Split Torsional Compliance

Split torsional coupler

• 

Libraries:
Powertrain Blockset / Drivetrain / Couplings
Vehicle Dynamics Blockset / Powertrain / Drivetrain / Couplings

Description

The Split Torsional Compliance block implements parallel spring-damper coupling between shafts. You can specify the type of coupling by selecting one of the Coupling Configuration parameters:

• Shaft split — Single input shaft coupled to two output shafts

• Shaft merge — Two input shafts coupled to a single output shaft

In fuel economy and emissions studies, you can use the Split Torsional Compliance block to model mechanical rotational compliance between common driveline elements such as motors, planetary gears, and clutches. For example, use the Shaft split configuration to couple a motor and two planetary gear sets. Use the Shaft merge configuration to couple a dual clutch transmission to an output shaft.

Shaft Split

For the Shaft split configuration, the block implements this schematic and equations.

$$\begin{array}{l}{T}_{in}=-({\omega }_{in}-{\omega }_{1out})b_1-({\omega }_{in}-{\omega }_{2out})b_2-{\theta }_1{k}_1-{\theta }_2{k}_2\\ T_{1out}=({\omega }_{in}-{\omega }_{1out})b_1+{\theta }_1{k}_1\\ T_{2out}=({\omega }_{in}-{\omega }_{2out})b_2+{\theta }_2{k}_2\\ \\ {\dot{\theta }}_1=({\omega }_{in}-{\omega }_{1out})\\ {\dot{\theta }}_2=({\omega }_{in}-{\omega }_{2out})\end{array}$$

To account for frequency-dependent damping, both damping terms incorporate a low-pass filter.

The equations use these variables.

Tin	Resulting applied input reaction torque
ωin	Input shaft rotational velocity
T1out	Resulting applied torque to first output shaft
ω1out	First output shaft rotational velocity
T2out	Resulting applied torque to second output shaft
ω2out	Second output shaft rotational velocity
θ1, θ2	First, second shaft rotation, respectively
b1, b2	First, second shaft viscous damping, respectively
k1, k2	First, second shaft torsional stiffness, respectively

Shaft Merge

For the Shaft merge configuration, the block implements this schematic and equations.

$$\begin{array}{l}{T}_{out}=(-{\omega }_{out}+{\omega }_{1in})b_1+(-{\omega }_{out}+{\omega }_{2in})b_2+{\theta }_1{k}_1+{\theta }_2{k}_2\\ T_{1out}=({\omega }_{out}-{\omega }_{1in})b_1-{\theta }_1{k}_1\\ T_{2out}=({\omega }_{out}-{\omega }_{2in})b_2-{\theta }_2{k}_2\\ \\ {\dot{\theta }}_1=({\omega }_{1in}-{\omega }_{out})\\ {\dot{\theta }}_2=({\omega }_{2in}-{\omega }_{out})\end{array}$$

To account for frequency-dependent damping, both damping terms incorporate a low-pass filter.

The equations use these variables.

Tout	Resulting applied output torque
ωout	Output shaft rotational velocity
T1in	Resulting reaction torque to first input shaft
ω1in	First input shaft rotational velocity
T2in	Resulting reaction torque to second input shaft
ω2in	Second input shaft rotational velocity
θ1, θ2	First, second shaft rotation, respectively
b1, b2	First, second shaft viscous damping, respectively
k1, k2	First, second shaft torsional stiffness, respectively

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	PwrR	For the Shaft split configuration, mechanical power from input shaft	PTR	$$P_{TR}= -T_R{\omega }_R$$
		PwrC1	For the Shaft split configuration, mechanical power from first output shaft	PTC1	$$P_{TC1}= -T_{C1}{\omega }_{C1}$$
		PwrC2	For the Shaft split configuration, mechanical power from second output shaft	PTC2	$$P_{TC2}= -T_{C2}{\omega }_{C2}$$
		PwrC	For the Shaft merge configuration, mechanical power from output shaft	PTC	$$P_{TC}= T_C{\omega }_C$$
		PwrR1	For the Shaft merge configuration, mechanical power from first input shaft	PTR1	$$P_{TR1}= T_{R1}{\omega }_{R1}$$
		PwrR2	For the Shaft merge configuration, mechanical power from second input shaft	PTR2	$$P_{TR2}= T_{R2}{\omega }_{R2}$$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrDampLoss	Mechanical damping loss	Pd	$$P_d=-\left(b_1{\left|{\dot{\theta }}_1\right|}^2+b_2{\left|{\dot{\theta }}_2\right|}^2\right)$$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredShft	Rate change in spring energy	Ps	$$P_s=\left(k_1{\theta }_1{\dot{\theta }}_1+k_2{\theta }_2{\dot{\theta }}_2\right)$$

