Variable Nip Roller - MapleSim Help

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Variable Nip Roller

Variable nip roller component

	Description
	The Variable Nip Roller component models a pair of rollers: a nip and a roller.

Usage

The Variable Nip Roller component must be between two Span components.

The Variable Nip Roller pulls the web with the possibility of slippage (depending on the applied normal force) using 1D rotational flange ${flange}_{c1}$ or ${flange}_{c2}$ under torque or velocity control.

The Variable Nip Roller is similar to the Nip Roller component; the main difference is the inclusion of the slippage dependent on both the tension and the normal force.

Nip Force

There are four methods available for the nip force. These are selected via the mode parameter.

Mode = Constant Force In this mode, the nip/roller force is given via a parameter ( $F_{nip}$ ) and is constant throughout the simulation.

Mode = Force Input In this mode, the nip/roller force is given via in input signal and can be varied according to the simulation targets. The input unit is specified by a new parameter (Force unit).

Mode = Displacement Input In this mode, the nip position on the local y-axis is given via an input signal and can be varied according to the simulation targets. The nip force is then calculated from a lookup table describing the force vs deformation.

Mode = Mechanical In this mode, the nip position on the local y-axis is defined via a 1D Mechanical Translation flange. Similar to the previous case, at zero displacement no force is applied. Compression and nip force is achieved by positive displacement of the nip. The same lookup table is above is used to define the overall stiffness. An additional parameter (d) is enabled to add damping to the sliding motion of the nip if needed.

	Configuration
	The Variable Nip Roller component requires the nip to be within the contact arc of the web and the roller. If this condition is not satisfied, MapleSim generates an assertion failure and the integration will not continue beyond t=0.

Equations

Consider the two rollers shown below.

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

$T_{a}$ , $T_{b}$	Upstream and downstream tensions
$v_{a}$ , $v_{b}$	Upstream and downstream web speeds
$τ_{1}, τ_{2}$	Motor torque applied to roller 1, 2
$R_{1}, R_{2}$	Roller 1 effective radius
$ω_{1}, ω_{2}$	Roller angular velocity
$J_{1}, J_{2}$	Moment of inertia of roller 1 and 2
$b_{1}$ , $b_{2}$	Bearing damping coefficients
$W$ , $t$	Web width and thickness
$β_{1}$ , $β_{2}$	Entry and exit wrap angles
$F_{n}$	Nip to roller normal force
$μ_{1}$ , $μ_{2}$	Roller/Web and Nip/Web coefficients of friction

For the roller:

$J_{1} \frac{d ω_{1}}{d t} + b_{1} ω_{1} = τ_{1} + R_{1} ΔT$

For the nip:

$J_{2} \frac{d ω_{2}}{d t} + b_{2} ω_{2} = τ_{2} + R_{2} μ_{2} F_{n} sgn (v_{b} - R_{2} ω_{2})$

and for the web:

$m_{arc} \frac{d v_{b}}{d t} = - ΔT - μ_{2} F_{n} sgn (v_{b} - R_{2} ω_{2}) + T_{b} - T_{a}$

where:

$ΔT = (\begin{array}{c} T_{a} (e^{(β_{1} + β_{2}) μ_{1}} - 1) + μ_{1} F_{n} e^{β_{2} μ_{1}} & v_{b} > R_{1} ω_{1} \\ - T_{b} (e^{(β_{1} + β_{2}) μ_{1}} - 1) - μ_{1} F_{n} e^{β_{1} μ_{1}} & v_{b} < R_{1} ω_{1} \end{array})$

and:

$m_{arc} = ρ \cdot W \cdot t \cdot R_{1} \cdot (β_{1} + β_{2})$

Connections

Name	Description	Modelica ID
${frame}_{a}$	Left web 3-D connection point	frame_a
${frame}_{b}$	Right web 3-D connection point	frame_b
${frame}_{c}$	Roller holder base frame	frame_c
${web}_{a}$	Left (entry) web transfer information port (blue)	web_a
${web}_{b}$	Right (exit) web transfer information port (green)	web_b
${flange}_{c1}$	Roller rotation flange	flange_c1
${flange}_{c2}$	Roller rotation flange	flange_c2
$f_{n}$	Nip force signal input Mode = Force input	fn
$disp$	Nip displacement input signal Mode = Displacement Input	disp
$flange$	Nip translation flange Mode = Mechanical	flange

Parameters

Web Properties

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

Settings

Name	Default	Units	Description	Modelica ID
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.	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. Available when Use fixed base = true	InitPos
$θ$	$0$	$\deg$	Rotation about z-axis. Available when Use fixed base = true	InitAng

Nip Actuation

Name	Default	Units	Description	Modelica ID
$Mode$	$Constant Force$		Select actuation mode. There are four options: 1. Constant force (Given by the parameter $F_{nip}$ ), 2. Force Input (Given by the input signal fn), 3. Displacement input (Given by the input signal disp), 4. Mechanical (in this mode the nip is moved via a 1D translational flange)	mode
$F_{nip}$	$0$	$N$	Force applied from the nip to web. Available when Mode = Constant Force	Fnip
Force unit	$N$		Unit of force used in the data and/or input	forceUnit
Disp. unit	$m$		Unit of displacement used in the data and/or input	dispUnit
Data source	$inline$		Data source. There are three options available: inline (the data is entered in the provided matrix parameter), attachment (the data file is attached to the model), and file (the data is provided via a specified file).	datasourcemode
$f (x)$	[-1, 0; 0, 0; 0.001, 10; 0.002, 30; 0.003, 1000]		Data set	table
$skip rows$	0		Number of rows to skip	skipRows
$Smoothness$	Linear interpolation		Smoothness of table interpolation: linear, cubic spline, or none	smoothness

