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Slitter Roller

Slitter Roller component

	Description
	The Slitter Roller component divides the upstream web to two or more webs in the downstream.

Usage

The roller component must be between the upstream Span component and multiple downstream (slitted) span components.

The Slitter Roller component can have between zero and 10 cuts. With zero cuts, the component acts like a regular Roller component. With one cut, the downstream will consists of two parallel adjacent spans.

The picture below shows an example of a 1 m wide web being cut into three downstream webs (two cuts). The slitting points are defined with respect to the far end of the web as shown.

Equations

Consider the roller shown below.

Assume the web velocity goes through a discontinuous velocity change at the $b$ (right) boundary.

$T_{a}$	Upstream tension
$T_{b1} \dots T_{b11}$	Downstream tension
$v_{a}$	Upstream speed
$v_{b1} \dots v_{b11}$	Downstream speed
$τ_{m}$	Motor torque (zero if modeling an idler roller)
$R$	Roller effective radius
$ω_{r}$	Roller angular velocity
$b$	Bearing damping coefficient
$W$	Web width
$β_{1} \dots β_{11}$	Wrap angle

Under a no-slip assumption, we have:

$R (T_{a} - \sum_{i = 1}^{n} T_{bi}) = τ_{m} - J \frac{\partial ω_{r}}{\partial t} - b ω_{r}$

$v_{a} = R ω_{r}$

Additional Features

	Eccentricity
	The roller eccentricity is enabled by checking the option Add eccentricity

	CAD-Based Mass and Inertia
	Instead of using the internally calculated roller mass and inertia (which assumes a cylindrical shape), one can select to use an external component to give the roller the required mass and inertia. This is accomplished by checking the option Use CAD as shown below:

Connections

Name	Description	Modelica ID
${frame}_{a}$	Left web 3D connection point	frame_a
${frame}_{b}, {frame}_{b1 .. b11}$	Right web 3D connection point	frame_b
${frame}_{c}$	Roller holder base frame	frame_c
${frame}_{d}$	External mass/inertia	frame_d
${web}_{a}$	Left (entry) web transfer information port	web_a
${web}_{b}, {web}_{b1 .. b11}$	Right (exit) web transfer information port	web_b
${flange}_{c}$	Roller rotation flange	flange_c
$v_{out}$	Sensor output	v_out

Parameters

Web Properties

Name	Default	Description	Modelica ID
Use default properties (WP1)	$true$	When checked (true), web properties are defined by the closest Web Properties block (WP1) found.	useDefault
Web Properties	$WP1$	Name of the Web Properties record	wp

Settings

Name	Default	Units	Description	Modelica ID
Number of cuts	$0$		number of cuts	n
Cut 1 location .. Cut 10 location		$m$	Location of a cutting edge w.r.t. the back edge. Values must be bigger than zero and less than the web width	z_cut1
Use alternative configuration	$false$		Choose between two possible solutions for the web/roll configuration	useAltConfig
Flip direction	$false$		Use this option when building web lines that go from right to left. See documentation for more information	flipDirection
Use fixed base	$false$		When checked (true), frame is fixed in the inertial coordinate frame	useFixedBase
$r$	$[0, 0]$	$m$	Location of frame_b with respect to ground	InitPos
$θ$	$0$	$rad$	Rotation about z axis	InitAng
Use sensor	$false$		When checked (true), a signal output is enabled for the web speed	useSensor
Output type	$1$		Select measured quantity	sensorType
Velocity output unit	[1]			toUnitV

[1] Maplesoft.Conversions.VelocityDim.m/s

Roller

Name	Default	Units	Description	Modelica ID
$D$	$0.2$	$m$	Diameter of the roller	D
Use CAD	$false$		when checked (true), mass and inertia are defined from an externally attached CAD component or a rigid body component	useCAD
$D_{i}$	$0$	$m$	Inner diameter of the roller (Inertia and visualization) [1]	Di
$L$	$1.2$	$m$	Roller length [1]	L
Use cylindrical geometry	$true$		When checked (true), roller inertia is calculated assuming a uniform cylindrical geometry [1]	useCylindricalGeometry
$ρ$	$2.7 \cdot 10^{3}$	$\frac{kg}{m^{3}}$	Roller density [2]	rho_roll
$m$	$1$	$kg$	Roller mass [3]	m
$J$	$5.0 \cdot 10^{−3}$	$kg m^{2}$	Roller rotational inertia [3]	J
$d$	$0$	$N m \frac{s}{rad}$	Bearing viscous damping constant	d

[1] Enabled when Use CAD is false.

[2] Enabled when Use cylindrical geometry is true and Use CAD is false.

[3] Enabled when Use cylindrical geometry is false and Use CAD is false.

