Automated Manual Transmission

Ideal automated manual transmission

Libraries:
Powertrain Blockset / Transmission / Transmission Systems

Description

The Automated Manual Transmission block implements an ideal automated transmission (AMT). An AMT is a manual transmission with additional actuators and an electronic control unit (ECU) to regulate clutch and gear selection based on commands from a controller. The number of gears is specified via an integer vector with corresponding gear ratios, inertias, viscous damping, and efficiency factors. The clutch and synchronization engagement rates are linear and adjustable.

Use the block for:

Power and torque capacity sizing
Determining gear ratio impact on fuel economy and performance

To determine the rotational drive shaft speed and reaction torque, the Automated Manual Transmission block calculates:

Clutch lock-up and clutch friction
Locked rotational dynamics
Unlocked rotational dynamics

To specify the block efficiency calculation, for Efficiency factors, select either of these options.

Setting Block Implementation

Setting	Block Implementation
`Gear only`	Efficiency determined from a 1D lookup table that is a function of the gear.
`Gear, input torque, input speed, and temperature`	Efficiency determined from a 4D lookup table that is a function of: Gear Input torque Input speed Oil temperature

Gear only

Efficiency determined from a 1D lookup table that is a function of the gear.

Gear, input torque, input speed, and temperature

Efficiency determined from a 4D lookup table that is a function of:

Gear
Input torque
Input speed
Oil temperature

Clutch Control

The AMT delivers drive shaft torque continuously by controlling the pressure signals from the clutch. If you select Control type parameter Ideal integrated controller, the block generates idealized clutch pressure signals. To use your own clutch control signals, select Control type parameter External control.

Clutch Lock-Up and Clutch Friction

Based on the clutch lock-up condition, the block implements one of these friction models.

If	Clutch Condition	Friction Model
$\begin{array}{l} ω_{i} \neq N ω_{d} \\ or \\ T_{S} < \| T_{f} - N w_{i} b_{i} \| \end{array}$	Unlocked	$\begin{array}{l} T_{f} = T_{k} \\ where, \\ T_{k} = F_{c} R_{e f f} μ_{k} \tanh [4 (\frac{w_{i}}{N} - w_{d})] \\ T_{s} = F_{c} R_{e f f} μ_{s} \\ R_{e f f} = \frac{2 (R_{o}^{3} - R_{i}^{3})}{3 (R_{o}^{2} - R_{i}^{2})} \end{array}$
$\begin{array}{l} ω_{i} = N ω_{t} \\ and \\ T_{S} \geq \| T_{f} - N b_{i} ω_{i} \| \end{array}$	Locked	T_f = T_s

The equations use these variables.

ω_t	Output drive shaft speed
ω_i	Input drive shaft speed
ω_d	Drive shaft speed
$b_{i}$	Viscous damping
F_c	Applied clutch force
N	Engaged gear
$T_{f}$	Frictional torque
$T_{k}$	Kinetic frictional torque
$T_{s}$	Static frictional torque
$R_{e f f}$	Effective clutch radius
$R_{o}$	Annular disk outer radius
$R_{i}$	Annular disk inner radius
μ_s	Coefficient of static friction
μ_k	Coefficient of kinetic friction

Locked Rotational Dynamics

To model the rotational dynamics when the clutch is locked, the block implements these equations.

$\begin{array}{l} {\dot{ω}}_{d} J_{N} = η_{N} T_{d} - \frac{ω_{i}}{N} b_{N} + N T_{i} \\ ω_{i} = N ω_{d} \end{array}$

The block determines the input torque, T_i, through differentiation.

The equations use these variables.

ω_i	Input drive shaft speed
ω_d	Drive shaft speed
N	Engaged gear
b_N	Engaged gear viscous damping
J_N	Engaged gear inertia
η_N	Engaged gear efficiency
T_d	Drive shaft torque
T_i	Applied input torque

Unlocked Rotational Dynamics

To model the rotational dynamics when the clutch is unlocked, the block implements this equation.

