This is a great thread. I wish I'd read it earlier, though -- the descriptions of power transfer in the basic descriptions for open, limited slip, and locked differentials are incorrect, however. These are common misconceptions, but wrong nonetheless. I work in terms of force and torque all day (structural engineer), so hopefully I can contribute a little more accurate explanation. I may change the order to make things a little easier to understand -- a limited slip actually makes more sense once you explain a locker, since it falls between an open and locked diff in operation.
differential is a differential with no restriction to prevent the two wheels from turning at different speeds. An open differential always applies exactly the same torque to both axles.
It is a common misconception that an open differential only supplies torque to the wheel with the least traction, but this simply isn't true. Both wheels will get the same amount of torque, and that torque will be limited by the least amount of traction available to either wheel. In other words, to provide a couple of examples:
- If you have one wheel on ice with a traction capacity of 50 lb-ft, and one on clean pavement with a traction capacity of 1000 lb-ft, both axles will get 50 lb-ft of torque, which probably won't be enough to move the vehicle. The wheel with traction is getting torque, just not enough. At 100 lb-ft of total torque applied at the differential, you get wheelspin on the wheel on ice, and you cannot apply any more torque to the axle.
- If you have one wheel in the air, both axles will get ZERO ft-lb of torque, since this is the traction capacity of the wheel in the air. You can apply NO torque to the axle, and obviously cannot move the vehicle.
locks the axles together, permitting NO difference in wheel speed between the two wheels. With a locker, each axle gets torque proportional to available traction
, up to the total limit of traction. For example:
- First, we take our previous ice example, with a traction capacity of 50 lb-ft for the wheel on ice, and 1000 lb-ft for the wheel on pavement. If you apply 500 lb-ft total to the differential, 50 lb-ft will go to the wheel on ice, and the remaining 450 lb-ft will go to the wheel on clean pavement. You can keep applying more torque to the axle, and it will continue sending that extra torque to the wheel on pavement, which will propel the vehicle forward until you reach the limit of traction on the good wheel. At the traction limit, you have 50 lb-ft on the icy tire and 1000 lb-ft on the good tire, giving you 1050 lb-ft to move the vehicle. Add more torque and the good tire just spins.
- Try our example with the bad-traction tire lifted into the air again. Now, you have ZERO torque capacity on one wheel, and 1000 lb-ft on the other. The locker will transfer all axle torque to the good tire, giving you 1000 lb-ft to move the vehicle before the good wheel starts to spin too.
Open differentials and lockers are simple to describe. LIMITED SLIP DIFFERENTIALS
are a little more complex. In operation, they fall partway between an open diff and a locker. The two important things to know about an LSD are bias ratio
is the measure of the maximum amount of torque the differential can transfer to the good wheel compared to the bad wheel. For most limited slip differentials, this is somewhere around 3:1 to 6:1, meaning the good wheel can get three to six times the torque as the wheel with bad traction. Open and locked differentials have a bias ratio too -- an open differential has a bias ratio of 1:1, meaning both axles must have equal traction, and a locker has a bias ratio of infinity:1, since you can transfer as much torque as you want to the good tire, even with zero torque on the bad wheel. Some front wheel drive LSD's (not that most folks here would care) are designed with much lower bias ratios on the order of 1.5:1 or 2:1, to prevent harsh engagement that would jerk the steering wheel around on varying terrain.
is the measure of a limited slip differential's ability to transfer torque to the good tire when there is NO traction on the bad tire. Not all LSD's have preload
, as it is a feature that must be designed in, and the amount of torque that can be transferred by preload only is very small compared to the torque transfer in a locker. For instance, I measured the preload in the 31 spline Trac-Loc differential in my Bronco at just over 100 lb-ft. The 28 spline Trac-Loc in my Mustang only has around 40 lb-ft when it's working properly, and is currently at around 20 lb-ft (worn out).
Now, on to our examples. We'll have to compare two different LSD's -- one with preload, and one without -- in order to illustrate how bias ratio and preload work together. We will assume a 5:1 bias ratio and 100 lb-ft of preload.
