How much slip across a diff simulates "Locked" 1

[TMcRally]

The Differential. You don't need to read this to answer the question, but if interested....

It is a remote selectable, variable slip, clutch plate differential from a Porsche Cayenne. The pressure on the clutch plates is achieved by a PWM electric motor. The electric motor rotates a plate that is separated by ball bearings from another plate on the same axis. The driven plate has freedom of movement around it's axis but not along the axis. The slave plate has freedom of movement along it's axis but not around it's axis.

The 5 ball bearings between these two plates locate in ramped grooves. The groves are such that when the driven plate is rotated from rest the ball bearing roll up the ramps and force the two plates apart.

The slave plate backs onto the clutch plate assembly and as it is push apart from the driven plate compresses the clutch assembly. The harder you drive the electric motor the greater the resistance to slip across the diff.

These are a rare item in Australia, in fact I understand they weren't an option here.

I have bought one from a Transyberia that was wrecked in Georgia, Europe and imported the differential and intend to retrofit it and control it completely independent from the Porsche electronics.

I hope to run 6 options in one program.
0=Off
5=Locked or sufficiently tight it behaves like it was locked.
1-4=steps inbetween.

Question.

If I am testing the slip across a differential with a torque wrench with the intention to set the slip to simulate locked, How much torque is locked ? I could run through the maths and calculate the potential torque based on total gearing ratios and engine output but I am confident that figure will be well above the grip level available in an off-road situation and therefore unnecessary.

Another way to consider it is how much torque is required to move a 2.5t vehicle up a 30° hill with large rocks.

How would I come up with a number as a start point? I'm going around and around in circles.

If I over estimate that number I am increasing inertia stress on the drive gear in axel hop situations and I am wasting options when selecting other levels with more slip.

Thanks

 

[gruntguru]

IMO its always best to start with max torque at the wheel from grip. Shift all the rear axle weight to one tyre (the other side has lifted off the ground so has zero torque), guess the mu and multiply by rolling radius and your favourite factor.

je suis charlie

 

[EdStainless]

Look up some of the old Trosen papers. They selected gear angles in order to control the degree of 'lockedness'.
It really depends on the type of driving that you will be doing.
I want to recall (but don't trust my memory) that in most conditions anything over 85% was considered 'locked'.
The two real exceptions are drag racing and true offroad work.

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P.E. Metallurgy, consulting work welcomed

 

[TMcRally]

Thanks all.

I'm going to start at 2,000Nm across the diff and see where we end up.

Yes in the Torsen papers the diminishing returns seemed to top out with a 10:1 bias ratio and seem to have a useable range from 2.5:1 to 6:1

Thanks for the directions, it was an interesting read.