An open differential does technically send equal amounts of torque through both wheels. This is precisely WHY the inside tire always lights up going around a corner under heavy throttle. Because the their is less weight on the tire, it will lose traction sooner and the same amount of torque will actually cause it to spin potentially faster than outside wheel (particularly under power). Keep in mind that torque and half shaft speed are not always the same thing...every single kind of differential allows the tires to spin at different rates, this is why its called a differential. A solid rear end (ala shifter kart) always spins the inside tire because the tires are forced to rotate at the same speed because there is no differential. A limited slip differential will be able to bias the torque to the outside tire somewhat when there is a difference in the speed of rotation.

Sorry for the lack of technicalities...posting from work and my brain is a little fried....

I could add that the reason LSD type differentials make a car more difficult to drive is because the differential uses the available grip of both tires better. In an open differential, the same torque is always applied to both tires, and since in every corner there is a weight shift from one side to the other, you have an uneven load on the tires. In a FWD car,the open differential will allow one tire to spin like crazy while another tire remains traction, causing mild understeer, an LSD increases understeer at the limit because by the time you completely lose traction if the differential is strong enough both tires will lose traction at almost the same time, meaning a total loss of grip for steering and braking purposes at the moment. Same thing applies to RWD except replace understeer with oversteer.

LSD's will make you potentially faster in the corners, unless you are a poor driver in a high powered car that has enough torque to overwhelm both drive tires simultaneously, than its a catastrophic loss of grip compared to in an open diff car.

 

Omairthman1,
Older clutch type diffs had a reputation for wearing out. Newer ones in some cases should last the life of the car. The cone type clutch diff in the later Miatas was a type of clutch diff. It was reported to last just fine. Conversely, in racing application the Torsen diffs would and did wear out. They were also sensitive to lubricants. Unlike the clutch diffs the Torsens were hard to tune or adjust.

Nunco,
Your post ended forcing me to think a lot more. In the end I’m almost sticking to my story but your questions were sharp and forced me to think a lot to make sure I was confident in my answers.

Since I started with the claim that open diffs always transmit equal torque to each wheel and built my discussion of the LSD on that claim let me offer some level of proof for that claim… then let me prove it not entirely true

First, proof the torque to each wheel of an open diff is equal. I don’t think this is the proof I had to show years back in my kinematics class but it still works. Look at the spider gear and the two output gears. The spider is the center of the three gears. The spider has two loads applied to it. They can be thought of as tangential forces applied to either side of the gear. The magnitude of each of those forces is proportional to the magnitude of the torque applied to the two axles. This is simply stating that the force applied to a gear tooth is proportional to the torque on the axle shaft. So the spider gear has two forces applied to it and those two forces are in opposite directions. One force will cause the diff to spin clockwise, the other counter clockwise. Well if those forces aren’t balanced the spider MUST accelerate (angular acceleration). The only way the spider gear can remain at the same speed (not rotating when the wheels are moving at the same speed or fixed angular rate when you are making a constant radius turn or have one wheel on ice etc) is if the loads on the spider are balanced. Hence so long as you are in a static state (constant speed turn, straight etc) the forces/torques on the two outputs of the diff MUST be equal.

So now it’s time to mess up what I just claimed. First, when you are transitioning from say a turn to straight (ie changing radius turn) or when the wheel starts to spin up, the forces will not be balanced. The proof is the one I gave above. If the spider gear changes speed it can only do so via an imbalance in the forced applied to it by the two output gears (along with the action of the input shaft). So during a transition in spider gear rotational speed the forces will not be perfectly balanced. However, I would speculate that those changes in force would be very small in most cases and the equal torque assumption is probably very safe.

The other disclaimer is that it is more accurate to say the torque ratio is fixed but it doesn’t have to be 50:50. I can’t think of any rational reason why you would want a non-50/50 diff on a 2WD car. You might want a non equal split on an open diff center diff. I can’t think of an example as I’ve only ever heard of center diffs that are either open 50:50 or LSD with some ratio (not necessarily 50:50). In any case with a change in the pitch radius of the meshing gears (or a change to a different open diff layout) you can get something other than 50:50 but the ratio will still be fixed. The open diff doesn’t ensure equal distribution of power, just equal torque.

On to the LSDs…
You caught me on something. When talking about the clutch loading I was working with the assumption that the left and right clutch packs always have the same actuation torque. This is true when looking at a ramp style clutch system.
http://www.motoiq.com/magazine_artic...ferential.aspx
In this example the clutches are squeezed by a pair of plates that are forced apart by a wedging action of the spider gear axle. So in these diffs both left and right clutch will always have the same clamping force thus the same locking torque.

In the diff I pictured the clamping pressure of each clutch pack is a function of the spreading force of the spider gears with respect to the output drives. What you said about uneven clutch loading had me thinking. In the end I don’t agree and feel that both clutches will still have the same clamping force. Here’s why.

The clamping force only comes from the torque transmitted through the spider gears, not the clutches. If the load on the left side drops the force on the left side of the spider gears will also have to drop. That means the force on the right side spider gears must drop because the spider gear force is always balanced. So long as it’s balanced then the spreading force of the gears must also be balanced thus the clutch torque is balanced.

