Roller - MapleSim Help

All Products Maple MapleSim

Home : Support : Online Help : MapleSim Toolboxes : MapleSim Web Handling Library : Rollers : Roller

Roller

Roller component

	Description
	The Roller component models a pull roller or an idler roller.

	Usage
	The Roller component must be between two Span components. Using the provided 1D rotational flange (flange_c) the Roller component can model a pull roller. Without any applied torque or setpoint velocity, the Roller models an idler roller.

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
$T_{b}$	Downstream tension
$v_{a}$	Upstream speed
$v_{b}$	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
$β$	Wrap angle

Under a no-slip assumption, we have:

$R (T_{a} - T_{b}) = τ_{m} - J \frac{\partial ω}{\partial t} - b ω$

$v_{a} = R ω_{r}$

When the Include slippage option is selected, the icon changes (as shown above) to indicate additional dynamics included in the Roller component. The difference between entry and exit tensions is given by:

$T_{a} - T_{b} = (\exp (μ β) - 1) {\begin{array}{c} T_{b} & v_{rel} > v_{0} \\ T_{b} \frac{v_{rel}}{v_{0}} & v_{rel} > 0 \\ 0 & R ω_{r} = v_{a} \\ T_{a} \frac{v_{rel}}{v_{0}} & v_{rel} > - v_{0} \\ - T_{a} & otherwise \end{array}$

where $v_{0}$ is a small positive velocity threshold and

$v_{rel} = R ω_{r} - v_{a}$

The Roller component has a parameter P under the Friction tab which is activated when slippage is enabled. The positive pressure P represents the uniform suction pressure on the contact arc of the web from the roller. This increases the maximum limit on tension difference as shown below:

$T_{a} - T_{b} = (\exp (μ β) - 1) {\begin{array}{c} T_{b} & v_{rel} > v_{0} \\ (T_{b} + P \cdot W \cdot R) \frac{v_{rel}}{v_{0}} & v_{rel} > 0 \\ 0 & R ω_{r} = v_{a} \\ (T_{a} + P \cdot W \cdot R) \frac{v_{rel}}{v_{0}} & v_{rel} > - v_{0} \\ - T_{a} & otherwise \end{array}$

Optionally, a velocity-dependent coefficient of friction can be used:

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

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: Note that the frame on the CAD part should be on its axis midpoint for the part to be correctly visualized.

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; enabled when Use fixed base = false	frame_c
${frame}_{d}$	Roller center frame for external rigid body/CAD connection; enabled when Use CAD = true	frame_d
${web}_{a}$	Left (entry) web transfer information port (blue)	web_a
${web}_{b}$	Right (exit) web transfer information port (green)	web_b
${flange}_{c}$	Roller rotation flange	flange_c1
${ecc}_{in}$	Eccentricity signal (in meters)	ecc_in

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
Include slippage	$false$		When unchecked (false), no-slip conditions are assumed	includeSlippage
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_c is disabled and the roller frame is fixed in the inertial coordinate frame (addition position and orientation parameters are enabled instead)	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

Roller

Name	Default	Units	Description	Modelica ID
$D$	$0.2$	$m$	Diameter of 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 roller	Di
$L$	$1.2$	$m$	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
$m$	$1$	$kg$	Roller mass; enabled when not using cylindrical geometry	m
$J$	$0.005$	$kg m^{2}$	Roller rotational inertia; enabled when not using cylindrical geometry	J
$d$	$0$	$\frac{N m s}{rad}$	Bearing viscous damping constant	d

Friction

Name	Default	Units	Description	Modelica ID
$μ_{c}$	$0.2$		Coulomb coefficient of friction	mu_c
Use constant coefficient of friction	$true$		Checked (true) means the coefficient of friction is constant with velocity, otherwise the following parameters are enabled [2]	useConstantCoF
$Peak$	$1$		Static friction is $Peak \cdot μ_{c}$	peak
$v_{s}$	$0.01$		Stribeck sliding velocity	vs
$n_{Decay}$	$2$		Decay exponent	nDecay
$μ_{d}$	$0$		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) [1]	P

[1] When slippage is not enabled, this parameter is only used in the calculation of the capstan tension limit summary variable.

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

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	useInputEccentricity
$e$	$0$	$m$	Roller eccentricity	ecc
$θ_{0}$	$0$	$\deg$	Initial eccentricity angle	theta_ecc0

Frame

Name	Default	Units	Description	Modelica ID
$m_{f}$	$1$	$kg$	Frame mass	m_frame
$J_{f}$	$0.01$	$kg m^{2}$	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
$r_{f}$	$[0, \frac{D}{2}]$	$m$	Offset in the XY plane; enabled when Add frame offset is true	rf

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	$20$		Band angle	band_angle
Show reaction force arrow	$false$		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		Force arrow color	forceColor
Force arrow transparency	$false$		When checked (true), the force arrow is transparent	forceTransparent
Show reaction torque arrow	$false$		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		Torque arrow color	torqueColor
Torque arrow transparency	$false$		When checked (true), the torque arrow is transparent	torqueTransparent

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 the roller	summary_Length
summary_Limit		0 = Tension limit is less than capstan limit or include slippage is true; 1 = Tension limit exceeds capstan limit (web will slip)	summary_Limit
summary_SlipVelocity	$\frac{m}{s}$	Slip velocity: web speed - roller surface speed	summary_SlipVelocity

Maple

Maple Add-Ons

MapleSim

MapleSim Add-Ons

Systems Engineering

Consulting Services

Maple T.A. and Möbius

Education

Industries

Automotive and Aerospace

Robotics

Machine Design & Industrial Automation

Other

Application Areas

Product Pricing

Purchasing

Institutional Student Licensing

Maplesoft Elite Maintenance (EMP)

Support

Product Training

Online Product Help

Webinars & Events

Publications

Content Hubs

Examples & Applications

Community

About Maplesoft

Media Center

User Community

Contact

Online Help

All Products Maple MapleSim

Maple

Powerful math software that is easy to use

Maple Add-Ons

MapleSim

Advanced System Level Modeling

MapleSim Add-Ons

Systems Engineering

Consulting Services

Maple T.A. and Möbius

Education

Industries

Automotive and Aerospace

Robotics

Machine Design & Industrial Automation

Other

Application Areas

Product Pricing

Purchasing

Institutional Student Licensing

Maplesoft Elite Maintenance (EMP)

Support

Product Training

Online Product Help

Webinars & Events

Publications

Content Hubs

Examples & Applications

Community

About Maplesoft

Media Center

User Community

Contact

Online Help

All Products Maple MapleSim