Gearbox

Ideal rotational gearbox

Libraries:
Powertrain Blockset / Drivetrain / Couplings

Description

The Gearbox block implements an ideal rotational gearbox. The block uses the gear inertias and damping to calculate the velocity response to the base and follower gear pair input torques.

In fuel economy and powertrain efficiency studies, you can use the Gearbox block to model ideal gear coupling and the power transfer between common driveline elements such as transmissions, engines, clutches, and differentials.

The Gearbox block uses these equations to approximate the transmission dynamics.

$\begin{array}{l} {\dot{ω}}_{B} J_{B} = ω_{B} b_{B} + η N T_{F} \\ {\dot{ω}}_{F} J_{F} = ω_{F} b_{F} + η T_{F} \end{array}$

This constraint equation reduces the system to a one DOF system.

$ω_{B} = N ω_{F}$

To express the ideal torque transfer, the block uses this relationship.

$η N T_{B} + T_{F} = 0$

Efficiency

To account for the block efficiency, use the Efficiency factors parameter. This table summarizes the block implementation for each setting.

Setting Implementation

Setting	Implementation
`Constant`	Constant efficiency that you can set with the Constant efficiency factor, eta parameter.
`Driveshaft torque, temperature and speed`	Efficiency as a function of base gear input torque, air temperature, and driveshaft speed. Use these parameters to specify the lookup table and breakpoints: Efficiency lookup table, eta_tbl Efficiency torque breakpoints, Trq_bpts Efficiency speed breakpoints, omega_bpts Efficiency temperature breakpoints, Temp_bpts For the air temperature, you can either: Select Input ambient temperature to create an input port. Set a Ambient temperature, Tamb parameter value. To select the interpolation method, use the Interpolation method parameter. For more information, see Interpolation Methods.

Constant

Constant efficiency that you can set with the Constant efficiency factor, eta parameter.

Driveshaft torque, temperature and speed

Efficiency as a function of base gear input torque, air temperature, and driveshaft speed. Use these parameters to specify the lookup table and breakpoints:

Efficiency lookup table, eta_tbl
Efficiency torque breakpoints, Trq_bpts
Efficiency speed breakpoints, omega_bpts
Efficiency temperature breakpoints, Temp_bpts

For the air temperature, you can either:

Select Input ambient temperature to create an input port.
Set a Ambient temperature, Tamb parameter value.

To select the interpolation method, use the Interpolation method parameter. For more information, see Interpolation Methods.

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	`PwrBase`	Mechanical power from base shaft	P_Base	$P_{B a s e} = η T_{B} ω_{B}$
		`PwrFlwr`	Mechanical power from follower shaft	P_Flwr	$P_{F l w r} = η T_{F} ω_{F}$
	`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	`PwrMechLoss`	Total power loss	P_ng	$\begin{array}{l} P_{n g} = - (P_{t} + P_{d}) + P_{s} \\ P_{t} = η T_{B} ω_{B} + η T_{F} ω_{F} \end{array}$
		`PwrDampLoss`	Power loss due to damping	P_d	$P_{d} = - (b_{F} {\| ω_{F} \|}^{2} + b_{B} {\| ω_{B} \|}^{2})$
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`PwrStoredShft`	Rate change of stored internal kinetic energy	P_s	$P_{s} = (ω_{B} {\dot{ω}}_{B} J_{B} + ω_{F} {\dot{ω}}_{F} J_{F})$

The equations use these variables.

T_B	Base gear input torque
T_F	Follower gear output torque
ω_B	Base gear angular velocity
ω_F	Follower gear angular velocity
J_B	Base gear rotational inertia
J_F	Follower gear rotational inertia
b_B	Base gear rotational viscous damping
b_F	Follower gear rotational viscous damping
N	Torque transmission gear ratio
η	Gear efficiency
P_t	Total power
P_d	Power loss due to damping
P_s	Rate change of stored internal kinetic energy

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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BTrq — Base gear input torque
`scalar`

Base gear input torque, T_B, in N·m.

Dependencies

To create this port, for Port Configuration, select Simulink.

FTrq — Follower gear output torque
`scalar`

Follower gear output torque, T_F, in N·m.

Dependencies

To create this port, for Port Configuration, select Simulink.

B — Base gear angular velocity and torque
two-way connector port

Base gear angular velocity, ω_B, in rad/s. Base gear torque, T_B, in N·m.

Dependencies

To create this port, for Port Configuration, select Two-way connection.

AirTemp — Ambient air temperature
`scalar`

Ambient air temperature, T_air, in K.

Dependencies

To enable this port:

Set Efficiency factors to Driveshaft torque, speed and temperature.
Select Input ambient temperature.

Output

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Info — Bus signal
bus

Bus signal containing these block calculations.

