Rear End

First an understanding of what is meant by a torque sensing differential or torque bias differential.  To help understand torque biasing differentials I'll define a few new terms:

Torque Handling Capacity - This is simply the amount of axle torque that a tire is able to transmit to forward acceleration without slipping.

Torque Handling Capacity Difference - When a car is going around a corner weight transfer will lighten the inside wheel, limiting the amount of axle torque that the tire is able to transfer to forward acceleration.  In this state there is a torque capacity difference between the inside tire and the outside tire. 

Torque Bias - This is the amount of torque across the differential required before it will allow differential action (one wheel to spin faster than the other).

Torque Biasing Differentials
There are two situations where the differential biasing differential will differentiate.  The first is under low power going around a corner where torque bias is relatively low (almost no torque input) and there is enough traction on the inside tire (due to scrubing) compared to the outside to overcome the low torque bias.  The second situation is usually under heavy throttle (or rain) and cornering where the inside tire will not be able to transfer the axle torque to the ground.   In this situation the outside wheel has a higher torque handling capacity than the inside wheel.  When the torque handling capacity difference is greater than the torque bias the differential will differentiate allowing the inside wheel to spin.

With a torque sensing differential the goal is pick a torque bias which prevents wheel spin but limits power on induced understeer.

Difference between Torque Bias and Limited Slip
A limited slip differential has a high initial torque bias (sometimes called preload) then VERY gradually increase (linear) as input torque is applied. On the other hand a Torsen or Tru Trac has almost no initial torque bias but the torque bias increases at a much faster rate (also linear) as input torque is increased. 

As an example - A Dana 60 limited slip has an initial torque bias of about 400 ft lbs. Meaning that if you were to jack up both wheels and had one person hold one wheel and another try to spin the other. The person trying to spin the wheel would have to apply 400 ft lbs to make it spin. As input torque is applied (you step on the gas) the torque bias increases very gradually to about 900 ft lbs before one tire will slip.

Now a Torsen (and Tru Trac) has about a 0 torque bias with zero input. So if you were to jack up both wheels and try to spin one while holding the other it should be almost effortless. However if you increase the input torque to say 1000 ft lbs, with a Torsen with a 3.5:1 torque bias you now require 555 ft lbs across the differential before it will differentiate.

1000 ft lbs therefore:
3.5:1 ratio, there 4.5 total
1000/4.5 = 222 on one wheel, 777 on the other
777 - 222 = 555 torque bias.

Now increase the input to 3000 ft lbs and the torque bias is 1667 ft lbs. 

Another advantage of the Torque Biasing differential is that when you lift off the throttle you have almost zero torque bias so less tendency to understeer. Drawback is that when you stomp on the gas it will be less stable (without preload). 

The limited slips also wear and as they do the torque bias they can apply quickly drops away severely limiting their effectiveness.

The TracTech Tru Trac is another torque biasing diff, biasing ratios between 2.5:1 and 3.5:1.  The Tru Trac is generally considered not strong enough for high horsepower race cars.  Then there is the Gold Trac which is the only torque biasing differential that is available with preload.  Preload is an initial torque bias.  This allows the unit to bias with light throttle and makes for more stable corner exits.  The preload is adjustable.  The Gold Trac works the same as a Torsen or Tru Trac, the only difference being that it has adjustable preload (a good thing).

Below is an email exchange with a Torsen engineer to determine the best torque bias to choose for the test car. There is only one torque bias available for the Ford 9".

                      quote:
 

                      -----Original Message-----
                      From: Greg Carter 
                      Sent: Wednesday, June 07, 2000 1:15 PM
                      To: 'xxx@torsen.com'
                      Subject: Choosing TBR for race car

                      Hi,

                      I am trying to calculate the ideal torque biasing ratio for my
                      application:

                      Ford 9"
                      Watts link, approximately 12" from ground pivot point. No rear
                      sway bar.
                      Rear Track width 60".
                      Road Race car.

                      So assuming car mass over the rear as 1 unit, 1.0 u for
                      coefficient of friction, car going around a corner, I have come
                      up with the following
                      ratio:

                      1/2 + 1/5 for outside tire
                      1/2 - 1/5 for inside tire

                      1/2 comes for the fact that 1/2 the weight of unit 1 is applied
                      at each wheel, 1/5 is the torque at the wheels to counter the
                      moment about the c of g (the mass of unit 1, 1 foot off the
                      ground). Distance between the two
                      wheels is 5 feet, so need 1/5 the force.

