Torsional Compliance

Parallel spring-damper

• 

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

Description

The Torsional Compliance block implements a parallel spring-damper to couple two rotating driveshafts. The block uses the driveshaft angular velocities, torsional stiffness, and torsional damping to determine the torques.

$$\begin{array}{l}{T}_R=-({\omega }_R-{\omega }_C)b-\theta k\\ T_C=({\omega }_R-{\omega }_C)b+\theta k\\ \\ \dot{\theta }=({\omega }_R-{\omega }_C)\end{array}$$

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	Mechanical power from driveshaft R	PTR	$P_{TR}= T_R{\omega }_R$
		PwrC	Mechanical power from driveshaft C	PTC	$$P_{TC}= T_c{\omega }_c$$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrDampLoss	Mechanical damping loss	Pd	$P_d=-b{\left|\dot{\theta }\right|}^2$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredShft	Rate change in spring energy	PS	$P_s=-\theta k\dot{\theta }$

The equations use these variables.

TR	Driveshaft R torque
TC	Driveshaft C torque
ωR	Driveshaft R angular velocity
ωC	Driveshaft C angular velocity
θ	Coupled driveshaft rotation
k	Driveshaft torsional stiffness
b	Rotational viscous damping
Pd	Power loss due to damping
Ps	Rate change of stored spring energy

Ports

Input

RSpd — Driveshaft R angular velocity

scalar

Input driveshaft angular velocity, in rad/s.

Dependencies

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

CSpd — Driveshaft C angular velocity

scalar

Output driveshaft angular velocity, in rad/s.

Dependencies

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

R — Angular velocity and torque

two-way connector port

Angular velocity in rad/s. Torque is in N·m.

Dependencies

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

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Variable	Units
Trq	R		Input driveshaft torque	TR	N·m
	C		Output driveshaft torque	TC	N·m
	Damp		Damping torque	$$T_s=b\dot{\theta }$$	N·m
	Spring		Spring torque	Td = kθ	N·m
Spd	R		Input driveshaft angular velocity	ωR	rad/s
	C		Output driveshaft angular velocity	ωC	rad/s
	deltadot		Difference in input and output driveshaft angular velocity	$$\dot{\theta }$$	rad/s
PwrInfo	PwrTrnsfrd	PwrR	Mechanical power from driveshaft R	PTR	W
		PwrC	Mechanical power from driveshaft C	PTC	W
	PwrNotTrnsfrd	PwrDampLoss	Power loss due to damping	Pd	W
	PwrStored	PwrStoredShft	Rate change of stored internal kinetic energy	Ps	W

Dependencies

To enable this port, select Output Info bus.

RTrq — Driveshaft R torque

scalar

Input drive shaft torque, in N·m.

Dependencies

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

CTrq — Driveshaft C torque

scalar

Applied output driveshaft torque, in N·m.

Dependencies

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

C — Angular velocity and torque

two-way connector port

Angular velocity in rad/s. Torque is in N·m.

Dependencies

To enable 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:

• RSpd

• CSpd

• RTrq

• CTrq

Specifying Two-way connection creates these ports:

• R

• C

Output Info bus — Selection

off (default) | on

Select to create the Info output port.

Torsional stiffness, k — Inertia

1e4 (default) | scalar

Torsional stiffness, in N·m/rad.

Torsional damping, b — Damping

1e2 (default) | scalar

Torsional damping, in N·m· s/rad.

Initial deflection, theta_o — Angular

0 (default) | scalar

Initial deflection, in rad.

Initial velocity difference, domega_o — Angular

0 (default) | scalar

Initial velocity difference, in rad/s.

Damping cut-off frequency, omega_c — Frequency

3000 (default) | scalar

Damping cut-off frequency, in rad/s.

Extended Capabilities

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

Version History

Introduced in R2017a