Understanding Automotive Differentials: How Do They Work?

In summary, without a limited slip differential, the torque on each wheel is the same but the power delivered will be different based on the traction available.
  • #1
bugatti79
794
1
Folks,

Is it true to say for standard "open" differentials that when a car is turning a corner that the torque is equal on both wheels but the power will be different based on the expression P=TW, assuming that there is sufficient traction for all wheels, ie no slip?

thanks
 
Engineering news on Phys.org
  • #2
Yes; because of the way open diffs are constructed, the torque to each wheel will always be the same, and because of the difference in distanced traveled by each wheel, the power delivered will be different.

This also applies to slip conditions.
 
  • #3
mender said:
Yes; because of the way open diffs are constructed, the torque to each wheel will always be the same, and because of the difference in distanced traveled by each wheel, the power delivered will be different.

This also applies to slip conditions.

Thanks. For limited slip differentials, the torque is the same on each wheel in tractive conditions but in slippery conditions torque can vary on each wheel due to torque biasing right?
 
  • #4
Torque biasing is kind of misleading when used to describe how a limited slip or locked diff works; that implies an active control of the torque according to the traction available when in actuality it is a wheel speed control.

All the LSD does is keep the wheel with no traction from moving faster than the one with traction by locking them together either with a ratcheting or a friction-based (worm gear or clutch) system. That has the benefit of not reducing the torque being applied to the wheel with traction to equal that of the wheel with less traction, as happens with an open diff as we already agreed.

Although some of the means of operation of the LSD can involve torque to actuate the locking mechanism, the main design objective is to keep both wheels rotating at the same speed. The different amount of torque being applied at the road surface is because of the differing traction available, not a torque biasing system per se.

Electronic traction control systems apply the appropriate brake to slow a spinning wheel and again synchronize wheel speeds but the result is essentially the same.
 
Last edited:
  • #5
bugatti79 said:
Thanks. For limited slip differentials, the torque is the same on each wheel in tractive conditions but in slippery conditions torque can vary on each wheel due to the differing traction available, not a torque biasing system per se.?

Ok just to clarify I have rephrased the above above based on your reply.

mender said:
All the LSD does is keep the wheel with no traction from moving faster than the one with traction by locking them together either with a ratcheting or a friction-based (worm gear or clutch) system. That has the benefit of not reducing the torque being applied to the wheel with traction to equal that of the wheel with less traction, as happens with an open diff as we already agreed.

Although some of the means of operation of the LSD can involve torque to actuate the locking mechanism, the main design objective is to keep both wheels rotating at the same speed. The different amount of torque being applied at the road surface is because of the differing traction available, not a torque biasing system per se.

Electronic traction control systems apply the appropriate brake to slow a spinning wheel and again synchronize wheel speeds but the result is essentially the same.

What I find a bit misleading and I believe some other people do too is when they refer to 'power' instead of 'torque' when describing differentials. Part of me is telling me that we can describe differential behaviour using either 'power' or torque because they are related by P=TW..but I don't think that is right...?
You could argue that if a wheel is spinning that it has some torque and also some power and so its suffice to use either for descriptive purposes etc...? Whats your view?

Thanks
 
  • #6
Proper usage of terms is important when discussing things exactly; unfortunately that doesn't happen much outside of forums like this!

Without having an example of the verbiage being used and the context it's hard to say what the best terms to use are but I'm sure you've noticed that sales brochures are more about selling than telling!
 
  • #7
One seldom mentioned effect of LSD (in rear wheel drive) is that understeer is generally promoted. This is good if the vehicle in question oversteers, but bad if it already understeers.

Respectfully submitted,
Steve
 
  • #8
mender said:
Proper usage of terms is important when discussing things exactly; unfortunately that doesn't happen much outside of forums like this!

Without having an example of the verbiage being used and the context it's hard to say what the best terms to use are but I'm sure you've noticed that sales brochures are more about selling than telling!


I like to think of torque which provides the movement of a component while the definition of power I use to describe the time element in keeping a component moving at a certain speed.

Just my 2 cents :-)


Dotini said:
One seldom mentioned effect of LSD (in rear wheel drive) is that understeer is generally promoted. This is good if the vehicle in question oversteers, but bad if it already understeers.

Respectfully submitted,
Steve

Interesting
 
  • #9
The extent to which the LSD locks the wheels together is a major factor in the wheels wanting to turn a corner. If the LSD is 100% locked up and the axle is effectively solid, the wheels will want to run straight ahead and resist turning.

Respectfully,
Steve
 
  • #10
mender said:
Torque biasing is kind of misleading when used to describe how a limited slip or locked diff works; that implies an active control of the torque according to the traction available when in actuality it is a wheel speed control. .

Can you explain why is it not technically correct to say that control of the 'torque' is the same as control of the wheel speed? If one controls the torque of a wheel then this automatically controls the wheel speed..?

mender said:
...the main design objective is to keep both wheels rotating at the same speed.

Under what conditions? The wheel speeds will be the same on a straight road and hence the torque assuming traction is the same on all wheels and this is equivalent to an open differential right?

