International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 01, January 2019, pp. 2085-2094, Article ID: IJMET_10_01_204
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=1
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
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THEORETICAL AND FINITE ELEMENT
INVESTIGATION FOR NOSING BRASS TUBES
AT ROOM TEMPERATURES
Rawaa Hamid Mohammed Al-Kalali, Dr. Omer Muwafaq Mohmmed Ali and Ethar
Mohamed Mahdi Mubarak
Middle Technical University –Institute of Technology –Baghdad-Iraq
ABSTRACT
In this paper the equation is derived theoretically connecting between the stress
due to forming and nosing ratio. A theoretical study was performed on the conical
nosing of the brass tube material at room temperature. The relationship between
forming stress, nosing ratio of tube is concluded. ANSYS is used to simulated 5° and
10° semi-die angles in a conical die to observed the stress and strain distributions in
the tube. The process has been carried out using brass tube with thickness 2mm under
states of cold process of nosing samples with a radius of (20)mm and length (120)mm.
A good match is obtained between the theoretical and the ANSYS results. It is noticed
that the well die is conical die having 10° semi angle of die.
Keywords: Nosing tube, Brass tube, Finite element method, ANSYS, Tube end
reduction, nosing ratio.
Cite this Article: Rawaa Hamid Mohammed Al-Kalali, Dr. Omer Muwafaq
Mohmmed Ali and Ethar Mohamed Mahdi Mubarak, Theoretical and Finite Element
Investigation for Nosing Brass Tubes at Room Temperatures, International Journal of
Mechanical Engineering and Technology, 10(1), 2019, pp. 2085-2094.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=1
1. INTRODUCTION
The process of nosing (tube end reduction) is one of the processes of mechanical forming of
metals and the diameter of the end of the circular tube is reduced by compressing it into a
conical mold or arc of the cavity to take the end of the tube shape of the mold cavity and have
a finite end with a diameter less than the original diameter of the specimen. This process is
used to form the end of the projectiles and the percentage of nosing is defined as the amount
of contraction in the finite end diameter divided by the original diameter of the specimen. The
process of nosing as any mechanical forming process can be carried out on cold or warm. It is
cold when the pipes are fitted with a good mechanical properties such as high hardness and
smooth surface and is carried out warm for the purpose of reducing the load required for the
process of nosing, especially when nosing pipes with relatively large diameters. The process
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Theoretical and Finite Element Investigation for Nosing Brass Tubes at Room Temperatures
of nosing is a complex process influenced by several factors, including the geometry of the
mold, the geometry of the specimen, the properties of its material, friction and lubrication,
and the speed of the process. In this process there is an undesirable phenomenon, namely, the
phenomenon of lateral swelling of the pipe walls at the entrance of the mold, especially when
using conical molds. Research published about the nosing process is generally low. It is
evident from the previous research of the nosing process that although more than one or more
of the same material has been used in several studies, the issue of the influence of strain
hardening on the process has not been addressed directly. C.T. Kwan et al.,(2004),[1],
utilized, the finite element analysis to study the partially laterally constrained of cold nosing
process for metal tubes with a conical die. Simulations for the tube nosing by the ANSYS/LSDYNA was completed. The impacts of the procedure parameters, for example, length of tube,
thickness of tube, fillet radius of die, angle of die, factor of friction, coefficient of strength and
exponent of the strain hardening of the billet material on the tube critical nosing ratio are
analyzed. Tests were completed with treated steel SUS304 tube billets at room temperature,
and the after effects of trials were contrasted and the FEM computations. B.P.P. Almeida et
al., (2006) [2] , the point of this paper is to revive and expand the essentials of tube
development and diminishment utilizing a die by methods for a thorough theoretical and
experimental examination. The accentuation is centered around understanding modes of
distortion and on setting up formability standards for the advantage of the individuals who
plan tubular parts in day by day rehearse. The theoretical examination is proficient by the use
of virtual prototyping demonstrating systems in view of the finite element technique and the
trial work is for the most part used for supporting and approving the theoretical examination.