HOW TO DRIVE WITH AN LSD
- First, an LSD with no preload on ice. Again, 50 lb-ft of traction on the ice, and 1000 lb-ft on the dry pavement side. In this case, you can apply a total traction of 300 lb-ft to the axle. You get 50 lb-ft on the bad wheel, and the 5:1 bias ratio lets you put 250 lb-ft on the good wheel. After that point, the LSD can't transfer any more torque (without proper LSD driving techniques I'll explain later), and any further attempts at applying the go-pedal just spins the wheel on ice and cooks the diff. You do, however, get 300 lb-ft to move the vehicle, which is three times better than you get with an open diff. You can get more than that if you know how to drive it, but I'll get there later.
- Same icy road, but with 100 lb-ft of preload. You can now transfer five times the torque on the bad wheel, plus the preload, to the good wheel. Hence, now you get 50 lb-ft on the bad wheel, and 250+100 lb-ft or 350 lb-ft on the good wheel. That's 400 lb-ft to move the vehicle, or four times better than the open diff.
- No preload, one wheel in the air. If you don't know what you're doing, you get zero traction -- the non-preloaded limited slip can't transfer torque without some resistance on one side. Five times zero is still zero. See the section on how to drive a limited slip diff to get around this.
- Preload, one wheel in the air. With no resistance on one wheel, the maximum torque you can transfer is equal to the preload, or 100 lb-ft. 100 lb-ft isn't impressive, but mathematically it's infinitely better than zero.
You can work around the limit of the differential's bias ratio with a little skill. Let's simplify this example and say we're only working with a rear limited slip differential. No preload, 5:1 bias ratio ... and one wheel in the air. You're stuck. What do you do?
Well, you lightly apply the emergency brake. What? I'm stuck and you want me to put the brakes on
? Are you nuts? Well, that's exactly what you do. You can accomplish the same thing with the foot brake while you're moving, but sometimes when you're stuck stuck, the e-brake works better because it doesn't increase drag at the front wheel.
Look at the basic physics of the situation. Assume you lightly apply the e-brake and get 200 lb-ft of resistance per side to turning the wheel, at both wheels (your brakes are capable of a LOT more than this). You now have a 200 ft-lb resistance on the wheel in the air. That means the diff can now transfer 5*200 or 1000 lb-ft to the axle for the wheel with good traction! Now, that wheel has 200 lb-ft of brakes on it too, so you lose a little, but you still have 800 lb-ft of traction on that one wheel to move the vehicle. Note that this requires an INPUT torque to the axle of 1200 lb-ft to overcome the drag from the brakes, but it gets you off the rock. You just don't want to do this all day, or you'll cook your brakes, and possibly other things.
This trick works for all limited differentials, including gear-type diffs like the True Trac, with the possible exception of viscous diffs. I'm not certain about the viscous diffs either, it may work there too. Besides, who the heck wants to use a viscous diff off-road?
If you learn to drive your LSD, rather than just hammering down the skinny pedal and praying you get there, you'll find they're not nearly as bad as some people claim. They're a LOT better than an open diff, and while they're not as good as a locker offroad, they're a very good compromise for those of us who have to drive our trucks on the street too. They're also a lot more friendly (and useful) on ice.
What remains is the mostly a copy from a post of mine on another board explaining the types of limited slip differential. If you want to include this information, feel free to copy, chop, or modify its format to suit this post -- so long, of course, as the information itself remains intact.
I don't have much time to do any editing of this this afternoon (spent all my free time above), so I'm just gonna fire away.
There are many different varieties of differential that could be called "gear driven," and some of them are very different. The Torsen diff is a worm-type differential, which means it counts on the fact that worm gears typically transfer torque better in one direction than the other. Most differentials do not use worm gears, which sets this type off into a class of its own. Other gear-type examples include the True Trac and Quaiffe.
Most typical limited slip differentials are a variation of the Salisbury type, with or without ramps, and using either one or more cones or clutches for lockup. The basic principle of the Salisbury is that transmitting the torque from the pinion gears (on the cross shaft) to the side gears (splined to the axles) causes a spreading force on the side gears, and if you put some sort of clutch between the side gear and the housing, you can use this spreading force to restrain the movement of the side gear relative to the housing (hence, limiting slip). If you add ramps, you can magnify the spreading force, and set it up to vary so that you have a higher interlock (bias ratio) under acceleration than under deceleration. If you add a spring between the side gears to ensure there is always some clutch lock-up force, you get preload, too.
Functionally nearly identical variations of the Salisbury include the Ford/Dana Trac-Lok, the Eaton Posi used by GM, the Auburn, and a number of others. The Dana Powr-Lok used in the D60 and D70 is an example of a Salisbury with ramps.