Under what conditions do you want wheel speeds to be the same in a LSD..?
 
  • #11
bugatti79 said:
If one controls the torque of a wheel then this automatically controls the wheel speed..?
Other way around; if one controls the wheel speed it will indirectly control the torque output to each wheel. Controlling the wheel speed is much simpler and cheaper than controlling the torque bias so that's the usual method.

bugatti79 said:
Under what conditions? The wheel speeds will be the same on a straight road and hence the torque assuming traction is the same on all wheels and this is equivalent to an open differential right?

Under what conditions do you want wheel speeds to be the same in a LSD..?
Ideally the wheel speeds should only be the same when traveling in a straight line, and would differ as the vehicle goes around a corner. However, controlling the wheel speed to allow for the proper difference in distance traveled during the corner while also compensating for differing traction is complicated, so the simpler control scheme of locking the two wheels together is the usual solution.

Here's an actual torque splitting/biasing differential:
http://en.wikipedia.org/wiki/Torsen
 
  • #12
mender said:
However, controlling the wheel speed to allow for the proper difference in distance traveled during the corner while also compensating for differing traction is complicated, so the simpler control scheme of locking the two wheels together is the usual solution.

Assuming there is tendency for either wheel to slip on soft ground on a corner. Your comment above wouldn't apply in the case of sufficient traction on both wheel while negotiating a corner..right?

thanks
 
  • #13
Right; for that, an open diff is better. When cornering (once the corner is initiated), having the wheels locked can increase the likelihood of oversteer by forcing one wheel to slip, reducing the amount of lateral traction available as a result.

That's why the brake/traction control system has caught on, it emulates an LSD on demand but doesn't interfere with normal differential action when not needed.
 
  • #14
I see most of the open diffs really just pushing the gears on the faster side of the axle.

If both are turning at the same speed, both sides are being propelled.

If one side starts to go faster, say because you are going around a corner, or, one tire is on ice and the other on dry pavement, the faster tire is simply still the one being pushed, and the other side is coasting.If its a LSD, the two sides are held together, but the faster side is still being pushed and the slower side is still coasting if the break away torque setting is exceeded, allowing the two sides to go different speeds. (The two sides are both pushing until the difference between them exceeds the ability to hold them together, then it differentiates as normal.)If its a full locker, then the two sides can't differentiate even when the stresses build up...and the tires have to chirp or skitter around the turn on pavement, etc.

There are other types, like a Torsen, etc...which have different means of proportioning the differentiation.

I have a really old chevy video illustrating how an open diff works. I like the way it really simplified how the gears worked.



:D
 
Last edited by a moderator:
  • #15
Not quite; in fact there is a small tendency to drive the slower tire more than the faster one because of the friction of the differential gears themselves, but I'm being pedantic. :smile:

1. An open diff drives both wheels all the time with the same torque whether in a straight line or cornering. Trying to accelerate with the inside tire on ice and the outside tire on pavement should prove to you that an open diff doesn't allow either tire to "coast".
2. An LSD typically uses clutch packs to resist different tire speeds with no preference to which tire is going slower or faster. Usually there is a break-away torque that is preset with spring pressure. Drive torque (stepping on the throttle) increases the break-away torque value by forcing the spider gears apart, putting more pressure on the clutch packs.
3. A Detroit style locker is the only diff that coasts or overruns on the inside tire. It has a ratcheting mechanism to allow that.
4. A spool is locked 100% of the time and is the one that causes the chirping.
 
Last edited:
  • #16
mender said:
Not quite.

1. An open diff drives both wheels all the time with the same torque whether in a straight line or cornering. Trying to accelerate with the inside tire on ice and the outside tire on pavement should prove to you that an open diff doesn't "coast"
2. An LSD typically uses clutch packs to resist different tire speeds with no preference to which tire is going slower or faster. Usually there is a break-away torque that is preset with spring pressure. Drive torque (stepping on the throttle) increases the break-away torque value by forcing the spider gears apart, putting more pressure on the clutch packs.
3. A Detroit style locker is the only diff that coasts or overruns on the inside tire. I t has a ratcheting mechanism to allow that.
4. A spool is locked 100% of the time and is the one that causes the chirping.

1. The tire on ice is faster, and spins, the other one on dry pavement just sits there - I called that coasting.

What do you mean by them getting the same torque...if that means they are both spinning in the above scenario, its the opposite of what I see.

2. - Yup3. - Yup

4. - Well, there are selectable lockers like air lockers, elockers, etc, that are like a spool when locked, and either open or like an LSD when not locked, depending on model.
 
  • #17
Tea Jay said:
1. The tire on ice is faster, and spins, the other one on dry pavement just sits there - I called that coasting.

What do you mean by them getting the same torque...if that means they are both spinning in the above scenario, its the opposite of what I see.
The torque that each tire exerts on the surface whether ice or pavement is the same; the slippery surface limits the torque to both tires, which is why a vehicle gets stuck with only one tire on ice. They are both being driven (no "coasting").
 
  • #18
mender said:
The torque that each tire exerts on the surface whether ice or pavement is the same; the slippery surface limits the torque to both tires, which is why a vehicle gets stuck with only one tire on ice. They are both being driven (no "coasting").