The equations use these variables.

TR	Shaft R torque
TC	Shaft C torque
ωR	Shaft R angular velocity
ωC	Shaft C angular velocity
θ	Coupled shaft rotation
k	Shaft torsional stiffness
b	Rotational viscous damping
Pt	Total mechanical power
Pd	Power loss due to damping
Ps	Rate change of stored spring energy

Ports

Input

RSpd — Input shaft speed

scalar

Input shaft rotational velocity, ω_in, in rad/s.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft split

C1Spd — First output shaft speed

scalar

First output shaft rotational velocity, ω_1out, in rad/s.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft split

C2Spd — Second output shaft speed

scalar

Second output shaft rotational velocity, ω_2out, in rad/s.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft split

CSpd — Input speed

scalar

Output shaft rotational velocity, ω_out, in rad/s.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft merge

R1Spd — First input shaft speed

scalar

First input shaft rotational velocity, ω_1in, in rad/s.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft merge

R2Spd — Second input shaft speed

scalar

Second input shaft rotational velocity, ω_2in, in rad/s.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft merge

R — Input shaft angular velocity and torque

two-way connector port

Input shaft angular velocity, ω_in, in rad/s and torque, T_in, in N·m.

Dependencies

To enable this port, select:

• Port Configuration>Two-way connection

• Coupling Configuration>Shaft split

R1 — First input shaft angular velocity and torque

two-way connector port

First input shaft angular velocity, ω_1in, in rad/s and torque, T_1in, in N·m.

Dependencies

To enable this port, select:

• Port Configuration>Two-way connection

• Coupling Configuration>Shaft merge

R2 — Second input shaft angular velocity and torque

two-way connector port

Second input shaft angular velocity, ω_2in, in rad/s and torque, T_2in, in N·m.

Dependencies

To enable this port, select:

• Port Configuration>Two-way connection

• Coupling Configuration>Shaft merge

Output

Info — Bus signal

bus

If you set Coupling Configuration to Shaft split, the Info bus contains these signals.

Signal			Description	Variable	Units
Trq	R		Input shaft torque	Tin	N·m
	C1		First output shaft torque	T1out	N·m
	C2		Second output shaft torque	T2out	N·m
	Damp	C1	First output shaft damping torque	b1ω1out	N·m
		C2	Second output shaft damping torque	b2ω2out	N·m
	Spring	C1	First output shaft spring torque	k1θ1	N·m
		C2	Second output shaft spring torque	k2θ2	N·m
Spd	R		Input shaft angular velocity	ωin	rad/s
	C1		First output shaft angular velocity	ω1out	rad/s
	C2		Second output shaft angular velocity	ω2out	rad/s
	deltadot1		Difference in input and first output shaft angular velocity	$${\dot{\theta }}_1$$	rad/s
	deltadot2		Difference in input and second output shaft angular velocity	$${\dot{\theta }}_2$$	rad/s
PwrInfo	PwrTrnsfrd	PwrR	Mechanical power from input shaft	PTR	W
		PwrC1	Mechanical power from first output shaft	PTC1	W
		PwrC2	Mechanical power from second output shaft	PTC2	W
	PwrNotTrnsfrd	PwrDampLoss	Mechanical damping loss	Pd	W
	PwrStored	PwrStoredShft	Rate change of stored internal torsional energy	Ps	W

If you set Coupling Configuration to Shaft merge, the Info bus contains these signals.

