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Cable

Cable component

The Cable component is very similar to the Chain as it models an extensible discretized chain. The Cable component, however, does have bending integrity. The Cable component has options for wind lift/drag and for connecting to a Pulley or Winch component.

 

Usage

Parameters

Connections

Usage

The Cable component can be used separately or together with a Pulley component or a Winch component. The Cable component can be used in series to transfer force along a given path.

Cable components generally create a stiff system of equations. As such the best solver choice for models containing cables is the variable-step Rosenbrock solver.

Material Flow Sign Convention

If the Boolean parameters Fixed end a and/or Fixed end b are set to false (unchecked), 1D translational flanges are added to enable material flow.

Discretization

The number of middle nodes making up a Cable component is a user-defined parameter, n. The total mass of the Cable is given by M=Lunstretchedλ; where Lunstretched is the time-varying length of the cable excluding any stretching, and λ is the linear density of the cable. Each middle node has mass Mn+1. The two end nodes each have half the mass of a middle node, M2n+1.

Wind

The Cable component has an option to enable wind forces. The wind speed in the global coordinate frame is provided via a 3-vector Real input signal. The following formulations are used to calculate the lift and drag on each segment:

cLi=cD0sinαi2cosαi

cDi=cD0sinαi3+πcF

where cLi and cDi are the lift and drag coefficients of the i-th segment, respectively. cD0 and cF are user defined base drag and friction coefficients. αi is the angle-of-attack for the i-th segment and is calculated from the wind velocity vector and the instantaneous velocity and orientation of the i-th cable segment.

The user has the option to replace the above formula with a lookup table defining cL and cD w.r.t. to α.

Reference: S. F. Hoerner, Fluid-Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance, Hoerner Fluid Dynamics Midland Park, NJ, 1965.

Basic

The initial length of a cable component is determined from the position of the multibody frames to which it is connected. Make sure the cable's multibody frames are connected to other elements with defined positions. See the example below.

Cables in Series

If the Boolean parameters Fixed end a and/or Fixed end b are set to false (unchecked), 1D translational flanges are added to enable material flow.

             

Cables and a Pulley

Before connecting a Cable to a Pulley or Winch on end a (frame_a) and/or on end b (frame_b), the boolean parameters Pulley on end a and/or Pulley on end b must be set to true (checked), respectively. When set to true (checked) the selections are indicated on the Cable icon with an orange circle and the corresponding multibody frame is turned to a 2-vector port.

             

Parameters

Formulation

Name

Condition

Default

Description

Modelica ID

n

 

5

Number of middle nodes. E.g., when n=5, there are 7 mass points.

n

Detail

Fixed end a=falseFixed end b=falsePulley on end a=truePulley one end b=true

1

Formulation detail level: (1) Level 1: No flow inertial reaction (low flow velocity or acceleration) (2) Level 2: Full formulation (high flow velocity or acceleration)

Detail

Use node frames

Fixed end a=falseFixed end b=falsePulley on end a=truePulley one end b=true

false

When checked (true) n frames for the middle nodes are enabled

useNodeFrames

Tangent to pulley

Pulley on end a=truePulley one end b=true

false

When checked (true) the cable segment connected to the pulley is forced to remain tangent to the pulley. Using this option will result in more realistic-looking simulations, however, the initialization may fail or the simulation may become unstable if the lengths of the cable segments are smaller than the radius of the pulley.

forceTangent

Properties

Name

Condition

Default

Units

Description

Modelica ID

λ

 

0.5

kgm

Linear density

lambda

EA

 

1000000

N

Axial rigidity: Modulus of elasticity (E) times area (A)

EA

dr

 

0.01

 

Damping ratio: c=drEA

dr

Pretension

 

false

 

When checked (true) the unstretched length is given by the initial length of the cable minus the pretension length.

usePretension

δL

Pretension=true

0.1

m

Pretension length

dL

EI

 

10

Nm2

Bending rigidity

EI

drb

 

0.01

 

Damping ratio [0,1] as a fraction of stiffness

drb

Wind

Name

Condition

Default

Units

Description

Modelica ID

Use wind

 

false

 

Enable wind calculations

useWind

Use data table

Use wind=true

false

 

When true (checked) lift and drag coefficients are defined as a function of the angle between cable segment and relative wind velocity.

useTable

cD0

Use wind=trueUse data table=false

1.1

 

Drag coefficient, cD=cD0sinα3+πcF and cL=cD0sinα2cosα

cD0

cF

Use wind=trueUse data table=false

0

 

Friction coefficient, cD=cD0sinα3+πcF

cF

data source

Use wind=trueUse data table=true

inline

 