If both are being driven, why is the one with traction (On dry pavement for example) just sitting there/not pushing the car, and the one on ice spinning?

The gears are only pushing the faster side as far as I know (As shown in the video I attached). Are you explaining something other than what the gears are doing?

When off road for example, this scenario is pretty common with open differentials. The faster side is the one being pushed by the differential, and, the side that is faster is moving...and the other one is no longer moving because the gears themselves are designed to only push the faster side. I know the differential is getting the rotation from the drive shaft, and proportioning it to the axles. If both axles are being rotated by this, shouldn't both tires be turning?

It sounds like you are saying that the differential is instead taking the rotation of the drive shaft, and applying it to both sides, but that it can't push any harder than the weakest side's torque. Physically, I believe that effect, but, don't see that as a direct gear engagement result, but as the collateral result of what happens if the gears are only pushing the faster axle shaft. I'm more of a suspension guy though, so if you can explain what I'm missing, I'd really appreciate it.
 
Last edited:
  • #19
Tea Jay said:
If both are being driven, why is the one with traction (On dry pavement for example) just sitting there/not pushing the car, and the one on ice spinning?

Its sitting there /not pushing the car because the other wheel that's slipping on ice is dictating what torque is going to be applied to both wheels ( Rememeber in an open diff the torque is always the same on each wheel).

Why is the slipping wheel dictating the torque? Because an open differential will find the path of 'least resistance' which is through the slipping wheel. The least resistance being the torque required to overcome the friction of the ice which is going to be less than the torque required to overcome the friction of the non slippy surface.

Hope this helps.
 
  • #20
To clarify what I am trying to understand - The differential is pushing on both sides, but only one of them moves (The one on ice for example). The one that moves can spin as fast as the rotation is being transferred, and the other one doesn't have to move at all.

I describe this as the differential propelling the faster side, and letting the other side "coast". (Coasting here is used by me to just mean the side that is not being rotated)

I believe your are pointing out that the "coasting" side is actually getting power too, just not enough to rotate it because it has more traction/resistance to overcome to be able to rotate.

Mechanically, I'm not sure I understand where this energy is going on the "coasting" side that is getting torque as the diff rotates. With a locker, the system winds up if there's a difference between the two sides, which is, as you mentioned, released by the tire's slippage, etc.

So, I'll get it if you explain the difference to me in terms of this example:

The tire that is not spinning is getting rotational input, but not enough to rotate it. The stationary tire is contributing more to getting the rig unstuck than if the rig had one wheel drive on the spinning tire's side.

If the above is true, then I understand what you mean. I just think of it as the diff pushing the faster side, mechanically...as that's the "Path of Least Resistance".
 
  • #21
mender said:
Other way around; if one controls the wheel speed it will indirectly control the torque output to each wheel. Controlling the wheel speed is much simpler and cheaper than controlling the torque bias so that's the usual method.Ideally the wheel speeds should only be the same when traveling in a straight line, and would differ as the vehicle goes around a corner. However, controlling the wheel speed to allow for the proper difference in distance traveled during the corner while also compensating for differing traction is complicated, so the simpler control scheme of locking the two wheels together is the usual solution.

Here's an actual torque splitting/biasing differential:
http://en.wikipedia.org/wiki/Torsen

I re-read the thread. We are saying (Believing) the same thing, I'm just oversimplifying it seems, as the essential differential function seems to be the same. "Coasting" does imply a lack of ANY propulsion, and that's of course inaccurate.

On this topic, especially in offroad circles, the use of the word "traction" is confusing sometimes. A locker is called a "Traction Aide" for example. Is this accurate, or is there a more accurate term?

I often think of the tires as having the traction...and that there should be a different term for the mechanical propulsion aspect.
 
Last edited:
  • #22
Please forgive me for bringing back this thread. This is actually one of the better diff discussions I've seen and thought I would add a bit. I apologize because not all of this is in order.

First, a bit about the open diff. Someone included a link to the old GM video on the open diff. That is a GREAT video and does an excellent job explaining what and why. It was also correctly mentioned by several that an open diff sends equal torque to both wheels. This of course is also true. I was debating with someone who didn't agree. Here is how I justified this view.

Consider the spider gears. These are the gears between the two axle outputs. Each output gear applies a load to the spider gear that would cause it to turn. We all know that if you have a force applied to an object it will want to move. We also know that if you don't have an opposing force the object will accelerate forever. Since we know the spider gear doesn't accelerate forever we can assume there is an equal but opposite force also acting on the gear. Well that equal but opposite force is the other output gear. Hence the spider pushes equally hard on both output gears thus equal torque.

What about relative speeds? Even though we normally don't think of it as such, a differential can be thought of as a mechanical math statement. The average speed of the two outputs equals the speed of the input. That's In=1/2 (Leftout+Rightout).

Tea Jay was discussing having traction and some confusion there. Really we might say "sufficient" traction. We can assume sufficient to be enough traction such that the wheel doesn't slip given the torque applied to the wheel. We can also think of how much torque the ground can apply to the tire. Even if the tire is slipping we know there is some resistance which will be seen as a torque resisting the turning of the wheel.



