# Limited Slip Differential (LSD)

Limited Slip Differential (LSD) is a type of differential that allows the individual drive shafts (left/right) to rotate at different speeds but provides an option to limit the difference between the two. This is accomplished by providing a mechanism that resists the speed differential between the shafts. This could be a clutch or viscous coupling-based design.

## LSD in MotionView Vehicle Libraries

In MotionView’s Car/Small truck and Heavy truck library, a viscous coupling is used between the left-right drive shafts to model the slip limit.

LSD can be included while building a vehicle model using the assembly wizard. The selection is available under Front diff lock and/or Rear diff lock on the “Additional Systems for Full Vehicle with driver model” page:
Once the model is built, the diff locks system is created under the respective axle’s drive System:

## LSD Model

The limited slip differential is modeled using a simple rotational force/torque. The torque is an expression that is a function of:
• A damping coefficient (DAMP_COEFF)
• Delta of rotational speeds of the shafts (OMEGA_DIFFERENCE)
• Desired allowable difference between shafts’ rotational speeds (ALLOWABLE_SPEED_DIFFERENCE)
• A numerical switch (1, 0) that is used to switch On/Off the locking torque (LOCK_STATE)

T = LOCK_STATE * DAMPING_COEFF * (| OMEGA_LEFT – OMEGA_RIGHT |)

To allow for a smooth transition while engaging the lock, a STEP() function is used in the above expression:

T = LOCK_STATE * STEP( OMEGA_DIFFERENCE, ALLOWABLE_SPEED_DIFFERENCE, ALLOWABLE_SPEED_DIFFERENCE + 0.1, DAMP_COEFF * OMEGA_DIFFERENCE )

The torque acts between the Left and Right halves of the drive shaft.

## Interface

For easy manipulation of the diff lock parameters, a Form has been provided in the system which can be used to edit the values. Outputs are also available for plotting during result post-processing.