Concave and Flat Expander Anti-Wrinkle Rollers:

Transcription

1 Concave and Flat Expander Anti-Wrinkle Rollers: For Better or For Worse? Timothy J. Walker (651) Office (651) Mobile (866) Fax NEW Stonebridge Road St Paul, Minnesota 55118

2 Concave and Flat Expander Rollers? Concave Roller Flat Expander

3 Two Roller-Based Tracking Rules Initial Position (centered) Misaligned Roller Diameter Variations

4 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.

5 Bending a Web Uses Lateral Force -σ x +σ x T x

6 Bending a Web Uses Lateral Force -σ x +σ x T x

7 Bending a Web Uses Lateral Force -σ x +σ x T x -σ x +σ x T

8 Bending a Web Uses Lateral Force -σ x +σ x T x -σ x +σ x T

9 Diameter-Based Tracking A reverse crowned roller has two opposing tapered section. Diameter variations strain the web and induce tension variations The asymmetrical tension exerts a moment or torque on the web.

10 Tracking & Diameter Variations web roller Responding to the crossweb tension variation, the web bends, but is not parallel. With poor traction the web stays nonparallel. With good traction web tracks to parallel.

11 Tracking & Diameter Variations web roller A poor traction reverse crown roller creates wrinkles. With good traction web tracks to parallel.

12 Tracking & Diameter Variations FOR WORSE FOR BETTER A poor traction reverse crown roller creates wrinkles. A good traction reverse crown roller spreads the web, preventing wrinkles.

13 Two Roller-Based Tracking Rules Initial Position (centered) Misaligned Roller Diameter Variations Good Traction Tracking Tight Side Tight Side

14 Two Roller-Based Tracking Rules Initial Position (centered) Misaligned Roller Diameter Variations Tight Side Tight Side Poor Traction Tracking

15 Two Roller-Based Tracking Rules Initial Position (centered) Misaligned Roller Diameter Variations Good Traction Tracking Tight Side Tight Side Poor Traction Tracking

16 Diameter-Based Spreader Initial Position (centered) Diameter Variations Poor Traction Diameter Spreader Tight Side Poor Traction Tracking

17 Diameter-Based Spreader Initial Position (centered) Diameter Variations Good Traction Diameter Spreader Good Traction Tracking Tight Side

18 Diameter-Based Spreader Initial Position (centered) Diameter Variations Good Traction Diameter Spreader Good Traction Tracking Tight Side

19 Diameter-Based Spreader Good Traction Diameter Spreader Tape Collars Reverse Crowned (Concave) Roller Good Traction Required

20 Misalignment-Based Spreader Initial Position (centered) Misaligned Roller Good Traction Misalignment Spreader Good Traction Tracking Tight Side

21 Misalignment-Based Spreader Initial Position (centered) Misaligned Roller Good Traction Misalignment Spreader Good Traction Tracking Tight Side

22 Misalignment-Based Spreader Good Traction Misalignment Spreader Bowed Roller Skewed Edge Nips Expander Roller Good Traction Required Flex Expander Roller

23 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.

24 The Friction Circle The total friction available, F, is equal to µ times N. µ = coefficient of friction, N = normal load (car weight) +µn Y µn X +µn X Slip occurs if the applied load exceeds the friction available in either direction, OR If the combined vector sum exceeds the limit. µn Y Neither one of these friction demands alone would create slip, but combined they exceed the friction circle limit.

25 AW Roller Friction Needs MD friction required to develop diameter-induced upstream crossweb tension variations θ Machine Direction Friction TD friction required to bend web laterally and follow parallel entry rule. T Transverse Direction Friction

26 How Reverse Crowned Rollers Work A reverse crowned roller can be machined into the roller cylinder or created by applying tape to a standard cylindrical roller.

27 Reverse Crowned Rollers A cylindrical roller pulls with uniform strain and tension. ε Width

28 Reverse Crowned Rollers ε ε A concave roller pulls with strain and tension varied proportional to the percent diameter variations. Width

29 Reverse Crowned Rollers Greater percent diameter variations creates greater strain and tension variations. ε= r/r ε Width Be careful not to drive the center to slackness or the edge to break or deformation stresses.

30 Reverse Crowned Rollers Effectiveness of diameter variations is dependent on roller friction. Arrows indicate tension/width by lane

31 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)

32 Tape Collar Guidelines 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%). Diameter Width

33 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.

34 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.

35 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.

36 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.

37 Expander Roller Spreading An expanding surface roller has two strong spreading mechanisms: 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). 2. On-Roller Spreading As the roller s surface expands, it will attempt to laterally expand the web, limited by the available friction.

38 Flat Expander On-Roller Spreading α Angle of expander roller end φ Roller vector angle at initial web edge contact β1 β2 Wrap angle of web initial contact Wrap angle to web final contact (all angles in radians) α φ w roller w web T Roller width halfway from min to max, in. Web width change from initial to final contact point, assuming no web-roller lateral slip. Web tension, lbs. µ Coefficient of friction or traction r w web Roller radius, in. Web width at contact point, in. +β w r2 -β w web = w r1 w roller (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.)

39 Flat Expander Roller Spreading 1. Pre-Roller Spreading If ( W W R, IN R, IN W) i = 2L 3 FL δ = = 3EI F = µ Tβ = 2L IN θ 4FL Etw IN R, IN 3 3 sinθ R, IN W MAX > W R, IN β w R,OUT w R,IN θ R,IN w i L δ 1/ 2 W = 3 2µ TβL 3 twe 4µ TβL = twe MAX 3 3

40 Flat Expander Roller Spreading Roller setup spreading goes up with: Roller Angle (OK) Entry Span Length (less well known) W R IN = LIN R, IN, 2 θ Potential spreading goes up with: 4µ TβL twe W MAX = 3 Friction Tension Length CUBED and down with increasing lateral stiffness, (including width CUBED) 3

41 Flat Expander On-Roller Spreading w roller = + w roller wr 0 rsinβ 1 sinα = r ( sin β β ) sin α 1 + sin 2 The roller vector and web strain are directly proportional to web/roller face width ratio. w web = w w web r0 w roller w φ1 web = cos β1 wr0 α α φ +β w r2 -β w web = w r1 w roller

42 Flat Expander On-Roller Spreading 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: Y-Force/width required to follow the rubber covering strain during contact. Force applied by tension-created friction: Y-Force/width available from friction created by web tension. T w w = w te µ T web y, req web avail r T w =

43 Flat Expander On-Roller Spreading Scenario #1: Frictional forces more than sufficient. If T w avail T > w y, req Web y-strain = = rsinα ( sinβ + β ) w roller FOR BETTER 1 sin 2 Scenario #2: Frictional forces are insufficient. If T w T < avail w y, req Web y-strain = µ T rte (Assumes no friction is lost to drive the roller.) Big NEGATIVE scenario #2: Relative motion between web and roller will cause wear and abrasion. FOR WORSE

44 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.

45 Concave and Flat Expander Rollers? Concave Roller Flat Expander FOR BETTER? FOR WORSE? It s up to you

46 Questions?

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