Lirio Schaeffer and Akberto M.G. Brito, (2007) [3], studied the experimentally and
theoretically examination including tube end extension, diminishment and reversal forms
utilizing a die. The material utilized in the exploratory tests is an AISI1010 carbon steel and
all the work is completed at room temperature. The theoretical examination is finished
utilizing FEM programming QFORM3D, the examination on the tube end framing forms
concentrated principally on understanding methods of misshapening and on setting up
formability limits for every one of them, the outcomes demonstrate that procedures for end
forming of thin walled tubes are effective just inside a minimized scope of process
parameters. L. Venugopal, (2012) [4], in this examination, the Taguchi technique is utilized
to locate the ideal procedure parameters for most extreme development of tube closes. The
different procedure parameters to be specific the punch – die cone edge, the development
proportion and the rubbing conditions are taken as the information procedure condition and
the yield; the greatest spiral relocation is fundamentally analyzing. Spiral development is the
expansion in distance across of the tube by the die estimated on the best most segment of the
tube over its boundary. The ideal blend of the procedure parameters is gotten through the flag
to noise ratio (S/N) examination and the investigation of change (ANOVA) techniques. it is
discovered that the most noteworthy factor is the die cone edge (α) and this factor contributes
43.56% on the aggregate yield reaction esteem while development proportion rp/ro contributes
8.89% and the oil has contributed 38.59% on the aggregate yield. Seyed Ghaem
Amirhosseini and Abbasniknejad Nadersetoudeh (2017),[5], contemplated the nosing
procedure of round metal tubes in void and polyurethane foam filled conditions on a
semispherical unbending die was analyzed by hypothetical and trial techniques. Another
hypothetical model of plastic disfigurement of roundabout metal tubes was shown amid the
nosing procedure on an inflexible semispherical die. Examination of hypothetical expectations
and the comparing exploratory estimations uncovers that anticipated load-defection and
disseminated energy-deformation outlines by hypothetical equations have a decent connection
with the relating test bends and it demonstrates verity of the hypothesis. Moreover, the test
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Rawaa Hamid Mohammed Al-Kalali, Dr. Omer Muwafaq Mohmmed Ali and Ethar Mohamed Mahdi
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results demonstrate that the nearness of polyethylene Teflon-limitations builds extreme axial
displacement of the forming procedure.
Therefore, the aim of the current research was to study the effect of die angle on the loads,
displacements and distortions during the process of cold cone tube nosing from both
theoretical and finite element aspects.
2. MATERIALS USED
The Brass was selected as a material with high strain hardening. Mechanical properties was
[6-7]:
Young Modulus (E) = 97 GPa
Poison’s ratio (𝜈 ) =0.31
Yield stress (𝜎𝑦 ) = 124 – 310 MPa
Hardening parameters, n= 0.52 , K=740
3. NOSING DIE AND SPECIMEN
Select the halves of the desired die were determined to have small angles not exceeding 10°,
so angle 10° was chosen and for the comparison within the same range, a second angle of 5°
was chosen, as in Fig.(1a). The external diameter of each sample was determined using (40)
mm with wall thickness (2) mm. The specimen length of the is calculated using three times
diameter for external diameter to fit the two halves die angles (5°, 10°). Fig.(1b) shows the
geometry of specimen.
a
b
Figure 1 nosing die and specimen dimensions (in mm)
4. THE THEORETICAL PART
Cold cone nosing tube is a complex process involving several variables. However, its basic
configuration relationship is the relationship between the forming stress P/Ao (the load
divided by the original specimen section area) and the nosing ratio (R) (the difference
between the average of end nose radius rn and the average radius of the original ro divided by
ro). i.e. R = (ro – rn)/ro. As well as the relationship between the stress of forming P/Ao and the
relative deformation for specimen S/ro.
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Theoretical and Finite Element Investigation for Nosing Brass Tubes at Room Temperatures
The relationship between the stress of forming P/Ao and ratio for nosing R is the most
important relationship where the relative load required to achieve a certain amount of nosing
is determined. The hypotheses to find this relationship:
1. neglect the effect of side swelling and plastic bending.
