The document discusses tube bending quality and presents a new index to evaluate cross-sectional quality. It introduces copper tube properties, applications, and technical standards. It then describes the tube free bending process and existing quality indicators. Preliminary bending simulations using standard tools produced quality results. Modified tools in new configurations in the FEM model reduced thinning and improved quality indicators compared to standard configurations.

1. Nono Convegno
9 Torino, 7-9 Settembre 2009
Tube Free Bending: a new index for the
control of the cross section quality
Alessia Mentella Matteo Strano Roberto Gemignani
alessia.mentella@unicas.it matteo.strano@polimi.it roberto.gemignani@blm.it
UNIVERSITY of CASSINO POLITECNICO di MILANO Stefano Farina
Dept. of INDUSTRIAL ENGINEERING Dept. of stefano.farina@blm.it
Cassino (FR), ITALY MECHANICAL ENGINEERING
Milano (MI), ITALY BLM GROUP
Cantù (CO), ITALY

2. 9
Nono Convegno
Torino, 7-9 Settembre 2009
OUTLINE
Introduction
• Chemical, physical and technological properties of copper
• Most typical applications of copper tubes
• Technical Standards
Rotary-draw bending
• Free bending: configuration of the tools
• Free bending: process limits and quality indicators
Design of Computer Experiment
• Preliminary results with standard tools
• Description of the FEM model and its experimental validation
• Results with modified tools and comparison
Modelling and improving the quality of the section
• Correlation analysis among the quality indicators and development
of a unique estimator
• Conclusions
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Nono Convegno
Torino, 7-9 Settembre 2009
INTRODUCTION
Chemical and Physical Properties
0.014%≤ P≤0.040% Cu-DHP Cu+Ag: min 99.90%
Valore
Parametro Chimico-fisico Caratteristica Applicazione
parametro
Elevata resistenza al fuoco Impianti idro-termo-
Temperatura di Fusione 1083°C
e alle alte temperature (A1) sanitari
Coefficiente di dilatazione 1,65*10-6 Ottimo per accoppiamenti Pareti e pavimenti
termica a 20°C m/(m*K) multimateriale radianti
Pannelli Radianti;
Conduttività Termica a 20°C 391 W/(m*K) Ottimo conduttore termico
Scamb. di calore
Resistività Elettrica a 20°C 0.0173 Macchine statiche e
Ottimo conduttore elettrico
(ricotto) Ohm mm2/m dinamiche
Potenziale E° Elevata resistenza alla Impianti marini
0.337 V
(Cu2++2e- Cu) corrosione offshore
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Nono Convegno
Torino, 7-9 Settembre 2009
INTRODUCTION
Copper tubes applications
Metal or Thermal conductivity
%
Alloy Wm-¹ C-¹
Ag 420 115
Cu 364 100
Au 299 82
Al 82 58
Bronze 58 ÷ 65 17
Brass 70 ÷ 116 19 ÷ 32
Zn 110 30
Ni 58 ÷ 65 19
Sn 64 18
Steel 29 ÷ 105 8 ÷ 29
Ti 16 5
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Torino, 7-9 Settembre 2009
INTRODUCTION
Copper tubes applications
GAS ACQUA POTABILE
Impianto idrosanitario
San Raffaele, Milano
CONDIZIONAMENTO/REFRIGERAZIONE
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INTRODUCTION
Technical Standards
• UNI EN 12449, 2001. Seamless, round tubes for general purposes.
• UNI EN 1057, 2006. Seamless, round copper tubes for water and gas in sanitary
and heating applications.
• UNI EN 12735-1/2, 2008. Seamless, round copper tubes for air conditioning and
refrigeration.
• UNI EN 13348, 2008. Seamless, round copper tubes for medical gases or vacuum.
• UNI EN 12415. Seamless, round copper tubes for heat exchangers.
• UNI EN 723, 1998. Combustion method for determination of carbon on the inner
surface of copper tubes or fittings.
• ISO 8491, 2005. Metallic materials – Tube bend test.
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7. 9
Nono Convegno
Torino, 7-9 Settembre 2009
ROTARY-DRAW BENDING
Free Bending: configuration of the tools
OD t OD 2
BF = =
RM OD t ⋅ RM
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8. 9
Nono Convegno
Torino, 7-9 Settembre 2009
ROTARY-DRAW BENDING
Free bending: process limits
1. Thinning at the extradoss fo the bend
2. Flattening at the extradoss of the bend
3. Collapse of the extradoss of the bend
2 3
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9. 9
Nono Convegno
Torino, 7-9 Settembre 2009
ROTARY-DRAW BENDING
Free bending: quality indicators
ODZ − ODX #Flex: number of curvature
O% = ⋅100 changes in each cross section.