On to the LSD.

I think the thing that is hard to get about the LSD is the operating equation is actually quite easy. The sum of the torque applied to the two axle shafts is equal to the torque applied to the diff housing (the input torque). The speeds of the two wheels again follows the equation above. The catch is the equation for right and left torque. This is actually a two part equation. In all the stuff I posted below I describe the case when there is relative movement between the left and right wheel, the cornering case. There is also the straight line case.

In the cornering case torque is sent to each wheel via both the spider gears and the clutches (or other limiting mechanism). I have the equations and derivation below but the critical take away, which others have said is a LSD causes a tenancy to understeer. That's because it transfers torque to the SLOWER wheel, ie the inside wheel.

I didn't cover the straight case. In the case of going straight case we don't know exactly how much torque went to each wheel. If we know the torque required to get the clutches in the diff to slide then we can know the difference in wheel torque was less than what was needed to break the clutches free. So for a diff that can send say 70% power to one wheel, we can know that if the total torque sent to the diff was 100 ft lb, the lesser tire had enough traction to resist at least 30 ft lbs of torque applied to the axle.

OK, enough bathering, here is more blathering... with pictures!

**********************


Just a few things starting with the open diff:
1. Torque is like force, it's how hard you twist something.
2. Power is force times velocity or in this case torque times rotational speed. If you push just as hard but move twice as fast you have twice the power.
3. An open diff always sends equal TORQUE to each wheel. ALWAYS.
4. Since an open diff sends equal torque to both wheels the wheel that spins faster gets more power. So that one wheel on ice gets the same torque as the wheel on dry ground but the ice wheel is the only one getting power since it's the only one spinning.
5. The torque applied to the rear wheels (not the power) determines how hard the tires are pushing the car forward.

So at this point we can figured out that with an open diff each rear wheel pushes just as hard. If one is one ice, neither can push that hard.

Limited slip diffs come in a few basic types. You have the old spring loaded clutch pack type. Those have a fixed locking torque. Locking torque is what makes the output shafts try to spin at the same speed as the diff housing. For a clutch pack diff the locking torque is the torque needed say turn the wheel when the car is on jacks and the transmission is in gear. Next you have speed sensitive diffs. These are ones where the locking torque is related to the difference in speed between the axles and the diff housing. They act like an open diff if both wheels are spinning at about the same speed but act like a LSD when one wheel spins up. Finally we have ramp clutch, torque sensing clutch packs, Torsen, Quaifee (sp?) and other torque sensing diffs. In these diffs the locking torque is proportional to the torque into the diff. So when you are on the gas the diff has a lot of locking torque. When you are off the gas the diff is rather open. Even those all these torque sensing diffs have different guts, as a black box they all work about the same way. Since the clutch pack version is the easiest to see I used it in these pictures.


Now on to the pictures...

1. A basic clutch pack diff. This diff uses the separation force of the output gears from the spider gears to load up the clutch discs. That means this example is using a torque sensing diff. Note that because the clutches are between the housing and output any time the housing is spinning faster than the output the output will feel a torque in the forward direction. The opposite is true in reverse. There are two ways torque can be applied from the housing to the output; 1. via the spider gears, 2. via the clutch plates. The total torque to the output is ALWAYS the sum of those two torques.
Dif1.jpg


2. The open diff. Without the clutches the torque sent to each wheel is ALWAYS equal. The wheel on ice can't handle any torque so no torque gets sent to the wheel with grip. I stressed this because EVEN when we add clutches the SPIDER GEARS always send equal torque to each wheel. The clutches make up the difference.
Dif2.jpg


3.Now we turn to the right (imagine we are looking at the back of the car). The right wheel slows, the left wheel speeds up. We have relative motion in the clutches. Since this is a torque sensing, not speed sensing, diff it doesn't mater if the speed difference is 1/2 RPM or 100 RPM, the torque the clutches apply to the output shaft is still just a function of input torque.
The right wheel is spinning slower than the diff. That means the torque on the right output shaft is forward (or trying to make the right wheel spin faster). The torque from the spider gears is also forward. So we have two forward torques added together. Call that T_spider + T_clutches.
The left wheel is going faster so the torque the clutch applies to the output shaft is in the reverse direction. The equation looks like this: T_spider - T_clutches. So in one case we have addition and in the other subtractions. It's pretty clear that the addition case (ie the inside wheel) is going to get more torque. More torque at the wheel means more force on the ground.
Since the inside wheel is pushing harder than the outside wheel the rear axle is creating an understeer moment. If the front wheels were on casters the car would try to straighten out! Of course the front wheels over power this with their own steering moment but this is why a LSD (and of course a spool which is like an LSD with REALLY REALLY high bias!) tend to make a car understeer. Its just most of the time the front wheels can compensate.
Dif4.jpg

