Concave and Flat Expander Anti-Wrinkle Rollers · 164 Stonebridge Road St Paul, Minnesota 55118...

WWW.TJWA.COM 164 Stonebridge Road St Paul, Minnesota 55118

Concave and Flat Expander

Anti-Wrinkle Rollers:

For Better or For Worse?

Timothy J. Walker

[email protected]

(651) 686-5400 Office

(651) 249-1121 Mobile

(866) 572-3139 Fax

NEW

TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com

Concave and Flat Expander Rollers?

Concave Roller

Flat Expander


Two Roller-Based Tracking Rules

Misaligned

Roller

Diameter

Variations

Initial

Position

(centered)


Parallel Entry Rule

A moving web will tend to

shift laterally enter parallel

to the downstream roller’s

surface vector.

The web will shift may fall

short of parallel entry, if

the traction forces are

insufficient.


Bending a Web Uses Lateral Force

-σx +σx

T

x



-σx +σx

T

x



-σx +σx

-σx +σx

T

T

x



-σx +σx

-σx +σx

T

T

x


Diameter-Based Tracking

Diameter variations

strain the web and

induce tension

variations

A reverse crowned

roller has two

opposing tapered

section.

The asymmetrical

tension exerts a

moment or torque

on the web.


Tracking & Diameter Variations

With poor traction

the web stays non-

parallel.

Responding to

the crossweb

tension

variation, the

web bends,

but is not

“parallel.”

With good traction

web tracks to

“parallel.”

web roller



With good traction

web tracks to

“parallel.”

web roller

A poor traction

reverse crown

roller creates

wrinkles.



A good traction

reverse crown roller

spreads the web,

preventing wrinkles.

A poor traction

reverse crown

roller creates

wrinkles.

FOR WORSE�� FOR BETTER☺☺☺☺



Tight

Side

Tight

Side

Misaligned

Roller

Diameter

Variations

Good

Traction

Tracking

Initial

Position

(centered)



Tight

Side

Tight

Side

Misaligned

Roller

Diameter

Variations

Initial

Position

(centered)

Poor

Traction

Tracking



Tight

Side

Tight

Side

Misaligned

Roller

Diameter

Variations

Good

Traction

Tracking

Initial

Position

(centered)

Poor

Traction

Tracking


Tight

Side

Diameter

Variations

Diameter-Based Spreader

Initial

Position

(centered)

Poor

Traction

Tracking

Poor Traction

Diameter

Spreader


Tight

Side

Diameter

Variations


Good

Traction

Tracking

Initial

Position

(centered)

Good Traction

Diameter

Spreader


Tight

Side

Diameter

Variations


Good

Traction

Tracking

Initial

Position

(centered)

Good Traction

Diameter

Spreader



Good Traction

Diameter

Spreader

Good

Traction

Required

�Tape Collars

� Reverse Crowned

(Concave) Roller


Misalignment-Based Spreader

Tight

Side

Misaligned

Roller

Good

Traction

Tracking

Initial

Position

(centered)

Good Traction

Misalignment

Spreader



Tight

Side

Misaligned

Roller

Good

Traction

Tracking

Initial

Position

(centered)

Good Traction

Misalignment

Spreader



Good

Traction

Required

Good Traction

Misalignment

Spreader

� Flex Expander Roller

� Expander Roller

� Skewed Edge Nips

� Bowed Roller


The Friction Circle

In driving, you use tire-road friction in two directions:

1. To accelerate or brake 2. To hold the car laterally

In a turn, you may use friction in both directions at once.


The Friction Circle

The total friction available, F, is equal to µ times N.µ = coefficient of friction, N = normal load (car weight)

Slip occurs if the applied load

exceeds the friction available in

either direction,

–OR–

If the combined vector sum

exceeds the limit.

++++µµµµNX−−−−µµµµNX

−−−−µµµµNY

++++µµµµNY

Neither one of these friction demands

alone would create slip, but combined

they exceed the friction circle limit.


AW Roller Friction Needs

T

Machine Direction

Friction

Transverse Direction

Friction

θθθθMD friction required to

develop diameter-induced

upstream crossweb

tension variations

TD friction required to bend

web laterally and follow

parallel entry rule.


How Reverse Crowned Rollers Work

…or created by applying

tape to a standard

cylindrical roller.

A reverse crowned roller

can be machined into the

roller cylinder…


Reverse Crowned Rollers

ε

Width

A cylindrical roller

pulls with uniform

strain and tension.



ε

Width

∆ε

A concave roller

pulls with strain and

tension varied

proportional to the

percent diameter

variations.



ε

Width

∆ε=∆r/r

Greater percent

diameter variations

creates greater strain

and tension variations.

Be careful not to drive

the center to slackness

or

the edge to break or

deformation stresses.



Effectiveness of diameter variations is

dependent on roller friction.

Arrows indicate

tension/width

by lane



Spreading fails from insufficient traction.Look out for:

• Small wrap angles

• Low tension

• Low traction coefficients

(from slippery materials or lubrication of smooth surfaces

at high speed, large diameters, and low tension)


Tape Collar GuidelinesDiameter

Width

•Choose tape with good friction and roughness.

