*Corr. Author’s Address: Faculty of Mechanical Eng. and Mechatronics, Phenikaa University, Yen Nghia, Ha Dong, Hanoi 12116, Vietnam, tu.doanh@phenikaa-uni.edu.vn 223
Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 223-230 Received for review: 2023-02-22
© 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2023-05-31
DOI:10.5545/sv-jme.2023.550 Original Scientific Paper Accepted for publication: 2023-06-22
The Double-Sided Upsetting of the End Thickenings  
on Rod Blanks
Do, A.T. – Chernyaev A.V .
Anh Tu Do
1,*
 – Aleksey Vladimirovich Chernyaev
2
1 
Faculty of Mechanical Engineering and Mechatronics, Phenikaa University, Vietnam 
2 
Tula State University, Russia
The known methods for the plastic shaping of axisymmetric parts with bilateral end thickenings and the die equipment used for their 
application have several significant drawbacks, which may reduce the quality of manufactured products, increase their cost, and limit the 
technological capabilities of production. As a rule, they provide alternate plastic shaping of end thickenings. In this paper, we propose a 
method of simultaneous stamping of end thickenings on a bar stock in split dies and a stamping device for its implementation. To establish 
the power modes of stamping we carried out the simulation of the process under study using the finite element method in the QForm software 
package. The dependencies of the stamping force on the geometric dimensions of the workpiece and friction conditions on the contact 
surfaces are established. The damageability of the workpiece material made of AA5056 alloy was assessed, and a diagram was obtained to 
determine the number of required stamping operations.
Keywords: cold forging, upsetting, end thickenings, force, material damageability
Highlights
• 	 A method is proposed for the simultaneous stamping of two end thickenings on a bar stock in split dies and a stamping device 
for its implementation. 
• 	 As a result of modeling, the nature of the influence of the geometric dimensions of the workpiece and friction conditions on the 
power mode of stamping was established. 
• 	 An assessment was made of the stress-strain state of the workpiece and the damage of the material at the final stage of 
stamping products from the alloy AA5056.
• 	 A diagram was obtained to determine the number of necessary operations for stamping axisymmetric parts with end 
thickenings from AA5056 alloy.
0  INTRODUCTION
Axisymmetrical parts with end thickenings and 
axial cavities are widely used in various industries. 
In particular, they are used as pistons in pumping 
equipment, elements of axial power transmission in 
diesel, hydraulic hammers, and pneumatic devices, 
and for the movements of actuators in various 
automated systems.
One way to obtain axisymmetrical parts is by 
machining. However, the low metal utilization factor 
and significant production time do not allow this 
method to be considered rational for use in series 
production. 
The most effective way to obtain this kind 
of part is by cold forming [1] to [6], which allows 
for obtaining parts with sufficient accuracy and 
minimal material loss. At the same time, productivity 
increases, and the resulting products have higher 
strength characteristics and wear resistance due to the 
hardening of the material.
The stamping of end thickenings can be performed 
using extrusion or closed die operations [7] to [10]. 
The thickening is formed, as a rule, on one of the 
product ends [11] and [12]. If it is necessary to obtain 
the thickening at both ends of the product, alternate 
plastic formations of end thickenings are used. In this 
case, complex stamping devices are employed, which 
require manual installation of blanks with pincers and 
removal of the forgings. Some devices have limited 
technological capabilities related to the size of the 
products, low productivity, and are not suitable for 
complex automation. 
One promising direction in the development of 
forging and stamping production is the method of 
stamping by extrusion in split dies, the implementation 
of which is carried out both on universal equipment 
and on special presses. Unlike traditional stamping 
methods, the die has one or more parting planes, 
along which the parts of the die fit snugly against each 
other during the deformation of the workpiece. This 
method can be used for cold, semi-hot, and hot metal 
processing. The use of forging in split dies makes it 
possible not only to obtain forgings of a more complex 
shape with high dimensional accuracy but also to 
exclude the formation of a burr and its subsequent 
trimming, to reduce machining allowances, and to 
increase the productivity of forging [13] and [14]. 
Thus, it is relevant to develop a method for the 
simultaneous double-sided cold forming of end 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 223-230
224 Do, A.T. – Chernyaev A.V.
thickenings on rod blanks and study a stamping device 
for its implementation.
We propose below a design of a punching device 
with split dies. This model enables the simultaneous 
deformation of both end thickenings on a rod blank. 
The results of theoretical studies of the stressed and 
deformed state and damageability of the workpiece 
material made of AA5056 alloy are also presented 
hereafter in order to make it possible to determine the 
required number of forming operations.
1  TECHNOLOGY
The procedure of simultaneous moulding of the front 
and rear end thickenings (ET) should be focused more 
on the technological processes of plastic moulding 
of axisymmetric parts with bilateral end thickenings 
(APWBET) (Fig. 1).
Fig. 1.  Axisymmetric part with end thickenings;  
a) before, and b) after machining
The design of the stamping device should provide 
specified simultaneous moulding of ET in one 
stroke to make it possible to use conventional press 
equipment. This forming is carried out by upsetting 
the movable separable die 4 on the meridional plane 
(Fig. 2). In this case, geometrical dimensions, the 
shape of semi-finished product 2 before upsetting of 
ET, as well as its position relative to the tool (split die) 
at the moment of the beginning of plastic deformation, 
should be such as to ensure filling of both distant 
(from punch 1) ET in cavity 5 of a split die and distant 
(in the cavity 3) of the same die [13].
The production technology of the APWBET 
can include operations of cutting off measured rod 
billets, preliminary upsetting, or direct extrusion of 
the middle part of the billet, and the final stamping 
of end thickenings of various profiles [14]. The final 
dimensions of the product are formed by machining 
operations. If the through hole in the product has a 
small diameter, it is advisable to stamp a solid billet 
with further registration of the central hole by drilling. 
The metal loss, in this case, is insignificant. Depending 
on the degree of deformation, stamping can be carried 
out in 1 or 2 passes. The regulating factor is the 
accumulated damageability of the workpiece material, 
which should not exceed the permissible values. Let us 
consider the process of obtaining the billet APWBET 
at one stamping position, which will significantly 
increase the productivity of its production as a result 
of reducing the number of shaping operations and the 
exclusion of intermediate annealing.
2  RESEARCH METHODS
Theoretical studies of force regimes and the stress-
strain state of the workpiece during stamping 
APWBET are carried out using the basic provisions 
of the theory of plasticity of a rigid-plastic, 
incompressible, hardening material in the QForm 
Fig. 2.  Simplified schematic of an upsetting device for simultaneous plastic forming of ET