Dif5.jpg


5. The above is true until the inside tire slips. This is the case where everyone says, "See the LSD sends the power to the wheel with grip!" Well yes but that's because it sends more power to the slower wheel. When the inside tire slips it speeds up. Makes sense, it doesn't have the road to slow it down. Of course all the math above holds true. The inside tire is now the fast tire. That means the torque to the inside tire is T_spider - T_clutch. Since the outside tire is now the slow one it's torque equation is: T_spider+T_clutch. So the non-slipping tire gets more torque and everyone is happy.
Dif6.jpg


But there is a problem in that last bit. When you are cornering hard the outside tire is doing all it can to keep the rear end of the car from sliding out. When the inside tire loses grip it speeds up which means we get a lot of torque quickly transferring to the outside tire. The poor outside tire had just enough grip to handle pushing the car forward and keeping the tail in line. So now we spin thanks to the quick transfer of torque from the inside tire to the tire with grip! Fortunately this typically happens slowly and progressively enough that we can balance things and drive the car on the edge. Make no mistake, the LSD makes the edge sharper even though it doesn't always make it faster.
 
  • #23
Sideways, that's a fantastic discussion, loved it.

You are great at explaining things.

:D

My context for the above is primarily off road based, but I agree with the on road examples as well.

As far as my question regarding the proper terminology for off road "Traction"; Do you think its wrong to call a locker a "Traction Aid"?

To me, the traction part is, or should be the part related to the rubber's grip on the substrate.

The diff's job seems to be torque biasing rather than traction.

I'm looking for a better way to label what a locker or LSD does than "Traction Aid", if that's warranted. Otherwise, I'll just go along with the convention.

:D

Any input?
 
  • #24
I really haven't thought it out enough to say. It doesn't aid traction in that it doesn't increase the tractive force a tire can apply via the ground. For example with the open diff and one tire on ice, the other tire has good traction but no torque with which to use the traction.

What the locker does is better enable you to use the full traction of a single tire. So I guess in that regard is does aid you to use what you have. Like many things I hate to too carefully scrutinize the transition from physics terms to popular vernacular.

The torque biasing part is also sometimes problematic. What a torque biasing diff normally does is use the input torque to the diff to control the resisting torque of the internal clutch or other mechanism. Thus the resisting torque of the clutch is a function of input torque vs a fixed value or a function of RPM difference as in a viscous LSD.

What a LSD does correctly do is distribute torque unevenly between the two driven wheels (or axles for a center diff). So with a LSD I can send 60%, 80% or with a locker even 100% of the torque to one wheel. The drawback is that, excepting brake based systems, all of these end up sending torque to the slower wheel. This makes sense when you are stuck in the sand. The one wheel spins up, the wheel that isn't spinning gets the lion's share of the torque and moves the car forward.
 
  • #25
Sounds like torque proportioning or distributing might be better then.

:D

A more torquey engine would also add more available torque to the drive wheel, but would not be considered a traction aid either.

Its not increasing traction, its increasing the torque available to use of the any traction found.
 
  • #26
Basically yes.

Aside from wear, the open diff plus computer controlled brakes is theoretically a better system even though many of the car people shudder at the idea. However, here's why it's good. The open diff always splits the torque. That means at any point in time we can send half the available torque to either wheel. Most of the time our concern is that we have more torque than one wheel can handle thus that wheel slips and the other wheel is thus limited to the low torque value of the slipping wheel. With a wheel brake we can increase the the torque an axle handles by adding the brake torque to the traction "torque" (of course that traction goes through a few steps before becoming a torque in the axle). With the brake torque and the traction torque added to 1/2 the engine torque we now can deliver the other 1/2 of the engine torque to the other wheel.

Even better we can do this when the wheel speeds aren't supposed to be the same. We can now effectively control torque and speed of both wheels. The speed is controlled because, theoretically, the speed of the engine (diff housing) is the average of the two wheels and, thanks to our traction brake system neither is slipping. We control torque to each wheel individually via two inputs. The first is the engine throttle. That determines the max torque to each wheel. The second is the brake application. Brake application determines the reduction in torque to either wheel. Thus torque to say the outside wheel is 1/2 engine torque while torque to the inner wheel is 1/2 engine-brake load.

This also has a critical advantage in that you don't have the sudden spike in torque like you do with a LSD as it starts to break free.

With a LSD we already said while cornering the slower wheel gets more torque. Unfortunately that also happens to be the unloaded wheel when you are cornering hard. If, due to cornering, the inside tire unloads to the point where it starts to slip (ie the torque is greater than the traction available) it will speed up. Well if you look at the formula for torque to the wheels you can see that if the inside tire speeds up then the clutch torque can drop to zero. That results in a sudden INCREASE in torque to the outside tire. Well that tire was already doing it's best to keep the rear end in line as you were turning. No it's like you were on the limit and VTEC just kicked in yo. You exceed the grip of the outside tire and the car spins. Not cool.

With off road things might be different. A true locker or LSD sometimes might be better than a brake based system (again ignoring the wear and brake heating issues). I said with the open diff you can only send 50% of the torque to any wheel. It may be there is a time when, say climbing a rock, where one wheel has PLENTY of traction but you need more than 50% of the engine torque to actually get the vehicle to move. I'm not an off roader so I'm just speculating.
 
