Roll Forming Handbook / Edited by George T. Halmos

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4.11.2 Correlation between Design

for Loading and Curving of Roll

Formed Products

During curving, the stresses must exceed the yield

stress to create permanent deformation. When

curving is made with rolls, the area of load is

concentrated in aline (Figure4.57). This creates

very highconcentrated loads, but curving must

be achievedwithout local buckling,web cripp-

ling,twisting,orother imperfections. Curving

products with holes, notches, and dimples is even

moredifﬁcult and complex.

To create apermanent curvature, the product

must be stressed beyond yield point, into the

plastic range. The inside partofthe section, more

or less between the neutral axis and the center of

curving radius, will be permanently shortened

bend

(a) (b) (c)

(d) (e) (f)

FIGURE 4.53 Sequence of wiping 908 bends across the

partwith blocks (a, b, and c) or rolls (e, f, and g).

(a) (b) (c) (d) (e)

clamp

wipe up

FIGURE 4.52 Wing bending two 908 bend across the part.

FIGURE 4.54 Complex corner bends for shelving.

Roll Forming Handbook4 -26

(compressed) and the outside partofthe section

will be permanently elongated (stretched). As

the material content does not change, the com-

pressed partofthe section will become thicker,

and the stretched, outside par twill become

thinner(Figure4.58).The refore,the cross-

section deforms and the neutral axis moves

closer to the inside during curving as aresult of

stresses developed in the thicker and thinner

sections. This effect is described in alater partof

this section. The friction between curving dies

and products, the stiffness of product, and the

behavior of material will also contribute to the

change in the position of neutral axis.

In the case of sections asymmetrical to the

curvingplane, twist will also de velop

(Figure4.59). The stretched, outside partofthe

section usually presents fewer problems. Stresses

seldom exceed the ultimate tensile stress because

the partispushed and pressed throughthe

curving die, unless the punched holes and notches

signiﬁcantly reducethe cross-section of the out-

side section. The limiting factors to curve product

to asmaller radius will usually be the buckling of

the inside part(Figure4.57band Figure4.60), the

crippling of the web,the twisting of the section, or

other product deformation.

The roll geometry(diameter,position, and

distanceofrolls) will also haveaneffect on

buckling.This effect will be discussed in alater

partofthis section.

Anotherrestriction on curvingisweb crippling.

An analogue with theIbeamexplainsweb

crippling. Thestrengthofasection(assuming the

same cross-section area)will be increased by

increasing thedistanceofthe material from the

neutralaxis(Figure 4.61). Thedistancecannotbe

increasedtoinﬁnity sinceoveracertain limitthe

webwillbetoo thin andwillcrippleunderthe load.

Figure4.62 shows some examples of web

crippling and section deformation under con-

centrated forces. Inclined forces created by a

deformed web mayinduce additional ﬂange

crippling.Thiseffectmakes any attemptto

calculate stresses even morecomplex.

The effect of other factors on curving, such as

stiffeners, type of corrugation, bending radius of

thesection,holes,cutouts,closed sections,

section asymmetricity, physical properties of

the material, lubrication, and bending equip-

ment will be mentioned later in this section.

FIGURE 4.55 Curving is in one plane.

FIGURE 4.56 Spiraling.

(b)

(a)

FIGURE 4.57 Curving with rolls create concentrated

load at the contact line.

Secondary Operations in the Roll Forming Line 4 -27

4.11.3 Minimum Curving Radius

The minimum radius of acurvedproduct is

limited by the physical characteristics of the

material (yield an dult imate strength,

elongation, work hardening),the compression

stiffness of the section (resistance against buck-

ling while pushed into the curving tools by the

roll former) the shape, the height to thickness

ratio,and sensitivity to surface marks. Conse-

quently,the smallest curving radius usually can

be established only by tests, after the curving

tooling is completed.

