9-Speed

Clutch schedule for a nine-speed transmission

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Libraries:
Simscape / Driveline / Transmissions

Description

The 9-Speed 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 nine-speed 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

Drive Ratios, Clutch Schedule, and Power Flow

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, drive-ratio expressions, drive-ratio default values, and the power-flow diagrams for each gear of the 9-Speed block. The schedule and gear ratios are based on the manufacturer data for the ZF 9HP nine-speed 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 power-flow 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

Examples

Transmission Testbed

A testbed with interchangeable transmissions. The transmission models vary from classic four speed transmissions to modern seven, eight, nine, and ten speed configurations. The efficiency and drive ratio can be adjusted by varying the components in each individual transmission configuration. The transmission choices are held in a variant subsystem and are selected by either using the hyperlinks in the model or right-clicking the Transmission subsystem, selecting Variant -> Override using, and the desired variant.

• Open Model

Ports

Input

Gear — Numerical input for the gear

scalar

Specify -1 for reverse, 0 for neutral, and 1–9 for the forward gears.

Data Types: single | double

Conserving

B — Base interface

mechanical rotational

Conserving port associated with the base shaft.

F — Follower interface

mechanical rotational

Conserving port associated with the follower shaft.

Parameters

Initial gear — Gear state at the beginning of simulation

Neutral (default) | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | Reverse

Sets the initial engagement or disengagement of the clutches using the clutch schedule. When the transmission is in neutral, there is no power flow from the base shaft to the follower shaft.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2015a