Variable Torque Distribution Center Differential

The front-rear torque distribution ratio is basically determined by the gear tooth ratio of center differential's compound planetary gears and varied by changing the degree of engagement of the hydraulically operated multi-plate clutch that connects the center differential output elements according to driving conditions and road surface conditions. The torque distribution ratio is calculated using the following equations which include torque distribution coefficients (determined by number of gear teeth), input torque to the center differential, and torque capacity of the multi-plate clutch as factors.

When the front wheel speed is higher than the rear wheel speed:
T_R = 0.545 X T_i + T_C

T_F = 0.455 X T_i - T_C

where
1. T_R : Rear wheel output torque
2. T_i : Input torque to center differential
3. T_C : Torque capacity of multi-plate clutch
4. T_F : Front wheel output torque
5. 0.545: Coefficient of rear wheel torque determined by number of gear teeth
6. 0.455: Coefficient of front wheel torque determined by number of gear teeth
Fig 1: Power Flow Chart: When Front Wheel Speed Is Higher Than Rear Wheel Speed
Courtesy of SUBARU OF AMERICA, INC.

Fig 2: Power Flow Through Center Differential: When Front Wheel Speed Is Higher Than Rear Wheel Speed
Courtesy of SUBARU OF AMERICA, INC.
When the rear wheel speed is higher than the front wheel speed:
T_R = 0.545 X T_i - T_C

T_F = 0.455 X T_i + T_C

Fig 3: Power Flow Chart: When Rear Wheel Speed Is Higher Than Front Wheel Speed
Courtesy of SUBARU OF AMERICA, INC.

Fig 4: Power Flow Through Center Differential: When Rear Wheel Speed Is Higher Than Front Wheel Speed
Courtesy of SUBARU OF AMERICA, INC.

< Calculation of front and rear wheel torques>

If the frictional resistance resulting from meshing of the planetary gears and sliding of rotational components are ignored, the torques distributed to the front and rear wheels are expressed by the following equations:
1. T_R = [(Z_P1 X Z_S2 ) / (Z_S1 X Z_P2 )] X T_i
2. T_F = [1 - (Z_P1 X Z_S2 ) / (Z_S1 X Z_P2 )] X T_i
where
1. Z_P1 : Number of teeth of 1st planetary gear
2. Z_P2 : Number of teeth of 2nd planetary gear
3. Z_S1 : Number of teeth of 1st sun gear
4. Z_S2 : Number of teeth of 2nd sun gear
5. T_i : Input torque
If the number of teeth in each component in each component is the same as that assumed in the equations on the previous page, the following ratios are the calculation results of the equations shown above.
1. T_R = 0.545 X T_i
2. T_F = 0.455 X T_i
As a result, the front-rear torque distribution ratio of the compound planetary gear set without an adjustment by the multi-plate clutch is 45.5 : 54.5.