How to calculate lockup/locking force in a salisbury differential?

[LCT]

I'm trying to find the ideal ramp angle, preload, and clutch setup for a salisbury type differential and I've come up with an equation to calculate locking force which depends on the following variables:

clutch radius
input torque
distance from spider gear to diff centerline
coefficient of friction in the clutches
number of clutches
ramp angle
torque difference between halfshafts
preload spring stiffness

since there isn't much available information on salisbury type differentials, I don't have a good way to check my work. Has anyone found/developed equations for this differential before? Or do most teams simply buy a few different ramp angles and preload springs and tune the diff setup from track testing?

[LCT]

I'm trying to find the ideal ramp angle, preload, and clutch setup for a salisbury type differential and I've come up with an equation to calculate locking force which depends on the following variables:

clutch radius
input torque
distance from spider gear to diff centerline
coefficient of friction in the clutches
number of clutches
ramp angle
torque difference between halfshafts
preload spring stiffness

since there isn't much available information on salisbury type differentials, I don't have a good way to check my work. Has anyone found/developed equations for this differential before? Or do most teams simply buy a few different ramp angles and preload springs and tune the diff setup from track testing?

[exFSAE]

I have no idea how you'd be able to validate that model without something like a diff dyno and a lot of test time.

Plus, even if you indeed had the diff modeled accurately, then how would you validate THAT within a vehicle model?

Are you making your own diff, or sourcing one? If the latter (I hope the latter!), could you not just supply the manufacturer with the lockup "curve" (rates) that you want, and see if they can help you?

Alternatively, the most practical and best solution may be to have a couple sets of ramps, clutches, and springs, and tune when you drive.

[scotty young Taylor Race]

LCT,

The best thing is to test differant ramps as well as clutch and plate stacks.
What diff are the internals out of.

scotty
Taylor Race Engineering
scotty@taylor-race.com

[TMG24]

We built a Salisbury in 07 from BMW internals and in 08 and 09 we bought Williams Racing Salisbury type diffs. We talked to the pros but the only way we found out what worked was by putting it on the car and beating the snot out of it. Data AQ is probably the best way to figure out what point in a turns radius your diff is locking and unlocking, same with straight line.