Torque split during operation of limited-slip differential

An open differential has a fixed torque split between the input and outputs. In most cases the relationship is:

• Trq _{out_1} = Trq _{out_2} , where 1 and 2 are typically the left and right drive wheels.

• Trq _in = Trq _{out_1} + Trq _{out_2} .

Thus the wheels always see the same torque even when spinning at different speeds, including the case where one is stationary. Note, the torque split can be unequal, though 50:50 is typical.

A limited-slip differential has a more complex torque-split and should be considered in the case when the outputs are spinning the same speed and when spinning at different speeds. The torque difference between the two axles is called Trq _d . (In this work it is called Trq _f for torque friction). Trq _d is the difference in torque delivered to the left and right wheel. The magnitude of Trq _d comes from the slip-limiting mechanism in the differential and may be a function of input torque (as in the case of a gear differential), or the difference in the output speeds (as in the case of a viscous differential).

The torque delivered to the outputs is:

• Trq ₁ = ½ Trq _in + ½ Trq _d for the slower output

• Trq ₂ = ½ Trq _in – ½ Trq _d for the faster output

When traveling in a straight line, where one wheel starts to slip (and spin faster than the wheel with traction), torque is reduced to the slipping wheel (Trq ₂ ) and provided to the slower wheel (Trq ₁ ).

In the case when the vehicle is turning and neither wheel is slipping, the inside wheel will be turning slower than the outside wheel. In this case the inside wheel will receive more torque than the outside wheel, which can result in understeer.

When both wheels are spinning at the same speed, the torque distribution to each wheel is:

• Trq _{(1 or 2)} = ½ Trq _in ±(½ Trq _d ) while

• Trq ₁ +Trq ₂ =Trq _in .

This means the maximum torque to either wheel is statically indeterminate but is in the range of ½ Trq _in ±( ½ Trq _d ).