Roll Forming Handbook / Edited by George T. Halmos

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11.1.2 Redundant Deformations

Metal strips are subjected to manyother deformations in addition to transversal bending. Metal strips are

enteredinto roll forming mills either in precut or coil form, and are gradually deformed into complicated

three-dimensional (3-D) shapes by aseries of contoured rolls beforethey are ﬁnally made into products.

Because of this process, various types of additiveredundant deformations are induced in the metal

(Figure11.2).

The additive redundantdeformations (hereinaftercalled “redundantdeformations”) are:

1. Longitudinal bending and bending back

2. Longitudinal elongation and/or shrinkage

3. Transversal elongation and/or shrinkage

4. Shear in the metal’splane

5. Shear in the direction of the metal’sthickness

6. Various combinations of the above (Figure11.2)

These redundantdeformations are superimposed on the transversal bending and they signiﬁcantly

inﬂuence the formation of the product’scross-section and shape. Manyproblems, which occur in roll

forming processes,are related to redundant deformations.

In order to properly design rolls, build suitable equipment, optimize processes, maintain stable

operation, improvequalityofproducts, attain highproductivity, and innovate overall aspects of roll

forming technology, the behavior of redundant deformations and their inﬂuence upon the product’s

Transversal Bending

FIGURE 11.1 Transversal bending of metal strip during roll forming.

(a),(a′ ),(a″ ):Longitudinal Elongation,

Shrinkage

(c),(c′ ):Longitudinal Bending,

Bending back

Shrinkage

(b),(b′ ):Transversal Elogation,

(c′ )

(c)

(b)

(b′ )

(a″ )

(a)

(a')

FIGURE 11.2 Additive redundant deformation of metal strip during roll forming.

Roll Forming Handbook11-2

shape should be systematically investigated and clariﬁed. The investigation should coverthe following

subjects:

1. Cause and magnitude of individual redundant deformation in metal strips.

2. Quantitativeand qualitative inﬂuence of redundant deformations on products’ shapes and

dimensions.

3. Effects of forming conditions, such as the mechanical properties, width, and thickness of the metal

strip,the number of passes, roll proﬁles,roll positions, rollgaps, pass line, and the geometryofthe

product’scross-section on magnitude and distribution featuresofredundant deformations.

4. Mechanism of occurrenceand inﬂuence of redundant deformations on product defects.

5. Methods to reduce redundant deformations.

6. Countermeasures to prevent product defects caused by redundant deformations.

7. Methods to maintain smooth and stable ﬂowofmetal sheets, improvequalityofproducts, and

attain highproductivity.

11.2 Causes of Redundant Deformations

11.2.1 Longitudinal Elongation or Shrinkage

In roll forming processes, strips are fed continuously into forming machines and are formed step-by-step

into products by pairs of contoured rolls. The strips are progressively bent in the transversal direction and

their cross-sectional proﬁle is gradually transformed to the required shape. In the process, the height (or

depth) of the transversal cross-section (hereinafter referred to simply as “cross-section”) of semiformed

strips increases fromthe initial height, equal to the strip thickness, to the height of the product’scross-

section. The width of its cross-section decreases from the initial strip width to the width of the product’s

cross-section.

This means that during roll forming,each portion of the strip shifts, moves and deforms in both

vertical and horizontal directions to form 3-D curved shapes (cur vedsurfaces; Figure 11.3). Every

portion of the strip moves along the entryguide to the ﬁrst rolls, then to the second rolls and on to the

last rollsalong the spatial ﬂow lines corresponding to the curvedsurface.

Both transversal edges and the adjacent areas of the strip (hereinafter referred to as “edge portions”)

usually movealong ﬂowlines which are longer than those for center portions and intermediate portions.

This is caused by the fact that, while the center partusually travels in astraight line, the edge portions

often rise vertically and, at the same time, shift horizontally toward the center of the cross-section

(Figure11.3). Because of the vertical rising and horizontal shifting,the edge portions usually elongate,

while the center and intermediate portions shrink in the longitudinal direction.