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 223-230
225 The Double-Sided Upsetting of the End Thickenings on Rod Blanks 
2D/3D software package based on the finite element 
method. Conditions accepted: stamping temperature 
20 °С; strain rate ξ = 1 s
-1
; Siebel friction model; 
lubricant - mineral oil; friction factor 0.15; test 
materials: 1010, C27400, AA5056; the number of 
finite elements of the workpiece mesh is 30,000. The 
number of forming operations was determined based 
on the value of damage capacity accumulated by the 
billet material based on the phenomenological fracture 
criterion considering the history of deformation.
3  FORGING POWER MODES
To assess the power modes of stamping of the 
APWBET, a simulation in the QForm 2D/3D software 
package was carried out. Stamping is performed in a 
die with split matrices. A cylindrical blank of length 
l = 28 mm and diameter d = 14.5 mm is deformed by 
two punches moving in the opposite direction (Fig. 
3). Under the influence of the tool, metal fills the 
cavities with the die, forming end thickenings. At the 
same time, an inner cavity is formed at the end of the 
workpiece, which serves as a marker for drilling a 
through hole (Fig. 4).
Fig. 3.  Schematic of the operation
The workpiece material was assumed to be rigid, 
hardened plastic. The studies were performed for 
workpieces made of the following materials: 1010, 
C27400, and AA5056. The hardening curves of the 
studied materials are shown in Fig. 5 [15].
Fig. 6 shows the graphical dependencies of the 
change in the force of the operation on the relative 
movement of the tool  where  and h is the current and 
final movements of the punches, respectively.
At the initial stage of stamping, an internal 
cavity of the radius is formed at the end of the blank, 
which is accompanied by a slight increase in the 
deformation force. This is followed by the stage of 
metal accumulation in the cavities of the split die with 
the formation of end thickenings, accompanied by a 
smooth increase in the force.
Fig. 4.  Sequence of shaping
Fig. 5.  Hardening curves of the studied materials  
(t = 20 °C , ξ = 1 s
–1
)
Fig. 6.  Force-to-travel plots for stamping the APWBET  
(μ = 0.1, R = 5 mm, r = 2 mm, d = 14.5 mm, D = 21.8 mm)
At the final stage, the final design of the contour 
of the workpiece by filling the angular sections of the 
die occurs, which is manifested by a sharp increase in 
the force of the operation. The technological force 
reaches its maximum value at the final moment of 
stamping h = 1 . In further studies, its maximum value 
is taken as the operation force. The main factors 
affecting the force modes of stamping of the APWBET 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 223-230
226 Do, A.T. – Chernyaev A.V.
are geometric parameters of the tool and workpiece: 
radius of curvature of the die cavity R, radius of 
curvature of the punch protrusion r, initial d and final 
D diameters of the workpiece, as well as friction 
conditions at the contact boundaries of the tool and 
workpiece, characterized by the friction coefficient μ. 
Theoretical studies of the forging force modes of the 
APWBET were performed in the following ranges of 
varying parameters: R = 3 mm, 5 mm, 7 mm, and 9 
mm; r = 1 mm, 2 mm, 3 mm, and 4 mm; µ = 0.05, 
0,10, 0.15, and 0.20. The diameter of the blank was 
taken as constant d = 14.5  mm, the diameter of the 
product  mm, which corresponds to the values of the 
relative diameter. The length of the blank and the 
product were taken l = 28 mm, L = 22 mm. The results 
of the calculations are shown in Fig. 7.
It was found that the greatest influence on the 
force of stamping in the studied ranges of variation 
of varying parameters has a relative diameter. 
The decrease from 0.66 to 0.6, which corresponds 
to the increase in the diameter size of the product 
and, therefore, the degree of deformation with the 
unchanged dimensions of the blank, leads to an 
increase in the stamping force by 20 % to 30 %. The 
diametrical size of the product is determined by the 
requirements of the drawing and is not a subject of 
optimization of the force modes. 
The radius of the inner cavities of the die R has a 
significant influence on the stamping force. Increasing  
R from 3 mm to 9 mm leads to a decrease in force by 
15 % to 20 %, which is explained by more favourable 
conditions of metal flow with less energy required to 
change the trajectory. Increasing R, if allowed by the 
product drawing and operating conditions, leads to a 
decrease in force and increases the die resistance.
Increasing the radius r of the internal cavity at 
the end of the blank from 1 mm to 4 mm leads to an 
increase in force by 5 % to 10 %. The value of the 
specified radius is not significant in the design of the 
product because later, the central part of the blank 
will form a through hole, and the cavity formed 
during stamping, which is a marking, will be removed 
into the waste. Therefore, to reduce the stamping 
force, it is advisable to assign smaller values r. An 
increase in friction on the contact surfaces of the 
tool and workpiece can result in a 10 % increase 
in force. To reduce friction, it is advisable to use 
lubricants designed for this purpose and provide 
Fig. 7.  Forging power modes of APWBET