${\dot{ω}}_{d} J_{N} = N T_{f} - ω_{d} b_{N} + T_{d}$

where:

ω_d	Drive shaft speed
N	Engaged gear
b_N	Engaged gear viscous damping
J_N	Engaged gear inertia
T_d	Drive shaft torque
T_i	Applied input torque

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Variable	Equations
`PwrInfo`	`PwrTrnsfrd` — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	`PwrEng`	Engine power	P_eng	$ω_{i} T_{i}$
		`PwrDiffrntl`	Differential power	P_diff	$ω_{d} T_{d}$
	`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	`PwrEffLoss`	Mechanical power loss	P_effloss	$ω_{d} T_{d} (η_{N} - 1)$
		`PwrDampLoss`	Mechanical damping loss	P_damploss	$- b_{N} ω_{d}^{2} - b_{i n} ω_{i}^{2}$
		`PwrCltchLoss`	Clutch power loss	P_mech	When locked: $0$ When unlocked: $- T_{k} (ω_{i} - N ω_{d})$
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`PwrStoredTrans`	Rate change in rotational kinetic energy	P_str	When locked: ${\dot{ω}}_{i} ω_{i} (J_{i n} + \frac{J_{N}}{N^{2}})$ When unlocked: $J_{i n} {\dot{ω}}_{i} ω_{i} + J_{N} {\dot{ω}}_{d} ω_{d}$

The equations use these variables.

b_N	Engaged gear viscous damping
J_N	Engaged gear rotational inertia
J_in	Flywheel rotational inertia
η_N	Engaged gear efficiency
N	Engaged gear ratio
T_i	Applied input torque, typically from the engine crankshaft or dual mass flywheel damper
T_d	Applied load torque, typically from the differential or drive shaft
ω_d	Initial input drive shaft rotational velocity
ω_i, ώ_i	Applied drive shaft angular speed and acceleration

Examples

Build Conventional Vehicle Model

Build a vehicle with an internal combustion engine using the conventional vehicle reference application.

Ports

Input

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Gear — Gear number to engage
`scalar`

Integer value of gear number to engage.

CltchCmd — Clutch command
`scalar`

Clutch pressure command.

Dependencies

To create this port, select Control type parameter External control.

EngTrq — Applied input torque
`scalar`

Applied input torque, T_i, typically from the engine crankshaft or dual mass flywheel damper, in N·m.

DiffTrq — Applied load torque
`scalar`

Applied load torque, T_d, typically from the differential or driveshaft, in N·m.

Temp — Oil temperature
`scalar`

Oil temperature, in K. To determine the efficiency, the block uses a 4D lookup table that is a function of:

Gear
Input torque
Input speed
Oil temperature

Dependencies

To create this port, set Efficiency factors to Gear, input torque, input speed, and temperature.

Output

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Info — Bus signal
bus

Bus signal contains these block calculations.

Signal			Description	Variable	Units
`Eng`	`EngTrq`		Input applied torque	T_i	N·m
`Eng`	`EngSpd`		Input drive shaft speed	ω_i	rad/s
`Diff`	`DiffTrq`		Output drive shaft torque	T_t	N·m
`Diff`	`DiffSpd`		Output drive shaft speed	ω_t	rad/s
`Cltch`	`CltchForce`		Applied clutch force	F_c	N
`Cltch`	`CltchLocked`		Clutch lock status, Boolean: Locked — `0` Unlocked — `1`	N/A	N/A
`Trans`	`TransSpdRatio`		Speed ratio at time t	$ϕ (t)$	N/A
	`TransEta`		Ratio of output power to input power	$η$	N/A
	`TransGearCmd`		Commanded gear	N_cmd	N/A
	`TransGear`		Engaged gear	N	N/A
`PwrInfo`	`PwrTrnsfrd`	`PwrEng`	Engine power	P_eng	W
	`PwrTrnsfrd`	`PwrDiffrntl`	Differential power	P_diff	W
	`PwrNotTrnsfrd`	`PwrEffLoss`	Mechanical power loss	P_effloss	W
		`PwrDampLoss`	Mechanical damping loss	P_damploss	W
		`PwrCltchLoss`	Clutch power loss	P_mech	W
	`PwrStored`	`PwrStoredTrans`	Rate change in rotational kinetic energy	P_str	W

EngSpd — Angular speed
`scalar`

Applied drive shaft angular speed input, ω_i, in rad/s.

DiffSpd — Angular speed
`scalar`

Drive shaft angular speed output, ω_d, in rad/s.

Parameters

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Control type — Specify control type
`Ideal integrated controller` (default) | `External control`

Dependencies

This table summarizes the port configurations.

Control Mode	Creates Ports
`External control`	`CltchCmd`

Efficiency factors — Specify efficiency calculation
`Gear only` (default) | `Gear, input torque, input speed, and temperature`

To specify the block efficiency calculation, for Efficiency factors, select either of these options.

Setting Block Implementation

Setting	Block Implementation
`Gear only`	Efficiency determined from a 1D lookup table that is a function of the gear.
`Gear, input torque, input speed, and temperature`	Efficiency determined from a 4D lookup table that is a function of: Gear Input torque Input speed Oil temperature

Gear only

Efficiency determined from a 1D lookup table that is a function of the gear.

