Transfer Case

Differential as a planetary bevel gear

Since R2021b

• 

Libraries:
Powertrain Blockset / Drivetrain / Final Drive Unit
Vehicle Dynamics Blockset / Powertrain / Drivetrain / Final Drive Unit

Description

The Transfer Case block implements a differential as a planetary bevel gear train. The block matches the driveshaft bevel gear to the crown (ring) bevel gear. You can specify:

• Carrier-to-driveshaft ratio

• Crown wheel location

• Viscous and damping coefficients for the axles and carrier

Use the Transfer Case block to:

• Dynamically couple the post-transmission driveshaft to the wheel axles or universal joints

• Model simplified or older drivetrains when optimal traction control does not require passive or active torque vectoring

• Model mechanical power splitting in generic gearbox and drive line scenarios

The block is suitable for use in hardware-in-the-loop (HIL) and optimization workflows. All the parameters are tunable.

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	Equations
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrDriveshft	Mechanical power from driveshaft	$$\eta T_d{\omega }_d$$
		PwrAxl1	Mechanical power from axle 1	$$\eta T_1{\omega }_1$$
		PwrAxl2	Mechanical power from axle 2	$$\eta T_2{\omega }_2$$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrMechLoss	Total power loss	$$\begin{array}{l}{\dot{W}}_{loss}= -(P_t+P_d)+P_s\\ \\ P_t=\eta T_d{\omega }_d+\eta T_1{\omega }_1+\eta T_2{\omega }_2\end{array}$$
		PwrDampLoss	Power loss due to damping	$$P_d=-\left(b_1\left|{\omega }_1\right|+b_2\left|{\omega }_2\right|+b_d\left|{\omega }_d\right|\right)$$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredShft	Rate change of stored internal energy	$P_s=-({\omega }_1{\dot{\omega }}_1{J}_1+{\omega }_2{\dot{\omega }}_2{J}_2+{\omega }_d{\dot{\omega }}_d{J}_d)$

Dynamics

The Transfer Case block implements these differential equations to represent the mechanical dynamic response for the crown gear, front axle, and rear axle.

Mechanical Dynamic Response	Differential Equation
Crown Gear	$${\dot{\omega }}_d{J}_d=\eta T_d-{\omega }_d{b}_d-T_i$$
Front Axle	${\dot{\omega }}_1{J}_1=\eta T_1-{\omega }_1{b}_1-T_{i1}$
Rear Axle	${\dot{\omega }}_2{J}_2=\eta T_2-{\omega }_2{b}_2-T_{i2}$

The equations use these variables.

N	Carrier-to-driveshaft gear ratio
Jd	Rotational inertia of the crown gear assembly
bd	Crown gear linear viscous damping
ωd	Driveshaft angular speed
η	Differential efficiency
J1	Axle 1 rotational inertia
b1	Axle 1 linear viscous damping
ω1	Axle 1 speed
J2	Axle 2 rotational inertia
b2	Axle 2 linear viscous damping
ω2	Axle 2 angular speed
Td	Driveshaft torque
T1	Axle 1 torque
T2	Axle 2 torque
Ti	Driveshaft internal resistance torque
Ti1	Axle 1 internal resistance torque
Ti2	Axle 2 internal resistance torque

Ports

Inputs

DriveshftTrq — Torque

scalar

Applied input torque, typically from the engine crankshaft, in N·m.

Axl1Trq — Torque

scalar

Axle 1 torque, T₁, in N·m.

Axl2Trq — Torque

scalar

Axle 2 torque, T₂, in N·m.

Temp — Temperature

scalar

Temperature, in K.

Dependencies

To enable this port:

• Set Efficiency factors to Driveshaft torque, speed and temperature.

• Select Input temperature.

TrqSplitRatioConstant — Front axle torque split ratio

scalar

Front axle torque split ratio.

Dependencies

To enable this port, select Input front axle torque split ratio, TrqSplitRatio.

SpdLockConstant — Axle speed lock

scalar

Axle speed lock.

