A. Mentella Esaform 2008

11° ESAFORM Conference
on
MATERIAL FORMING
April 23-25, 2008
Lyon, France

A new method for feasibility study and
determination of the loading curves in the
rotary draw-bending process
A. Mentella1, M. Strano2, R. Gemignani3
1 alessia.mentella@unicas.it
2m.strano@unicas.it
3roberto.gemignani@blm.it

UNIVERSITÀ DEGLI STUDI DI CASSINO
Dipartimento di Ingegneria Industriale
BLM S.p.A. CASSINO (FR), ITALY

on
MATERIAL FORMING
April 23-25, 2008
Lyon, France

Table of contents
Conventional • Stretch bending – Rotary-draw bending – Compression bending
bending methods
Rotary-draw • Bending process – System configurations – Applications - Defects
bending
• Development of a computational methodology for the determination of the
Aim of the work optimal displacement curves of booster and pressure die
Algorithm • Presentation of the computational methodology
presentation
Finite element • Description of the FEM model
modeling
FE Model • Results of experimental test, using a stainless steel (AISI 304) tube
validation
Application of the • Results obtained in 3 different bending operations
method

Università degli Studi di Cassino
BLM S.p.A.

on
MATERIAL FORMING
April 23-25, 2008
Lyon, France

Conventional bending methods
Stretch bending Rotary-draw bending Compression bending

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MATERIAL FORMING
April 23-25, 2008
Lyon, France

Rotary-draw bending

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MATERIAL FORMING
April 23-25, 2008
Lyon, France

Rotary-draw bending
Basic tooling for simplest cases More complex tooling for hardest cases
Booster

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MATERIAL FORMING
April 23-25, 2008
Lyon, France

Rotary-draw bending
Main applications of cold formed metal tubes

Cold air intake
component

Bull bar
Aluminum 2024, 5052, 6061
Inconel 600, 625, 718
Stainless Steel 304, 316, 321
Cres 21-6-9
Exhaust Hastelloy-X
System Titanium

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MATERIAL FORMING
April 23-25, 2008
Lyon, France

Rotary-draw bending
Main applications of cold formed metal tubes
Fluid lines and conditioning Furnishing Design

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MATERIAL FORMING
April 23-25, 2008
Lyon, France

Rotary-draw bending
Main defects and failures in tubular parts

Hump at end
of the bend Wrinkling throughout bend,
Tool marks on extended into wiper die area Overbend at 90°
centerline of bend
Heavy wrinkles through bend
area and linear scratches in grip
area indicating, clamp slippage

Excessive collapse Excessive collapse
with or without wrinkling Mandrel balls hump after tubing is pulled
throughout the bend off mandrel balls

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on
MATERIAL FORMING
April 23-25, 2008
Lyon, France

Rotary-draw bending
Process parametres and Pressure die/booster configurations

A B C

A: pressure die only (A1 stationary, A2 follower, A3 boosted)

B: pressure die(boosted) with connected booster block

C: pressure die (C1 follower, C2 boosted) and indipendent axial booster

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MATERIAL FORMING
April 23-25, 2008
Lyon, France

The C configurations, with Very limited studies or procedures are
independent booster, provide available in the scientific literature
the greatest process flexibility providing criteria for selecting the axial
and performance. assist of the rotary draw bending process

A constant axial load is
Aim of the generally applied to control
the independent booster
work
A displacement control is
generally used when the
pressure die is boosted
Development a simple computational methodology,
that enables to rapidly obtain feasible, close to
The proposed method is based
optimal velocity curves for the most critical cases, on displacement control of
when configuration c2 must be adopted. both booster and pressure die.

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MATERIAL FORMING
April 23-25, 2008
Lyon, France

Algorithm presentation
INPUT VALUES AND ASSUMPTIONS

vM = ω ⋅ RM (tangential velocity of the bend die = axial velocity of the tube at the section
immediately before the bending region, if no axial assist is provided )
vS = vM ⋅ γ S (tangential velocity of the pressure die)
strictly correlated to vM
v B = vM ⋅ γ B (tangential velocity of the booster)

γ S γB Factors used for tuning a proportional
law between vM and the tools velocity

ε1 + ε 2 + ε 3 = 0 ε1
 ⇒ − = %th ⇒ ε1 = 2th% (axial strain, assuming volume constancy)
 ε 2 = %th = ε 3 2

