ObjectConnectorCoordinateSpringDamper

A 1D (scalar) spring-damper element acting on single ODE2 coordinates and connecting to coordinate-based markers. NOTE that the coordinate markers only measure the coordinate (=displacement), but the reference position is not included as compared to position-based markers!; the spring-damper can also act on rotational coordinates.

Interface

Python names: ObjectConnectorCoordinateSpringDamper or CoordinateSpringDamper, and VCoordinateSpringDamper for its visualization
Markers it acts on: those providing Coordinate: MarkerNodeCoordinate, MarkerNodeODE1Coordinate, MarkerNodeRotationCoordinate, MarkerBodiesRelativeTranslationCoordinate, MarkerBodiesRelativeRotationCoordinate, MarkerBodyCable2DShape, MarkerBodyCable2DCoordinates

Parameters

The parameters of the item; in a dictionary, its type is ‘ConnectorCoordinateSpringDamper’:

name	type	default	description
name	String	‘’	connector’s unique name
markerNumbers	ArrayMarkerIndex	[ invalid (-1), invalid (-1) ]	list of markers used in connector
stiffness	Real	0.	(symbol: \(k\)) stiffness [SI:N/m] of spring; acts against relative value of coordinates
damping	Real	0.	(symbol: \(d\)) damping [SI:N/(m s)] of damper; acts against relative velocity of coordinates
offset	Real	0.	(symbol: \(l_\mathrm{off}\)) offset between two coordinates (reference length of springs), see equation
activeConnector	Bool	True	flag, which determines, if the connector is active; used to deactivate (temporarily) a connector or constraint
springForceUserFunction	ObjectConnectorCoordinateSpringDamperSpringForceUserFunction	0	(symbol: \(\mathrm{UF} \in \Rcal\)) A Python function which defines the spring force with 8 parameters, see equations section / see description below
visualization	VObjectConnectorCoordinateSpringDamper		parameters for visualization of item

Visualization parameters

The parameters of VObjectConnectorCoordinateSpringDamper, given as visualization:

name	type	size	default	description
show	Bool		True	set true, if item is shown in visualization and false if it is not shown
drawSize	float		-1.	drawing size = diameter of spring; size == -1.f means that default connector size is used
color	Float4	4	[-1.,-1.,-1.,-1.]	RGBA connector color; if R==-1, use default color

Drawing

Drawn as all connectors; a spring of diameter drawSize between the positions of the markers, if they have one, drawn as the spring of ObjectConnectorSpringDamper.

Settings beyond those of all connectors: connectors.curveTiling, connectors.drawSimplified, connectors.springNumberOfWindings, general.cylinderTiling.

Output variables

Available as OutputVariableType in sensors, Get...Output() and other functions:

output variable	symbol	description
Displacement	\(\Delta q\)	relative scalar displacement of marker coordinates
Velocity	\(\Delta v\)	difference of scalar marker velocity coordinates
Force	\(f_{SD}\)	scalar force in connector
PotentialEnergy	\(V = \frac{1}{2} k\, (\Delta q - l_\mathrm{off})^2\)	elastic energy of the spring; zero if the connector is not active; raises for a springForceUserFunction

Detailed description

Definition of quantities

intermediate variables	symbol	description
marker m0 coordinate	\(q_{m0}\)	current displacement coordinate which is provided by marker m0; does NOT include reference coordinate!
marker m1 coordinate	\(q_{m1}\)
marker m0 velocity coordinate	\(v_{m0}\)	current velocity coordinate which is provided by marker m0
marker m1 velocity coordinate	\(v_{m1}\)

Connector forces

Displacement between marker m0 to marker m1 coordinates (does NOT include reference coordinates),

\[ \Delta q= q_{m1} - q_{m0} \]

and relative velocity,

\[ \Delta v= v_{m1} - v_{m0} \]

If activeConnector = True, the scalar spring force vector is computed as

\[ f_{SD} = k \left( \Delta q - l_\mathrm{off} \right) + d \cdot \Delta v \]

If the springForceUserFunction \(\mathrm{UF}\) is defined, \(\fv_{SD}\) instead becomes (\(t\) is current time)

\[ f_{SD} = \mathrm{UF}(mbs, t, i_N, \Delta q, \Delta v, k, d, l_\mathrm{off}) \]

and iN represents the itemNumber (=objectNumber).