Dependencies

To enable this port, select Input axle speed lock, SpdLock.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Units
Driveshft	DriveshftTrq		Driveshaft torque	N·m
	DriveshftSpd		Driveshaft speed	rad/s
Axl1	Axl1Trq		Axle 1 torque	N·m
	Axl1Spd		Axle 1 speed	rad/s
Axl2	Axl2Trq		Axle 2 torque	N·m
	Axl2Spd		Axle 2 speed	rad/s
PwrInfo	PwrTrnsfrd	PwrDriveshft	Mechanical power from driveshaft	W
		PwrAxl1	Mechanical power from axle 1	W
		PwrAxl2	Mechanical power from axle 2	W
	PwrTrnsfrd	PwrMechLoss	Total power loss	W
		PwrDampLoss	Power loss due to damping	W
	PwrStored	PwrStoredShft	Rate change of stored internal energy	W

DriveshftSpd — Angular speed

scalar

Driveshaft angular speed, ω_d, in rad/s.

Axl1Spd — Angular speed

scalar

Axle 1 angular speed, ω₁, in rad/s.

Axl2Spd — Angular speed

scalar

Axle 2 angular speed, ω₂, in rad/s.

Parameters

Block Options

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:	DiffEffModelPopup
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.

Input ambient temperature — Create input port

off (default) | on

Select to create input port Temp for the 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 front axle torque split ratio, TrqSplitRatio — Create input port

off (default) | on

Select to create input port TrqSplitRatioConstant for the front axle torque split ratio.

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

Input axle speed lock, SpdLock — Create input port

off (default) | on

Select to create input port SpdLockConstant for the axle speed lock.

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

Crown wheel (ring gear) located — Specify crown wheel connection

To the left of center-line (default) | To the right of center-line

Specify the crown wheel connection to the driveshaft.

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:	shaftSwitchMask
Values:	To the left of center-line (default) | To the right of center-line
Data Types:	character vector

Carrier to drive shaft ratio, Ndiff — Ratio

4 (default) | scalar

Carrier-to-driveshaft gear ratio, N, 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:	Ndiff
Values:	4 (default) | scalar
Data Types:	double

Carrier inertia, Jd — Inertia

.1 (default) | scalar

Rotational inertia of the crown gear assembly, J_d, in kg·m^2. You can include the driveshaft inertia.

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:	Jd
Values:	.1 (default) | scalar
Data Types:	double

Carrier damping, bd — Damping

1e-3 (default) | scalar

Crown gear linear viscous damping, b_d, 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:	bd
Values:	1e-3 (default) | scalar
Data Types:	double

Axle 1 inertia, Jw1 — Inertia

.1 (default) | scalar

Axle 1 rotational inertia, J₁, 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:	Jw1
Values:	.1 (default) | scalar
Data Types:	double

Axle 1 damping, bw1 — Damping

1e-3 (default) | scalar

Axle 1 linear viscous damping, b₁, 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:	bw1
Values:	1e-3 (default) | scalar
Data Types:	double

Axle 2 inertia, Jw2 — Inertia

.1 (default) | scalar

Axle 2 rotational inertia, J₂, 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:	Jw2
Values:	.1 (default) | scalar
Data Types:	double

Axle 2 damping, bw2 — Damping

1e-3 (default) | scalar

Axle 2 linear viscous damping, b₂, 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:	bw2
Values:	1e-3 (default) | scalar
Data Types:	double

Axle 1 initial velocity, omegaw1o — Angular velocity

0 (default) | scalar

Axle 1 initial velocity, ω_o1, 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:	omegaw1o
Values:	0 (default) | scalar
Data Types:	double

Axle 2 initial velocity, omegaw2o — Angular velocity

0 (default) | scalar

Axle 2 initial velocity, ω_o2, 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:	omegaw2o
Values:	0 (default) | scalar
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.

Ambient temperature, Tamb — Ambient temperature

297.15 (default) | scalar

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:	Tamb
Values:	297.15 (default) | scalar
Data Types:	double

Dependencies

To enable this parameter:

• Set Efficiency factors to Driveshaft torque, speed and temperature.

• Clear Input ambient temperature.

Front axle torque split ratio, TrqSplitRatio — Front axle torque split ratio

0.5 (default) | scalar

Front axle torque split ratio.

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:	TrqSplitRatio
Values:	0.5 (default) | scalar
Data Types:	double

Dependencies

To enable this parameter, clear Input front axle torque split ratio, TrqSplitRatio.

Axle speed lock, SpdLock — Axle speed lock

0 (default) | scalar

Axle speed lock. Set this value to 0 to make the front and rear axle rotational speed not fixed. Set this value to 1 to make the front and rear axle rotational speed fixed.

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:	SpdLock
Values:	0 (default) | scalar
Data Types:	double

Dependencies

To enable this parameter, clear Input axle speed lock, SpdLock.

Extended Capabilities

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

Version History

Introduced in R2021b