• Tape build up depends on web strain and roller diameter.

• Try building up roller radius about 2-3 times web strain (commonly about 0.3%).


Concave Roller Tips #1

Don’t Go Slack or Over-Twist

Avoid creating center slackness and excessive

shear.

A concave roller’s profile should be based on web

width, thickness, modulus, and roller diameter.



Apply Firmly.

Concave roller need to create a crossweb tension

variation in the upstream span.

Design for enough lane-by-lane traction to support

induced upstream-to-downstream tension

variations.



Relieve Excess Gas (Air)

To ensure good traction,…

…especially with increase air lubrication (a function

of speed, diameter, tension, porosity, and

roughness),…

…concave roller need to have an appropriate

surface texture or roughness.


Flat Expander Rollers

A flat expander roller’s surface is made of

polymer bands or a rubber sleeve.

The surface expands

laterally under the

wrapping web.

The result is diverging

surface vectors and two

spreading mechanisms –

pre-roller and on-roller

web spreading.


Expander Roller Spreading

An expanding surface roller has two strong spreading mechanisms:

2. On-Roller Spreading

As the roller’s surface expands, it

will attempt to laterally expand the

web, limited by the available friction.

1. Pre-Roller Spreading

The web will track outward to align its edges

to enter parallel to surface vector of the

roller’s initial contact point (parallel entry rule).


Flat Expander On-Roller Spreading

α Angle of expander roller end

φ Roller vector angle at initial web

edge contact

β1 Wrap angle of web initial contact

β2 Wrap angle to web final contact

(all angles in radians)

ααααφφφφ

+β

-β wweb= wr1wroller

wr2

wroller Roller width halfway from min to max, in.

∆wweb Web width change from initial to final

contact point, assuming no web-roller

lateral slip.

T Web tension, lbs.

µ Coefficient of friction or traction

r Roller radius, in.

wweb Web width at contact point, in.

(β1 and β2 angles are measured from tangent line halfway between minimum or maximum rubber expansion.

Positive and negative β-angles are upstream and downstream from reference point.)


Flat Expander Roller Spreading

INRININR

INRINiINR

LW

LWW

,,

,,

2

sin2)(

θ

θ

=∆

=−

1. Pre-Roller Spreading

wR,IN Lwi

wR,OUT

θθθθR,IN

If…

Etw

LTW

Etw

LT

TF

Etw

FL

EI

FL

MAX 3

3

3

3

2/1

3

33

4

2

4

3

βµ

βµδ

βµ

δ

=∆

=

=

==

INRMAX WW ,∆>∆

ββββ


Flat Expander Roller Spreading

INRININR LW ,, 2 θ=∆Roller setup spreading goes

up with:

Etw

LTWMAX 3

34 βµ=∆

• Roller Angle (OK)

• Entry Span Length (less well known)

Potential spreading goes up with:

• Friction

• Tension

• Length CUBED

• …and down with increasing lateral stiffness,

(including width CUBED)



ααααφφφφ

+β

-β wweb= wr1wroller

wr2

αβ sinsin 10 rww rroller +=

( )21 sinsinsin ββα +=∆ rw roller

roller

r

webweb w

w

ww ∆

=∆

0

1

0

1 cos βαφ

=

r

web

w

w

The roller vector and web

strain are directly proportional

to web/roller face width ratio.



tEw

w

w

T

web

web

reqy

∆=

, r

T

w

T

avail

µ=

Y-Force/width required to

follow the rubber covering

strain during contact.

Y-Force/width available from

friction created by web

tension.

Q: Will the web and the rubber spread together?

A: Only if applied force exceed TD stress/strain needs.

Force required to follow

rubber stretching:

Force applied by

tension-created friction:



(Assumes no friction is

lost to drive the roller.)

reqyavail w

T

w

T

,

>

reqyavail w

T

w

T

,

<

If…

If…

Web y-strain = ( )21 sinsinsin ββα +=∆ rwroller

Web y-strain =rtE

Tµ

Big NEGATIVE scenario #2: Relative motion between web and

roller will cause wear and abrasion.

Scenario #1: Frictional forces more than sufficient.

Scenario #2: Frictional forces are insufficient.

FOR WORSE��

FOR BETTER☺☺☺☺


Flat Expander Tips #1 & 2

Drive Safely

Ensure sufficient traction via friction coefficient, wrap angle, and tension to provide to turn the high drag roller and exert spreading forces on the web.Add a drive belt to reduce web friction load.

Don’t over stretch

Avoid unnecessary wear by stretching the expanding sleeve beyond the available traction’s ability to expand the web.


Concave and Flat Expander Rollers?

Concave Roller Flat Expander

FOR WORSE��?

FOR BETTER☺☺☺☺?

It’s up to you ��…


Questions?

[email protected]

651-686-5400

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Concave and Flat Expander Anti-Wrinkle Rollers · 164 Stonebridge Road St Paul, Minnesota 55118...

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