Signal			Description	Variable	Units
Trq	C		Output shaft torque	Tout	N·m
	R1		First input shaft torque	T1in	N·m
	R2		Second input shaft torque	T2in	N·m
	Damp	R1	First input shaft damping torque	b1ω1in	N·m
		R2	Second in shaft damping torque	b2ω2in	N·m
	Spring	R1	First input shaft spring torque	k1θ1	N·m
		R2	Second in shaft spring torque	k2θ2	N·m
Spd	C		Output shaft angular velocity	ωout	rad/s
	R1		First input shaft angular velocity	ω1in	rad/s
	R2		Second input shaft angular velocity	ω2in	rad/s
	deltadot1		Difference in first input and output shaft angular velocity	$${\dot{\theta }}_1$$	rad/s
	deltadot2		Difference in second input and output shaft angular velocity	$${\dot{\theta }}_2$$	rad/s
PwrInfo	PwrTrnsfrd	PwrC	Mechanical power from output shaft	PTC	W
		PwrR1	Mechanical power from first input shaft	PTR1	W
		PwrR2	Mechanical power from second input shaft	PTR2	W
	PwrNotTrnsfrd	PwrDampLoss	Mechanical damping loss	Pd	W
	PwrStored	PwrStoredShft	Rate change of stored internal torsional energy	Ps	W

Dependencies

To enable this port, select Output Info bus.

RTrq — Input shaft torque

scalar

Input shaft torque, T_in, in N·m.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft split

C1Trq — First output shaft torque

scalar

First output shaft torque, T_1out, in N·m.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft split

C2Trq — Second output shaft torque

scalar

Second output shaft torque, T_2out, in N·m.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft split

CTrq — Output shaft torque

scalar

Output shaft torque, T_out, in N·m.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft merge

R1Trq — First input shaft torque

scalar

First input shaft torque, T_1in, in N·m.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft merge

R2Trq — Second input shaft torque

scalar

Second input shaft torque, T_2in, in N·m.

Dependencies

To enable this port, set both of these parameters:

• Port Configuration to Simulink

• Coupling Configuration to Shaft merge

C1 — First output shaft angular velocity and torque

two-way connector port

First output shaft angular velocity, ω_1out, in rad/s and torque, T_1out, in N·m.

Dependencies

To enable this port, select:

• Port Configuration>Two-way connection

• Coupling Configuration>Shaft split

C2 — Second output shaft angular velocity and torque

two-way connector port

Second output shaft angular velocity, ω_2out, in rad/s and torque, T_2out, in N·m.

Dependencies

To enable this port, select:

• Port Configuration>Two-way connection

• Coupling Configuration>Shaft split

C — Output shaft angular velocity and torque

two-way connector port

Output shaft angular velocity, ω_out, in rad/s and torque, T_out, in N·m.

Dependencies

To enable this port, select:

• Port Configuration>Two-way connection

• Coupling Configuration>Shaft merge

Parameters

Block Options

Port Configuration — Specify configuration

Simulink (default) | Two-way connection

Specify the port configuration.

Coupling Configuration — Specify configuration

Shaft split (default) | Shaft merge

Specify the coupling type.

Output Info bus — Selection

off (default) | on

Select to create the Info output port.

Coupling 1

Torsional stiffness, k1 — Stiffness

5e4 (default) | scalar

Rotational inertia, k₁, in N·m/rad.

Torsional damping, b1 — Damping

1e2 (default) | scalar

Torsional damping, b₁, in N·m· s/rad.

Damping cutoff frequency, omega1_c — Frequency

3000 (default) | scalar

Damping cutoff frequency, in rad/s.

Coupling 2

Torsional stiffness, k2 — Stiffness

5e4 (default) | scalar

Rotational inertia, k₂, in N·m/rad.

Torsional damping, b2 — Damping

1e2 (default) | scalar

Torsional damping, b₂, in N·m· s/rad.

Damping cutoff frequency, omega2_c — Frequency

3000 (default) | scalar

Damping cutoff frequency, in rad/s.

Extended Capabilities

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

Version History

Introduced in R2017b