Gear, input torque, input speed, and temperature

Efficiency determined from a 4D lookup table that is a function of:

Gear
Input torque
Input speed
Oil temperature

Dependencies

Setting Parameter To Enables

Setting Parameter To	Enables
`Gear only`	Efficiency vector, eta
`Gear, input torque, input speed, and temperature`	Efficiency torque breakpoints, Trq_bpts Efficiency speed breakpoints, omega_bpts Efficiency temperature breakpoints, Temp_bpts Efficiency lookup table, eta_tbl

Gear only

Efficiency vector, eta

Gear, input torque, input speed, and
                                        temperature

Efficiency torque breakpoints, Trq_bpts

Efficiency speed breakpoints, omega_bpts

Efficiency temperature breakpoints, Temp_bpts

Efficiency lookup table, eta_tbl

Transmission

Input shaft inertia, Jin — Inertia
`.01` (default) | `scalar`

Input shaft inertia, in kg·m^2.

Input shaft damping, bin — Damping
`.001` (default) | `scalar`

Input shaft damping, in N·m·s/rad.

Initial input velocity, omegain_o — Angular velocity
`0` (default) | `scalar`

Angular velocity, in rad/s.

Gear number vector, G — Specify number of transmission speeds
`[-1, 0, 1, 2, 3, 4, 5]` (default) | `vector`

Vector of integer gear commands used to specify the number of transmission speeds. Neutral gear is 0. For example, you can set these parameter values.

To Specify	Set Gear number, G To
Four transmission speeds, including neutral	`[0,1,2,3,4]`
Three transmission speeds, including neutral and reverse	`[-1,0,1,2,3]`
Five transmission speeds, including neutral and reverse	`[-1,0,1,2,3,4,5]`

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Efficiency torque breakpoints, Trq_bpts — Breakpoints
`[25, 50, 75, 100, 150, 200, 250]` (default) | `vector`

Torque breakpoints for efficiency table, in N·m.

Dependencies

To enable this parameter, set Efficiency factors to Gear, input torque, input speed, and temperature.

Efficiency speed breakpoints, omega_bpts — Breakpoints
`[52.4 78.5 105 131 157 183 209 262 314 419 524]` (default) | `vector`

Speed breakpoints for efficiency table, rad/s.

Dependencies

To enable this parameter, set Efficiency factors to Gear, input torque, input speed, and temperature.

Efficiency temperature breakpoints, Temp_bpts — Breakpoints
`[313 358]` (default) | `vector`

Temperature breakpoints for efficiency table, in K.

Dependencies

To enable this parameter, set Efficiency factors to Gear, input torque, input speed, and temperature.

Gear ratio vector, N — Ratio of input speed to output speed
`[-4.47, 1, 4.47, 2.47, 1.47, 1, 0.8]` (default) | `vector`

Vector of gear ratios (that is, input speed to output speed) with indices corresponding to the ratios specified in Gear number, G. For neutral, set the gear ratio to 1. For example, you can set these parameter values.

To Specify Gear Ratios For	Set Gear number, G To	Set Gear ratio, N To
Four transmission speeds, including neutral	`[0,1,2,3,4]`	`[1,4.47,2.47,1.47,1]`
Five transmission speeds, including neutral and reverse	`[-1,0,1,2,3,4,5]`	`[-4.47,1,4.47,2.47,1.47,1,0.8]`

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Transmission inertia vector, Jout — Gear rotational inertia
`[0.128 0.01 0.128 0.1 0.062 0.028 0.01]` (default) | `vector`

Vector of gear rotational inertias, with indices corresponding to the inertias specified in Gear number, G, in kg·m^2. For example, you can set these parameter values.

To Specify Inertia For	Set Gear number, G To	Set Inertia, J To
Four gears, including neutral	`[0,1,2,3,4]`	`[0.01,2.28,2.04,0.32,0.028]`
Inertia for five gears, including reverse and neutral	`[-1,0,1,2,3,4,5]`	`[2.28,0.01,2.28,2.04,0.32,0.028,0.01]`

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Transmission damping vector, bout — Gear viscous damping coefficient
`[.003 .001 .003 .0025 .002 .001 .001]` (default) | `vector`

Vector of gear viscous damping coefficients, with indices corresponding to the coefficients specified in Gear number, G, in N·m·s/rad. For example, you can set these parameter values.