Variable torque when the wheels are spinning the same speed…
I believe you are correct that with a LSD you can have essentially an unknown distribution of torque between the left and right wheels IF both wheels are going the exact same speed. If both wheels aren’t going the same speed then the force required to overcome the clutch friction will always be T_clutch. T_clutch may be fixed as in a spring clutch or variable as in the ramp diff I linked to above. Regardless, the torque required to spin the output with respect to the diff housing is always T_clutch.

So we have one wheel on sand, the other on pavement. We give the car just a bit of gas. Well both wheels are only being asked to push just a little. The same force is applied to each contact patch. Since no slipping is occurring each tire is applying the same force thus an even distribution. If we start pushing just a bit too hard for the sand then the tire will slip if ever so minutely. The moment we have a difference in wheel speeds we MUST have overcome whatever the locking torque happens to be. That is always the case. If the output moves at a different speed that the case it must have overcome the clutch friction thus the T_clutch.

Where things could get fuzzy is if we can get an unequal load but equal speed on the wheels. Two tires in snow or mud might do this. However, since it could only occur at times when the wheels speeds are equal I’m not sure it would mater much. Still, I’m not overly convinced of my explanation. I mean if we consider a spool nothing more than a LSD with a VERY high clutch torque and that can transfer 100% of the torque to either wheel at all times then we clearly can send all the torque to one wheel even when both spin at the same speed. Beyond saying it would ONLY happen at equal wheel speeds thus even the slightest amount of slip of one wheel (0.0001 RPM difference) would render the point moot.

Side point, a spool can send 100% of the power to either wheel. Think of a 4x4. One wheel is off the ground, the other still pushes the truck forward.


Outside wheel having more torque…
Nope, this one is definitely not the case IF we aren’t slipping. As before we said the spider gears WILL deliver equal torque to the left and right output shafts. The clutches will either ADD or REMOVE net torque from the shafts depending on the speed of the shaft vs the diff housing. If the wheel is going FASTER than the diff housing the clutch will apply a torque which tries to slow the output hence T_spider-T_clutch. Conversely the clutch will always try to speed up a slower wheel (T_spider + T_clutch). So in normal non-slipping turns the inside tire gets more torque. If the inside tire is slipping the outside wheel gets more torque.

Note that the above is very different than an open diff. In the open diff we ALWAYS see equal torque at both wheels. When both tires have good grip that means both push just as hard. When one is on ice neither push hard. With the LSD we have the INSIDE tire pushing harder at first but then the non-slipping tire pushes harder (either due to say sand or a hard turn unloading the inside tire). This is very different than an open diff.


Viscous diffs…
So far I have mostly used clutch diffs in my discussion because they are easy to understand. Some have a spring pack and a fixed T_clutch. In others T_clutch varies with input torque. Either way a key point is IF the output shafts aren’t moving at the exact same speed as the diff housing then the output torque is T_spider+/-T_clutch.

Well the viscous diff makes that a bit more complex. We can still think of the locking torque as “T_clutch” though in this case it’s T_Viscous_clutch. The problem is the torque of T_clutch is now a function of the delta between the left and right output shafts. So all the same equations apply. The inside wheel still gets T_spider+T_Viscous_clutch. The outside still gets T_spider-T_Viscous_clutch. However, if the difference in wheel speeds is very small, say a normal right hand turn or a freeway cloverleaf then then V_left_V_right (rotational velocities) is small thus T_Viscous_clutch is small and the diff basically behaves like a traditional open diff. Since we are unlikely to see a big wheel speed difference when neither wheel is slipping most of the time the diff behaves like an open diff. Only when you peg leg it or have a wheel on ice do you notice the T_Viscous_clutch but by that time you have already lost speed in that corner.

Viscous diffs are superior when your wheels aren’t slipping because they don’t have the large, under power, understeer moment the torque sensing diffs can give you. However, they also only serve to limit, not stop peg leg turns thus they aren’t great for racing. An advanced hydraulic diff might have the ability to fix that issue but that’s outside of the scope of this post.



Budgy,
I’m not sure I fully agree with your “why LSD is harder” part. First, I think we should be clear, LSD doesn’t mean the car will be hard to drive. You didn’t say that but I want to make sure people understand I’m not saying that either. I think the problem with a LSD, or perhaps tradeoff is the better term, is that a LSD first creates an understeer moment which means you need to turn into the turn more then can quickly transition into an oversteer moment just at the time you have your front wheels turned in to counter an understeer moment.

I disagree that the LSD uses the grip of the tires better. That is only true some times. IF you don’t need it then it’s inferior. Even if they were legal a LSD in a FF racecar wouldn’t make sense. Those cars are finely balanced and typically have more grip than power (far more grip than any road legal car, only 116hp and power to weight that many road cars can best). A FF rarely would lack for traction coming out of a turn. However, the added understeer moment would require a bit more turn in when exiting a turn. That would ask a bit more of the front wheels and may slow the car.