OD
A0 − A
A% = ⋅100
A0
MD0 − HD
HD% = ⋅100 SEC-45° - α=π/2
MD0
4A
HD =
P
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Nono Convegno
Torino, 7-9 Settembre 2009
DESIGN OF COMPUTER EXPERIMENTS
Preliminay results with standard tools
Difficulty
Geometrical input data and ratios Results
factor
OD t RM OD/t RM/OD BF O% HD% A% #Flex
8 1 22 8.0 2.8 2.9 2.5 19.2 2.4 1
8 1 14 8.0 1.8 4.6 7.0 22.2 7.8 0.5
6 0.75 10 8.0 1.7 4.8 7.6 22.7 8.7 0.5
E
8 1 12 8.0 1.5 5.3 9.5 24.4 11.3 1
A
9.52 0.67 25 14.2 2.6 5.4 4.9 20.2 4.0 1
S
8 0.5 22 16.0 2.8 5.8 4.7 20.1 3.8 0.5
Y
7.2 0.7 12.5 10.3 1.7 5.9 7.8 22.1 7.7 1
9.52 0.8 15 11.9 1.6 7.6 11.4 24.2 10.8 1
8 0.5 14 16.0 1.8 9.1 11.5 23.4 9.0 1
D 12 0.75 18 16.0 1.5 10.7
I 9.52 0.67 12.5 14.2 1.3 10.8
F 15 1 19.5 15.0 1.3 11.5
F 16 0.9 24 17.8 1.5 11.9
I 18 1 27 18.0 1.5 12.0
C 12.7 0.7 18 18.1 1.4 12.8
U 18 1 23.4 18.0 1.3 13.8 OD t OD 2
L 22 0.9 35 24.4 1.6 15.4 BF = =
T 18 0.7 27 25.7 1.5 17.1 RM OD t ⋅ RM
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11. 9
Nono Convegno
Torino, 7-9 Settembre 2009
DESIGN OF COMPUTER EXPERIMENTS
Modified pressure and bending die
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DESIGN OF COMPUTER EXPERIMENTS
FEM model description
4-nodes shell elements
Cu-DHP R220
with 5 integration points σ(εp)=K(ε0+ εp)n Material
(annealed)
throughout the thickness Young’s modulus E [MPa] 110000
Elongation A% 0.6
Tensile strenght Rm [MPa] 220
Elastic strain ε0 0.0003027
Initial Yield stress σ0 [MPa] 33.310
Ultimate tensile stress σf [MPa] 336
Hardening exponent n 0.315
Strenght coefficient K [MPa] 426.07
Poisson’s ratio ν 0.343
Density ρ 7.85E-09
CONTACT Contact Interface Static f. c. Dynamic f. c.
• Surface to surface Tube/Pressure
0.57 0.35
• Coulomb friction model and bend dies
Tube/Wiper die 0.30 0.15
Tube/Clamp die 1.99 1.99
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13. 9
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Torino, 7-9 Settembre 2009
DESIGN OF COMPUTER EXPERIMENTS
Experimental validation of the FEM model
OD t RM
BF
(mm) (mm) (mm)
18 1 27 12
0° 90°
45°
SECTION O%SIM O%EXP
0° 10% 9.4%
45° 18.3% 22.2%
90° 4.6% 5.3%
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14. 9
Nono Convegno
Torino, 7-9 Settembre 2009
DESIGN OF COMPUTER EXPERIMENTS
Experimental validation of the FEM model
176.4 mm2
90°
OD t RM
(mm) (mm) (mm) 0°
45°
16 0.9 24
123.4 mm2
SECTION O%SIM O%EXP
0° 10.9% 9.4%
45° 18.6% 17.5%
90° 4.6% 5.6%
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15. 9
Nono Convegno
Torino, 7-9 Settembre 2009
DESIGN OF COMPUTER EXPERIMENTS
Results with modified pressure and bending dies
Configuration 0 Configuration 1 Configuration 2
RE=RM RE=RM+0.5 RE=RM+0.5
Standard pressure-die Retracted pressure-die Milled pressure-die
BF O% HD% A% #Flex O% A% HD% #Flex O% A% HD% #Flex
7.6 11.4 24.2 10.8 1 11.4 9.26 23.6 0.5 11.6 11.15 24.3 1.0
9.1 11.5 23.4 9.0 1 12.1 7.23 23.1 1.25 11.2 9.02 23.3 1.0
10.7 18.3 27.2 14.6 1.75 17.3 11.7 25.8 1.25 17.4 13.9 26.7 1.5
10.8 19.6 28.3 16.4 2.5 21.3 15.2 28.1 2 18.6 15.6 27.7 2.25
11.5 20.9 28.9 17.2 2.5 19.8 14.7 27.7 2 20.1 16.5 28.4 2.25
11.9 19.5 27.6 14.9 2.25 18.7 12.2 26.3 1.75 18.6 14.3 27.1 2
12.0 19.7 27.7 15.1 2.75 18.3 12.1 26.2 2.25 18.1 14.2 27.0 2.25
12.8 21.8 29.0 16.7 2.25 22.6 14.2 27.8 1.25 20.4 15.7 28.1 1.75
13.8 25 31.1 19.7 2.25 27.7 19.3 31.2 2.75 23.9 18.8 30.4 2.25
15.4 25.3 30.4 18.0 2.5 22.6 15.0 28.5 2 23.7 17.0 29.5 2.5
17.1 29.5 32.9 21.2 3 severe wrinkling 27.7 19.8 31.8 2.75
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16. 9
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Torino, 7-9 Settembre 2009
MODELLING AND IMPROVING THE QUALITY
OF THE SECTION
Correlation analysis among the quality indicators and
development of a unique estimator
OD/t has a very limited
OD t OD 2 impact on the quality of OD t OD 2
BF = = the cross section, and BFnew = =
RM OD RM ⋅ t virtually no effect in the (RM OD ) RM 1.5 ⋅ t 0.5
3
“easy” part of the plan.