To Specify Damping For	Set Gear number, G To	Set Damping, b To
Four gears, including neutral	`[0,1,2,3,4]`	`[0.001,0.003,0.0025, 0.002,0.001]`
Five gears, including reverse and neutral	`[-1,0,1,2,3,4,5]`	`[0.003,0.001,0.003, 0.0025,0.002,0.001,0.001]`

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Efficiency vector, eta — Gear efficiency
`[0.9, 0.9, 0.9, 0.9, 0.9, 0.95, 0.95]` (default) | `vector`

Vector of gear mechanical efficiency, with indices corresponding to the efficiencies specified in Gear number, G. For example, you can set these parameter values.

To Specify Efficiency For	Set Gear number, G To	Set Efficiency, eta To
Four gears, including neutral	`[0,1,2,3,4]`	`[0.9,0.9,0.9,0.9,0.95]`
Five gears, including reverse and neutral	`[-1,0,1,2,3,4,5]`	`[0.9,0.9,0.9, 0.9,0.9,0.95,0.95]`

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Dependencies

To enable this parameter, set Efficiency factors to Gear only.

Efficiency lookup table, eta_tbl — Gear efficiency
`array`

Table of gear mechanical efficiency, η_N as a function of gear, input torque, input speed, and temperature.

Dependencies

To enable this parameter, set Efficiency factors to Gear, input torque, input speed, and temperature.

Initial output velocity, omegaout_o — Transmission
`0` (default) | `scalar`

Transmission initial output rotational velocity, ω_to, in rad/s. If you select Start simulation with clutch locked, the block ignores the Initial output velocity, omega_o parameter value.

Initial gear, G_o — Engaged gear
`0` (default) | `scalar`

Initial gear to engage, G_o.

Clutch and Synchronizer

Clutch pressure time constant, tauc — Time
`.02` (default) | `scalar`

Pressure input filter time constant, τ_c, in s.

Synchronization time, ts — Time
`.25` (default) | `scalar`

Time required for gear selection and synchronization, t_s, in s.

Clutch time, tc — Time
`.5` (default) | `scalar`

Time required to engage and disengage the clutch during shift events, t_c, in s.

Dependencies

To create this parameter, select Control type parameter Ideal integrated controller.

Effective clutch radius, R — Radius
`.2` (default) | `scalar`

The effective radius, $R_{e f f}$ , used with the applied clutch friction force to determine the friction force, in m. The effective radius is defined as:

$R_{e f f} = \frac{2 (R_{o}^{3} - R_{i}^{3})}{3 (R_{o}^{2} - R_{i}^{2})}$

The equation uses these variables.

$R_{o}$	Annular disk outer radius
$R_{i}$	Annular disk inner radius

Clutch force gain, K_c — Force
`5e3` (default) | `scalar`

Open loop lock-up clutch gain, K_c, in N.

Clutch static friction coefficient, mus — Coefficient
`0.6` (default) | `scalar`

Dimensionless clutch disc coefficient of static friction, μ_s.

Clutch kinematic friction coefficient, muk — Coefficient
`0.4` (default) | `scalar`

Dimensionless clutch disc coefficient of kinetic friction, μ_k.

Start simulation with clutch locked — Select to initially lock clutch
`off` (default) | `on`

Select to lock clutch initially.

Dependencies

To create this parameter, select Control type parameter Ideal integrated controller.

Automated Manual Transmission

Description

Clutch Control

Clutch Lock-Up and Clutch Friction

Locked Rotational Dynamics

Unlocked Rotational Dynamics

Power Accounting

Examples

Build Conventional Vehicle Model

Ports

Input

Gear — Gear number to engage scalar

CltchCmd — Clutch command scalar

Dependencies

EngTrq — Applied input torque scalar

DiffTrq — Applied load torque scalar

Temp — Oil temperature scalar

Dependencies

Output

Info — Bus signal bus

EngSpd — Angular speed scalar

DiffSpd — Angular speed scalar

Parameters

Control type — Specify control type Ideal integrated controller (default) | External control

Dependencies

Efficiency factors — Specify efficiency calculation Gear only (default) | Gear, input torque, input speed, and temperature

Dependencies

Input shaft inertia, Jin — Inertia .01 (default) | scalar

Input shaft damping, bin — Damping .001 (default) | scalar

Initial input velocity, omegain_o — Angular velocity 0 (default) | scalar

Gear number vector, G — Specify number of transmission speeds [-1, 0, 1, 2, 3, 4, 5] (default) | vector

Efficiency torque breakpoints, Trq_bpts — Breakpoints [25, 50, 75, 100, 150, 200, 250] (default) | vector

Dependencies

Efficiency speed breakpoints, omega_bpts — Breakpoints [52.4 78.5 105 131 157 183 209 262 314 419 524] (default) | vector