When arectangular,ﬂat bariscurved

edgewise (Figure4.63), then theoretically the

neutral axis remains in the middle of the sec-

tion; the compression stresses at the inside

ﬁber are equal to the tension stresses at the

outside ﬁber.Inreality, the compression of

the inner ﬁber thickens the material, while the

outside ﬁber is getting thinner.Therefore, the

true stress at the inside will be smaller and at

the outside larger.The larger outside stresses

will elongate the material more and makeit

even thinner.Atthe same time, the thicker

inside ﬁber thetruestresses canactually

decrease,thusstoppingfurther change in

thickness.

As an effect of these changes, created by the

true stresses, the neutral axis is gradually moving

towards the inside. This hypothetical phenom-

enon is similar to the moving of the neutral axis

in the direction of the bending radius during

brake and roll forming.

actual

theoretical

FIGURE 4.58 The inside of the curved partisthicker, and

the outside is thinner.

R R

symmetrical

asymmetrical

FIGURE 4.59 Section asymmetrical to the curving plane will develop atwist.

FIGURE 4.60 Buckling of the inside of the curvedpart.

weakest strongest web buckles

FIGURE 4.61 Webbuckling of Ibeam.

Roll Forming Handbook4 -28

The theoretical strain of the outside ﬁber

during curving (Figure 4.64)is

£ p 2 D

£ p ¼ p ð D

2 D

¼ h

Total elongation ¼ p h

Percentage elongation e ¼

p h

£ 100

£ 100%

ð 4 : 1 Þ

In other words, the theoretical elongation of the

outside ﬁber equals to the ratio of the section

height divided by the radius of neutral axis. Because under actual conditions, the neutral axis is moving

closer to the center of the curving radius, the actual elongation (strain) on the outer ﬁber is larger than the

theoretically calculated value. On the other hand, the compression from the roll forming mill, pushing

the section through the resistance of the curving tool, marginally increases the compression stress in the

section. This effect is not very signiﬁcant because the stress created by the pushing is considerably below

the yield stress.

As an example, take a2-in. (50-mm) deep section, made out of 0.030-in. (0.75-mm) thick material,

curved into 11-in. (280-mm) diameter.This results in an approximately 10-in. (25-mm) neutral axis

diameter,creating a(2(10) £ 100 ¼ 20%) theoretical elongation in the outer ﬁber and 40% compression in

the inner ﬁber.Toachieve this, the outside ﬁber must be exposed to permanent elongation of over 20%,

without necking (see stress–strain diagram in Figure6.4). At the same time, the inside of the thin section

must be compressed by 20% without wrinkling (buckling). Considering the increased strain on the outside

ﬁber caused by the movement of the neutral axis towards the center of the curving radius, to curve this deep

section to the speciﬁed radius will be extremely difﬁcult, if not impossible.

before

after

FIGURE 4.62 Typical web buckling (crippling) of different cross-section.

theoretical and

actual

stress distribution

theoretical actual

position of neutral axis

FIGURE 4.63 Curving rectangular bar edgewise.

FIGURE4.64 Theoretical approach of calculat ing

stresses in atubular part.

Secondary Operations in the Roll Forming Line 4 -29

4.11.4 Curving Precut Parts

Separately

Precut sheets, plates, hot-rolled,orrollformed

sections must be curvedwith driven curving

units. Typical arrangements, wherematerial is

moved by the curving rolls, are the symmetric

or asymmetric pyramidorpinch roll type

three-roll curving (Figure4.65), four-roll units

(Figure4.66), or two-roll curving equipment

with elastic roll (Figure 4.67).

Curving precut parts is labor intensive,and

both the front and the tail end of the cur ved

product remains straight (Figure4.68). The length

of the straight section depends on the geometry

(rolldistanceand roll diameter) of the curving

unit. Curving precutparts with curving shoes is

not practical.

4.11.5 Curving in Roll Forming

Mill with Rolls

In thecase of rollforming,the productis

continuously pushed through the curving tooling

by the roll forming mill. Figure4.69 shows two

possible methods of curving without additional

curving stands.These methods canbeused

for products with relatively large curving radii.

