Documentation

Torsional Compliance

Parallel spring-damper

• Library:
• 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.

$\begin{array}{l}{T}_{R}=-\left({\omega }_{R}-{\omega }_{C}\right)b-\theta k\\ {T}_{C}=\left({\omega }_{R}-{\omega }_{C}\right)b+\theta k\\ \\ \stackrel{˙}{\theta }=\left({\omega }_{R}-{\omega }_{C}\right)\end{array}$

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionVariableEquations

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

PwrC

Mechanical power from driveshaft C

PTC

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

• Positive signals indicate an input

• Negative signals indicate a loss

PwrDampLoss

Mechanical damping loss

Pd

${P}_{d}=-b{|\stackrel{˙}{\theta }|}^{2}$

PwrStored — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

PwrStoredShft

Rate change in spring energy

PS

${P}_{s}=-\theta k\stackrel{˙}{\theta }$

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

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Input driveshaft angular velocity, in rad/s.

Dependencies

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

Output driveshaft angular velocity, in rad/s.

Dependencies

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

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

Dependencies

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

Output

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Bus signal containing these block calculations.

SignalDescriptionVariableUnits
Trq

R

Input driveshaft torque

TRN·m

C

Output driveshaft torque

TCN·m

Damp

Damping torque

${T}_{s}=b\stackrel{˙}{\theta }$

N·m

Spring

Spring torque

Td = kθ

N·m

Spd

R

Input driveshaft angular velocity

C

Output driveshaft angular velocity

Difference in input and output driveshaft angular velocity

$\stackrel{˙}{\theta }$

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 create this port, select Output Info bus.

Input drive shaft torque, in N·m.

Dependencies

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

Applied output driveshaft torque, in N·m.

Dependencies

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

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

Dependencies

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

Parameters

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Block Options

Specify the port configuration.

Dependencies

Specifying Simulink creates these ports:

• RSpd

• CSpd

• RTrq

• CTrq

Specifying Two-way connection creates these ports:

• R

• C

Select to create the Info output port.

Torsional stiffness, in N·m/rad.

Torsional damping, in N·m· s/rad.

Initial deflection, in rad.

Initial velocity difference, in rad/s.

Damping cut-off frequency, in rad/s.

Extended Capabilities

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