  • #27
slideways said:
Basically yes.

Aside from wear, the open diff plus computer controlled brakes is theoretically a better system even though many of the car people shudder at the idea. However, here's why it's good. The open diff always splits the torque. That means at any point in time we can send half the available torque to either wheel. Most of the time our concern is that we have more torque than one wheel can handle thus that wheel slips and the other wheel is thus limited to the low torque value of the slipping wheel. With a wheel brake we can increase the the torque an axle handles by adding the brake torque to the traction "torque" (of course that traction goes through a few steps before becoming a torque in the axle). With the brake torque and the traction torque added to 1/2 the engine torque we now can deliver the other 1/2 of the engine torque to the other wheel.

Even better we can do this when the wheel speeds aren't supposed to be the same. We can now effectively control torque and speed of both wheels. The speed is controlled because, theoretically, the speed of the engine (diff housing) is the average of the two wheels and, thanks to our traction brake system neither is slipping. We control torque to each wheel individually via two inputs. The first is the engine throttle. That determines the max torque to each wheel. The second is the brake application. Brake application determines the reduction in torque to either wheel. Thus torque to say the outside wheel is 1/2 engine torque while torque to the inner wheel is 1/2 engine-brake load.

This also has a critical advantage in that you don't have the sudden spike in torque like you do with a LSD as it starts to break free.

With a LSD we already said while cornering the slower wheel gets more torque. Unfortunately that also happens to be the unloaded wheel when you are cornering hard. If, due to cornering, the inside tire unloads to the point where it starts to slip (ie the torque is greater than the traction available) it will speed up. Well if you look at the formula for torque to the wheels you can see that if the inside tire speeds up then the clutch torque can drop to zero. That results in a sudden INCREASE in torque to the outside tire. Well that tire was already doing it's best to keep the rear end in line as you were turning. No it's like you were on the limit and VTEC just kicked in yo. You exceed the grip of the outside tire and the car spins. Not cool.

With off road things might be different. A true locker or LSD sometimes might be better than a brake based system (again ignoring the wear and brake heating issues). I said with the open diff you can only send 50% of the torque to any wheel. It may be there is a time when, say climbing a rock, where one wheel has PLENTY of traction but you need more than 50% of the engine torque to actually get the vehicle to move. I'm not an off roader so I'm just speculating.

You are correct.

Off road, the brake based systems tend to at least require programming changes to allow some spin, to "get going".

What happens off road for example on systems that have poor programming, is that the truck will just sit there shuddering. Essentially, as soon as some torque is applied, the system senses slippage and brakes the spinning tire...and if none of the tires has enough traction on its own to make the rig MOVE, well, the poor things sit there shivering and shuddering as each tire tries to rotate, goes faster than another tire, and is promptly braked.

By allowing some initial spin/rotation to occur, it also allows the other tires to try to pitch in on the propulsion thing, so some momentum can be gained.This is also why, from a propulsion stand point, the front lockers can outperform the rear lockers.

Essentially, the locker really only helps if one side slips, by allowing the OTHER side to keep pushing you up the hill, etc.

The tires that slip the MOST though are the front tires, which are more lightly loaded, and tend to have less wheel travel to stay on the terrain.

So, lockers help the axle which slips the most, more than they help the axle that slips the least...and if it doesn't slip at all, the locker is not a factor.Of course, its a lot harder to STEER a locked front end.

:D
 
Last edited:
  • #28
slideways said:
Consider the spider gears. These are the gears between the two axle outputs. Each output gear applies a load to the spider gear that would cause it to turn. We all know that if you have a force applied to an object it will want to move. We also know that if you don't have an opposing force the object will accelerate forever. Since we know the spider gear doesn't accelerate forever we can assume there is an equal but opposite force also acting on the gear. Well that equal but opposite force is the other output gear. Hence the spider pushes equally hard on both output gears thus equal torque.




Now on to the pictures...

1. A basic clutch pack diff. This diff uses the separation force of the output gears from the spider gears to load up the clutch discs. That means this example is using a torque sensing diff. Note that because the clutches are between the housing and output any time the housing is spinning faster than the output the output will feel a torque in the forward direction. The opposite is true in reverse. There are two ways torque can be applied from the housing to the output; 1. via the spider gears, 2. via the clutch plates. The total torque to the output is ALWAYS the sum of those two torques.
Dif1.jpg


2. The open diff. Without the clutches the torque sent to each wheel is ALWAYS equal. The wheel on ice can't handle any torque so no torque gets sent to the wheel with grip. I stressed this because EVEN when we add clutches the SPIDER GEARS always send equal torque to each wheel. The clutches make up the difference.
Dif2.jpg

.

Very impressive post I must say. Thanks! I am still having trouble visualizing how the torque is split 50:50 relative to the axle input pinion in an open diff.

If we look at the case of vehicle moving in a straight line then we know that the diff housing which is rigidly attached to crown wheel rotate as one unit with no relative rotation of the spiders inside.

Now since the spider pinion is in mesh with a spider gear on either side we know that the force and hence the torque on the left spider gear (left half shaft) will be the same as that on the right (right half shaft).