Curving,however, is more frequently carried

out with aseparate three-roll unit attached to the

end of the mill. In case of continuous roll

forming,the cur ving rolls are usually not driven.

To avoid,oratleast minimize, the chances of

productbucklingbetween thelast pass of

forming rolls and the curving tools, the two

units should be located as close to each other as

possible. As an alternative solution, the product

could be supported all around to avoid buckling.

The process of removing the last piece(end of

coil) from anondriven curving units must be

considered at the design stage.

FIGURE 4.66 Four-rollcurving unit.

FIGURE 4.67 Curving with elastic (bottom) roll.

asymmetricalsymmetrical pinch roll type

FIGURE 4.65 Three-roll curving units.

FIGURE 4.68 The front and tail ends of precut parts,

curved in athree-roll curving unit, remain straight.

Roll Forming Handbook4 -30

The application of standard,three-roll, pyramid-

roll curving mechanisms wit hcenter rolladjust-

ment for radius should be avoided. Figure4.70a

shows the incorrect, two-way bending created by

this type of unit. The preferable method is to adjust

curvature with the third roll only (Figure4.70b).

As mentioned before, owing to compression and

curving die pressure, buckling is the most frequent

limiting factor when light-gaugeproductsare

curved. Buckling is inﬂuenced by manyfactors.

Improvingthe curving conditions will allow

curving products with considerably smaller radii.

The effect of some of the inﬂuencing factors

can be explained by reviewing curving of simple

corrugated panels. The term “minimum curving

radius”refers to the smallest radius to which aroll

formed product can be curvedwithout developing

undesirable deformation which can be harmful to

the strength or degrading to appearance from a

speciﬁc material with given curving equipment.

4.11.5.1 Thickness

The thinner the material, the larger the minimum

curving radius will be because it is moredifﬁcult to

compress thin material than thick material.

In aclose-centered, three-roll curving unit, the

variation in thickness, even within one coil, will

change curving radius (increase in thickness will

reduce the curving radius as shown in Figure 4.71).

4.11.5.2 Height

The higher the section is, the larger the minimum

curving radius.The relationbetween section

height ð H Þ ; curving radius ð R Þ ; and material thick-

ness ð t Þ is shown in Figure4.72 [417].

4.11.5.3 Product Shape

The larger the ﬂat, compressed areas, the more

prone willbethe section for buckling.

4.11.5.4 Bending Radius

Products with larger bending radii, especially in

the compressed partofthe section, can be curved

to smaller radius. Forexample, if a1/2-in. deep sinus corrugated section (shown in Figure4.73)can be

curved to,say,a10-in. (200-mm) radius, then a1/2-in. deep section with sharp corners formed from the

same material maybecurved only to 200 in. (5000 mm) without buckling.

It follows that asection with curvedinside and straight outside surfacescan be curvedclose to the same

radius as the fully sinus corrugated panel (Figure4.74).

In other words, sections with large inside bend radii (inside refers to the partofthe section closer to

the center of curving radius), withnoorminimum ﬂat inside surface,can be curvedtoasmall radius

(Figure4.75).

(a)

(b)

FIGURE 4.69 Continuous cur ving in the roll forming

mill.

(a) incorrect

(b) correct

FIGURE 4.70 Incorrect (a) and correct (b) application

of athree-roll curving unit attached to arollformer.

FIGURE 4.71 Effect of material thickness change to

curving radius.

Secondary Operations in the Roll Forming Line 4 -31

4.11.5.5 Effective Stiffener Ribs

Because the buckling develops in the compressed

(inside) surfaces, stiffener ribs in these areas

canhelptoreducebuckling.Panelswith

longitudi nal stiffener ribs will haveabetter

chancetobecurvedtosmaller radii than panels

without these ribs.

