Iconic Diagrams\Mechanical\Translation\Components
Default
Stiffness
Frequency
Domains: Continuous. Size: 1-D. Kind: Iconic Diagrams (Translation).
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.
Ports |
Description |
p_high p_low |
Two ports of the spring (Translation). |
Causality |
|
preferred force out |
|
Variables |
|
x |
compression of the spring [m] |
Parameters |
|
k d |
Stiffness [N/m] damping [N.s/m] |
Initial Values |
|
x_initial |
The initial extension of the spring [m]. |
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.
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]. |
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.
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]. |