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Question about torque through a differential.
4

Question about torque through a differential.

Question about torque through a differential.

(OP)
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.

RE: Question about torque through a differential.

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.

RE: Question about torque through a differential.

(OP)
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!

RE: Question about torque through a differential.

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.

RE: Question about torque through a differential.

(OP)
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.   

RE: Question about torque through a differential.

2
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).  

RE: Question about torque through a differential.

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.

RE: Question about torque through a differential.

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.

RE: Question about torque through a differential.

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.

RE: Question about torque through a differential.

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.

RE: Question about torque through a differential.

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.  

RE: Question about torque through a differential.

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.

RE: Question about torque through a differential.

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?

RE: Question about torque through a differential.

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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RE: Question about torque through a differential.

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

RE: Question about torque through a differential.

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.
 

RE: Question about torque through a differential.

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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RE: Question about torque through a differential.

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.

RE: Question about torque through a differential.

(OP)
Lionel,

If I understand you, you are saying that if one motor is stopped, the other motor will see no load change?

My current design is using two electric motors on a 24V power supply that is restricted to a maximum of 2 amps. So based on your example above, I would not have to size one motor to handle the total required output torque? In other words, each motor has no idea whether or not the other motor has stopped working?

To take it one step further, you are saying that I could essentially lock one side of the diff and use it as a 2:1 reduction?
  

RE: Question about torque through a differential.

The one remaining motor, IF IT RETAINS THE SAME SPEED will also require the same torque.

The output will retain the original torque but the speed will be halved so the power will be halved.

The 2:1 reduction in speed gives a 2:1 multiplication in torque at the output.

Removing drive from one motor halves the total input power. The change in effective drive ratio corrects for the loss in torque at the expense of speed or distance travelled. This of course presumes that it is accepted that power equals torque times speed.

Regards
Pat
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RE: Question about torque through a differential.

Pat - It's OK, I'll confirm that you're not confused.

Compositepro - no, the torque load on the remaining motor does not double.

Sean - YES. To go back to your first post, your co-worker is correct.

The differential must always have the same torque on both input shafts and it always adds the torque on both input shafts together to the torque on the output side. Don't confuse the stopped motor as meaning there is not any input torque applied to that shaft. The stopped input shaft still has the same torque applied, it's just applied at 0rpm via a brake of some sort instead of being applied at a rotating speed via a motor. If you didn't have any input torque applied to one of the shafts then you'd get no output torque (both input shafts would just rotate opposite directions).

So, thinking about it like above, it's not technically a torque multiplier or torque doubler, it's a torque adder. Funny though, since T1 = T2 and Tout = T1 + T2 you always get Tout = 2 x T1 and so it always does doubles the torque of a single input shaft.

This is why I posted it's a HP adder. You don't remove any torque from the differential input shaft when you stop the motor, you just remove HP.
 

RE: Question about torque through a differential.

(OP)
Lionel,

OK, so in THIS case it would act as a 2:1 reduction.

If, for example, the motors were not identical (T1 does not equal T2), then the reduction ratio would depend on the ratio of the motor sizes, correct?

I think the confusion for me from the beginning was that I was being told a differential will ALWAYS add a 2:1 reduction regardless of input.

Also, you stated in your first post:

'This type of gearbox could be considered a constant torque unit which more or less adds the HP and speed of the motors together.'

So in your example of two 1500RPM/500ft*lb motors, shouldn't your differential be outputting 1000ft*lbs at 3000RPM when both motors are running? And then when one motor goes down, you'd have 1000ft*lbs at 1500RPM?

RE: Question about torque through a differential.

I am just extremely grateful that I have never had to teach this stuff to students.

And then we have various strange compound configurations of epicyclic gear trains to think about......

RE: Question about torque through a differential.

The gearbox and more or less are important parts of that comment. I was making a general comment about a gearbox that used a differential.

What is this 2:1 reduction? What speed you are comparing the output speed to?

The differential itself adds 1/2 the speed of each input to get the final output speed.

S(out) = 0.5 x S(input1) + 0.5 x S(input2)

If you use the sum of the input speeds then the differential is always a 2:1 reducer. If you have matched motors and compare the output speed to a single motor's input speed then it's a 1:1 when both motors are running and 2:1 when one motor is running.

And I thought some simple numbers in an example would make the relationships clear.
 

RE: Question about torque through a differential.

(OP)
First of all, thanks for all your help and taking the time to fully explain this. I really appreciate it.

What I meant by THIS case is that because both motors happen to be the same, the ratio ends up being 2:1. But this isn't necessarily the case for all situations.

For example (assuming I'm understanding what you've said up to this point):

If you have two different motors:
M1 = 100ft*lbs @ 500RPM
M2 = 20ft*lbs @ 500RPM

Then your output with both motors running = 120ft*lbs @ 500RPM. With only one motor running, this would change to 120ft*lbs @ 100RPM (a reduction of 5:1 -- 100/20)

You could also have varying input speeds as well:
M1 = 100ft*lbs @ 500RPM
M2 = 20ft*lbs @ 200RPM

Then your output with both motors running = 120ft*lbs @ 350RPM ((500/2)+(200/2)). If one motor fails in this scenario, then your output would change to 120ft*lbs @ 70RPM (a reduction of 5:1 -- 100/20).

I know this might be going slightly beyond the scope of my initial question, but I'm trying to fully understand the fundamentals here.

Thanks again!

RE: Question about torque through a differential.

No, you apparently don't understand at all. The torque from both input shafts (motors) must always be equal and it always sums to 2x a single input shaft torque at the output. The input speeds added together is 2x the output speed (or inputs speeds added together divided by 2 equals the output speed).

In both examples
Output = 120ft-lbs both running means each motor = 60ft-lbs.
M1 stopped you can get 40ft-lbs out.
M2 stopped you can get 200ft-lbs out.

Example #1
If either motor stops then the output speed is 250rpm.

Example #2
If M1 stops then the output speed is 100rpm.
If M2 stops then the output speed is 250rpm.


Once again, here are the formula to follow.

T(out) = T(input1) + T(input2)
       where T(input1) must be equal to T(input2)

S(out) = 0.5 x S(M1) + 0.5 x S(M2)

T is the torque and S is the speed.

I have no idea how to make this any clearer.
 

RE: Question about torque through a differential.

Are these Induction motors?  

RE: Question about torque through a differential.

(OP)
Tmoose -- no, these are DC servo motors.

Lionel -- OK, torque must be equal on both inputs. That being true, how could you have a torque higher than the rated torque of a motor on one side? Wouldn't the whole system be reduced to the max output of 2X the smallest motor?

In other words, in both the above examples, you could only expect 40ft*lbs (2x20ft*lbs) at the output. The 80ft*lb difference between the two motors would essentially 'bleed off'? Just like in a car when you hit an ice patch on one tire with this type of differential.  

RE: Question about torque through a differential.

It appears you figured out the problem with your example.

RE: Question about torque through a differential.

(OP)
...it was definitely a long journey, but I think I finally got there.

Thanks for all the help!

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