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SpringDamper

Library

Iconic Diagrams\Mechanical\Translation\Components

Default

Stiffness

Frequency

Use

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

Description - Default

This model represents an ideal translational spring with damper. The element has a preferred force out causality. The corresponding constitutive equations then contain an integration. The element can also have the non-preferred velocity out causality. The constitutive equations then contain a derivation. The spring-damper model has separate high and low ports. The equations are

p.F = p_high.F = p_low.F

p.v = p_high.v - p_low.v

Force out causality (preferred):

x = int(p.v);

p.F = k*x + d*p.v;

Velocity out causality:

p.v = ddt(x);

x = (p.F - d*p.v)/k;

A positive force will compress the spring damper. The length x is positive when the spring damper is compressed. It is negative when the spring damper is stretched.

Interface - Default

Ports

Description

p_high

p_low

Two ports of the spring (Translation).

Causality

preferred force out

Variables

x

compression of the spring [m]

k

d

Stiffness [N/m]

damping [N.s/m]

Initial Values

x_initial

The initial extension of the spring [m].

Description - Stiffness

This model represents another implementation of the ideal translational spring with damper. The damping value (d) is calculated on the basis of a known stiffness (k), relative damping (b) and mass reference (m). The mass is only used to compute the damping (no actual mass is used in this component).

The element has a preferred force out causality. The corresponding constitutive equations then contain an integration. The element can also have the non-preferred velocity out causality. The constitutive equations then contain a derivation. The spring-damper model has separate high and low ports. The equations are

p.F = p_high.F = p_low.F

p.v = p_high.v - p_low.v

Force out causality (preferred):

x = int(p.v);

p.F = k * x + d*p.v;

d = 2*b*sqrt(k*m);

Velocity out causality:

p.v = ddt(x);

x = (p.F - d*p.v)/k;

d = 2*b*sqrt(k*m);

A positive force will compress the spring damper. The length x is positive when the spring damper is compressed. It is negative when the spring damper is stretched.

Interface - Stiffness

Ports

Description

p_high

p_low

Two ports of the spring (Translation).

Causality

preferred force out

Variables

x

d

compression of the spring [m]

damping [N.s/m]

Parameters

k

b

m

Stiffness [N/m]

Relative damping []

Reference mass [kg]

Initial Values

x_initial

The initial extension of the spring [m].

Description - Frequency

This model represents another implementation of the ideal translational spring with damper. The stiffness (k) is calculated on basis of a known resonance frequency. The damping value (d) is calculated on the basis of the calculated stiffness (k), relative damping (b) and mass reference (m). The mass is only used to compute the damping (no actual mass is used in this component).

The element has a preferred force out causality. The corresponding constitutive equations then contain an integration. The element can also have the non-preferred velocity out causality. The constitutive equations then contain a derivation. The spring-damper model has separate high and low ports. The equations are

p.F = p_high.F = p_low.F

p.v = p_high.v - p_low.v

Force out causality (preferred):

x = int(p.v);

p.F = k * x + d*p.v;

k = m*(2*pi*F)^2;

d = 2*b*sqrt(k*m);

Velocity out causality:

p.v = ddt(x);

x = (p.F - d*p.v)/k;

k = m*(2*pi*f)^2;

d = 2*b*sqrt(k*m);

A positive force will compress the spring damper. The length x is positive when the spring damper is compressed. It is negative when the spring damper is stretched.

Interface - Frequency

Ports

Description

p_high

p_low

Two ports of the spring (Translation).

Causality

preferred force out

Variables

x

k

d

compression of the spring [m]

stiffness [N/m]

damping [N.s/m]

Parameters

b

f

m

Relative damping []

Resonance frequency [Hz]

Reference mass [kg]

Initial Values

x_initial

The initial extension of the spring [m].