Due to how the powerflow works on the 722.6, Calculating from Input to output is done in order of group 1,3,2 and calculating from output to input is done in order of group 2,3,1.
- I - Input speed
- Q - Output speed
- N2 - Speed reported by the N2 speed sensor (Monitors Group 1 gear planetary carrier)
- N3 - Speed reported by the N3 speed sensor (Monitors Group 1 gear sun gear)
- an - Ring gear teeth of group n
- bn - Sun gear teeth of group n
- cn - Planetary gear teeth of group n
- Ry - Ring gear speed of group n
- Sy - Sun gear speed of group n
- Py - Planetary speed of group n
R1=I.
S1=N3⟹0.0.
P1=N2.
R3=P1.
S3=0.0.
P3=a3+b3a3×P1.
R2=P3.
S2=0.0.
P2⟹Q=a2+b2a2×P3.
R1=I.
S1=N3⟹I.
P1=N2⟹I.
R3=c1.
S3=0.0.
P3=a3+b3a3×P1.
R2=c3.
S2=0.0.
P2⟹Q=a2+b2a2×P3.
R1=I.
S1=N3⟹I.
P1=N2⟹I.
R3=P1.
S3=P1.
P3=P1.
R2=c3.
S2=0.0.
P2⟹Q=a2+b2a2×P3.
R1=I.
S1=N3⟹I.
P1=N2⟹I.
R3=P1.
S3=P1.
P3=P1.
R2=P3.
S2=P3.
P2⟹Q=P3.
R1=I.
S1=N3⟹0.0.
P1=N2.
R3=P1.
S3=a3(a3×I)+(s3×I)−(a3×P1).
P3=I.
R2=I.
S2=S3.
P2⟹Q=a2+b2(a2×I)+(b2×S3).
¶ Calculating speeds of engaging and disengaging elements during shifts
These equations are derived depending on what the actual and target gear is. This is done so that the TCU can monitor the engagement and release of the clutch groups during a gear change.
The speed of brake B2 is calculated in all gears as it has an influence on the output shaft rotation speed.
¶ Drive 1-2 and 2-1
Difference: B1 and K1
The progress of K1 engagement is monitored as the delta between S1 and P1. When K1 is locked and B1 is off, S1=P1, if K1 is off and B1 is on, then S1=0 and P1=N2.
VK1=N2−N3
VB1=N3
VB2=0.0
¶ Drive 2-3 and 3-2
Difference: K2 and K3
Since one side of K2 (Locked to R1) is already being driven by the input shaft, K2's relative velocity should be 0 when R2's speed is equal to R1. Therefore, this can be very easily be expressed as the difference between the input shaft speed, and the estimated input shaft speed based on the output gearbox speed. If this number falls below 0, then it implies that R2's rotation speed is higher than the input shaft speed.
VK2=I−(Ratio[D3]∗Q)
Firstly, Ratio[D2]−Ratio[D3] is used to calculate the difference in ratios from D2 to D3, which mechanically is only caused by the rear planetary set locking up to a 1:1 ratio. (R3 is always being driven by the Input shaft in D2 and D3), and P3 is then also locked to the input shaft speed via K2.
It is also known that if K3 is applied (In D2), then S3's rotation speed would be 0, as K3 is locked to the stationary B2 brake. This means that (Ratio[D2]×Q)−I should give us the rotational speed of K3 when in D2. We can multiply this number by Ratio[D3] to account for the difference in sun gear speeds.
VK3=Ratio[D2]−Ratio[D3]Ratio[D3]×((Ratio[D2]×Q)−I)
VB2=0.0
¶ Drive 3-4 and 4-3
Difference: B2 and K3
Almost the same equation and principle is used as when calculating the speed of K3 for the 2-3 and 3-2 shift group. But since K2 remains locked (Thus the rear planetary remains at the same relative rotation speed as in D3)
VB2=Ratio[D3]−Ratio[D4]Ratio[D4]×((Ratio[D3]×Q)−I)
It is the inverse of the speed of B2 with respect to the input shaft speed. So its a very simple formula:
VK3=I−VB2
¶ Drive 4-5 and 5-4
Since this is the same switching groups as the 1-2 and 2-1 shift groups, the same formulas are used, but the B2 rotation speed is calculated in the same way as in the 3-4 and 4-3 shifts.
VK1=N2−N3
VB1=N3
VB2=Ratio[D3]−Ratio[D4]Ratio[D4]×((Ratio[D3]×Q)−I)
Sn=anPan+Pbn−Rbn