quality constraints can be set. Moreover, the dimensional
stability of a final produced profile, with springback compensation,
is another critical issue for the quality of a roll
forming product.
Quality constraints are defined as the functions of redundant
deformations during processing. These constraints are
checked through FEM responses within the optimization
methodology. The FEM of the cold roll forming process is
built based on the determined optimum set of the energy
efficiency indicator levels, which serve as the basis for the
modeling approach by Paralikas et al. [31]. The quality constraints
(Fig. 6) are (1) longitudinal strains distribution on
cross section (elongation and shrinkage peaks) and unevenness
of distribution of strains between the flange and the web
of the profile for the checking of longitudinal bow and twist,
(2) average values of longitudinal strains peaks (elongation
and shrinkage) at edge of profile for checking longitudinal
bow and twist, (3) longitudinal strains peaks, not surpassing
the yield point of the profile’s material at edge for checking
longitudinal bow and edge waviness, (4) major strain on
FLD for checking edge cracking, (5) strains in thickness
direction for checking edge cracking, and (6) dimensional
error on the final produced profile with springback.
The longitudinal strains distribution on cross section
(flange and web) can affect the bow and twist of roll
formed profiles. Any uneven distribution between the
flange and the web can cause undesired defects, such
as bow and twist [27]. Thus, the difference in the mean
values of a distribution of longitudinal strains, between
the flange and the web (at elongation and shrinkage
peaks), should be minimized as:
Δ"
ðwebflangeÞ
long
! min ð3Þ
Moreover, another critical quality constraint to prevent bow
and twist is the minimization of the average value of the maximum
longitudinal strains (elongation and shrinkage) at the edge
of the profile. This quality constraint can be described as:
"peaks
long
! min ð4Þ
Longitudinal strain peaks (elongation and compression) at
the edge of the roll formed profile are responsible for main
defects, such as edge wave (buckling) and warping (bow)
[27]. If elastic longitudinal strains at the edge of the profile
surpass the yield point of a material, then plastic deformations
are accumulated at the edge and may result in waviness and
bow defects. There is an elastic strain range (Δσstrain) (Fig. 7)
that elastic longitudinal strains should not exceed. Thus, all
longitudinal strain peaks (elongation and shrinkage) should
not surpass the yield point of the material and the compressive
strength in order to avoid edge buckling:
"TYP > 8"peak
long > "CYP ð5Þ
The mapping of major and minor strains in the roll
formed profile on material FLC can predict any warping
(bow) and twisting defects [27]. The failure modes assigned
to the FLC are shown in Fig. 8, and the forming window
appears under the critical forming point FLC0. Different
areas, around FLC, provide information about the deformation
state of the produced profile and their effects on the
product and the defects produced. Such defects can be
fracture, tearing, shearing, and wrinkling that can generate