The magnitude and transversal distribution pattern of the longitudinal elongation and shrinkage are

balanced to maintain an equilibrium of the longitudinal forces acting on the transversal cross-section of the

strip.The longitudinal forces acting on the cross-section of the semiformed strip are equal to the sum of the

longitudinal stress induced on its cross-section by the longitudinal elongation and shrinkage. The

longitudinal forces between stands are also inﬂuenced by tension or compression caused by the rolls.

The relativelength of the ﬂowline, along which each portion of strip moves from one roll stand to the

next, depends upon the working conditions, such as the number of rolls, roll proﬁles, roll positions,

horizontal distancebetween stands, and geometr yofthe product’scross-section. Therefore, the ﬂowline

of the edge portion is not always longer than that of other portions. Forexample, when the ﬂowline of

the center portion is longer than that of the edge portion, the center portion tends to elongate and the

edge portion tends to shrink in the longitudinal direction.

11.2.2 Transversal Elongation and Shear in Strip’sPlane

Products with wide cross-sections are roll formed from wide metal coils. The edge portions and, to a

lesser degree, intermediate portions of those products are pulled by rolls in the transversal direction and

Behavior of Metal Strip During Roll Forming 11-3

forced to shift towardthe center of semiformed cross-sections, unless the products are formed only at

their edge. This transversal shifting is usually induced by the transversal bending of the center portions of

the coils (Figure11.4).

When the coil is wide, the forcerequired to pull the edge and intermediate portions toward the center

of the semiformed cross-section becomesquite large, because aconsiderable amount of shear deforma-

tion in the coil’s plane is required to shift the ﬂat portions in the transversal direction.

Because of the large transversal tensile force necessaryfor this pulling,transversal elongation occurs in

the metal. If the convex rollispushed against the coil surface so strongly that it locally reduces the metal

thickness, then considerable transversal elongation can occur at the bend lines. The transversal tensile

forcecreated by transversal bending has astrong effect on transversal elongation.

Furthermore,when the top of convex(male) rolls exerts excessiveforceonthe inside surface of the

bending corner,asortofbulging deformation takes place(Figure11.5). Both longitudinal and transversal

elongation occurs in this case. Excessivetransversal elongation, as shown in the following sections, can

result in manykinds of defects.

As mentioned above, shear deformations occur at the edges and intermediate portions when they

are pulled and forced to shift in the transversal direction. The shear deformation can signiﬁcantly

inﬂuence the shape of the corner portion (bend line) as well as the springback deformation of the cutoff

end (ﬂare). When it is excessive, it causes asortofpermanent buckling of the corner portion and

distortion of cutoffends.

Tensile Stress

Flow Line

(Relatively Short)

Compressive Stress

Elongation

Shrinkage

#(i +1)–roll

# i –roll

′

(0′ )

(0)

# i –roll

Flow Line

(Relatively long)

FIGURE 11.3 Mechanism of occurrenceoflongitudinal elongation and shrinkage of metal strip.

Roll Forming Handbook11-4

11.2.3 Longitudinal Bending or

Bending Back

When ametal strip enters into arollgap,each

portion of the strip moves along individual

spatial ﬂow lines, respectively inclining in the

longitudinal direction. Some of those ﬂowlines

are close to the peripheryofthe convex roll and

others are close to that of the concave roll

(Figure11.6). For example, at the breakdown

formingpassesfor ERW(electricresistance

welded) pipes, both edge portions of the strip

usually enter the roll gaps along the ﬂow lines

closetothe concave rolls, while thecenter

portion of the strip ﬂows into the roll gaps

along the convex rolls.

