Wrinkles in a running web^[1] are a constant source of problems and waste in printing, coating, slitting, laminating, and sheeting; in any converting process, in fact, for which a flat surface is required.  Converters, as an industry, have been chasing wrinkles and methods for eliminating them from the earliest days of web processing.  Usually the available “cures” are in vain since they fail to address the fundamental problems in the web and its transport.

All wrinkles are caused by unsupported shear stresses in the web. 
A misaligned machine will cause wrinkles, but wrinkles will still form in a machine with so called perfect geometry.

There are three basic types of wrinkles that can be found in a running web: longitudinal, diagonal and trace wrinkles.  These are distinguished from one another by the origins of the shear stresses that caused them.  Any viable cure for wrinkles must relieve these underlying shear stresses.

ANATOMY OF A WRINKLE

Since no web is intentionally sheared, any shear stresses arising in it must be fed by the tension in the web.  To get any web to unwind from its parent roll and to guide it into a converting process, it must run over rollers which direct it into the process in the correct orientation.  If the web is to remain in contact with these rollers and be guided by them, i.e., kept "on the road", it must be pulled tight against them. 

The law of belting says that all running webs^[2] must meet their rolls perpendicular to the roll but it is friction at the roll face which drives the web to this particular orientation and this friction force is derived from web tension.  Whenever a running web is tensioned,  tensile stresses in the web must resist that tension, and if these tensile stresses are not uniform across the web then shear stresses arise, wrinkles can form, and the web will not present itself to the intended process as a flat sheet.

To see why shear stresses cause wrinkles, examine any small patch of a running web as shown in the figure below and examine the stresses acting on its boundary.  If the patch is in pure shear, then a patch within the patch rotated exactly 45° will be in pure tension on two sides and pure compression on the other two^[3].  If the original patch is allowed to deform under the shear stress, it will become diamond-shaped as shown to the right in the figure.  The inner patch will get narrower and longer under the tension and compressive stresses.  The web, however, is very thin (by definition, or it is a plate), so it buckles when it is compressed.  Buckling is simply the web evading the com­pressive stress by bending out of plane instead of compressing, and that bend out of plane:  , is a wrinkle.

Shear Stresses in a Tensioned Web of Paper, Film or Foil.

The three major causes of undesired sheer stresses are:

a)  excessive tension in the web, which causes longitudinal or machine-direction wrinkles in the central portion of the web between rolls;

b)   baggy edges in the web, which means a skewed tension distribution exists which causes diagonal wrinkles radiating from one edge near every roll into the unsupported region of the web;

c)   non-flatness of the web which causes small “pockets” of shear stress and random-appearing “trace” wrinkles throughout the body of the web except on the rolls.

The first of these is cured by reducing the gross tension in the web^[4], the second by introducing a Tension Profile Control system into the web path wherever web flatness is critical, and the third by providing alternating flotation and anchorage patterns under the web as it passes over rolls.  Each of these is explained in more detail below.

Longitudinal Wrinkles

When any material is pulled in one direction, it shrinks in the other two.  Similarly, if a block of material is compressed, its lateral dimensions increase by an amount proportional to the compression.  The ratio of the change in the loaded direction to the change in the off-axis dimensions is called Poisson’s ratio^[5].  If a sheet of material is pulled in one dimension, both its thickness and width must either change or lateral stresses must develop to prevent the change.  If the change is permitted by the circumstances, the situation is called plane stress, but if one of the lateral deformations is prevented by surrounding material, the situation is called plane strain.  In a thin, wide web, both situations exist, and the combination produces shear stresses.

Near the edge of a sheet, lateral deformations are not limited by surrounding material because of the free edge.  In the middle of the sheet however, a narrowing element of the web pulls neighboring elements toward it and tensile stresses arise to do so.  As it passes over a roll, the web is forced to be flat, but in mid-span the web is free.  If the web was tensioned without moving, it would neck down, shown in dashed lines in the figure below, getting narrower in the mid-span than at the supporting roll faces.  The curvature of the edges would exert a tension in the center to stabilize it.  However, if the web is running over the rolls under tension, then each little patch of web meeting the roll must pass straight around a circumferential line on the roll^[6], and the curvature of the edges of the web will be straightened out to the solid lines shown in the figure i.e., the whole web will get narrower.  The tension stresses in the mid-span area between rolls which were trying to pull the edges of a stationary web toward the center are relieved by wrinkle formation in the center of the web, away from the flattening effects of the rolls.  The region of wrinkling is roughly elliptical as shown.

“Necking down” of a web under tension

Diagonal Wrinkles

If tensions are not high enough to cause longitudinal tension wrinkles, diagonal wrinkles may still form.  These are wrinkles which radiate upstream and downstream from one edge of the web where it passes over a roll. 