Signal			Description	Variable	Units
Base	`BaseTrq`		Base gear input torque	T_B	N·m
Base	`BaseSpd`		Base gear angular velocity	ω_B	rad/s
Flwr	`FlwrTrq`		Follower gear torque	T_F	N·m
Flwr	`FlwrSpd`		Follower gear angular velocity	ω_F	rad/s
PwrInfo	`PwrTrnsfrd`	`PwrBase`	Mechanical power from base shaft	P_Base	W
	`PwrTrnsfrd`	`PwrFlwr`	Mechanical power from follower shaft	P_Flwr	W
	`PwrNotTrnsfrd`	`PwrMechLoss`	Total gear power loss	P_ng	W
	`PwrNotTrnsfrd`	`PwrDampLoss`	Power loss due to damping	P_d	W
	`PwrStored`	`PwrStoredShft`	Rate change of stored internal kinetic energy	P_s	W

BSpd — Input gear angular velocity
`scalar`

Base gear angular velocity, ω_B, in rad/s.

Dependencies

To create this port, for Port Configuration, select Simulink.

FSpd — Output gear angular velocity
`scalar`

Follower gear angular velocity, ω_F, in rad/s.

Dependencies

To create this port, for Port Configuration, select Simulink.

F — Output gear angular velocity and torque
two-way connector port

Follower gear angular velocity, ω_F, in rad/s. Follower gear torque, T_F, in N·m.

Dependencies

To create this port, for Port Configuration, select Two-way connection.

Parameters

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Block Options

Port Configuration — Specify configuration
`Simulink` (default) | `Two-way connection`

Specify the port configuration.

Dependencies

Specifying Simulink creates these ports:

BSpd
FSpd
BTrq
FTrq

Specifying Two-way connection creates these ports:

Efficiency factors — Specify configuration
`Constant` (default) | `Driveshaft torque, speed and temperature`

To account for the block efficiency, use the Efficiency factors parameter. This table summarizes the block implementation for each setting.

Setting Implementation

Setting	Implementation
`Constant`	Constant efficiency that you can set with the Constant efficiency factor, eta parameter.
`Driveshaft torque, temperature and speed`	Efficiency as a function of base gear input torque, air temperature, and driveshaft speed. Use these parameters to specify the lookup table and breakpoints: Efficiency lookup table, eta_tbl Efficiency torque breakpoints, Trq_bpts Efficiency speed breakpoints, omega_bpts Efficiency temperature breakpoints, Temp_bpts For the air temperature, you can either: Select Input ambient temperature to create an input port. Set a Ambient temperature, Tamb parameter value. To select the interpolation method, use the Interpolation method parameter. For more information, see Interpolation Methods.

Constant

Constant efficiency that you can set with the Constant efficiency factor, eta parameter.

Driveshaft torque, temperature and speed

Efficiency as a function of base gear input torque, air temperature, and driveshaft speed. Use these parameters to specify the lookup table and breakpoints:

Efficiency lookup table, eta_tbl
Efficiency torque breakpoints, Trq_bpts
Efficiency speed breakpoints, omega_bpts
Efficiency temperature breakpoints, Temp_bpts

For the air temperature, you can either:

Select Input ambient temperature to create an input port.
Set a Ambient temperature, Tamb parameter value.

To select the interpolation method, use the Interpolation method parameter. For more information, see Interpolation Methods.

Interpolation method — Method
`Flat` | `Nearest` | `Linear point-slope` | `Linear Lagrange` | `Cubic spline`

For more information, see Interpolation Methods.

Dependencies

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

Output shaft rotates in same direction as input — Rotation
`off` (default) | `on`

Select to specify that the output shaft rotates in the same direction as the input.

Input ambient temperature — Create input port
`off` (default) | `on`

Select to create input port AirTemp for the ambient air temperature.

Dependencies

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

Input to output gear ratio, N — Ratio
`2` (default) | `scalar`

Base-to-follower gear ratio, dimensionless.

Input shaft inertia, J1 — Inertia
`.01` (default) | `scalar`

Base shaft inertia, in kg·m^2.

Output shaft inertia, J2 — Inertia
`.01` (default) | `scalar`

Follower shaft inertia, in kg·m^2.

Input shaft damping, b1 — Damping
`.001` (default) | `scalar`

Base viscous shaft damping, in N·m· s/rad.

Output shaft damping, b2 — Damping
`.001` (default) | `scalar`

Follower viscous shaft damping, in N·m· s/rad.

Input shaft initial velocity, w1_o — Initial velocity
`0` (default) | `scalar`

Base shaft initial velocity, in rad/s.

Efficiency

Constant efficiency factor, eta — Efficiency
`1` (default) | `scalar`

Constant efficiency, η.

Dependencies

To enable this parameter, set Efficiency factors to Constant.

Efficiency lookup table, eta_tbl — Lookup table
`M`-by-`N`-by-`L` array

Dimensionless array of values for efficiency as a function of:

M input torques
N input speed
L air temperatures

Each value specifies the efficiency for a specific combination of torque, speed, and temperature. The array size must match the dimensions defined by the torque, speed, and temperature breakpoint vectors.

Dependencies

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

Efficiency torque breakpoints, Trq_bpts — Torque breakpoints
`[25, 50, 75, 100, 150, 200, 250]` (default) | `1`-by-`M` vector

Vector of input torque, breakpoints for efficiency, in N·m.