4.11.5.6 Matching Curving Tool and

Proﬁle

Curving rollpressurecan also create or contrib-

ute to buckling.Therefore, it is importantthat

rolls, which exertgreat pressure, should conform

to the full surfaceofthe section, and not just

touch it at afew points (Figure4.76).

Occasionally,the bending radius of the roll

formed product is larger than the matching radius

on the male curving roll (see Figure 4.77a). This

mismatch can be the result of incorrect setup,

worn forming rolls, or using new or incorrectly

designed curving rolls. The reforming of the bend

lines by curving rolls with different radius will

result in distortedproducts. Toolarge aradius

on the female die can haveequally detrimental

effects (Figure4.77b).

4.11.5.7 Product Width(Coverage)

It is important that the roll formed proﬁle should

match the curving die exactly.Curving dies not

matching the roll formed proﬁle maycompletely

reform theproduct.The result will be a

straight productedge instead of acurvedone

(see Figure4.78).

If, on the other hand, the twoedges of the

ﬁnished panel are curvedtothe correct radius,

but the center is straight or has averylarge

radius,thenthisprobl em is mostprobably

caused by an excessive deﬂection of the curving

roll shafts (Figure4.79).

BUCKLING

GOOD

CURVING

log

FIGURE 4.72 Effect of height and thickness on curving.

min

=10

min

=200

FIGURE 4.73 It is more difﬁcult to curve products with

aﬂat inside surface than with aradiused one.

very large

min

small

min

smaller

min

FIGURE 4.74 Products with curved inside elements can be cur ved to smaller radius.

Rlarge

Rsmall

FIGURE 4.75 Asmall change in product design can help

reducing minimum curving radius.

Roll Forming Handbook4 -32

4.11.5.8 Center Distance of Curving

Rolls

Most products will haveless of achancetobuckle

if the curving rolls are closertoeach other

(Figure4.80). The bending moment required for

permanent deformation is the result of the force

on the curving rollmultiplied by the distancefrom

the next roll.The closer the rollsare (the smaller

the distanceis), the larger the forces are required

to generate this bending moment ð M

Þ M

¼ bP

: The smaller the distances “ a ”and “ b ”

are, the greater P

and P

forces are required.

The larger the curving forces are, the larger

the shaft diameters required. The diameter of the

curving rolls placed on larger shafts will be also

larger.The larger the rolls are, the fur ther they have

to be placed, which contradicts the ﬁrst require-

ment of putting the rolls as close as possible.

To ﬁnd the optimum solution, sometimes either the minimum curving radius has to be compromised

or curving shoes havetobeused. Curving shoes will be discussed in alater partofthis section.

One waytocompromise forces and diameters is to have an asymmetrical curving roll arrangement, as

shown on Figure4.81.For example, if a ¼ 6 : 4in. (160 mm) and b ¼ 0 : 4in. (10 mm) and the diameter of

“B” roll is 8in. (200 mm), then the forces on the “A”roll will be 1/16 of the forces on the “B” roll.This

will allow asmall shaft and asmall “A”roll,thus minimizing the “ a ”roll distance.

4.11.5.9 Effect of Inside Curving Roll Diameter

The curving rolldiameter has little effect on buckling because during curving the roll contacts the

product only in aline (Figure4.82). In special cases, however, when the product is literally wrapped

around the inside roll, the chances of buckling can be reduced (Figure4.83). However,ifthe productis

curved over 1808 ,then its removal can be tricky.

4.11.5.10 Elastic Outside Pressure Roll

Figure4.84ashows how the above-mentioned wrapped around effect can be achieved using arubber,

urethane, or other elastic outside roll.Using elastic rollcan minimize or eliminate buckling caused by

(a) Full line contact

with rolls

(b) Point contacts

with rolls

FIGURE 4.76 Full contact between the product and

curving rolls reduces buckling.

