Clutch schedule for a ninespeed transmission
Simscape / Driveline / Transmissions
The 9Speed block consists of four planetary gear sets and six clutches. The follower shaft connects to the planet gear carrier of the fourth planetary gear. Three of the clutches determine the power flow path for the base shaft. The other three clutches serve as brakes, grounding various gears of the planetary sets to the transmission housing.
This diagram shows a ninespeed transmission. The labels for the gear components are superimposed on the input and output gears. The table lists the gear and clutch components that are labeled in the diagram.
Label  Component 

P.G.1–P.G.4  Planetary gears, 1–4 
R  Ring gear 
C  Planet gear carrier 
S  Sun gear 
A, B, E  Forward clutches that control the power flow path 
C, D, F  Forward, braking clutches 
The drive ratio between the transmission input and output shafts follows from the elementary gear ratios specified for the gear blocks. The elementary gear ratios are
$${g}_{x}=\frac{{N}_{{R}_{x}}}{{N}_{{S}_{x}}},$$
where:
N_{Rx} is the number of teeth in the planetary ring gear x, where x = 1, 2, 3, and 4.
N_{Sx} is the number of teeth in the planetary sun gear x, where x = 1, 2, 3, and 4.
The table shows the clutch schedule, driveratio expressions, driveratio default values, and the powerflow diagrams for each gear of the 9Speed block. The schedule and gear ratios are based on the manufacturer data for the ZF 9HP ninespeed automatic transmission.
The letters in the clutch schedule columns denote the brakes and clutches. A value
of 1
denotes a locked state and a value of 0
an unlocked state. The clutch schedule generates these signals based on the Gear
port input signal. The signals are scaled through a Gain block and used as actuation
inputs in the clutch blocks.
The powerflow diagrams show the power flow paths between input and output shafts for each gear setting. Power flow is shown in orange. Connections to the transmission housing (a mechanical ground) are shown in black.
Gear  Clutch Schedule  Drive Ratio Equation  Default Ratio  Power Flow  

A  B  C  D  E  F  
9  0  1  0  1  1  0  $$\frac{1+{g}_{4}}{1+{g}_{3}+{g}_{4}\left(\frac{{g}_{3}}{1{g}_{1}{g}_{2}}\right)}$$  0.48 

8  0  0  1  1  1  0  $$\frac{1+{g}_{4}}{1+{g}_{3}+{g}_{4}}$$  0.58 

7  1  0  0  1  1  0  $$\frac{1+{g}_{4}}{1+{g}_{3}\left(\frac{{g}_{3}}{1+{g}_{2}}\right)+{g}_{4}}$$  0.70 

6  1  0  1  0  1  0  $$\frac{1+{g}_{4}}{1+{g}_{3}+{g}_{4}\left(\frac{{g}_{1}{g}_{3}}{1+{g}_{1}}\right)}$$  0.81 

5  1  1  0  0  1  0  $$1$$  1 

4  1  0  0  0  1  1  $$\frac{1+{g}_{4}}{{g}_{4}}$$  1.38 

3  1  1  0  0  0  1  $$\frac{\left(1+{g}_{3}\right)\left(1+{g}_{4}\right)}{{g}_{3}{g}_{4}}$$  1.91 

2  1  0  1  0  0  1  $$\frac{\left(1+{g}_{1}\right)\left(1+{g}_{3}\right)\left(1+{g}_{4}\right)}{{g}_{1}{g}_{3}{g}_{4}}$$  2.84 

1  1  0  0  1  0  1  $$\frac{\left(1+{g}_{2}\right)\left(1+{g}_{3}\right)\left(1+{g}_{4}\right)}{{g}_{3}{g}_{4}}$$  4.70 

R  0  1  0  1  0  1  $$\frac{\left(1{g}_{1}{g}_{2}\right)\left(1+{g}_{3}\right)\left(1+{g}_{4}\right)}{{g}_{3}{g}_{4}}$$  3.80 

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