Thus, each portion of the strip is bent in the

longitudinal direction before entering into the

roll gap and they are bent back to alongitudinal

straight shape at the center or exit side of the roll

gap.This repeated longitudinal bending and

Corner Portion Not-Formed

(Flat) Portion

Transversal

Tension

Transversal

Shifting

FIGURE 11.4 Mechanism of generation of transversal tensile forceacting to metal strip.

Bulging of Corner

Forming

Force

FIGURE 11.5 Bulging deformation of corner portion of

product.

Behavior of Metal Strip During Roll Forming 11-5

bending back is especially extensive at the edge portion of the strip.The repeated longitudinal bending

and bending back under the longitudinal tensile force(or tensile stress), which is usually hig hatthe edge

portion, contributes to the longitudinal elongation. The effect is similar to the progressive elongation of

metal strips subjected to roller leveling.

11.3 Effects of Redundant Deformations on Product Defects

The redundantdeformations signiﬁcantly inﬂuence the transversal bending of the strip necessaryto

achieve the required cross-section of the product. They also affect stresses and strains induced in metal

strips, springback deformations after forming ,and the distribution of residual stresses in the products.

In other words, the redundant deformations cause avarietyofdefects in the products, such as

longitudinal bow, camber or twist, edge wave,center (or pocket) wave, herringbone effect, thinning,

cracking,splitting, ﬂare (distortion of cutoffend), and dimensional inaccuracy (Figure11.7).

The mechanisms of the occurrence of these defects are summarized in the following sections.

11.3.1 Longitudinal Bow and Twist

Longitudinal bow, camber,and twist are the most frequent defects in narrowroll formed products. As

shown in Figure 11.8,these defects are caused by nonuniform transversal distribution of the longitudinal

membrane strain, or in other words, the nonuniform longitudinal elongation and shrinkage of the strip.

This nonuniformity is one of the fundamental characteristics of deformation of the strip during roll

forming.The magnitude and direction of bow, camber,and twist followthe variation in the distribution

pattern of the membrane strain (Figure 11.8).

The transversal nonuniformity of the longitudinal membrane strain is moreorless inevitable. It

cannot be avoided whereﬂat metal strips are roll formed into products with cross-sections having heights

(depths) and widths different from those of ﬂat metal strips. Therefore, in roll formed products, the

longitudinal elongation or shrinkage will not become uniform in the transversal direction. This is an

inevitable phenomenon related to 3-D deformations of the strips during roll forming.

However,the magnitude of longitudinal membrane strain can be reduced and its unavoidable

transversal nonuniform distribution can be rendered ineffectual by using proper conditions, in terms of

number of rolls, roll proﬁles, roll positions, pass line, horizontal (between-stand) distance, and others.

Therefore, the longitudinal bowcamber and twist can be prevented or at least reduced by the following

methods:

Longitudinal

Bending Back

Flow Line

Longitudinal

Bending

FIGURE 11.6 Mechanism of occurrenceoflongitudinal bending of metal strip.

Roll Forming Handbook11-6

1. The appropriate number of passes should be used (Figure11.9). When the number of passes is too

small, the amount of transversal bending deformation caused by each pair of rolls tends to become

excessive. In such cases, the strip is bent too much and too abruptly in the transversal direction, and some

portions of it, such as the ﬂange portion and edge portion are forced to rise steeply.Consequently,the

difference between the spatial length of their ﬂowlines and that of others becomes large. This causes

enlargement of the nonuniformity of the longitudinal membrane strain distributing in the transversal

direction.

If an adequate number of passes are used, then the strip is formed gradually and the longitudinal

membrane strain can be reduced to an ineffective level.However,when too manypasses are used, the cost

of the forming mill, the tooling,and the setup time will be unnecessarily increased.

Various methods havebeen proposed to determine the appropriate the number of rolls. However,

most of them havebeen based on experience, rough approximation, and assumptions.