(b)(a)

curving

outer curving roll

reformed corners

product after

curving

product before

inner curving roll

product before

outer curving roll

reformed corners

curving

product after

curving

inner curving roll

FIGURE 4.77 Nonmatching curving tool radius and bend radius will distortthe product.

Secondary Operations in the Roll Forming Line 4 -33

holes and notches. To reduce the effect of the variation in shape caused by the ﬂuctuation in material

thickness and properties, it is advisable to use an additional steel radius controlling roll (Figure4.84b).

When elastic curving roll is installed in arollforming line, it should not be placed directly under

the top or over the bottom curving roll to avoid curving the productatﬁrst in the opposite direction

(Figure4.85).

4.11.5.11 Buckling and Bending of Flanges

Compressed ﬂanges havethe tendency to buckle. The simplest way to minimize the effect of buckling,

thus curving the product to asmaller radius, is to add astiffener bend or rib to the ﬂange as shown

on Figure4.86.Ifthe product design cannot be modiﬁed, then we recommend envelopingthe ﬂanges

(legs) in the curving rollsinanareaaslarge as possible (Figure4.87). At the same time, the entryofthe

leg (ﬂange) into the envelopingslot should be facilitated. Ironing out of the buckled ﬂange creates

considerable friction and tool wear.Therefore, the ﬂange rolls should be made from high-quality,

wear-resistant tool steel, and rollsshould be split at the anticipated wear line. Split rollscan be easily

remachined and reconstituted to the original shape.

In case of cur ving channels withlegs out, the outside ﬁber of the ﬂanges will haveconsiderable tension.

The tension tries to pull the legs either out or in as shown Figure4.88.After bending in or out, the outside

ﬁber of the leg willbecloser to the center of curving, thus having asmaller circumference, which results in a

smaller tension. The tendency of having the legs bent in (or out) increases when the curving radius is

reduced, when the leg is longer,when the material is thinner,and the further the ang le is from 908 .

Good ﬂanging rolls or sometimes additional rolls can minimize this bending out (or in) tendency.

4.11.5.12 Sections with Hidden Bend Lines

Bends made during rollforming provide the strength and stiffness of the section. Therefore,itisbest

to curve asection with the curving rolls in contact with the bend lines. To illustrate this statement, let us take

bottom roll

top roll

profile

(a) matching

bend lines will be

"reformed"

(b) not matching

FIGURE 4.78 One edge of the curved panel can be straight if the productproﬁle does not match the curving rolls.

Roll Forming Handbook4 -34

a“hat” section and a“C” section made from the

same material, same blank size, same thickness,

and formed to similar dimensions. Both sections

with havethe same inertia and section modules,

and will be curvedtothe same radius. The two

sections are shown on Figure 4.89.The center

curving roll of the Csection (Figure4.89b) cannot

touch the “hidden”corners; therefore, during

curving, it can distortthe shape. Therefore,ahat

section (Figure 4.89a) can be curvedtoasmaller

radius than asimilarCsection. Generally

speaking, it is difﬁcult to curveany section

wherethe curving tool is not touching the bend

lines. To overcome th is problem, frequently

curving shoes are applied instead of rolls (see

Section 4.11.9).

4.11.5.13 Fully Closed Sections

Fully closed, welded sections giveagood chance

to be curved, althoughbend lines cannot be

reached in the inside. Experienceshows that it is

relatively easy to curve some of the welded,

shallowsections, such as bicycle rims. In the case

of asmall curving radius or thin wall thickness,

deformation typical of tubes curvedinconven-

tional ways will prevail as shown in Figure4.90.

Mandrels, used in precut tube bending,are

sometimes applied to eliminate buckling.

FIGURE 4.79 To oweak curving rolls will bend, yielding

products with two curvededges and astraightcenter.

FIGURE 4.80 Shortdistance between curving rolls reduces the buckling tendency but increases the forces.

FIGURE 4.81 Asymmetrical roll arrangement may provide the smallest curving radius.

Secondary Operations in the Roll Forming Line 4 -35