Data source

datasourcemode

table

Use wind=trueUse data table=true

 

 

Data set. First column: Angle of Attack (in rad), Second column: Lift coefficient, Third column: Drag coefficient

table

data

Use wind=trueUse data table=true

 

 

Attached data set. First column: Angle of Attack, Second column: Lift coefficient, Third column: Drag coefficient.

data

skip rows

Use wind=trueUse data table=true

0

 

Number of rows to skip

skipRows

smoothness

Use wind=trueUse data table=true

Linear segments

 

Smoothness of table interpolation

smoothness

ρair

Use wind=true

1.2

kgm3

Air density

rho_air

D

Use wind=true

0.04

m

Cable effective diameter

D

Connections

Name

Condition

Default

Description

Modelica ID

Pulley on end a

 

false

When checked (true) the cable is to be connected to a pulley at frame_a

toPulley_a

Pulley on end b

 

false

When checked (true) the cable is to be connected to a pulley at frame_b

toPulley_b

Fixed end a

Pulley on end a=false

true

When checked (true) the cable is fixed to frame_a. When unchecked (false) a 1D mechanical flange is enabled for material flow.

fixed_a

Fixed end b

Pulley on end b=false

true

When checked (true) the cable is fixed to frame_b. When unchecked (false) a 1D mechanical flange is enabled for material flow.

fixed_b

Welded at end a

Pulley on end a=false

false

When checked (true), the cable bending reactions at frame_a.

welded_a

Welded at end b

Pulley on end b=false

false

When checked (true), the cable bending reactions at frame_b.

welded_b

Visualization

Name

Condition

Default

Units

Description

Modelica ID

Show visualization

 

true

N

Show visualization

showVisualization

Transparent

Show visualization=true

false

 

Transparent

transparent

radius

Show visualization=true

0.02

m

Cable radius. This radius is only used for the cylindrical visualization of the cable

radius

Color mode

Show visualization=true

Single color

 

Choose color option: (1) Single color, (2) Two colors: Tension and No tension, (3) Multi-color: Color based on tension value

colorMode

Cable color

Show visualization=trueColor mode=2

gray

 

Cable color 1

color

2nd rope color

Show visualization=trueColor mode2,3

red

 

Cable color 2

color2

τmin

Show visualization=trueColor mode=3

0

N

Minimum Tension: color 1

minTension

τmax

Show visualization=trueColor mode=3

1000

N

Maximum Tension: color 2

maxTension

Force arrows

 

false

 

When checked (true), arrows are added at end points  to visualize tension.

show Tension

Scale

Tension visualization=true

1

 

Force scale (N to m)

tensionscale

Color

Tension visualization=true

cyan

 

Force arrow color

tensioncolor

Transparent

Tension visualization=true

false

 

Force arrow transparency

tensiontransparent

Flow rate arrow

Fixed end a=falseFixed end b=falsePulley on end a=truePulley on end b=true

false

 

When checked (true), an arrow is added to visualize material flow speed and direction

showFlow

Scale

Fixed end a=falseFixed end b=falsePulley on end a=truePulley on end b=trueFlow visualization=true

1

 

Speed scale (m/s to m)

speedscale

Color

Fixed end a=falseFixed end b=falsePulley on end a=truePulley on end b=trueFlow visualization=true

magenta

 

Flow arrow color

flowcolor

Transparent

Fixed end a=falseFixed end b=falsePulley on end a=truePulley on end b=trueFlow visualization=true

false

 

Flow arrow transparency

flowtransparent

Summary Variables

Name

Default

Description

Modelica ID

Force unit

N

Unit in which the summary variables summary_Tension_a and summary_Tension_b are expressed

forceUnitSummary

Connections

Name

Condition

Description

Modelica ID

framea

Pulley on end a=false

End a multibody frame.

frame_a

frameb

Pulley on end a=false

End b multibody frame.

frame_b

frameap

Pulley on end a=true

End a a 2-Vector multibody frame. For use with a Pulley or Winch component.

frame_ap

framebp

Pulley on end b=true

End b a 2-Vector multibody frame For use with a Pulley or Winch component.

frame_bp

flangea

Fixed end a=falsePulley on end a=true

End a 1D translational flange for cable flow.

flange_a

flangeb

Fixed end b=falsePulley on end b=true

End b 1D translational flange for cable flow.

flange_b

wind

Use wind=true

3-vector signal input for wind velocity in global coordinate frame.

wind

See Also

Pulley

Winch

Winch3D

Chain

Rope

Ropes and Pulleys Library Overview