If we look at the picture, essentially the crown wheel, housing with its gears is one piece...right?

So is it not the case that whatever torque the crown wheel is delivering is the same along the axle half shafts...? I just don't understand how the axle half shafts torque is half axle input torque.
 
  • #29
bugatti79 said:
Very impressive post I must say. Thanks! I am still having trouble visualizing how the torque is split 50:50 relative to the axle input pinion in an open diff.

If we look at the case of vehicle moving in a straight line then we know that the diff housing which is rigidly attached to crown wheel rotate as one unit with no relative rotation of the spiders inside.

Now since the spider pinion is in mesh with a spider gear on either side we know that the force and hence the torque on the left spider gear (left half shaft) will be the same as that on the right (right half shaft).

If we look at the picture, essentially the crown wheel, housing with its gears is one piece...right?

So is it not the case that whatever torque the crown wheel is delivering is the same along the axle half shafts...? I just don't understand how the axle half shafts torque is half axle input torque.
I think its because the torque is applied evenly, and if both sides rotate at the same speed in response to the input, the gear pushes on both sides evenly.

If one side rotates faster in response to the torque input (Because that side had less resistance/is slipping, or, is on the outside of a turn, etc...) then it is now the side that is being pushed at the limiting factor.

The OTHER side is being pushed at this factor as well, but the available torque may be inadequate to push the vehicle, or to rotate the tire against the greater resistance.

If you watch the video I posted, it does a pretty good job of showing how that torque is applied mechanically. I also needed Sideways' explanation to fully grasp MECHANICALLY about the torque split though.

Combine both parts, and I think it will make sense for you too.

Look closest at the part that starts at about 3:50 - 6:10, that's the part that is immediately relevant to your question...its the KEY to the principle.
 
Last edited by a moderator:
  • #30
bugatti79 said:
Very impressive post I must say. Thanks! I am still having trouble visualizing how the torque is split 50:50 relative to the axle input pinion in an open diff.

If we look at the case of vehicle moving in a straight line then we know that the diff housing which is rigidly attached to crown wheel rotate as one unit with no relative rotation of the spiders inside.

Now since the spider pinion is in mesh with a spider gear on either side we know that the force and hence the torque on the left spider gear (left half shaft) will be the same as that on the right (right half shaft).

If we look at the picture, essentially the crown wheel, housing with its gears is one piece...right?

So is it not the case that whatever torque the crown wheel is delivering is the same along the axle half shafts...? I just don't understand how the axle half shafts torque is half axle input torque.

If I understand the question correctly, you are OK with the idea that the left and right axle torque is the same. But I think you are confusing something I have said. I think the confusion is the statement that the sum of the left and right torque is that of the crown gear. So if the engine applies 100 N-m to the crown then the left + right shaft torque = 100 N-m. This doesn't mean that each wheel sees 100 N-m.

Think of a seesaw. Put a 30kg kid on each end. The pivot has to support 60kg. The crown gear has to apply enough torque for both wheels. If that torque split is even then the torque to each wheel is 1/2 that of the crown gear.
 
  • #31
Torque is the same while speed of each wheel is different.
 
  • #32
slideways said:
If I understand the question correctly, you are OK with the idea that the left and right axle torque is the same. But I think you are confusing something I have said. I think the confusion is the statement that the sum of the left and right torque is that of the crown gear. So if the engine applies 100 N-m to the crown then the left + right shaft torque = 100 N-m. This doesn't mean that each wheel sees 100 N-m.

Think of a seesaw. Put a 30kg kid on each end. The pivot has to support 60kg. The crown gear has to apply enough torque for both wheels. If that torque split is even then the torque to each wheel is 1/2 that of the crown gear.

See attached my sketch. I have difficulty understanding how the torque is split 50:50 in the case of straight line driving in which the crownwheel/diff housing and diff gears are all rotating as one, ie just one rigid bar...
 

Attachments

  • IMAG0160.jpg
    IMAG0160.jpg
    15.4 KB · Views: 475
  • #33
Go the other way then; let's put the car in the air on a hoist and a guy at each wheel with a lever attached to the wheel. Pretend it's not a diff but is forced to act as a solid bar and the driveshaft is locked (automatic in park).

How much torque is there at the carrier if one guy is applying 40 N-m on one wheel? Now have the other guy exert 60 N-m in the same direction on the other wheel; how much torque is acting on the carrier now? Is it any different than if both guys were at the same wheel and still applying the same amount as before? The forces are balanced, so it's always 100 at the carrier because that's the total of the forces being applied.

If a mechanism allows the forces to be applied equally to two (or more) "resistances", the force applied at each is the original force divided by the number of resistances. That's why a four wheel drive doesn't accelerate any faster in four wheel drive than it does in two wheel drive; the power input is the same but the torque at each of the wheels in four wheel drive is half as much as at the rear wheels in two wheel drive. That's also what keeps the tires from spinning in four wheel drive when they would spin in two wheel drive.
 