In recent years, some mathematical models of rollforming wereproposed and computer-aided

simulation techniques weredeveloped for investigating the deformation characteristics of metal strip in

roll forming processes. By using such techniques, the overall behavior of the longitudinal membrane strain

which occurs in the strip can be analyzed and evaluated much more exactly and consistently than before.

As the mathematical models and simulation techniques become moreadvanced, the effects of the

number of rolls on deformation features of metal strips can be systematically analyzed, and the required

number of rolls can be better determined.

2. In addition to the number of passes, the roll proﬁles and roll positions should be checked. If

necessary, they havetobemodiﬁed to reduce the longitudinal membrane strain (Figure 11.10). When the

Warping (Bow)

Edge Wave (Buckling)

Center (Pocket) Wave

End Cross-Section

Corner Buckling

(Herring Bone)

Non-Uniform

Spring Back

Intermediate

Cross-Section

(End Effect)

Flare

Twisting

Cracking

FIGURE 11.7 Schematic illustration of defects of products.

Behavior of Metal Strip During Roll Forming 11-7

employed roll proﬁles and roll positions are not suitable for the smooth ﬂowofeach portion of the strip,

the magnitude and nonuniformity of longitudinal membrane strain tend to increase. The inﬂuenceofthe

roll proﬁles and roll positions on the behavior of the longitudinal membrane strain is very complicated.

It is too difﬁcult to clarify the relationships between them merely by trail and error.Toestablish those

relationships, investigation based on the mathematical theoryand application of the computerized

simulation technique is indispensable. The effects of rollproﬁles and roll positions on the deformation

FIGURE 11.8 Relationshipbetween transvers al distributionoflongitudinalmembrane strain “ 1

”and

longitudinal warp or twist of product; (a) longitudinal bow; (b) longitudinal twist.

Product' sCross-Section

Longitudinal Bow

Longitudinal Membrane Strain

(+): Elongation

Width

( − ): Shrinkage(a)

(+)

( − )

Twisting

Longitudinal Membrane Strain

Width

(+): Elongation

( − ): Shrinkage(b)

( − )

(+)

Roll Forming Handbook11-8

featuresofmetal strips, especially on the behavior of the longitudinal membrane strain, can be predicted

consistently and systematically by utilizing the abovetechniques. As aresult, suitable roll proﬁles and roll

positions can be designed to reduce the longitudinal membrane strain.

3. Entryguides and intermediate guides can be utilized effectively to reduce the longitudinal

membrane strain (Figure 11.11). Proﬁles and positions of such guides can be designed moreeasily than

those of forming rolls. Setting up the guides and changing the ﬂowlines is relatively simple. At the same

time, they control the spatial lengths of the ﬂowlines. As aresult, the magnitude of longitudinal

membrane strain is reduced and the undesirable effects of transversal nonuniformity can be minimized

or eliminated.

Membrane Strain

Case(a):

Case(a)

Case(b)

Web

Flange Flange

Case(b):

Entry Guide

Metal Sheet

By many

roll-stands,

By small number

of roll stands,

:Longitudinal

(+)

( − )

FIGURE 11.9 Effect of number of roll stands on the magnitude of “ 1

: ”

(+)

(–)

FIGURE 11.10 Effects of roll proﬁle and roll position on transversal distribution of “ 1

: ”

Behavior of Metal Strip During Roll Forming 11-9

11.3.2 Edge Wave

The edge wave,caused by asortofelastic or

elastoplastic buckling,isafrequent defect. It

takes placenot only in ﬁnished products, but also

in semiformed metal sheets moving from one

pass to the next. It reduces product qualityand,

in some cases, makes it difﬁcult to maintain a

suitable roll forming operation.

In the manufactureofERW pipes and tubes,

thecompl etepreve ntionofedgewaveis

important.Once edgewavetakes place, for

instance, at the breakdown pass or ﬁn pass

forming stage, complete and reliable welding of

the edges becomes verydifﬁcult or impossible

(Figure11.12). Therefore,toobtain agood weld,

edge waveshould be prevented.