The wrinkles form a fan starting at the roll contact point and radiating away from the roll toward the center of the web.  The source of these wrinkles is camber or curvature in the web.

A web rolled onto a flat surface.

Imagine that a roll of material is unwound onto a flat surface under near-zero tension.  If one end is fastened to the floor and the roll is unwound along a straight path, one edge may exhibit an irregular cockled edge.  This is a characteristic "baggy edge".  Should a significant length be cut from the roll and left free of any tensions on a flat surface, it wanders from a straight path even though it had been slit straight and wound on a straight-sided roll.  The rolls of material were originally slit and rewound under tension; without that tension they would meander in very gentle curves either steadily to the left or right, or in a sinuous way as shown, greatly exaggerated, in the figure above.  Because of this lateral curvature in the web, it would prefer to run in an arc, so running under tension over parallel rolls is equivalent to bending the web as straight as it was when it was slit.

Stresses induced by lateral bending  in web straightening.  The arrow lengths correspond to the magnitude of the tension at that location along the base or zero lines.  Arrows to the right are positive or tensile, to the left are negative or compressive.  The figures are drawn for a web in which the original curvature was upward, with the short side at the top of the figure.

The figure directly above shows a web under tension stretched from left to right.  If the web was originally curved upward (center of curvature at the top of the page) then pulling it straight induces two sets of stresses which can be considered separately.  If the web was perfectly straight, pulling it through the machine would induce the same stresses everywhere across the web as shown on the left.  If the web is curved, however, straightening it induces “bending” stresses which are tensile above the center and compressive below as shown in the center diagram.  These could not actually be induced by themselves because the web would not withstand the compression, but this is the component of total stress due to bending only.  On the right is the total stress picture.  The total stress is high enough so that the baggy side is under positive tension, but the tension profile is quite skewed.  The real world produces errors which are clearly non-linear but, for the sake of simplicity, the arguments are presented for a linear condition which are good approximations at this stage.

Part of the forced straightening is due to tension, and part is due to side forces developed at the rolls which shift the web into line.  Since these side forces are friction forces, they must be proportional to the normal forces between the web and the roll, they are highest on the tight side.  The wrinkles that develop are not unlike those which would be expected if a long span of web was grasped by one edge and pulled away from center toward that side.  A “fan” pattern of wrinkles would develop radiating away from the gripped point.  On a real roll this is not a point  but a region, so the wrinkles fan out from the tight side, not from a single point, as shown in the figure below.

Diagonal wrinkles caused by a near-side baggy edge condition.  The far side is tight.

In extreme situations, the web could have a baggy edge, one edge that did not tighten at all unless the short side was stretched to match the long side.  Steady curvature is most common in webs slit from the edges of the parent roll, while sinuous curvature will be found in center or near center cuts from the parent.  The webs least likely to show this effect are those run at full production width, but they can then have two baggy edges and a tight middle which usually results in longitudinal wrinkles.

Whether severe or slight, the cure for diagonal wrinkles is tension profile control; the active cocking and steering of a roll to equalize the path length and reduce the straightening forces and hence the shear in the web due to its curvature.  The efficacy of this cure is proven by hundreds of installations of tension profile control systems, and the side benefit is that total tension can usually be reduced as well so that longitudinal wrinkles become less of a problem, or vanish altogether.

Consider a sheet of material which is straight, but which is not perfectly flat.  Because of distortions in their manufacture, real webs have small regions which vary slightly, perhaps less than the thickness of the web, out of plane.  These regions amount to “bubbles” in the web that cannot be seen, although their area may be hand-sized or bigger, because their depth is very small.  These are often the result of uneven drying of paper products or of non-uniform thickness in films.  When this web is tensioned and run over rolls, two things happen to it to generate what are called trace wrinkles.

The stress field around a slack region in the web.

First, as shown in the figure above, the loose area or bubble does not carry its share of the tension in the web since it does not tighten up until other portions of the web are already carrying significant portions of the load.  This leads to a non-uniform stress profile as shown on the left below, with the edges of the bubble actually enduring a stress concentration.  In addition, the web is permitted to shrink laterally in the bubble region, but not as easily in the regions away from the edges and the bubbles, and both conditions produce shear stresses.  Wrinkles of both the longitudinal and the diagonal types can then be induced to form, and it is the perverse nature of webs that if wrinkles can form they do.  If the slack regions are not too large, these “trace” wrinkles are not too large either, but they are random and very persistent.

Secondly, as the web encounters a roll in the machine, the high tension on either side of a bubble binds the sides to the roll while the bubble itself is free to squirm or creep on the roll.  This can feed an adverse stress situation from one side of the roll contact patch to the other and can exacerbate the tension profile problem on either side; the anchorage entirely prevents the bubble from relaxing laterally under the straightening effects of the web’s curvature around the roll.

