concave and flat expander anti-wrinkle rollers · 164 stonebridge road st paul, minnesota 55118...
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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
(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
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Two Roller-Based Tracking Rules
Misaligned
Roller
Diameter
Variations
Initial
Position
(centered)
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Bending a Web Uses Lateral Force
-σx +σx
T
x
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Bending a Web Uses Lateral Force
-σx +σx
T
x
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Bending a Web Uses Lateral Force
-σx +σx
-σx +σx
T
T
x
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Bending a Web Uses Lateral Force
-σx +σx
-σx +σx
T
T
x
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Tracking & Diameter Variations
With good traction
web tracks to
“parallel.”
web roller
A poor traction
reverse crown
roller creates
wrinkles.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Tracking & Diameter Variations
A good traction
reverse crown roller
spreads the web,
preventing wrinkles.
A poor traction
reverse crown
roller creates
wrinkles.
FOR WORSE���� FOR BETTER☺☺☺☺
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Two Roller-Based Tracking Rules
Tight
Side
Tight
Side
Misaligned
Roller
Diameter
Variations
Good
Traction
Tracking
Initial
Position
(centered)
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Two Roller-Based Tracking Rules
Tight
Side
Tight
Side
Misaligned
Roller
Diameter
Variations
Initial
Position
(centered)
Poor
Traction
Tracking
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Two Roller-Based Tracking Rules
Tight
Side
Tight
Side
Misaligned
Roller
Diameter
Variations
Good
Traction
Tracking
Initial
Position
(centered)
Poor
Traction
Tracking
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Tight
Side
Diameter
Variations
Diameter-Based Spreader
Initial
Position
(centered)
Poor
Traction
Tracking
Poor Traction
Diameter
Spreader
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Tight
Side
Diameter
Variations
Diameter-Based Spreader
Good
Traction
Tracking
Initial
Position
(centered)
Good Traction
Diameter
Spreader
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Tight
Side
Diameter
Variations
Diameter-Based Spreader
Good
Traction
Tracking
Initial
Position
(centered)
Good Traction
Diameter
Spreader
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Diameter-Based Spreader
Good Traction
Diameter
Spreader
Good
Traction
Required
�Tape Collars
� Reverse Crowned
(Concave) Roller
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Misalignment-Based Spreader
Tight
Side
Misaligned
Roller
Good
Traction
Tracking
Initial
Position
(centered)
Good Traction
Misalignment
Spreader
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Misalignment-Based Spreader
Tight
Side
Misaligned
Roller
Good
Traction
Tracking
Initial
Position
(centered)
Good Traction
Misalignment
Spreader
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Misalignment-Based Spreader
Good
Traction
Required
Good Traction
Misalignment
Spreader
� Flex Expander Roller
� Expander Roller
� Skewed Edge Nips
� Bowed Roller
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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…
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Reverse Crowned Rollers
ε
Width
A cylindrical roller
pulls with uniform
strain and tension.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Reverse Crowned Rollers
ε
Width
∆ε
A concave roller
pulls with strain and
tension varied
proportional to the
percent diameter
variations.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Reverse Crowned Rollers
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Reverse Crowned Rollers
Effectiveness of diameter variations is
dependent on roller friction.
Arrows indicate
tension/width
by lane
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Reverse Crowned Rollers
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)
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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%).
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Concave Roller Tips #2
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Concave Roller Tips #3
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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).
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.)
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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)
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Flat Expander On-Roller Spreading
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Flat Expander On-Roller Spreading
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:
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Flat Expander On-Roller Spreading
(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☺☺☺☺
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
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.
TJWalker+Associates, Inc., Copyright 2004 www.tjwa.com
Concave and Flat Expander Rollers?
Concave Roller Flat Expander
FOR WORSE����?
FOR BETTER☺☺☺☺?
It’s up to you ����…
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