Collaboration diagram for RundDorg:

Author: Jørgen Haavind Jensen

Date: Q4 2011 JHJ: Initial version.

Cable model with bending/torsional stiffness and winch-functionality. The cable is discretized as "6 degrees of freedom" rigid cylinders which are connected with axial and angular constraints. For high bending stiffness the cable will work as a truss/beam.

The constraints are regularized with a compliant variation of the Baumgarte method. In effect the cylinders can be thought of as connected with axial and angular springs like a traditional spring-mass-damper model, but high frequency dynamics are filtered out which reduces some of the numerical instability problems associated with high stiffness cables.

The cable solves full collision detection and reaction forces, both self-collision and other geometry that can be added through other SimObjects. Additionally the cable itself includes the collision geometry of a full winch drum.

Note: The hydrodynamic load model does not currently include the effect of added mass.

Configuration parameters

Parameter	Default	Comment
CableLength	-	Total cable length [m]
NumElements	-	Number of discrete rigid mass elements in cable [#]
CableDiameter	-	Nominal cross sectional diameter [m]
TensileCrossSectionArea	Assumes the nominal area encircles 7 circular strands in a hexagonal pattern	cross sectional area of load bearing material [m^2]
TensileCrossSectionSecondAreaMoment	Assumes the nominal area encircles 7 circular strands in a hexagonal pattern	second area moment of load bearing material [m^4]
TensileCrossSectionTorsionalAreaMoment	Assumes the nominal area encircles 7 circular strands in a hexagonal pattern	torsional area moment of load bearing material [m^4]
YoungsModulus	2*10^11 (200GPa)	Young's modulus of load bearing material [Pa],[N/m^2]
ShearModulus	YoungsModulus/2.6	Shear modulus of load bearing material [Pa],[N/m^2]
DisplacementCrossSectionArea	90% of nominal area	fluid displacement cross section area [m^2]
CableWeight	TensileCrossSectionArea*7900kg/m^3	Cable weight per meter [kg/m]
CableFrictionCoefficient	1.2	Skin friction coefficient for the cable
RegulatorFrequencyCoefficient	-	Time response coefficient of the structure. A typical value would be less than 1/timestep, but it depends on the integrator method used.
StructuralDampingCoefficient	1.0	Structural damping factor. A value of 1 gives critical damping.
TensionStabilityFactor	1.0	Numerical stabilizer for when the cable is under heavy load. Increases effective bending stiffness, and decreases bending frequency response. Values from 1.0 and up.
WinchLength	-	Inner length of the winch drum
WinchInnerRadius	-	Inner radius of the winch drum
WinchOuterRadius	-	Outer radius the winch drum
WinchFrictionCoefficient	0.8	Skin friction coefficient for the winch drum
InitialCableLengthOnWinch	0	For setting initial conditions. Determines how much cable should be already on the winch. [m]
InitialCableWindingOnWinch	RightWinding	Should the first layer of the initial winding be "RightWinding" or a "LeftWinding"?
WayPointN	-	Intermediate waypoints for initializing cable. An arbitrary number of waypoints (starting from #1) can be included. Cable elements are distributed in a hanging catenary shape between waypoints (the winch position and free end position are implied start/end-points). Takes 4 numbers, where the first three are coordinates and the last one is the length of cable to distribute between that waypoint and the last. [m]

Input ports

Tag	Size	Comment
WinchPosition	3	Position of winch. [m]
WinchVelocity	3	Velocity of winch. [m]
WinchOrientation	4	Orientation of winch. [Quaternion(w,x,y,z)]
WinchAngularVelocity	3	Angular velocity of winch. [rad/s]
EndPosition	3	Position of endpoint. [m]
EndVelocity	3	Velocity of endpoint. [m/s]
EndConnectionStrength	1	Relative strength of endpoint connection. Typically between [0,1]
InternalConnections	2	Interface for cutting/splicing cable. The port can be used to adjust the relative strength of one internal connection at a time. The first value is the index number of the constraint to adjust, and the second is the relative strength to apply, typically between [0,1].

Output ports

Tag	Size	Comment
WinchForce	3	Reaction force on winch. [N]
WinchTorque	3	Reaction torque on winch. [Nm]
EndForce	3	Reaction force on endpoint. [N]

States

Tag	Size	Comment
posN	3	The position of element N, from 0 -> NumElements-1. [m]
velN	3	The velocity of element N, from 0 -> NumElements-1. [m/s]
omegaN	3	The angular velocity of element N, from 0 -> NumElements-1. [rad/s]
thetaN	4	The quaternion(w,x,y,z) orientation of element N, from 0 -> NumElements-1. [quaternion(w,x,y,z)]

This SimObject is referred to as RundDorg