Clearly, the trace wrinkle problem diminishes if the gross tension in the web is reduced sufficiently and tension profile problems are addressed.  Since the tension in the web establishes the friction forces on the rolls of the machine, however, lateral control of the web can be lost if the tension is reduced too much.  The tension required to maintain control increases with increasing web speed because the web can float on a film of  air.

SQUEEZE FILMS AND ROLL VENTING

The figure below shows a side view of a web approaching a 90° wrap over a roll.  Both the spinning roll and the running web drag air along with them, and before the web can make contact with the roll face, this “entrained” air must be squeezed out from between them.  As it gets thinner, this film of air called a “squeeze film” becomes very hard to displace.  If the air film is not extremely thin by the end of its contact with the roll, the web will float on the roll and can slide sideways at will.  The law of belting no longer applies  . . . and under extreme conditions the roll will actually stop.  In the figure below, any increase in web speed will cause complete loss of control, but even when the speed is below that point, the friction forces between air and the web are negligible compared to those expected and lateral stability is compromised.

Side view of web floating away from a roll face at high speed.

To solve the web flotation problem without excessive tensions requires roll venting.  Vented rolls have grooves of some sort in their faces to allow air entrapped between the roll face and the running web to escape.  Conventionally, venting practices dictates a great number of grooves cut circumferentially across the entire roll face.  This assures that the web will make solid contact with the roll face as air squeezes into the grooves and escapes around the roll.  At the edges of these venting grooves, the entrained air is squeezed out very quickly by the web tension, and the web is well-anchored laterally.

A Cure for Trace Wrinkles

Conventionally vented rolls with closely spaced circumferential grooves are awkward to produce because they require a sequence of cuts.  A helical groove with a small pitch is sometimes threaded onto the roll face.  This geometry is rarely used however, because it is believed to cause a lateral web  shift.  To avoid this effect while retaining the continuous cut characteristic of a helix, an even number of threads can be cut, half with a right-hand pitch and half with a left-hand pitch.  This creates a symmetric diamond pattern of grooves and pads on the roll face as shown in the figure below.^[7]  When this pattern was actually tried in practice, however, it revealed a serendipitous benefit: all longitudinal and trace wrinkles disappeared. 

Since the test application had the most troublesome form of trace wrinkles, a heat-set wrinkle formed in a drying operation, the test was particularly convincing.

Support Pattern on a Diamond Vented Roll Face.

Although heat-set wrinkles and gage-band wrinkles^[8] usually disappear on the roll faces, they reappear immediately in all of the free spans in the same place on the web.  They can be particularly troublesome because the web material has been permanently deformed where they appear and the troublesome shear stress causing the trace wrinkles is built into the web.  Their disappearance in the body of the web near a diamond-vented roll therefore means that the roll pattern interacting with the air is responsible for the cure.  The vent pattern is therefore permitting shear stresses in the running web to relax before they build up to wrinkle the web.

If the web speed is high enough, this venting pattern will allow web contact as shown by the shading in the figure.  Even if the web speed is too slow for flotation, a hole pattern placed in the “diamonds” and supplied with air from the interior of the roll can augment the entrained air at the leading edges of the dia­monds without floating the web and will produce the pattern shown.  If this is a view above a roll looking down on the contact patch with the web traveling from bottom to top, then air is being entrained at the lower edge of the figure and escaping to the crossed grooves.  Even though the roll is vented, the diamonds whose wide part is at the leading edge of the contact patch are entraining air which squeezes out into the funnel of grooves.  The web is hardly anchored at the mouth of the funnel but it rapidly gets a moderate grip on the roll face which increases in strength as the grooves are approached.

In the diamonds whose leading edge is pointed, contact has been made earlier with the grooves diverging and the entrained (or blown) air has farther to go to the groove.  A thin air film forms in these regions which does not squeeze out as quickly as in the convergent regions.  The web contact in these regions is minimal and the web is free to “squirm” in these areas and relax small regions of shear stress between the adjacent anchor regions.  Bear in mind, however, that the pattern shown in the figure is not stationary because the roll is turning.  In only a fraction of a turn the regions of anchorage and flotation will have moved laterally (sideways one pitch of the screws) and longitudinally as well.  This can be imagined by sliding the contact patch along an unrolled or developed roll face.  Clearly, an oscillating pattern of support and anchorage is produced on the running web which maintains control of the web path through adequate contact, but at the same time allows small regions of the web to “squirm” on the roll face.  This squirming relaxes the local shear stresses, but cannot treat a gross tension profile error where the problem is full width except by allowing the web to creep over to one side or the other slightly and thus reduce the shear a bit.  Tension profile control is still required.

With the rolls relaxing shear stresses at every wrap, conditions that would cause major wrinkles can be incrementally relaxed from roll to roll.  As this happens, even the regions of the web between rolls can relax a bit and both the trace wrinkle problem and the longitudinal wrinkle problem are eliminated.

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