2. consider a homogeneous distortion.
3. consider the Coulomb friction.
4. Consider the thin walls of the specimen.
5. Considering the constant wall thickness
An element from specimen’s wall [8] during the nosing tube process as shown in Fig.(2).
Figure 2 equilibrium element of tube wall during nosing
Where the element is defined by a small angle. It has a thickness t and lies on the distance
r of the longitudinal axis of the sample and is subjected to longitudinal stress 𝜎𝛼 and
circumferential stress 𝜎𝜃 and thickness stress 𝜎𝑡 . As a result of contact with the surface of the
die with the specimen surface, a friction force of 𝜇𝜎𝑡 per unit area is generated.
The equilibrium equation of forces is in the direction of 𝜎𝑡
𝑑𝑟
𝛽
𝜎𝑡 (𝑟. 𝑑𝜃 𝑠𝑖𝑛𝛼) − 2𝜎𝜃 . cos (𝛼 + 2 ) 𝑠𝑖𝑛
𝑑𝜃
𝑑𝑟
(𝑡. 𝑠𝑖𝑛𝛼)
2
=0
(1)
Because of the angles 𝑑𝜃 and β are small as well as result for multiplying the small
quantities, the equilibrium equation becomes:
𝜎𝑡 . 𝑟 = 𝜎𝜃 . 𝑐𝑜𝑠𝛼. 𝑡
𝑡
𝜎𝑡 = (𝑟 . 𝑐𝑜𝑠𝛼) . 𝜎𝜃
(2)
Eq.(2) shows that 𝜎𝑡 is much lower than 𝜎𝜃 for thin-walled samples. The equilibrium
equation of forces towards 𝜎𝛼 is:
(𝜎𝛼 + 𝑑𝜎𝛼 )(𝑟 + 𝑑𝑟)(𝑡 + 𝑑𝑡)𝑑𝜃 − 𝜎𝛼 . 𝑡. 𝑟. 𝑑𝜃 − 𝜎𝜃 (𝑡 −
𝑑𝑟
) 𝑑𝜃. 𝑠𝑖𝑛𝛼
𝑠𝑖𝑛𝛼
𝑑𝑟
− 𝜇𝜎𝑡 (𝑟. 𝑑𝜃 𝑠𝑖𝑛𝛼) = 0 (3)
Simplified eq.(3), it can be get:
𝑑(𝜎𝛼 .𝑟.𝑡)
𝑑𝑟
𝑟
− 𝜎𝜃 . 𝑡 − 𝜇𝜎𝑡 𝑠𝑖𝑛𝛼 = 0
(4)
Substitute 𝜎𝑡 from Eq.(1) into Eq.(3), with constant wall thickness :
𝑑(𝜎𝛼 .𝑟)
𝑑𝑟
− 𝜎𝜃 (1 + 𝜇𝑐𝑜𝑡𝛼) = 0
(5)
Since the continuation of the nosing process requires that 𝜎𝜃 reach to the yield stress for
metal in the circumferential direction. The use of von Mises's theory with the neglect of 𝜎𝑡
and 𝜇𝜎𝑡 and the assumption that |𝜎𝛼 | < |𝜎𝜃 | . Within this range, a certain value was
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determined for the yield stress using Von Mises yield criterion. The best approximation of the
values given by the von Mises curve is given in the same range:
𝜎𝜃 = 𝜎𝑦 = 1.1𝜎𝑜
(6)
Where
𝜎𝑜 …. the uniaxial yield stress
Substituting Eq.(6) into Eq.(3) :
𝑑(𝜎𝛼 .𝑟)
𝑑𝑟
− 1.1𝜎𝑜 (1 + 𝜇𝑐𝑜𝑡𝛼) = 0
(7)
Integrating Eq.(7)
𝜎𝛼 = 1.1𝜎𝑜 (1 + 𝜇𝑐𝑜𝑡𝛼) +
𝐶
𝑟
(8)
Where c is the constant, and can be found where 𝜎𝛼 = 0 , at r=ro, thus:
𝐶 = 1.1𝜎𝑜 (1 + 𝜇𝑐𝑜𝑡𝛼)𝑟𝑛
(9)
Substitute Eq.(9) into Eq.(8) , it can be get :
𝑟
𝜎𝛼 = 1.1𝜎𝑜 (1 + 𝜇𝑐𝑜𝑡𝛼) + (1 − 𝑟𝑛 )
(10)
According to Eq.(10), the maximum longitudinal stress was on r = ro , i.e at die entrance ,
thus:
𝑟
𝜎𝛼)𝑚𝑎𝑥 = 1.1𝜎𝑜 (1 + 𝜇𝑐𝑜𝑡𝛼) + (1 − 𝑟𝑛 )
(11)
𝑜
Therefore, the requested load for nosing process is
𝑃 = 𝜎𝛼)𝑚𝑎𝑥 . 𝐴𝑜 . 𝑐𝑜𝑠𝛼
(12)
Where Ao represent the original cross section of specimen.
