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.

Schematic diagram of shaft split rotational compliance

$\begin{array}{l} T_{i n} = - (ω_{i n} - ω_{1 o u t}) b_{1} - (ω_{i n} - ω_{2 o u t}) b_{2} - θ_{1} k_{1} - θ_{2} k_{2} \\ T_{1 o u t} = (ω_{i n} - ω_{1 o u t}) b_{1} + θ_{1} k_{1} \\ T_{2 o u t} = (ω_{i n} - ω_{2 o u t}) b_{2} + θ_{2} k_{2} \\ {\dot{θ}}_{1} = (ω_{i n} - ω_{1 o u t}) \\ {\dot{θ}}_{2} = (ω_{i n} - ω_{2 o u t}) \end{array}$

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

The equations use these variables.

T_in	Resulting applied input reaction torque
ω_in	Input shaft rotational velocity
T_1out	Resulting applied torque to first output shaft
ω_1out	First output shaft rotational velocity
T_2out	Resulting applied torque to second output shaft
ω_2out	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.

Schematic diagram of shaft merge rotational compliance

$\begin{array}{l} T_{o u t} = (- ω_{o u t} + ω_{1 i n}) b_{1} + (- ω_{o u t} + ω_{2 i n}) b_{2} + θ_{1} k_{1} + θ_{2} k_{2} \\ T_{1 o u t} = (ω_{o u t} - ω_{1 i n}) b_{1} - θ_{1} k_{1} \\ T_{2 o u t} = (ω_{o u t} - ω_{2 i n}) b_{2} - θ_{2} k_{2} \\ {\dot{θ}}_{1} = (ω_{1 i n} - ω_{o u t}) \\ {\dot{θ}}_{2} = (ω_{2 i n} - ω_{o u t}) \end{array}$

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

The equations use these variables.

T_out	Resulting applied output torque
ω_out	Output shaft rotational velocity
T_1in	Resulting reaction torque to first input shaft
ω_1in	First input shaft rotational velocity
T_2in	Resulting reaction torque to second input shaft
ω_2in	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	P_TR	$P_{T R} = - T_{R} ω_{R}$
		`PwrC1`	For the `Shaft split` configuration, mechanical power from first output shaft	P_TC1	$P_{T C 1} = - T_{C 1} ω_{C 1}$
		`PwrC2`	For the `Shaft split` configuration, mechanical power from second output shaft	P_TC2	$P_{T C 2} = - T_{C 2} ω_{C 2}$
		`PwrC`	For the `Shaft merge` configuration, mechanical power from output shaft	P_TC	$P_{T C} = T_{C} ω_{C}$
		`PwrR1`	For the `Shaft merge` configuration, mechanical power from first input shaft	P_TR1	$P_{T R 1} = T_{R 1} ω_{R 1}$
		`PwrR2`	For the `Shaft merge` configuration, mechanical power from second input shaft	P_TR2	$P_{T R 2} = T_{R 2} ω_{R 2}$
	`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	`PwrDampLoss`	Mechanical damping loss	P_d	$P_{d} = - (b_{1} {\| {\dot{θ}}_{1} \|}^{2} + b_{2} {\| {\dot{θ}}_{2} \|}^{2})$
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`PwrStoredShft`	Rate change in spring energy	P_s	$P_{s} = (k_{1} θ_{1} {\dot{θ}}_{1} + k_{2} θ_{2} {\dot{θ}}_{2})$

The equations use these variables.

T_R	Shaft R torque
T_C	Shaft C torque
ω_R	Shaft R angular velocity
ω_C	Shaft C angular velocity
θ	Coupled shaft rotation
k	Shaft torsional stiffness
b	Rotational viscous damping
P_t	Total mechanical power
P_d	Power loss due to damping
P_s	Rate change of stored spring energy

Ports

Input

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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

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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	T_in	N·m
	`C1`		First output shaft torque	T_1out	N·m
	`C2`		Second output shaft torque	T_2out	N·m
	`Damp`	`C1`	First output shaft damping torque	b₁ω_1out	N·m
	`Damp`	`C2`	Second output shaft damping torque	b₂ω_2out	N·m
	`Spring`	`C1`	First output shaft spring torque	k₁θ₁	N·m
	`Spring`	`C2`	Second output shaft spring torque	k₂θ₂	N·m
Spd	`R`		Input shaft angular velocity	ω_in	rad/s
	`C1`		First output shaft angular velocity	ω_1out	rad/s
	`C2`		Second output shaft angular velocity	ω_2out	rad/s
	`deltadot1`		Difference in input and first output shaft angular velocity	${\dot{θ}}_{1}$	rad/s
	`deltadot2`		Difference in input and second output shaft angular velocity	${\dot{θ}}_{2}$	rad/s
PwrInfo	`PwrTrnsfrd`	`PwrR`	Mechanical power from input shaft	P_TR	W
		`PwrC1`	Mechanical power from first output shaft	P_TC1	W
		`PwrC2`	Mechanical power from second output shaft	P_TC2	W
	`PwrNotTrnsfrd`	`PwrDampLoss`	Mechanical damping loss	P_d	W
	`PwrStored`	`PwrStoredShft`	Rate change of stored internal torsional energy	P_s	W