Roller

Name	Default	Units	Description	Modelica ID
$D_{1}$	$0.2$	$m$	Diameter of roller 1	D1
$D_{i1}$	$0$	$m$	Inner diameter of roller 1	Di1
$D_{2}$	$D_{1}$	$m$	Diameter of roller 2	D2
$D_{i2}$	$0$	$m$	Inner diameter of roller 2	Di2
$L$	$1.2$	$m$	Roller length	L
Use cylindrical geometry	$true$		When checked (true), roller inertia is calculated assuming a uniform cylindrical geometry	useCylindricalGeometry
$ρ$	$2.7 \cdot 10^{3}$	$\frac{kg}{m^{3}}$	Roller density; enabled when using cylindrical geometry	rho_roll
$m_{1}$	$1$	$kg$	Roller 1 mass; enabled when not using cylindrical geometry	m1
$m_{2}$	$1$	$kg$	Roller 2 mass; enabled when not using cylindrical geometry	m2
$J_{1}$	$0.005$	$kg m^{2}$	Roller 1 rotational inertia; enabled when not using cylindrical geometry	J1
$J_{2}$	$0.005$	$kg m^{2}$	Roller 2 rotational inertia; enabled when not using cylindrical geometry	J2
$d_{1}$	$0$	$\frac{N m s}{rad}$	Bearing viscous damping constant for roller 1	d1
$d_{2}$	$0$	$\frac{N m s}{rad}$	Bearing viscous damping constant for roller 2	d2

Nip Guide (available if Mode = Mechanical)

Name	Default	Units	Description	Modelica ID
$d$	$0$	$\frac{N s}{m}$	Translational damping constant	Kdamper_slider
${IC}_{s, v}$	Ignore		Indicates whether to ignore, try to enforce, or strictly enforce the translational initial conditions	MechTranTree_slider
$s_{0}$	$0$	$m$	Initial displacement of the joint at the start of the simulation	InitPos_slider
$v_{0}$	$0$	$\frac{m}{s}$	Initial velocity of the joint at the start of the simulation	InitVel_slider

Friction - web/Roller 1

Name	Default	Units	Description	Modelica ID
$μ_{c}$	$0.2$		Coulomb coefficient of friction	mu_c1
$v_{0}$	$1 \cdot 10^{−4}$	$\frac{m}{s}$	Tight/slack side switching velocity boundary	v01
Use constant coefficient of friction	$true$		Checked (true) means the coefficient of friction is constant with velocity, otherwise the following parameters are enabled [1]	useConstantCoF1
$Peak$	$1$		Static friction is ${Peak}_{μ_{c}}$	peak1
$V_{s}$	$0.01$		Stribeck sliding velocity	vs1
$n_{Decay}$	$2$		Decay exponent	nDecay1
$μ_{d}$	$0$		Viscous coefficient of friction	mu_d1

$[1] μ (v_{rel}) = μ_{d} |v_{rel}| + μ_{c} + μ_{c} (Peak - 1) \exp (- {|\frac{v_{rel}}{v_{s}}|}^{n_{Decay}}) &semi;$

Friction - web/Roller 2

Name	Default	Units	Description	Modelica ID
Use same as Roller 1	$true$		When checked (true), the same coefficient of friction is assumed between the web and roller 2 as roller 1	useSame
$μ_{c}$	$0.2$		Coulomb coefficient of friction	mu_c2
$v_{0}$	$1 10^{−4}$	$\frac{m}{s}$	Tight/slack side switching velocity boundary	v02
use constant coefficient of friction	$true$		Checked (true) means the coefficient of friction is constant with velocity, otherwise the following parameters are enabled [1]	useConstantCoF2
$Peak$	$1$		Static friction is ${Peak}_{μ_{c}}$	peak2
$v_{s}$	$0.01$		Stribeck sliding velocity	vs2
$n_{Decay}$	$2$		Decay exponent	nDecay2
$μ_{d}$	$0$		Viscous coefficient of friction	mu_d2

Frame

Name	Default	Units	Description	Modelica ID
Reference frame	Middle of the gap		Select option for the location of the ${frame}_{c}$ (holder). There are three options available: Middle of the gap, Center of roller 1, and Center of roller 2	Ref_pos
$m_{f}$	$1$	$kg$	Frame mass	m_frame
$J_{f}$	$0.01$	$kg m^{2}$	Frame inertia	J_frame
$Y$	$0$	$m$	Offset from the reference point in the Y direction	Y

Visualization

Name	Default	Units	Description	Modelica ID
Show roller 1	$true$		When checked (true), a visualization of roller 1 is created	showVisualization_roller
Show roller 2	$true$		When checked (true), a visualization of roller 2 is created	showVisualization_second
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	$20$	$\deg$	Band angle	band_angle
Show frame	$false$		When checked (true), a visualization of the frame is created	showVisualization_frame
Transparent frame	$false$		When checked (true), the roller visualization is transparent	transparent_frame
Frame color	Orange		Frame color	color_frame

Advanced Settings

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

Summary Variables

Name	Units	Description	Modelica ID
summary_WrapAngle	$rad$	Wrap angle	summary_WrapAngle
summary_Length	$m$	Length of the web in contact with roller	summary_Length
summary_SlipVelocity1	$\frac{m}{s}$	Difference between the web velocity and the surface velocity of Roller 1 (in m/s)	summary_SlipVelocity1
summary_SlipVelocity2	$\frac{m}{s}$	Difference between the web velocity and the surface velocity of Roller 2 (in m/s)	summary_SlipVelocity2

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