The relationship connected the stress of forming and ratio for nosing can be found by
substituting the R equation into Eq.(11). Hence Eq.(12) will be:
𝑃
𝐴𝑜
= 1.1𝜎𝑜 (1 + 𝜇𝑐𝑜𝑡𝛼)(𝑐𝑜𝑠𝛼)𝑅
(13)
A relationship between the forming stress and relative axial displacement of the sample
𝑆
(𝑟 ) can be determined. By determining the relationship between (𝑟 ) and the nosing ratio
𝑆
𝑜
𝑜
R. Assuming that the total height of the sample remains almost constant via the nosing
𝑆
procedure, therefore, the relationship between 𝑟 and R :
𝑜
𝑆
𝑅 = ( ) 𝑡𝑎𝑛𝛼
𝑟𝑜
Assume the flow stress according to Ludwik equation[9], and that the circumferential
stress equal to the equivalent stress and the circumferential strain equal to equivalent strain.
Hence Eq.(4), will be in the form :
𝑑
[𝜎 . 𝑟 (1.5𝑡𝑜
𝑑𝑟 𝛼
𝑡
𝑟
𝑛
𝑡
− 2𝑟𝑜 𝑟)] = 𝜎𝑦 [1 + 𝑘 (𝑙𝑛 𝑟𝑛 ) ] (1 + 𝜇𝑐𝑜𝑡𝛼)((1.5𝑡𝑜 − 2𝑟𝑜 𝑟)… (14)
𝑜
𝑜
𝑜
Using 4th order Rang-Kutt [10] to solving the differential equation(14) with dependent
boundary condition and with n=1.
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Theoretical and Finite Element Investigation for Nosing Brass Tubes at Room Temperatures
5. FINITE ELEMENT ANALYSIS VIA ANSYS
Simulating of the two different cone angle (5◦, 10◦) are investigated. Finite element analysis
software ANSYS 15 was used; the stroke steps on rigid cones are expressed as an explicit
problem. During each step, many solutions (sub-load steps) are achieved to provide the
pressure. At each sub- load, a number of equilibrium iterations are achieved to get a
convergence solution. [11].
The rigid cone is modeled as rigid body. Contact process in ANSYS 15 was utilized to
model a complex interference between the specimen and cone, the 2D contact element
TARGE169 was used, to represent 2D (cone set) surfaces that were associated with the
deformable body (specimen) indicated via 2D elements of contact (CONTA175).
Element PLANE182 is used for two dimension model of solid structures (specimen) that
shown in Fig.(3). The used element as either a plane element (plane stress, plane strain or an
axisymmetric element), in the present study, an axisymmetric option is used (keyopt(3)=1).
PLANE182 is introduced through four nodes, at each node two degrees of freedom:
translations in the directions x and y. The element has plasticity, hyper elasticity, stress
stiffening, large deflection, and large strain capabilities [12].
Figure 3 Element Plane182 [12]
The material properties required for this element was depended on the application, i.e.
[13];
 Linear or nonlinear.
 Isotropic, orthotropic, anisotropic.
 Constant temperature or temperature-dependent.