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INPUT VALUES AND ASSUMPTIONS
The maximum principal true strain at the tube extrados (axial strain ε1), if
assuming isotropic material behaviour and no shift of the neutral axis, can be
roughly calculated as:
  OD− t  
 α ⋅  RM +  − d0 
ε1 = ln 1 = ln 
l 2   = ln1+ OD− t − ∆
 
l0  α ⋅ RM   2⋅ RM 
 
 
where :
• α is the bend angle;
• Δ is the normalized amount of the reduction in lenght of external ∆ = d 0
fiber, due to the axial assist of the pressure die and the booster. α ⋅ RM

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OD − t ε1 OD − t 2th %
∆ = 1+ − e = 1+ −e
2 ⋅ RM 2 ⋅ RM
The total axial stroke d of the tube at the extrados, immediately before the bending
region, can be written as:
The term a⋅RM is mainly due to the bend die and the term
d = γ ⋅ α ⋅ RM = α ⋅ RM + d 0
d0 is mainly due to the assist tools.

A correction factor can now be calculated as:
α ⋅ RM + d 0 d0 OD − t
γ= = 1+ = 1+ ∆ = 2 + − exp(2th%)
α ⋅ RM α ⋅ RM 2 ⋅ RM

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The factor γ can be interpreted as the amount of extra axial feed which must be
provided by the assist tools, if the target maximum thinning thmax must be reached
and, therefore, can be used to find the values of γS and γB.
The axial assist effect should be distributed between the booster and the pressure
die.

γS >γB
Because the pressure die acts mostly on the extrados, while the
booster acts on the whole tube section.
CONSTRAINS

(γ S + γ B ) ≈ 1.1⋅ γ Otherwise, not all the displacement of the booster
and of the pressure die could be transformed into
displacement of the tube at the section immediately
2 before the bending region.

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on
MATERIAL FORMING
April 23-25, 2008
Lyon, France

Finite Element Modeling
σ (ε p ) = K (ε e + ε p ) n

Material AISI 304
Ultimate tensile strength σf 788 MPa
Extensibility A% 53
Poisson’s ratio ν 0.28
Pressure die Initial yield stress σs 205 MPa
Hardening exponent n 0.224
Mandrel balls Strenght coefficient K 954 MPa
Clamp Young’s modulus E 196.5 GPa
Mandrel body
Contact interface Static f. c. Dynamic f. c.
Booster
Tube/Pressure and bend dies 0.57 0.35
Tube/Wiper die 0.30 0.15
Bend die Tube/Clamp die 1.99 1.99
Tube/Mandrel 0.075 0.055
Tube
Ball/Mandrel (spherical joint) 0.055 0.055

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Model validation by experiment
Outside diameter, OD 35mm
Initial Thickness, t 0.8mm
Mean radius of the bend, RM 40mm
Bend angle, α 90°

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Lyon, France

Model validation by experiment

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Application of the method
By running several FEM analyses with different combinations of γS and γB, the
γ S = max (1.25 ⋅ γ , 1)
following rules have been identified as optimal:

γ B = max (0.92 ⋅ γ , 1)
PROCESS DATA CASE 1 CASE 2 CASE 3
Outside diameter, OD 35mm 85mm 76mm
Initial Thickness, t 0.8mm 2mm 1.5mm
Mean radius of the bend, RM 35mm 85mm 114mm
Bending angle, α 90° 90° 90°
Difficulty Ratio FD=(OD2)/(t⋅RM) 43.75 42.5 33.8
Booster coefficient, γB 1.05 1.05 1.0
Pressure die coefficient, γS 1.42 1.42 1.25
Target maximum thinning, thMAX 0.15 0.15 0.14
Output maximum thinning, thMAX 0.15 0.14 0.14

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MATERIAL FORMING
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Conclusions
The amount of axial displacement of the assist tools (booster and pressure
die), expressed through the parameters γS and γB, is particularly important
in critical bending conditions. In fact, experiments and simulations show that
the maximum thinning decreases as γS and γB increase.
However, these values cannot be indefinitely increased, since
wrinkling may occur, especially as γB increases.

The study proposed a method for determining γS and γB.

The method has been evaluated by successfully applying it to three
different critical bending operations.

BLM S.p.A.

A. Mentella Esaform 2008

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A. Mentella Esaform 2008