Unwind Drum
Unwind drum component
Description
Usage
Equations
Connections
Parameters
Summary Variables
The Unwind Drum component models an unwind drum with variable roll radius and inertia.
The Unwind Drum component must be at the start of a web line.
Using the provided 1D rotational flange (flange_c) the Unwind Drum component can be equipped with a motor or a brake.
Consider the drum shown below:
Tb
Downstream tension
vb
Downstream speed
τ
Motor torque (= zero if modeling an idler roller)
ω
Angular velocity (positive means unwind)
Rc
Core radius
R⁡t
Instantaneous roll radius
dB
Bearing damping coefficient
th
Web thickness
W
Web width
The time-varying roll radius is given by the following differential equations:
dR⁡tdt={−ω⁢th2⁢πUse stepwise=false−ω⁢th2⁢δ__φ0<φ<δ__φ0otherwise
where φ is the rotation of the drum between 0 and 2⁢π. When the Use stepwise option is selected, the roll radius decreases only over a portion of each turn defined by δφ.
−Tb⁢R⁡t=τm−J⁡t⁢d⁢ω⁢1d⁢t−dB⁢ω;
vb=R⁢ω
The roll inertia consists of the core inertia, Jc, and roll variable inertia, J⁡t:
J⁡t=Jc+π2⁢ρ⁢W⁢R⁡t4−Rc4
Note: If R⁡t≤Rc, an assertion is triggered, terminating the simulation.
Name
Modelica ID
frameb
Right web 3-D connection point
frame_b
framec
Drum holder base frame; enabled when Use fixed base=false
frame_c
framed
Drum frame (for attaching CAD)
frame_d
webb
Exit web transfer information port
web_b
flangec
Drum rotation flange
flange_c
Rmax
Real output; drum and web radius [m]
eccin
Eccentricity signal (in meters)
ecc_in
reset
Boolean signal to trigger roll radius reset
Web Properties
Default
Units
Use Default Properties (WP1)
true
When checked (true), web properties are defined by the closest Web Properties block found
useDefault
WP1
Name of the record containing the web properties (enabled when Use default properties = false)
wp
Drum
Dinit
0.4
m
Initial roll diameter
D_init
D
0.1
Core diameter
Di
0
Core inner diameter
L
1.2
Drum length
Use cylindrical geometry
When checked (true), roller inertia is calculated assuming a uniform cylindrical geometry
useCylindricalGeometry
ρ
2.7·103
kgm3
Drum core density; enabled when using cylindrical geometry
rho_roll
1
kg
Drum mass; enabled when not using cylindrical geometry
J
0.005
kg⁢m2
Drum rotational inertia; enabled when not using cylindrical geometry
d
N⁢m⁢srad
Bearing viscous damping constant (both rollers)
Use CAD
false
When checked (true), mass and inertia are defined from an externally attached CAD component or a rigid body component
useCAD
Use reset
The roll diameter is reset to D_init with an external signal
useReset
Use stepwise
When checked (true), the roll diameter is changed over a portion of each rotation (instead of changing continuously)
useStepwise
φ0
deg
Offset of angle; enabled when Use stepwise is true
phi0
δφ
90
Merge angle; enabled when Use stepwise is true
phi1
Settings Parameters
Use alternative configuration
Choose between two possible solutions for the web/roll configuration
useAltConfig
Flip direction
Use this option when building web lines that go from right to left
flipDirection
Use fixed base
When checked (true), frame_c is disabled, the frame is fixed in the inertial coordinate frame, and position and/or orientation parameters are enabled
useFixedBase
r
0,0
Location of frame_b with respect to ground. Available when Use fixed base = true
InitPos
θ
Rotation about z-axis. Available when Use fixed base = true
InitAng
Enable radius sensor
When checked (true), drum outer radius is provided via an output signal
useSensor
Eccentricity
Add eccentricity
When checked (true), a parameter is enabled for the roller eccentricity
addEccentricity
Use input
When checked (true), eccentricity is given by an input signal in meters
useInputEccentricity
e
Roller eccentricity
ecc
θ0
Initial eccentricity angle
theta_ecc0
Frame
mf
Frame mass
m_frame
Jf
0.01
Frame inertia
J_frame
Add frame offset
When checked (true), frame connection point is placed at an offset w.r.t. the roll center
addFrameOffset
rf
0,D2
Offset in the XY plane
Visualization
Show drum visualization
When checked (true), a visualization is produced for the drum
showVisualization_drum
Transparent drum
When checked (true), the drum visualization is transparent
transparent_drum
Drum color
Blue
Color of the drum
color_drum
Band color
Yellow
Color of a radial band on the drum
color_band
Band angle
20
band_angle
Show reaction force arrow
When checked (true) an arrow is shown for the reaction force
showReactionForce
Force arrow scale
1000
Force scale (N to M)
forceScale
Force arrow color
Cyan
forceColor
Force arrow transparency
When checked (true), the force arrow is transparent
forceTransparent
Show reaction torque arrow
When checked (true) an arrow is shown for the reaction torque
showReactionTorque
Torque arrow scale
100
Torque scale (N to M)
torqueScale
Torque arrow color
Magenta
torqueColor
Torque arrow transparency
When checked (true), the torque arrow is transparent
torqueTransparent
summary_Radius
Roll radius
summary_Layers
Number of layers
See Also
Sources and Sinks
Web Handling Library
Download Help Document