# forcing a differential

Discussion in 'Physics' started by strantor, Jun 21, 2012.

1. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
(mechanical question alert) This is sort of a continuation of my previous thread about theoretical 3 wheeled vehicles.

I've been giving some more thought to it, and mainly about mechanical solutions to the division of power between 2 wheels.

The ordinary (not LSD) differential of a car allows for one wheel of the car to spin faster & the other slower, with a constant power input. But, using a that same differential (or another type) is there a way to force unequal speed between the 2 wheels for a constant power input?

I'm pretty sure that if brakes were applied to one side, it would slow down on that side and speed up on the other side, which would accomplish the goal, but the vehicle would be working against itself for a period of time (inefficient). So what is the 'as close to lossless as possible' way to do it?

I considered placing a mechanical speed variator in parallel with the diferential, which would force unequal speed, but variators can o nly be adjusted while running. This would need to work from a stop.

Thanks for any ideas

2. ### davebee Well-Known Member

Oct 22, 2008
539
47
This sounds possible, but seems like it will need a completely different mechanical linkage than a differential.

What if each wheel was driven separately through a continuously variable transmission?

3. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
I was originally considering 2 seperately controlled electric motors. I've started to depart from that idea and towards the differential idea because it doesn't seem entirely safe for the steering to be set up that way. What if something happens to just one motor? What if the semiconductors in one controller fail shorted and one side of the car takes off like a bullet and causes the vehicle to spiral out of control at highway speed?

2 seperate CVTs sounds like it's on the same page as 2 seperate motors. I don't know much abot CVTs, but I assume this. I assume that 2 seperate *anything*s leaves the door open for catastrophe.

This is why I'm on the trail of a differential solution, because if the wheels are mechanically linked, then should something happen, it would happen to both sides. Now, I realize I sound like I'm contradicting myself, as I said before I want one side to spin faster than the other, by means of effecting one side in one way and the other side in the other way, but let me explain.

I'll conjure up a magic black box and call it a "speed diverter". The speed diverter has 2 shafts on it, and we can think of these as input or ouput shafts. It just (by magical mechanical means) sets a ratio of speed between it's 2 shafts. The absolute speed of the 2 shafts is irrelevant, the black box only care about ratio. It has a 1 turn adjustment wheel. All the way to the left, left speed = 0%, right speed = 100%. half way between left & center, left speed = 25%, right speed= 75%. Mid way, left speed = 50%, right speed = 50%, and so on.

If the differential were driven by a motor with no outside forces acting on it, I predict the result would be unpredictable. The division of speed would probably favor which ever wheel had the least rolling resistance and rather than drive in a straight line, the vehicle would meander off in some odd direction.

Now, we couple the 2 shafts of the speed diverter to the 2 axle shafts of the differential, and the division of speeds is mechanically forced to favor the setpoint of the speed diverter over the wheel with the least rolling resistance. At this point, we should be able input rotational power into the differential and control the wheel speeds via the speed diverter.

for the part where I don't contradict myself: with this speed diverter in place, if something were to happen to one wheel, say the brakes apply to one side only, on the left side, both wheels will be decelerated; the right wheel will be slowed in relation to the left wheel, at the rate determined by the stpoint of the speed diverter. If the driver is going straight, the speed diverter is in center position (50/50 split) and the wheels will be slowed at the exact same rate. If this brake failure happened during a turn (say, 25/75 split) then both wheels would be slowed at the ratio of 25/75 and the vehicle would maintain the same arc through the turn.

So I guess I'm looking for this conjured up speed diverter. Does it exist?

Or I'm still open to suggestion, if you think the CVTs still would work, I would like to hear more. Or any keywords for the 'completely different mechanical linkages' that you might have in mind.

4. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
It should turn like this:

Here's an example I cobbled together from google images' collection of clipart.

so if the ratio were 2:1 as drawn, the wheel on the left should be completing 2 revolutions for every 1 revolutions of the wheel on the right, and the rotations of the incoming power shaft (assuming 1:1 gearing in the differential) should be exactly in the middle between the two, at 1.5 revolutions for every 2 revs of left wheel and every 1 rev of right wheel.

I believe this should give me an arc as shown in the first pic, with R being equal to B.
Would you concur?

File size:
18.2 KB
Views:
64
File size:
174.4 KB
Views:
60
5. ### cork_ie Active Member

Oct 8, 2011
428
73
Yes there is a device known as differential lock see http://en.wikipedia.org/wiki/Locking_differential, which can be used if say one driving wheel got stuck in mud or snow. There is also another device known as a limited slip differential which will automatically lock the differential when the slip on one side exceeds a certain limit .
The modern ESP brake systems can also accomplish the same effect to distribute the torque to the vehicles wheels by automatically applying/releasing the brakes with varying pressure to different wheels as required and controlling the engine power output. This can help to straighten up a car in a skid or slide and restore grip when there is excessive slip .

6. ### Biff383 Active Member

Jun 6, 2012
50
19
A clutch on each side of the ring gear might work for you. Disengage the clutch on the side you don't want to power. Also on the what if scenario what if a tie rod end falls off on a conventional steering system...

7. ### davebee Well-Known Member

Oct 22, 2008
539
47
In a conventional differential, if you could control the rotation of the two little gears attached to the rotating cage, then you should be able to control the differential wheel rotation rate.

When the gears are fixed relative to the cage, the car goes straight. When the car is in a constant turn, the little gears rotate at a constant rate. To make a turn of some angle, then go back to driving straight, the little gears would turn by some angle, then be fixed again.