Dependencies

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

Efficiency speed breakpoints, omega_bpts — Speed breakpoints
`[52.4 78.5 105 131 157 183 209 262 314 419 524]` (default) | `1`-by-`N` vector

Vector of speed, breakpoints for efficiency, in rad/s.

Dependencies

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

Efficiency temperature breakpoints, Temp_bpts — Temperature breakpoints
`[290 358]` (default) | `1`-by-`L` vector

Vector of ambient temperature breakpoints for efficiency, in K.

Dependencies

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

Air temperature, Tair — Ambient air temperature
`297.15` (default) | `scalar`

Ambient air temperature, T_air, in K.

Dependencies

To enable this parameter:

Set Efficiency factors to Driveshaft torque, speed and temperature.
Clear Input ambient temperature.

Extended Capabilities

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

Version History

Introduced in R2017a

Gearbox

Description

Efficiency

Power Accounting

Examples

Build Conventional Vehicle Model

Ports

Input

BTrq — Base gear input torque scalar

Dependencies

FTrq — Follower gear output torque scalar

Dependencies

B — Base gear angular velocity and torque two-way connector port

Dependencies

AirTemp — Ambient air temperature scalar

Dependencies

Output

Info — Bus signal bus

BSpd — Input gear angular velocity scalar

Dependencies

FSpd — Output gear angular velocity scalar

Dependencies

F — Output gear angular velocity and torque two-way connector port

Dependencies

Parameters

Port Configuration — Specify configuration Simulink (default) | Two-way connection

Dependencies

Efficiency factors — Specify configuration Constant (default) | Driveshaft torque, speed and temperature

Interpolation method — Method Flat | Nearest | Linear point-slope | Linear Lagrange | Cubic spline

Dependencies

Output shaft rotates in same direction as input — Rotation off (default) | on

Input ambient temperature — Create input port off (default) | on

Dependencies

Input to output gear ratio, N — Ratio 2 (default) | scalar

Input shaft inertia, J1 — Inertia .01 (default) | scalar

Output shaft inertia, J2 — Inertia .01 (default) | scalar

Input shaft damping, b1 — Damping .001 (default) | scalar

Output shaft damping, b2 — Damping .001 (default) | scalar

Input shaft initial velocity, w1_o — Initial velocity 0 (default) | scalar

Constant efficiency factor, eta — Efficiency 1 (default) | scalar

Dependencies

Efficiency lookup table, eta_tbl — Lookup table M-by-N-by-L array

Dependencies

Efficiency torque breakpoints, Trq_bpts — Torque breakpoints [25, 50, 75, 100, 150, 200, 250] (default) | 1-by-M vector

Dependencies

Efficiency speed breakpoints, omega_bpts — Speed breakpoints [52.4 78.5 105 131 157 183 209 262 314 419 524] (default) | 1-by-N vector

Dependencies

Efficiency temperature breakpoints, Temp_bpts — Temperature breakpoints [290 358] (default) | 1-by-L vector

Dependencies

Air temperature, Tair — Ambient air temperature 297.15 (default) | scalar

Dependencies

Extended Capabilities

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

Version History

See Also

BTrq — Base gear input torque
`scalar`

FTrq — Follower gear output torque
`scalar`

B — Base gear angular velocity and torque
two-way connector port

AirTemp — Ambient air temperature
`scalar`

Info — Bus signal
bus

BSpd — Input gear angular velocity
`scalar`

FSpd — Output gear angular velocity
`scalar`

F — Output gear angular velocity and torque
two-way connector port

Port Configuration — Specify configuration
`Simulink` (default) | `Two-way connection`

Efficiency factors — Specify configuration
`Constant` (default) | `Driveshaft torque, speed and temperature`

Interpolation method — Method
`Flat` | `Nearest` | `Linear point-slope` | `Linear Lagrange` | `Cubic spline`

Output shaft rotates in same direction as input — Rotation
`off` (default) | `on`

Input ambient temperature — Create input port
`off` (default) | `on`

Input to output gear ratio, N — Ratio
`2` (default) | `scalar`

Input shaft inertia, J1 — Inertia
`.01` (default) | `scalar`

Output shaft inertia, J2 — Inertia
`.01` (default) | `scalar`

Input shaft damping, b1 — Damping
`.001` (default) | `scalar`

Output shaft damping, b2 — Damping
`.001` (default) | `scalar`

Input shaft initial velocity, w1_o — Initial velocity
`0` (default) | `scalar`

Constant efficiency factor, eta — Efficiency
`1` (default) | `scalar`

Efficiency lookup table, eta_tbl — Lookup table
`M`-by-`N`-by-`L` array

Efficiency torque breakpoints, Trq_bpts — Torque breakpoints
`[25, 50, 75, 100, 150, 200, 250]` (default) | `1`-by-`M` vector

Efficiency speed breakpoints, omega_bpts — Speed breakpoints
`[52.4 78.5 105 131 157 183 209 262 314 419 524]` (default) | `1`-by-`N` vector

Efficiency temperature breakpoints, Temp_bpts — Temperature breakpoints
`[290 358]` (default) | `1`-by-`L` vector

Air temperature, Tair — Ambient air temperature
`297.15` (default) | `scalar`

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