Gearbox

Ideal rotational gearbox

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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.

$$\begin{array}{l}{\dot{\omega }}_B{J}_B={\omega }_B{b}_B+\eta N{T}_F\\ {\dot{\omega }}_F{J}_F={\omega }_F{b}_F+\eta T_F\end{array}$$

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

$${\omega }_B=N{\omega }_F$$

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

$$\eta N{T}_B+T_F=0$$

Efficiency

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

Setting	Implementation
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	PBase	$P_{Base}= \eta T_B{\omega }_B$
		PwrFlwr	Mechanical power from follower shaft	PFlwr	$$P_{Flwr}= \eta T_F{\omega }_F$$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrMechLoss	Total power loss	Png	$$\begin{array}{l}{P}_{ng}= -(P_t+P_d)+P_s\\ \\ P_t=\eta T_B{\omega }_B+\eta T_F{\omega }_F\end{array}$$
		PwrDampLoss	Power loss due to damping	Pd	$P_d=-\left(b_F{\left|{\omega }_F\right|}^2+b_B{\left|{\omega }_B\right|}^2\right)$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredShft	Rate change of stored internal kinetic energy	Ps	$P_s=\left({\omega }_B{\dot{\omega }}_B{J}_B+{\omega }_F{\dot{\omega }}_F{J}_F\right)$

The equations use these variables.

TB	Base gear input torque
TF	Follower gear output torque
ωB	Base gear angular velocity
ωF	Follower gear angular velocity
JB	Base gear rotational inertia
JF	Follower gear rotational inertia
bB	Base gear rotational viscous damping
bF	Follower gear rotational viscous damping
N	Torque transmission gear ratio
η	Gear efficiency
Pt	Total power
Pd	Power loss due to damping
Ps	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

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

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Variable	Units
Base	BaseTrq		Base gear input torque	TB	N·m
	BaseSpd		Base gear angular velocity	ωB	rad/s
Flwr	FlwrTrq		Follower gear torque	TF	N·m
	FlwrSpd		Follower gear angular velocity	ωF	rad/s
PwrInfo	PwrTrnsfrd	PwrBase	Mechanical power from base shaft	PBase	W
		PwrFlwr	Mechanical power from follower shaft	PFlwr	W
	PwrNotTrnsfrd	PwrMechLoss	Total gear power loss	Png	W
		PwrDampLoss	Power loss due to damping	Pd	W
	PwrStored	PwrStoredShft	Rate change of stored internal kinetic energy	Ps	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

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:

• B

• F

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	port_config
Values:	Simulink (default) | Two-way connection
Data Types:	character vector

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
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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	input_config
Values:	Constant (default) | Driveshaft torque, speed and temperature
Data Types:	character vector

Interpolation method — Method

Flat | Nearest | Linear point-slope | Linear Lagrange | Cubic spline

For more information, see Interpolation Methods.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	InterpMethod
Values:	Flat | Nearest | Linear point-slope | Linear Lagrange | Cubic spline
Data Types:	character vector

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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	dirSwitch
Values:	off (default) | on
Data Types:	character vector

Input ambient temperature — Create input port

off (default) | on

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	extTamb
Values:	off (default) | on
Data Types:	character vector

Dependencies

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

Input to output gear ratio, N — Ratio

2 (default) | positive scalar

Base-to-follower gear ratio, dimensionless.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	N
Values:	2 (default) | positive scalar
Data Types:	double

Input shaft inertia, J1 — Inertia

.01 (default) | positive scalar

Base shaft inertia, in kg·m^2.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	J1
Values:	.01 (default) | positive scalar
Data Types:	double

Output shaft inertia, J2 — Inertia

.01 (default) | positive scalar

Follower shaft inertia, in kg·m^2.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	J2
Values:	.01 (default) | positive scalar
Data Types:	double

Input shaft damping, b1 — Damping

.001 (default) | positive scalar

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	b1
Values:	.001 (default) | positive scalar
Data Types:	double

Output shaft damping, b2 — Damping

.001 (default) | positive scalar

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	b2
Values:	.001 (default) | positive scalar
Data Types:	double

Input shaft initial velocity, w1_o — Initial velocity

0 (default) | scalar greater than or equal to 0

Base shaft initial velocity, in rad/s.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	w1_o
Values:	0 (default) | scalar greater than or equal to 0
Data Types:	double

Efficiency

Constant efficiency factor, eta — Efficiency

1 (default) | positive scalar

Constant efficiency, η.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	eta
Values:	1 (default) | positive scalar
Data Types:	double

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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	eta_tbl
Values:	M-by-N-by-L array
Data Types:	double

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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Trq_bpts
Values:	[25, 50, 75, 100, 150, 200, 250] (default) | 1-by-M vector
Data Types:	double

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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	omega_bpts
Values:	[52.4 78.5 105 131 157 183 209 262 314 419 524] (default) | 1-by-N vector
Data Types:	double

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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Temp_bpts
Values:	[290 358] (default) | 1-by-L vector
Data Types:	double

Dependencies

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

Air temperature, Tair — Ambient air temperature

297.15 (default) | scalar greater than 0

Ambient air temperature, T_air, in K.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Tair
Values:	297.15 (default) | scalar greater than 0
Data Types:	double

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