The specimen’s material is brass and the plastic response was modeled using the Von
Mises yield criterion.
The element shape is specified, mapped mesh was existed, and Fig.(4) shown the mapped
meshing. The mesh of the problem is an essential step via that the geometry of the model is
transferred to finite element model (FEM).
(a) die angle 𝛼 = 5°
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(b) die angle 𝛼 = 10°
Figure 4 nosing tube model for 𝛼 = 5° and 10°
In concentrate the contact between two bodies, the surface of one body is traditionally
taken as a contact surface and the surface of the other body as a target surface. The "contact target" combine idea has been broadly utilized in finite element analysis. For rigid-flexible
contact, the contact surface is related with the deformable body; and the target surface could
be the inflexible surface. For flexible-flexible contact, both contact and target surfaces are
related with deformable bodies. The contact and target surfaces constitute a "contact Pair".
ANSYS provides both rigid-to-flexible and flexible-to-flexible surface-to-surface contact
elements. These contact components utilize "target surface" and "contact surface" to construct
a contact combine. The target surface is demonstrated with either TARGE169 or TARGE170
(for 2-D or 3-D, separately). [12].
6. RESULTS AND DISCUSSION
The metal stream is mind boggling and delicate to the frictional requirement at the die workpiece interaction. Generally wall thickness increases, and the shell shrinks in length after the
task (depend on friction). The state of the external surface of the shell takes after the nosing
die profile whereas the internal surface isn't bolstered amid the nosing procedure. The
relationship between load and displacement is complicated because it includes all that events
between sample and die, i.e. side swelling and contraction in the sample outside the die plus
the nosing inside the die.
Fig.(5) illustrated the relationship between the forming stress (P/Ao) with relative axial
displacement of specimen (S/ro) with 𝛼 = 5 ° 𝑎𝑛𝑑 10°, theoretically and ANSYS . It is
noticeable in the Fig.(5) that for the same P/Ao value S/ro is larger for angle 5° while the
opposite is true for angle 10°. Side swelling is expected to play a major role in this difference,
with a greater effect of an angle of 10° compared to an angle of 5°. Fig.(6) illustrated the
equivalent stress and strain distribution.
Figure 5 Theoretical and ANSYS relationship between the forming stress (P/Ao) with relative axial
displacement of specimen (S/ro) with 𝛼 = 5 ° 𝑎𝑛𝑑 10°
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Theoretical and Finite Element Investigation for Nosing Brass Tubes at Room Temperatures
(a) Die angle 𝛼 = 5°
(b) Die angle 𝛼 = 10°
Figure 6 Equivalent stress and strain distribution in nosing tube for 𝛼 = 5° and 10°
Fig.(7) illustrated the relationship between the forming stress and nosing ratio. R is one of
the most important variables in the nosing process, representing the amount of nosing
obtained, regardless of the half-angle of the die compared to the relative axial displacement of
the S/ro. The theoretical analysis of the nosing process is directly dependent on R. Fig.(7)
shows an increasing slop for all curves from the point of origin. It is further noted that the
curve for angle 5° is higher than the curve for angle 10°. It is clear that the curves seem much
closer to the values and shape (increasing slop). Thus, the best theoretical equation compared
with ANSYS results is the equation based on strain hardening linearity.
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Differences between finite element analysis via ANSYS software and theoretical curves
can be attributed to certain aspects of theoretical analysis such as the nature of equivalent
stress and the possibility of different stresses and strains across the sample wall. However, the
main cause of the differences is expected to be due to the nature of the friction and the method
of determining the coefficient of friction. Forming stress values in all theoretical equations are
sensitive to any change in the μ value for the small angles of the expression (1+ μcotα) in all.
In this study the friction coefficient of the brass is taken = 0.035 .
Figure 7 Theoretical and ANSYS relationship between the forming stress with nosing ratio (R) with
𝛼 = 5 ° 𝑎𝑛𝑑 10°
7. CONCLUSIONS
1. The ideal angle of die for the conical dies is (10°)
2. Good agreement is evident between theoretical and ANSYS results with average
discrepancy 15%.
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