Edge wavesare also frequently observedduring

roll forming of wide ﬂoor decks, sidings, and roof

decks formed from thin metal (Figure11.13).

The edge wave is caused by excessively large

longitudinalmem branestrain, whichoccurs

locally at the edge portion of the coil. When, as

aresult of small thickness or the geometryofthe

cross-section, large edge elongation is unavoid-

able and the longitudinal stiffness of the edge

portion of the partially or fully formed product is

small, edge wave tends to occur.

Edge wave is caused by elastic or elastoplastic buckling.The mechanism that creates the buckling is

very simple. In general, at the initial stage of forming,the longitudinal elongation inevitably takesplaceat

the edge portion of the strip,because the edge portion has to moveboth in the vertical and transversal

directions. Additional elongation takesplacewhen the edge portion enters the roll gap.However,the

elongated edge portion must shrink again when it exits the roll gap,because the longitudinal length of

each portion of the semiformed strip or product should be equal to keep the product straight. When the

local edge elongation becomes excessive, it becomes very difﬁcult or impossible for the elongated edge

Forming Roll

(+)

( − )

Forming Roll

EntryGuide Roll

Guide Rolls

FIGURE 11.11 Modiﬁcation of ﬂow lines by guide rolls

for reducing “ 1

: ”

Stage II

Shrink

Stage I

EEC

Edge Buckling

(Edge Wave)

FIGURE 11.12 Schematic illustration of edge buckling (edge wave) taking place during roll forming of ERWpipes.

Roll Forming Handbook11-10

portion to shrink smoothly.Insome cases, at the

exit of the roll gap,the compressive stress acting

upon the edge portion exceeds the critical value

and, as aresult, buckling (edge wave)occurs.

To preventedgewav e, thelongitudinal

elongation of the edge portion should be reduced

below the critical value by using asufﬁcient

number of rolls, roll proﬁles,roll positions, guides

andacorrect pass line. Effective simulation

techniques are available to ﬁnd the required

number of rolls, their proﬁles and positions. One

helpful technique will be explained later.

Some other countermeasures can be taken to

prevent edge waves, as described below:

1. The ﬁrst edge wave reducing/preventing method is called the “local heating method” (Figure 11.14).

The edge waves are caused by localized edge elongation, which is plastic deformation. Therefore, to

prevent edge waves, the contribution of the plastic deformation should be reduced by utilizing the effect

of thermal deformation induced by local heating of the strip.

Forinstance,ifthe edge portion is heated between roll stands, then the local thermal longitudinal

elongation (expansion) can be sufﬁciently close to the plastic edge elongation caused by the longitudinal

force. Owing to the thermal elongation, the plastic elongation of the edge por tion becomes relatively

small. Consequently,the magnitude of the plastic longitudinal shrinkage of the edge portion occurred at

the exit of the rollgap is reduced. Therefore,with the drop of temperature,the shrinkage of the edge

portion occurs smoothly and edge waves can be prevented.

2. The second one is called the “preforming method.”Although the longitudinal edge elongation can

be reduced by using suitable rolls, it is almost impossible to prevent nonuniform elongation and

shrinkage completely.

In this method, metal coils are preformed by either a“roller preformer” or aspecial, frequently called,

“shape-correcting”leveler (Figure11.15). The roller preformer or leveler has several crowned rolls or roll

EntryGuide

# n − roll

#(n − 1)− roll

#2− roll

#1− roll

Shrink

Elongate

Edge Buckling

(Edge Wave)

FIGURE 11.13 Atypical edge wavewhich occurs in

products made from coils with large width and small

thickness.

(a) Center Heating

Reducing of Strain

Balancing of Strain

Plastic Strain

(b) Edge Heating

Heater

Thermal

Strain

Thermal

Strain

FIGURE 11.14 “Local heating method” for preventing edge wave.

Behavior of Metal Strip During Roll Forming 11-11