Conversely I think the LSD makes you faster in cases where you have more power than grip. That would include low powered cars with crap tires or high powered cars. The problem is the LSD makes the edge sharper. That’s fine when we are driving on a race track but not so fine when driving in the rain. Also, LSD’s have some level of compromise in their setup. The Infiniti Pro Series race cars use ramp-clutch pack LSDs. They will change the ramp profiles depending on the track. Clearly one setup is not idea for the same car when the track is changed. The same is true for road cars. The perfect LSD for an S2000 on a dry track with stickies may be a nightmare in the rain with all season tires.

Don’t take all of what I have said to mean a LSD is a bad thing in a car. Most of the time it does make you go faster and does get the job done. It’s not a perfect solution. You might have missed it but this discussion came out of the McLaren thread. There was a critical comment that McLaren would have been better with a LSD instead of the brake based system they used. I actually think that, from a performance POV, if well executed a brake system is superior to a LSD in just about every way. It’s an open diff when an open diff is better yet it is a good LSD when we want a LSD. The drawbacks I can see are (presumably); cost, increased brake pad wear, who says it’s easy to get it right.

Good discussion all!

 

Would the Torsen LSD in an NB Miata be a negative then? Or would it still help the car. I understand this is really general.

 

It's a definite maybe! Really, it depends on tires, alignment, driving conditions, what you are looking for out of the car. I've found the LSD makes the car faster in most conditions but sometimes makes it feel less natural. It is also a bad pairing with hard tires so if you buy a second hand Miata with a LSD, get rid of the crap tires. You also might notice a chirp from the inside tire if you make a sharp U-turn, that's the diff.

 

NuncoStr8,
I would be interested to know if at this point I sold you the way I described the operation of a LSD.

 

In my many years of experience with autoX, where there are no straight lines and the goal is to drive the car at 10/10ths speed at every moment, any car with an LSD will always be faster than that same car without the LSD. Always. Without exception.

When Lotus released the Elise LSD option in mid 2005, most serious autoXers retrofitted their non-LSD Elise with the new stock-legal part, and they were significantly faster than the non-LSD Elises. Even in a car like the Elise, where the weight of the mid-engine affords the car incredibly good rear traction without an LSD, that traction is still significantly improved WITH an LSD.

Andrew

 

aklucsarits,
What you are saying is generally true. It doesn't actually conflict with anything I just said. LSDs almost never will improve handling. At best they don't harm it. However, they often do help when you have relatively high power vs relatively low grip. This is almost always the case with an autocross where you are in low gears and often have the power to spin the inside tire of an open diff car.

The catch is don't confuse track times with "handling" I know of a Formula Continental driver that adjusted the air pressure in his tires down a bit. The net result was the car didn't handle as well. He felt the car was less precise and somewhat squirmy vs the original higher pressure. However the car was also faster around the track because the tires were better able to grip the road. He prefered the FEEL of the higher pressure setup but the extra grip of the lower pressure setup. If the objective is always fastest lap times then with most streetcars some type of LSD is going to be best. Of course what is best for a dry autocross may not be "best" for other times such as what feels good when driving on wet roads. If the objective is natural feeling (as was Lotus's intent with the orignal Elise) then often an open diff is a better option. If the cars in question have a lot of grip but not so much power (as is the case with FF) then often open diffs are actually faster.

If we don't care about cost and if we can make all the electronics work then an electronic diff is probably the best solution. It solves one of the big issues I outlined above. Rather than sending torque to the inside wheel in "non-slip" cases, it removes torque from the wheel that's about to slip only when it's about to slip. The rest of the time it can send even torque to both wheels.

 

Actually the more grip you have, the greater the need for LSD. The greater the cornering grip, the more you unload the inside drive wheel. Even with low hp, if you have enough grip to unload the inside wheel you'll get inside wheelspin.

I don't think so. With the brake system, you're just throwing away the drag on the spinning wheel. With a clutch-type LSD, the "drag" on the inside wheel that's trying to spin is transmitted to the outside wheel. If you have GOBS of power (enough to overwhelm both tires anyway), no biggie. If your power/weight is more modest, the clutch lsd has a big advantage over a virtual lsd using the braking system.

My 2x $.02 = $.04!

 

Besides the effective power loss with the brake-based "electronic LSD" systems, the most serious problem with such systems is that they are terrible for prolonged performance driving because they cause and exacerbate brake overheating.

Mini Cooper Ss are no longer available with the mechanical LSD option. The LSD used to be a $500 a la carte build option that was pretty much the best bargain on the Mini options list. In 2011s model year, the LSD was discontinued and a new brake-based "Electronic LSD" replaced it. Strangely, the new "Electronic LSD", even though it was nothing more than software code in the ECU, also costs $500. Minis with the LSD are fantastic track day cars because they are lightweight cars and come with phenomenal brakes from the factory. Overheating brakes are rarely a serious issue with a Mini on a track day. The owners of 2011+ Minis with the Electronic LSD report that, regardless of what brake pads or fluid they use, the brakes overheat and turn to mush within 2 or 3 laps due to all the extra braking generated by the Electronic LSD.

Andrew

 

Yeah, that too! Even on a supercar like the new McLaren, I see this as cost-savings over real performance. Boo/hiss!