                      So:
                      .7/.3 ~ 2.3:1 TBR. Would a 3.5:1 work best, to account for
                      less than ideal traction (bumps) etc?

                      I don't have the actual car weight as it is still being built. The
                      engine develops approximately 800 ft lbs of torque.

                      Thanks for any help.

                      Greg Carter
 

                Zexel Torsen Engineer reply

                      quote:
 

                      -----Original Message-----
                      From: xxx
                      Sent: Wednesday, June 07, 2000 2:07 PM
                      To: 'Greg Carter'
                      Subject: RE: Choosing TBR for race car
 

                      We've found that normally a bias ratio between 2.8 and 4.0:1
                      to be best for most race cars. The key is keeping the inside
                      rear wheel firmly planted on the track. If it does so with out
                      any major traction loss from unloading (obviously, the weight
                      transfer will pick it up some), then the lower end of the range
                      will work. If, like a lot of Mustangs or Camaros, that wheel
                      gets
                      picked up quite a bit, then a higher bias is needed to
                      overcome the loss of traction on that lifted side. Also, a
                      higher bias will always send more torque to the high traction
                      side, so that maybe beneficial in and of itself.

                      If the bias is too high, however, the differential will tend to
                      act much like a locker, which induces understeer in turns. For
                      reference, by too high, I mean 5 or 6:1 or higher. Ultimately,
                      though, the bias ratio is already chosen for you (assuming
                      you intend to use a Torsen). The 9" differential we make is
                      about 3.5:1, and doesn't come in other ratios. This should
                      work quite well for most race cars.
 

                My question on torque ratings

                      quote:
 

                      -----Original Message-----
                      From: Greg Carter 
                      Sent: Wednesday, June 07, 2000 3:00 PM
                      To: xxx
                      Subject: RE: Choosing TBR for race car
 

                      Well that sure makes selection easy! One other thing, just
                      want to check on the torque limits for the unit.

                      Assume a CoF of 1.0 and almost 100% of the weight transfers
                      to the rear at max acceleration I would need it to handle:

                      3000 lbs x 1.0 x tire radius (26"/2) = 39000 in-lbs or 3250
                      ft-lbs of output torque to break the tires free in ideal traction
                      conditions.

                      Using a safety factor of 2 (dumping the clutch, shifting gears,
                      yahoo driving, etc.) I would like to have a unit that could
                      handle 6500 ft-lbs.

                      The engine produces 800+ ft-lbs of torque x 3.06 (1st gear) x
                      3.5 (rear end) = 8570 ft-lbs, so the max torque is definitely
                      limited by traction.

                      Will the unit withstand this amount of torque?

                      Thanks again.

                      Greg Carter
                      Entrust Technologies - http://www.entrust.com 
 

                His reply

                      quote:
 

                      -----Original Message-----
                      From: xxx@torsen.com] 
                      Sent: Wednesday, June 07, 2000 3:54 PM
                      To: 'Greg Carter'
                      Subject: RE: Choosing TBR for race car
 

                      Actually, the way the differential is rated is short duration
                      torque (engine torque X gear ratios), plus impact torque,
                      which adds a "shock" factor for clutch dumps, etc. Impact
                      torque is an instantaneous torque spike that occurs from a
                      sudden loading. The factor used is something like 3 or 3.5
                      (depends on a number of things), although impact IS
                      ultimately limited by wheelspin. If you could prevent
                      wheelspin, the impact torque would be short duration X 3
                      (8570 X 3 = 25710 lbft). Eeek, that's high. Fortunately, its
                      limited by wheelspin. And, of course, your assumptions are
                      probably a worse case then actual. If 6500 lbft is what your
                      after (because of the wheelspin), your in luck. The diff can
                      withstand about 9000 lbft with no trouble. Our testing has
                      shown that the pinion shaft will fail before the
                      diff does (we've seen them fail around 8800 lbft). So, to make
                      a long story short, it should work, unless you manage to
                      dump all your torque into it with no wheelspin...