Last edited:
  • #34
bugatti79, I don't think you can assume that the axle shaft is solid from one side to the other in the case of straight line driving. The appearance is the same but it is not the case.
-
I would say it is similar to hooking a chain from one corner of the front of the vehicle to the other corner of the front in a fashion that allows the chain to loop out ahead of the vehicle about 20 feet. Pull on it while allowing the loop to slide back and forth on whatever you are pulling it with and you can guarantee the force on the chain will be split in half. Anchor the loop chain to whatever is pulling it so it cannot slide and you no longer have that guarantee.
 
  • #35
bugatti79 said:
See attached my sketch. I have difficulty understanding how the torque is split 50:50 in the case of straight line driving in which the crownwheel/diff housing and diff gears are all rotating as one, ie just one rigid bar...

They aren't really rotating as one. Think of it as balanced. A seesaw with two 30kg kids is balanced but that doesn't mean the thing can't pivot. The only way it stays balanced is if the load on each side is equal.

Take a look at the video Tea Jay posted. Notice the part where he attached a single spoke to each wheel (3:45) and where he pushes each with a bar (4:20). What he is illustrating with the bar that can't pivot is a welded seesaw. He shows how holding one wheel will stop the bar. I think that should be easy to see. Because the bar is locked in the center, you can't spin it and both wheels turn at the same speed. This is the welded axle case.

At 4:51 he puts the bar on a pivot. Now it's like the seesaw. If the bar is going to not rotate the loads on either end must be equal. So if the load the bar applies to each side is equal then the torque to each wheel must be equal. Does that clear up the straight line case?

Now when we corner the bar (gear) does spin but it does so at a constant speed. Well let's think of angular acceleration. If the gear spins at a constant speed that means all the forces are balanced. The gear teeth on the left side have to push with equal but opposite force with respect to the right or the gear will not just spin but accelerate. So if it's not accelerating, then the forces must be equal thus the torques are equal. This second explanation is perhaps a bit to brief but I think if you understand the first one it's easier to see this one.
 
<h2>1. How does a differential work?</h2><p>A differential is a mechanical device that allows the wheels of a vehicle to rotate at different speeds while still receiving power from the engine. It works by using a set of gears to distribute power from the engine to the wheels, while also allowing the wheels to rotate at different speeds when turning.</p><h2>2. What is the purpose of a differential?</h2><p>The purpose of a differential is to allow the wheels of a vehicle to rotate at different speeds while still receiving power from the engine. This is necessary for smooth turning and to prevent the wheels from slipping or skidding on the road.</p><h2>3. How do I know if my differential is malfunctioning?</h2><p>Signs of a malfunctioning differential include unusual noises, such as whining or grinding, when turning or driving, vibrations or shuddering while driving, and difficulty turning or steering the vehicle. If you experience any of these symptoms, it is important to have your differential checked by a mechanic.</p><h2>4. What is the difference between an open and a limited slip differential?</h2><p>An open differential, also known as a standard differential, distributes power evenly to both wheels. A limited slip differential, on the other hand, uses a series of clutches or gears to distribute power to the wheels with the most traction, allowing for better handling and control on slippery or uneven surfaces.</p><h2>5. How often should I have my differential serviced?</h2><p>It is recommended to have your differential serviced every 30,000-50,000 miles or as specified in your vehicle's owner's manual. Regular maintenance can help prevent major issues and prolong the lifespan of your differential.</p>

1. How does a differential work?

A differential is a mechanical device that allows the wheels of a vehicle to rotate at different speeds while still receiving power from the engine. It works by using a set of gears to distribute power from the engine to the wheels, while also allowing the wheels to rotate at different speeds when turning.

2. What is the purpose of a differential?

The purpose of a differential is to allow the wheels of a vehicle to rotate at different speeds while still receiving power from the engine. This is necessary for smooth turning and to prevent the wheels from slipping or skidding on the road.

3. How do I know if my differential is malfunctioning?

Signs of a malfunctioning differential include unusual noises, such as whining or grinding, when turning or driving, vibrations or shuddering while driving, and difficulty turning or steering the vehicle. If you experience any of these symptoms, it is important to have your differential checked by a mechanic.

4. What is the difference between an open and a limited slip differential?

An open differential, also known as a standard differential, distributes power evenly to both wheels. A limited slip differential, on the other hand, uses a series of clutches or gears to distribute power to the wheels with the most traction, allowing for better handling and control on slippery or uneven surfaces.

5. How often should I have my differential serviced?

It is recommended to have your differential serviced every 30,000-50,000 miles or as specified in your vehicle's owner's manual. Regular maintenance can help prevent major issues and prolong the lifespan of your differential.

Similar threads

  • Mechanical Engineering
Replies
20
Views
1K
  • Mechanical Engineering
Replies
12
Views
11K
Replies
1
Views
4K
  • Mechanical Engineering
Replies
2
Views
1K
  • Mechanical Engineering
Replies
4
Views
4K
  • Mechanical Engineering
Replies
7
Views
1K
  • Engineering and Comp Sci Homework Help
3
Replies
102
Views
4K
Replies
2
Views
1K
  • Mechanical Engineering
Replies
9
Views
6K
  • Mechanical Engineering
Replies
6
Views
6K
Back
Top