There is a nice review about slip which can give you some clues about your problem

http://link.springer.com/referenceworkentry/10.1007%2F978-3-540-30299-5_19

I think you should check how your torque could affect to the multiple possible things which could generate slip behavior.

I was wondering what domain you are discussing. Torque is easily understood as force x distance with the component of the force at right angles to the distance. Slip is the difference between two velocities, of pretty well anything. Slip in a mechanical system is the speed difference between two moving parts. Slip in Adolfo's article is the difference in speed between the solid and liquid at the boundary. Slip in an induction motor is the difference in speed between the rotor and the driving rotating magnetic field. There are numerous others, I'm sure! Which are you particularly interested in?

If two wheels or shafts are bolted together with a flange face, then there is a frictional torque that will prevent the flanges from slip. If the applied torque goes beyond  the frictional torque threshold then the slip will happen. This torque is controlled by the frictional coefficient and the bolt preload.

This torque can be found by integrating (mu.p.dA.r) over the contact surface, where mu is friction coefficient p is pressure, r is radius and A is area.

whenever load increases speed will decrease .at N=Ns condition S=0 as well as T=0.because torque directly propotional to slip for low slip region .for high slip region torque is inversly propotional to slip .torque increases slip will decrease.

the slipping speed of the shifting element is zero, the torque capacity is bigger than the actual

torque transferred by the shifting element.

When the actual torque exceeds the torque capacity,

the shifting element will begin slipping and the actual torque is equal to the friction torque.