Ordinarily the gears are floating, subject to the forces applied to them by the wheels. So yes, clutches or brakes on one wheel could force the car to rotate, but it wouldn't be very controlled.

But suppose the little gears were attached to shafts of powerful stepping motors. Then each step of the motors would correspond to turning the car by some angle, then it would return to travelling straight. A constant rotation of the stepping motors would correspond to the car driving in a circle.

Do you think that might work?

8. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
Intriguing idea, and I agree. I hadn't thought of that. I assume it would need sliprings, sloshing around in a mixture of nonconductive oil and conductive sediment of metal filings/dust. Would need to make sure the oil is changed according to schedule. or possibly sealed sliprings rated for submersion. I will need to think about this more, but it sounds very good. Thank you.

9. ### WBahn Moderator

Mar 31, 2012
24,221
7,544
There are a couple of approachs to what you are trying to do.

First, you can use a planetary arrangement, which gives your three shafts - the sun, the spider, and the ring gear. You use two for the input/output and size the gears so that if the other (the control shaft) is held stationary the speed ratio is 1:1. If you turn the control shaft on direction, the output shaft turns faster than the input shaft and if you turn it the other the output shaft turns slower. This is the same approach that is used in things such as Constant Speed Gear Boxes (such as on the F-15) or the chair spacing adjustment section on a high speed detachable chair lift.

You could conceivable also use a standard differential noting that the normal drive shaft establishes the average (the common mode) speed of the two axle shafts but, other than that, they are allowed to move one faster/one slower than the average by the same amount (the differential speed). So if you used on axle as the input and the other axle as the output, if the drive shaft is held stationary the output shaft will turn at the same speed as the input shaft but in the opposite direction (easy to take care of). So, once again, if you rotate the normal drive shaft one direction the output shaft will turn faster and if you rotate it the other direction the output shaft will turn slower.

10. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
Like this?

If I've got that right, it's pretty close to davebee's idea but slightly harder for me to wrap my head around. I'll need to digest it. I think that with both of things you guys suggested, the effect of the turn will be dependent on speed. So the speed of whatever turning mechanism (stepper, servo, whatever) would need to be increased linearly with speed. That's conjecture not based on any math, do you think it's on the right track?

If the drawing I've made confirms to you that I've understood what you are conveying, then I think this is the superior idea so far. Trying to cram servos inside a differential doesn't sound fun.

File size:
128.3 KB
Views:
38
11. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
hmmmm.... I'm thinking I got the 2 driveshafts (what would be driveshafts in an ordinary car) wrong. I think they would be fighting eachother the way I drew them. If I used gear/gear instead of pully/belt I think they would cancel eachother out.

I think I should remove one driveshaft from the equation, just lock it down, so it's only purpose is to reverse direction. Then, use the remaining driveshaft solely to control the steering.

is that right?

This is a mindbender for me...

12. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
Here's a graphical representation, with an additional question...

Rather than lock that second shaft down, could driving torque be applied there? I'm lost now....

I think I need to get a differential and play with it.

File size:
136.7 KB
Views:
23
13. ### WBahn Moderator

Mar 31, 2012
24,221
7,544
That looks like something worth looking into, although I think we may have to turn the shafts in opposite directions. I would need to think on it some more.

strantor likes this.
14. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
Wow I've given you something that you need a while to think about? I don't feel quite so stupid now. (that's a compliment, not sarcastic)

I've gone over it quite a few times in my head; It's tough to follow but I'm 74% confident that driving torque could be input to one driveshaft and steering controlled by the other. Totally independent of eachother.

15. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
I talked myself down to 13% confidence on the drive home from work. I really wish my mind's eye were a better simulator. BTW do you know of some software I can use to simulate this?

16. ### WBahn Moderator

Mar 31, 2012
24,221
7,544
If you put drive torque into one of them, then you are more or less right back where you started with a normal differential arrangment because the outboard wheel can turn faster or slower as in the normal arrangement.

From a power efficiency standpoint, I'm guessing that you are going to be better off with a planetary arrangment.

17. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
agreed.
I'll have to look into that.

18. ### gerty AAC Fanatic!

Aug 30, 2007
1,237
344
You do realize that you are forcing unequal speed when you turn..
you demonstrate this in your post #4 drawing.

After typing that, are you looking to use this unequal speed for steering?

19. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,998
3,085
I think you are thinking about a differential being used in the traditional manner in the rear of a car, and yes, in that case, you could say that unequal speed is "forced" by the road. I word this in a different way; I say that the differential used in this manner allows for unequal speed of the wheels. In this case, the automobile is not in control of ratio of speeds between the wheels, as evidenced by runaway burnouts in wet weather.
I wish to have the operator be able to control the ratio of speeds between the wheels, and use this control as a scheme for steering in the absence of all linkages, unions, pivoting wheels, etc.

20. ### WBahn Moderator

Mar 31, 2012
24,221
7,544
I think you are going to have problems if you don't at least have pivoting wheels. A rigidly mounted wheel wants to track straight ahead. Turning two wheels at different speeds on a common axis is not too much of a problem and the object can turn about the vertical axis that passes through the common axis pretty freely. But if you add another wheel that does not share that common axis, then it will fight you. This is true even in aircraft that use differential braking on the main gear to steer -- the nose/tail wheel still needs to pivot.

In a conventional four wheeled vehicled, the two front wheels not only need to pivot, but they need to pivot by different amounts. because you want the axes of all four wheels to pass through a common point at the center of the turn. The steering linkages, such as the Ackerman steering arm, are pretty amazing when you understand the subtleties of what they do.