With respect to the newly proposed factor BFnew, a new index Qcs, calculated as
a linear combination of the four considered parameters, has been developed:
Qcs = β1 ⋅ O % + β 2 ⋅ A% + β 3 ⋅ HD % + β 4 ⋅# Flex
βi ≥ 0 ∀i = 1...4
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17. 9
Nono Convegno
Torino, 7-9 Settembre 2009
MODELLING AND IMPROVING THE QUALITY
OF THE SECTION
Correlation analysis among the quality indicators and
development of a unique estimator
3.5 30
3.0 RM/OD
25
OD/t
2.5
20
Rm/OD
2.0
OD/t
15
1.5
10
1.0
0.5 5
0.0 0
0 5 10 15 20 25
Qcs
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18. 9
Nono Convegno
Torino, 7-9 Settembre 2009
MODELLING AND IMPROVING THE QUALITY
OF THE SECTION
Correlation analysis among the quality indicators and
development of a unique estimator
Qcs = β1 ⋅ O % + β 2 ⋅ A% + β 3 ⋅ HD % + β 4 ⋅# Flex
The best fit linear regression model (R2=0.972) between Qcs and BFnew is obtained when
β1 = 0.218; β 2 = 1.286; β 3 = 0; β 4 = 0.776
r O% A% HD% #Flex QCS
O% 1 Qcs = A%+ # Flex
A% 0.976 1.000
(β1 = 0; β 2 = 1; β3 = 0; β 4 = 1)
HD% 0.991 0.995 1
#Flex 0.924 0.871 0.900 1
QCS 0.9833 0.9981 0.997 0.900 1
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19. 9
Nono Convegno
Torino, 7-9 Settembre 2009
MODELLING AND IMPROVING THE QUALITY
OF THE SECTION
Correlation analysis among the quality indicators and
development of a unique estimator
35
O%
2
R = 0.959
18
30 A%
Flex
16 R2 = 0.858
Difficulty Factors
Qcs 2
R = 0.949 14 BFnew
Quality Indicators
25 HD%
12 BF
2
R = 0.970
20 10
2
R = 0.967
conventional 8
15 tooling 6
modified tooling R2 = 0.970
4
10
2
5 0
2
R = 0.781 0 5 10 15 20 25
0 QCS
0 2 BF new 4
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20. 9
Nono Convegno
Torino, 7-9 Settembre 2009
MODELLING AND IMPROVING THE QUALITY
OF THE SECTION
Conclusions
• NO INTERNAL MANDREL for copper tubes with round cross section for hydro-thermo-sanitary
applications.
strong tendency of the tube to collapse ovalization and reduction of area
aesthetical problems and head losses
• A new index can be chosen, QCS=A%+#Flex, which synthetically and effectively represents
all quality parameters of the cross section.
• A new bending difficulty factor has been introduced, Bfnew , which shows a good correlation
with the traditional quality parameters and an excellent correlation to QCS.
• In order to enhance the quality of the cross section of the bent tube, it is necessary to re-
design the tooling configuration, for difficult to bend tubes (BFnew>2); for easy to bend tubes
(BFnew<2), the standard tooling must be preferred.
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21. Nono Convegno
9 Torino, 7-9 Settembre 2009
Tube Free Bending: a new index for the
control of the cross section quality
Alessia Mentella Matteo Strano Roberto Gemignani
alessia.mentella@unicas.it matteo.strano@polimi.it roberto.gemignani@blm.it
Stefano Farina
stefano.farina@blm.it
THANK YOU FOR YOUR ATTENTION!