Eccentricity

Name	Default	Units	Description	Modelica ID
Add eccentricity	$false$		When checked (true), a parameter is enabled for the roller eccentricity	addEccentricity
Use input	$false$		When checked (true), eccentricity is given by an input signal in meters [1]	useInputEccentricity
$e$	$0$	$m$	Roller eccentricity [2]	ecc
$θ_{0}$	$0$	$rad$	Initial eccentricity angle [1]	theta_ecc0

[1] Enabled when Add eccentricity is true.

[2] Enabled when Add eccentricity is true and Use Input is false.

Friction

Name	Default	Units	Description	Modelica ID
$μ_{c}$	$0.20$		Coulomb coefficient of friction. When slippage is not enabled, this parameter is only used in the calculation of the capstan tension limit summary variable.	mu_c
Use constant coefficient of friction	$true$		When unchecked (false), a velocity-dependent formulation is used for the coefficient of friction [1]	useConstantCoF
$Peak$	$1$		peak$μc$ = Maximum friction force at zero sliding velocity	peak
$v_{s}$	$1 \cdot 10^{−2}$	$\frac{m}{s}$	Stribeck sliding velocity	vs
$n_{Decay}$	$2$		Decay exponent	nDecay
$μ_{d}$	$0$	$\frac{s}{m}$	Viscous coefficient of friction	mu_d
$v_{0}$	$1 \cdot 10^{−4}$	$\frac{m}{s}$	Tight/slack side switching velocity boundary	v0
$P$	$0$	$Pa$	Surface pressure (positive is suction). When slippage is not enabled, this parameter is only used in the calculation of the capstan tension limit summary variable.	P

[1] Enabled when Include Slippage is true.

[2] Enabled when Use constant coefficient of friction is true and

Visualization

Name	Default	Units	Description	Modelica ID
Show roller	$true$		When checked (true), a visualization of the roller is created	showVisualization_roller
Transparent roller	$false$		When checked (true) the roller visualization is transparent	transparent_roller
Roller color	Blue		Roller color	color_roller
Band color	Yellow		Band color	color_band
Band angle	20	$degree$	Band angle	band_angle
Show frame	$true$		When checked (true), a visualization of the frame is created	showVisualization_frame
Transparent frame	$false$		When checked (true) the frame visualization is transparent	transparent_frame
Frame color	Orange		Frame color	color_frame
Show base shaft	$false$		When checked (true), additional shaft visualization is added to the base frame	showShaft
Show reaction force arrow	$false$		When checked (true), ground reaction force is visualized with an arrow	showReactionForce
Force arrow scale	$1000$	$1$	Force scale (N to m)	forceScale
Force arrow color	Cyan		Force arrow color	forceColor
Force arrow transparency	$false$		Force arrow transparency	forceTransparent
Show reaction torque arrow	$false$		When checked (true), ground reaction force is visualized with an arrow	showReactionTorque
Torque arrow scale	$100$	$1$	Torque scale (Nm to m)	torqueScale
Torque arrow color	Magenta		Torque arrow color	torqueColor
Torque arrow transparency	$false$		Torque arrow transparency	torqueTransparent

Frame

Name	Default	Units	Description	Modelica ID
$m_{f}$	$0$	$kg$	Frame mass	m_frame
$J_{f}$	$0$	$kg m^{2}$	Frame inertia	J_frame
Add frame offset	$false$		When checked (true), frame connection point is placed at an offset w.r.t. the roll center	addFrameOffset
$r_{f}$	$[0, 0]$	$m$	Offset in the XY plane	rf

Advanced Settings

Name	Default	Units	Description	Modelica ID
Use effective radius	$false$		When checked (true), the roller radius is padded with half of the thickness of the web	useEffectiveRadius

Summary Variables

Name	Units	Description	Modelica ID
summary_WrapAngle	[1]	Wrap angle	summary_WrapAngle
summary_Length	[1]	Length of the web in contact with the roller	summary_Length
summary_Limit		Between 0 and 1; 0 means tension limit is less than capstan limit or include slippage is true; 1 means tension limit exceeds capstan limit (web will slip)	summary_Limit
summary_SlipVelocity	[1]	Slip velocity: v_web - w_rollerR_eff	summary_SlipVelocity
summary_SlipRatio		(roller surface speed - web speed)/(roller surface speed)	summary_SlipRatio
summary_RollerAngularVelocity	[1]	Roller angular velocity	summary_RollerAngularVelocity
summary_WebSpeed	[1]	Web speed	summary_WebSpeed
summary_RollerSurfaceSpeed	[1]	Roller surface speed	summary_RollerSurfaceSpeed

[1] Units are set in the corresponding Web Properties block (under the Summary variables section)

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