Dependencies

Efficiency temperature breakpoints, Temp_bpts — Breakpoints [313 358] (default) | vector

Dependencies

Gear ratio vector, N — Ratio of input speed to output speed [-4.47, 1, 4.47, 2.47, 1.47, 1, 0.8] (default) | vector

Transmission inertia vector, Jout — Gear rotational inertia [0.128 0.01 0.128 0.1 0.062 0.028 0.01] (default) | vector

Transmission damping vector, bout — Gear viscous damping coefficient [.003 .001 .003 .0025 .002 .001 .001] (default) | vector

Efficiency vector, eta — Gear efficiency [0.9, 0.9, 0.9, 0.9, 0.9, 0.95, 0.95] (default) | vector

Dependencies

Efficiency lookup table, eta_tbl — Gear efficiency array

Dependencies

Initial output velocity, omegaout_o — Transmission 0 (default) | scalar

Initial gear, G_o — Engaged gear 0 (default) | scalar

Clutch pressure time constant, tauc — Time .02 (default) | scalar

Synchronization time, ts — Time .25 (default) | scalar

Clutch time, tc — Time .5 (default) | scalar

Dependencies

Effective clutch radius, R — Radius .2 (default) | scalar

Clutch force gain, K_c — Force 5e3 (default) | scalar

Clutch static friction coefficient, mus — Coefficient 0.6 (default) | scalar

Clutch kinematic friction coefficient, muk — Coefficient 0.4 (default) | scalar

Start simulation with clutch locked — Select to initially lock clutch off (default) | on

Dependencies

Start simulation with synchronizer locked — Select to initially lock synchronizer off (default) | on

Extended Capabilities

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Version History

See Also

Gear — Gear number to engage
`scalar`

CltchCmd — Clutch command
`scalar`

EngTrq — Applied input torque
`scalar`

DiffTrq — Applied load torque
`scalar`

Temp — Oil temperature
`scalar`

Info — Bus signal
bus

EngSpd — Angular speed
`scalar`

DiffSpd — Angular speed
`scalar`

Control type — Specify control type
`Ideal integrated controller` (default) | `External control`

Efficiency factors — Specify efficiency calculation
`Gear only` (default) | `Gear, input torque, input speed, and temperature`

Input shaft inertia, Jin — Inertia
`.01` (default) | `scalar`

Input shaft damping, bin — Damping
`.001` (default) | `scalar`

Initial input velocity, omegain_o — Angular velocity
`0` (default) | `scalar`

Gear number vector, G — Specify number of transmission speeds
`[-1, 0, 1, 2, 3, 4, 5]` (default) | `vector`

Efficiency torque breakpoints, Trq_bpts — Breakpoints
`[25, 50, 75, 100, 150, 200, 250]` (default) | `vector`

Efficiency speed breakpoints, omega_bpts — Breakpoints
`[52.4 78.5 105 131 157 183 209 262 314 419 524]` (default) | `vector`

Efficiency temperature breakpoints, Temp_bpts — Breakpoints
`[313 358]` (default) | `vector`

Gear ratio vector, N — Ratio of input speed to output speed
`[-4.47, 1, 4.47, 2.47, 1.47, 1, 0.8]` (default) | `vector`

Transmission inertia vector, Jout — Gear rotational inertia
`[0.128 0.01 0.128 0.1 0.062 0.028 0.01]` (default) | `vector`

Transmission damping vector, bout — Gear viscous damping coefficient
`[.003 .001 .003 .0025 .002 .001 .001]` (default) | `vector`

Efficiency vector, eta — Gear efficiency
`[0.9, 0.9, 0.9, 0.9, 0.9, 0.95, 0.95]` (default) | `vector`

Efficiency lookup table, eta_tbl — Gear efficiency
`array`

Initial output velocity, omegaout_o — Transmission
`0` (default) | `scalar`

Initial gear, G_o — Engaged gear
`0` (default) | `scalar`

Clutch pressure time constant, tauc — Time
`.02` (default) | `scalar`

Synchronization time, ts — Time
`.25` (default) | `scalar`

Clutch time, tc — Time
`.5` (default) | `scalar`

Effective clutch radius, R — Radius
`.2` (default) | `scalar`

Clutch force gain, K_c — Force
`5e3` (default) | `scalar`

Clutch static friction coefficient, mus — Coefficient
`0.6` (default) | `scalar`

Clutch kinematic friction coefficient, muk — Coefficient
`0.4` (default) | `scalar`

Start simulation with clutch locked — Select to initially lock clutch
`off` (default) | `on`

Start simulation with synchronizer locked — Select to initially lock synchronizer
`off` (default) | `on`

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