is 0.0854 % for EEF_V1 and 0.0693 % for EEF_V2, as
resulting in 18.8 % decrease. The average values of the
peaks for shrinkage are -0.1108 % for EEF_V1 and
-0.0962 % for EEF_V2, resulting in 13.1 % decrease.
Moreover, all the peaks of longitudinal strains for elongation
and shrinkage are within the elastic limits of
DP600 material, as:
0:175% > 8"peak
long > 0:175% ð10Þ
The major peak of strains has been decreased by 13.9 %
from the EEF_V1 to the EEF_V2 solution (Fig. 14) since it
meets the constraint of the quality characteristics:
"max
1
¼ 0:194 < FLC0 ¼ 0:223 ð11Þ
The peak of the strains in thickness direction has been
reduced by 8.4 % as a result of the EEF_V2 solution
(Fig. 15):
"min
3
¼ 0:163 > UEPDP600 ¼ 0:179 ð12Þ
The cross-sectional dimensional error on the flange has
been decreased by 45.3 % from the EEF_V1 to EEF_V2
solution (Fig. 16). The dimensional error of the EEF_V2
is within the typical tolerance of the cold roll forming
process, as:
Dflange
error
¼ 0:239 < 0:8 ¼ Tsection ð13Þ
7 Benchmarking study
A paradigm of the extensive usage of a U-channel
profile is the mounting brackets of solar panels [32,
33], as shown in detailed views in Fig. 17. Such mounting
brackets as well as the pole require about 10 m of
the U-channel profile each.
For the application of the case study, benchmarking data
for the cold roll forming process of a U-channel profile
should be set. Such benchmarking data will be used for their
comparison with robust optimization results, as they indicate
the level of energy efficiency enhancement of an optimum
solution. Benchmarking data, as shown in Table 10,
are the most common data used by cold roll forming machine
builders and engineers from literature and market [26,
27, 34–37].
The control factors of the benchmark study are listed
in Table 10, as the bending angle concept, roller diameter,
line velocity, roll stations inter-distance, and roll
gap (clearance). The noise factors are listed in Table 4,