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

Signal			Description	Variable	Units
Trq	`C`		Output shaft torque	T_out	N·m
	`R1`		First input shaft torque	T_1in	N·m
	`R2`		Second input shaft torque	T_2in	N·m
	`Damp`	`R1`	First input shaft damping torque	b₁ω_1in	N·m
	`Damp`	`R2`	Second in shaft damping torque	b₂ω_2in	N·m
	`Spring`	`R1`	First input shaft spring torque	k₁θ₁	N·m
	`Spring`	`R2`	Second in shaft spring torque	k₂θ₂	N·m
Spd	`C`		Output shaft angular velocity	ω_out	rad/s
	`R1`		First input shaft angular velocity	ω_1in	rad/s
	`R2`		Second input shaft angular velocity	ω_2in	rad/s
	`deltadot1`		Difference in first input and output shaft angular velocity	${\dot{θ}}_{1}$	rad/s
	`deltadot2`		Difference in second input and output shaft angular velocity	${\dot{θ}}_{2}$	rad/s
PwrInfo	`PwrTrnsfrd`	`PwrC`	Mechanical power from output shaft	P_TC	W
		`PwrR1`	Mechanical power from first input shaft	P_TR1	W
		`PwrR2`	Mechanical power from second input shaft	P_TR2	W
	`PwrNotTrnsfrd`	`PwrDampLoss`	Mechanical damping loss	P_d	W
	`PwrStored`	`PwrStoredShft`	Rate change of stored internal torsional energy	P_s	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

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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

Split Torsional Compliance

Description

Shaft Split

Shaft Merge

Power Accounting

Ports

Input

RSpd — Input shaft speed scalar

Dependencies

C1Spd — First output shaft speed scalar

Dependencies

C2Spd — Second output shaft speed scalar

Dependencies

CSpd — Input speed scalar

Dependencies

R1Spd — First input shaft speed scalar

Dependencies

R2Spd — Second input shaft speed scalar

Dependencies

R — Input shaft angular velocity and torque two-way connector port

Dependencies

R1 — First input shaft angular velocity and torque two-way connector port

Dependencies

R2 — Second input shaft angular velocity and torque two-way connector port

Dependencies

Output

Info — Bus signal bus

Dependencies

RTrq — Input shaft torque scalar

Dependencies

C1Trq — First output shaft torque scalar

Dependencies

C2Trq — Second output shaft torque scalar

Dependencies

CTrq — Output shaft torque scalar

Dependencies

R1Trq — First input shaft torque scalar

Dependencies

R2Trq — Second input shaft torque scalar

Dependencies

C1 — First output shaft angular velocity and torque two-way connector port

Dependencies

C2 — Second output shaft angular velocity and torque two-way connector port

Dependencies

C — Output shaft angular velocity and torque two-way connector port

Dependencies

Parameters

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

Coupling Configuration — Specify configuration Shaft split (default) | Shaft merge

Output Info bus — Selection off (default) | on

Torsional stiffness, k1 — Stiffness 5e4 (default) | scalar

Torsional damping, b1 — Damping 1e2 (default) | scalar

Damping cutoff frequency, omega1_c — Frequency 3000 (default) | scalar

Torsional stiffness, k2 — Stiffness 5e4 (default) | scalar

Torsional damping, b2 — Damping 1e2 (default) | scalar

Damping cutoff frequency, omega2_c — Frequency 3000 (default) | scalar

Extended Capabilities

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

Version History

See Also

RSpd — Input shaft speed
`scalar`

C1Spd — First output shaft speed
`scalar`

C2Spd — Second output shaft speed
`scalar`

CSpd — Input speed
`scalar`

R1Spd — First input shaft speed
`scalar`

R2Spd — Second input shaft speed
`scalar`

R — Input shaft angular velocity and torque
two-way connector port

R1 — First input shaft angular velocity and torque
two-way connector port

R2 — Second input shaft angular velocity and torque
two-way connector port

Info — Bus signal
bus

RTrq — Input shaft torque
`scalar`

C1Trq — First output shaft torque
`scalar`

C2Trq — Second output shaft torque
`scalar`

CTrq — Output shaft torque
`scalar`

R1Trq — First input shaft torque
`scalar`

R2Trq — Second input shaft torque
`scalar`

C1 — First output shaft angular velocity and torque
two-way connector port

C2 — Second output shaft angular velocity and torque
two-way connector port

C — Output shaft angular velocity and torque
two-way connector port

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

Coupling Configuration — Specify configuration
`Shaft split` (default) | `Shaft merge`

Output Info bus — Selection
`off` (default) | `on`

Torsional stiffness, k1 — Stiffness
`5e4` (default) | `scalar`

Torsional damping, b1 — Damping
`1e2` (default) | `scalar`

Damping cutoff frequency, omega1_c — Frequency
`3000` (default) | `scalar`

Torsional stiffness, k2 — Stiffness
`5e4` (default) | `scalar`

Torsional damping, b2 — Damping
`1e2` (default) | `scalar`

Damping cutoff frequency, omega2_c — Frequency
`3000` (default) | `scalar`

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