratio between these two shafts and the third shaft will be determined by the pinion/ring gear ratio. Where do you find this 2:1 torque ratio?

 

[patprimmer]

Refer to the classic laws of mechanical advantage and the laws of conservation of energy.

Also the final drive of a car is inaccurately called the differential, even if the differential action is locked.

The final drive normally contains a differential gear set in addition to a crown wheel and pinion gear set. The differential is only the component that allows the wheels to turn at different speeds relative to each other, but still maintain the overall average speed of the crown wheel.

In the OPs example the differential drives the crown wheel whereas in a car final drive the crown wheel drives the differential.

Regards
Pat
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[Compositepro]

Pat I think you are confused. Please explain your reasoning. I've explained mine. I think you will find that you can't.

 

[LionelHutz]

Geeze, the ring and pinion is not the differential. Heck, in a non-standard application it would likely be a set of helical gears or a whole gearbox.

So, as an example, lets say these are 1500rpm motors with a rated 500ft-lbs output.

Start with both motors running. Each motor is inputting 1500rpm and is capable of 500ft-lbs of torque. The differential will be outputting 1500rpm and is capable of 1000ft-lbs. The differential is not doing any torque multiplying, it is just simply coupling the 2 motors together.

Now, stop one motor. The running motor is inputting 1500rpm and is capable of 500ft-lbs of torque. The differential is outputting 750rpm and is still capable of 1000ft-lbs of torque. The differential is now using a 2:1 gear ratio to 1/2 the speed and double the torque.

The differential output is always as above. The fact that the differential may drive another gear set with some other ratio has no bearing on this discussion.

 

[patprimmer]

I do not think I am confused.

I have explained it in first principles.

Lionel has elaborated on that explanation with example.

A differential allows shafts to turn at different speeds relative to each other, hence the name differential.

Regards
Pat
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[Compositepro]

Okay, I see what you guys are trying to say. When one "wheel" shaft is locked so it cannot turn, the differential is basically a 2:1 gearbox (times the pinion ratio). The actual torques will depend on the nature of the load and how it varies with speed, and on the capability of the motors to drive the load. If the load is constant torque, then when one of two (constant speed)drive motors stops, the output shaft will drop to 1/2 speed and the torque load on the remaining motor will double.