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WOLFRAM SYSTEM MODELER

Spring

Linear translational spring with optional mass

Diagram

Wolfram Language

In[1]:=

SystemModel["Modelica.Mechanics.MultiBody.Forces.Spring"]

Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Linear spring acting as line force between frame_a and frame_b. A force f is exerted on the origin of frame_b and with opposite sign on the origin of frame_a along the line from the origin of frame_a to the origin of frame_b according to the equation:

f = c*(s - s_unstretched);

where "c" and "s_unstretched" are parameters and "s" is the distance between the origin of frame_a and the origin of frame_b.

Optionally, the mass of the spring is taken into account by a point mass located on the line between frame_a and frame_b (default: middle of the line). If the spring mass is zero, the additional equations to handle the mass are removed.

In the following figure a typical animation of the spring is shown. The blue sphere in the middle of the spring characterizes the location of the point mass.

model Examples.Elementary.SpringWithMass

Parameters (10)

animation	Value: true Type: Boolean Description: = true, if animation shall be enabled
showMass	Value: true Type: Boolean Description: = true, if point mass shall be visualized as sphere if animation=true and m>0
c	Value: Type: TranslationalSpringConstant (N/m) Description: Spring constant
s_unstretched	Value: 0 Type: Length (m) Description: Unstretched spring length
m	Value: 0 Type: Mass (kg) Description: Spring mass located on the connection line between the origin of frame_a and the origin of frame_b
lengthFraction	Value: 0.5 Type: Real Description: Location of spring mass with respect to frame_a as a fraction of the distance from frame_a to frame_b (=0: at frame_a; =1: at frame_b)
numberOfWindings	Value: 5 Type: Integer Description: Number of spring windings
s_small	Value: 1e-10 Type: Distance (m) Description: Prevent zero-division if distance between frame_a and frame_b is zero
fixedRotationAtFrame_a	Value: false Type: Boolean Description: = true, if rotation frame_a.R is fixed (to directly connect line forces)
fixedRotationAtFrame_b	Value: false Type: Boolean Description: = true, if rotation frame_b.R is fixed (to directly connect line forces)

Inputs (6)

width	Default Value: world.defaultForceWidth Type: Distance (m) Description: Width of spring
coilWidth	Default Value: width / 10 Type: Distance (m) Description: Width of spring coil
color	Default Value: Modelica.Mechanics.MultiBody.Types.Defaults.SpringColor Type: Color Description: Color of spring
specularCoefficient	Default Value: world.defaultSpecularCoefficient Type: SpecularCoefficient Description: Reflection of ambient light (= 0: light is completely absorbed)
massDiameter	Default Value: max(0, (width - 2 * coilWidth) * 0.9) Type: Diameter (m) Description: Diameter of mass point sphere
massColor	Default Value: Modelica.Mechanics.MultiBody.Types.Defaults.BodyColor Type: Color Description: Color of mass point

Connectors (2)

	frame_a	Type: Frame_a Description: Coordinate system a fixed to the component with one cut-force and cut-torque
	frame_b	Type: Frame_b Description: Coordinate system b fixed to the component with one cut-force and cut-torque

frame_a

Type: Frame_a

Description: Coordinate system a fixed to the component with one cut-force and cut-torque

frame_b

Type: Frame_b

Description: Coordinate system b fixed to the component with one cut-force and cut-torque

Components (3)

	world	Type: World Description: World coordinate system + gravity field + default animation definition
	lineForce	Type: LineForceWithMass Description: General line force component with an optional point mass on the connection line
	spring	Type: Spring Description: Linear 1D translational spring

world

Type: World

Description: World coordinate system + gravity field + default animation definition

lineForce

Type: LineForceWithMass

Description: General line force component with an optional point mass on the connection line

spring

Type: Spring

Description: Linear 1D translational spring

Used in Examples (13)

	FreeBody Modelica.Mechanics.MultiBody.Examples.Elementary Free flying body attached by two springs to environment
	InitSpringConstant Modelica.Mechanics.MultiBody.Examples.Elementary Determine spring constant such that system is in steady state at given position
	PendulumWithSpringDamper Modelica.Mechanics.MultiBody.Examples.Elementary Simple spring/damper/mass system
	PointGravityWithPointMasses Modelica.Mechanics.MultiBody.Examples.Elementary Two point masses in a point gravity field (rotation of bodies is neglected)
	SpringDamperSystem Modelica.Mechanics.MultiBody.Examples.Elementary Simple spring/damper/mass system
	SpringMassSystem Modelica.Mechanics.MultiBody.Examples.Elementary Mass attached with a spring to the world frame
	SpringWithMass Modelica.Mechanics.MultiBody.Examples.Elementary Point mass hanging on a spring
	ThreeSprings Modelica.Mechanics.MultiBody.Examples.Elementary 3-dim. springs in series and parallel connection
	HeatLosses Modelica.Mechanics.MultiBody.Examples.Elementary Demonstrate the modeling of heat losses
	PrismaticConstraint Modelica.Mechanics.MultiBody.Examples.Constraints Body attached by one spring and two prismatic joints or constrained to environment
	RevoluteConstraint Modelica.Mechanics.MultiBody.Examples.Constraints Body attached by one spring and revolute joint or constrained to environment
	SphericalConstraint Modelica.Mechanics.MultiBody.Examples.Constraints Body attached by one spring and spherical joint or constrained to environment
	UniversalConstraint Modelica.Mechanics.MultiBody.Examples.Constraints Body attached by one spring and universal joint or constrained to environment