Re: torque and diffs

[Orin Eman <orin@wolfenet.com>]

Nice example.

Just for fun, here are the applicable formulae for diffs.
They are always true if no acceleration is involved.
If anything is accelerating, you have to put in some
moment of inertia * angular acceleration terms and it gets messy.

Ta, Tb, Trg are torques at shaft a, shaft b and the ring gear.

Ta + Tb = Trg
|Ta - Tb| <= Tf

Tf is the torque due to friction between the two driveshafts.

Open diff, Tf is 0, Therefore Ta = Tb
Locked diff, Tf is essentially infinite, therefore no constraints
on Ta or Tb other than Ta + Tb = Trg
Limited slip, Tf constrains the difference between Ta and Tb.

Orin.

> Take the example of a four wheel drive pickup with the front locking hubs.  
> It has essentially a locked center diff.  The front drive shafts are always 
> spinning, it is in locking the hubs that torque is transfered to the 
> wheel/ground.  With hubs free wheeling, all available torque goes to the 
> rear, the front driveshafts will spin at the same speed as the rear.  With 
> the front hubs locked to the front driveshafts, front and rear still spin at 
> the same speed, but torque is now going to the front wheels also.  The 
> center diff remained locked the entire time, the only thing that changed is 
> the torque required to spin front and rear wheels at the same speed.  Taking 
> the above quotation would mean that a system as described above, in front 
> hubs freewheeling mode, only half of the available torque would be moving 
> the vehicle which is obviously not the case.  In other words, if a locked 
> diff split torque 50%, then the same truck on a rear dyno with front hubs 
> freewheeling might show 100 lb ft (or Nm, units don't matter) now lock the 
> front hubs, put it on a four wheel dyno and it would show 200 lb ft? It 
> would still show 100 lb ft of total torque. Wrong.  Open diffs evenly 
> distribute torque, individual axle speed can vary, locked diffs evenly 
> distribute axle speed, torque can vary.  If there is no (or very little) 
> resistance on any given wheel, with a locked diff causing the wheels to spin 
> at the same speed, no (or very little) torque will be at the wheel without 
> traction, hence the torque must go to the other wheel.  Try to put 50 lb ft 
> of torque on a stripped bolt, can't do it, in the same manner a wheel with 
> no traction can't receive any torque.
> -Matt Martinsen
> Seattle, WA



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