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springdamper

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springdamper

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Iconic Diagrams\Mechanical\Rotation\Components

Implementations

Default

Stiffness

Frequency

Use

Domains: Continuous. Size: 1-D. Kind: Iconic Diagrams (Translation).

Description - Default

This model represents an ideal rotational spring with damper. The element has a preferred torque out causality. The corresponding constitutive equations then contain an integration. The element can also have the non-preferred angular velocity out causality. The constitutive equations then contain a derivation. The port p of the spring model has separate high and low terminals. The equations are:

 

p.T = p_high.T = p_low.T

p.omega = p_high.omega - p_low.omega

 

Torque out causality (preferred):

 

phi = int(p.omega);

p.T = c * phi + d*p.omega;

 

Angular velocity out causality:

 

p.omega = ddt(phi);

phi = (p.T - d*p.omega)/c;

Interface - Default

Ports

Description

p_high

p_low

Two ports of the spring (Rotation).

Causality

 

preferred torque out

An angular velocity out causality results in a derivative constitutive equation.

Variables

 

phi

torsion of the spring [rad]

Parameters

 

c

d

Rotational stiffness [Nm /rad]

Damping [Nms/rad]

Initial Values

 

phi_initial

The initial torsion of the spring [rad].

Description - Stiffness

This model represents an ideal rotational spring with damper. The damping value (d) is calculated on the basis of a known stiffness (c), relative damping (b) and reference inertia (J). The inertia is only used to compute the damping (no actual mass is used in this component).

 

The element has a preferred torque out causality. The corresponding constitutive equations then contain an integration. The element can also have the non-preferred angular velocity out causality. The constitutive equations then contain a derivation. The port p of the spring model has separate high and low terminals. The equations are:

 

p.T = p_high.T = p_low.T

p.omega = p_high.omega - p_low.omega

 

Torque out causality (preferred):

 

phi = int(p.omega);

p.F = c * phi + d*p.omega;

d = 2*b*sqrt(c*J);

 

Angular velocity out causality:

 

p.omega = ddt(phi);

phi = (p.T - d*p.omega)/c;

d = 2*b*sqrt(c*J);

Interface - Stiffness

Ports

Description

p_high

p_low

Two ports of the spring (Rotation).

Causality

 

preferred torque out

An angular velocity out causality results in a derivative constitutive equation.

Variables

 

phi

d

torsion of the spring [rad]

damping [Nms/rad]

Parameters

 

c

b

J

Rotational stiffness [Nm /rad]

Relative damping []

Moment of inertia [kgm^2]

Initial Values

 

phi_initial

The initial torsion of the spring [rad].

Description - Frequency

This model represents an ideal rotational spring with damper. The stiffness (c) is calculated on basis of a known resonance frequency (f). The damping value (d) is calculated on the basis of the stiffness, relative damping (b) and reference inertia (J). The inertia is only used to compute the damping (no actual mass is used in this component).

 

The element has a preferred torque out causality. The corresponding constitutive equations then contain an integration. The element can also have the non-preferred angular velocity out causality. The constitutive equations then contain a derivation. The port p of the spring model has separate high and low terminals. The equations are:

 

p.T = p_high.T = p_low.T

p.omega = p_high.omega - p_low.omega

 

Torque out causality (preferred):

 

phi = int(p.omega);

p.T = c * phi + d*p.omega;

c = J*(2*pi*f)^2;

d = 2*b*sqrt(c*J);

 

Angular velocity out causality:

 

p.omega = ddt(phi);

phi = (p.T - d*p.omega)/c;

c = J*(2*pi*f)^2;

d = 2*b*sqrt(c*J);

Interface - Frequency

Ports

Description

p_high

p_low

Two ports of the spring (Rotation).

Causality

 

preferred torque out

An angular velocity out causality results in a derivative constitutive equation.

Variables

 

phi

c

d

torsion of the spring [rad]

rotational stiffness [Nm /rad]

damping [Nms/rad]

Parameters

 

f

b

J

Resonance frequency [Hz]

Relative damping []

Moment of inertia [kgm^2]

Initial Values

 

phi_initial

The initial torsion of the spring [rad].