If activeConnector = False, \(f_{SD}\) is set to zero.

NOTE { that until 2023-01-21 (exudyn V1.5.76), the CoordinateSpringDamper included the parameters dryFriction and dryFrictionProportionalZone. These parameters have been removed and they are only available in CoordinateSpringDamperExt, HOWEVER, with different names. In order to use CoordinateSpringDamperExt instead of the old CoordinateSpringDamper with the same friction behavior, we recoomend:

USE CoordinateSpringDamperExt.dynamicFrictionForce INSTEAD of CoordinateSpringDamper.dryFriction
USE CoordinateSpringDamperExt.frictionProportionalZone INSTEAD of CoordinateSpringDamper.dryFrictionProportionalZone
CoordinateSpringDamperExt.frictionProportionalZone has a different behavior in case that it is zero; thus use 1e-16 in this case, to get as close as possible to previous behaviour
the variables stiffness, damping and offset have the same interpretation in both objects
keep every other friction, sticking and contact variables in CoordinateSpringDamperExt as default values
user functions obtained a new interface in CoordinateSpringDamperExt, which just needs to be adapted }

Userfunction: springForceUserFunction(mbs, t, itemNumber, displacement, velocity, stiffness, damping, offset) A user function, which computes the scalar spring force depending on time, object variables (displacement, velocity) and object parameters . The object variables are passed to the function using the current values of the CoordinateSpringDamper object. Note that itemNumber represents the index of the object in mbs, which can be used to retrieve additional data from the object through mbs.GetObjectParameter(itemNumber, ...), see the according description of GetObjectParameter.

arguments / return	type or size	description
`mbs`	MainSystem	provides MainSystem mbs in which underlying item is defined
`t`	Real	current time in mbs
`itemNumber`	Index	integer number \(i_N\) of the object in mbs, allowing easy access to all object data via mbs.GetObjectParameter(itemNumber, …)
`displacement`	Real	\(\Delta q\)
`velocity`	Real	\(\Delta v\)
`stiffness`	Real	copied from object
`damping`	Real	copied from object
`offset`	Real	copied from object
return value	Real	scalar value of computed force

Example:

#see also mini example! NOTE changes above since 2023-01-23
def UFforce(mbs, t, itemNumber, u, v, k, d, offset):
    return k*(u-offset) + d*v

Mini example

#define user function:
#NOTE: removed 2023-01-21: dryFriction, dryFrictionProportionalZone
def springForce(mbs, t, itemNumber, u, v, k, d, offset): 
    return 0.1*k*u+k*u**3+v*d

nMass=mbs.AddNode(Point(referenceCoordinates = [2,0,0]))
massPoint = mbs.AddObject(MassPoint(mass = 5, nodeNumber = nMass))

groundMarker=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= nGround, coordinate = 0))
nodeMarker  =mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= nMass, coordinate = 0))

#Spring-Damper between two marker coordinates
mbs.AddObject(CoordinateSpringDamper(markerNumbers = [groundMarker, nodeMarker], 
                                     stiffness = 5000, damping = 80, 
                                     springForceUserFunction = springForce)) 
loadCoord = mbs.AddLoad(LoadCoordinate(markerNumber = nodeMarker, load = 1)) #static linear solution:0.002

#assemble and solve system for default parameters
mbs.Assemble()
mbs.SolveDynamic()

#check result at default integration time
exu.sys['testResult'] = mbs.GetNodeOutput(nMass, 
                                             exu.OutputVariableType.Displacement)[0]

Examples (Ex) and TestModels (TM) that show this item, with weblink to github: tutorialSpringDamper.py (Ex), coordinateSpringDamper.py (Ex), plotSensorExamples.py (Ex), slidercrankWithMassSpring.py (Ex), CoordinateSpringDamperTest.py (TM)