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 223-230
227 The Double-Sided Upsetting of the End Thickenings on Rod Blanks 
careful treatment of the surfaces of the inner cavity of 
the die. During operation, it is necessary to monitor 
the condition of the working surfaces of the tool, to 
prevent wear and formation of scuffs, leading to an 
increase in force and deterioration of the appearance 
of products. 
4  DAMAGEABILITY OF WORKPIECE MATERIAL
The processes of cold forging (CF) are characterized 
by high specific forces at significant degrees of 
deformation and are accompanied by significant strain 
hardening and accumulation of microdamage. The 
quality of products obtained by CF and the reliability 
of their operation depend on the level of accumulated 
damageability [16] and [17]. 
Material damageability ω during plastic 
deformation is often evaluated by the criterion 
proposed by Kolmogorov [17]. As a characteristic 
of material damageability, the degree of plasticity 
resource utilization is taken as a ratio of accumulated 
strain intensity to its limiting value on given 
characteristics of the stress and strain state of 
the elementary volume in the centre of plastic 
deformation:
 







d
i
i
i
1
0
, (1)
where ε
i
 is the effective strain at a given stage of 
deformation; [ε
i
] is the effective strain at the moment 
of failure, depending on the stress state index. 
 



3
i
, (2)
where σ is mean stress, and σ
i
 effective stress. The 
value [ε
i
], as a rule, is found from experimentally 
obtained diagrams of ultimate plasticity.
To justify the number of necessary stamping 
operations, the stress and strain states of the blank in 
the process of forming were studied using the QForm 
2D/3D software package. Fig. 8 shows the distribution 
patterns σ
i
, ε
i
, σ, and ω the final stage of the forging of 
APWBET of AA5056 alloy.
It was found that compressive stresses 
predominate in the deformation centre, which creates 
favourable conditions in terms of deformation without 
failure, contributing to the healing of micro-defects 
caused by plastic deformation and preventing the 
exhaustion of the plasticity resource of the material 
[16]. The greatest values ω are reached in the marginal 
areas of the end thickenings (points P
1
 and P
2
). Further 
studies were carried out on these points. Values σ, σ
i
, 
and ε
i
 were calculated employing the QForm software 
package. The limiting values depending on η were 
set in the form of a data table for the corresponding 
Fig. 8.  Distribution σ
i
, ε
i
, σ, and ω at the final stage of stamping (material is AA5056 alloy; μ = 0.1, R = 5 mm, r = 2 mm, d =0.66)

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 223-230
228 Do, A.T. – Chernyaev A.V.
subprogram of the complex QForm according to the 
results of the approximation of the limit plasticity 
diagram [17]. An example of the calculation of the 
damageability for points P
1
 and P
2
 when stamping 
the APWBET of AA5056 alloy is shown in Fig. 9. 
The plasticity limit diagram [ε
i
] and the deformation 
trajectories at points P
1
 and P
2
 are shown. For the 
example under consideration, at point
 P
1
:  η = –1.8,  ε
i
 = 0.61,  ε
np
 = 1.67,  ω = 0.36;
 P
2
:  η = –1.6,  ε
i
 = 0.47,  ε
np
 = 1.61,  ω = 0.29.
It was found that the values d and R have 
the greatest influence on the damageability of the 
workpiece material. Their decrease in the studied 
range ω decreases by 30 % to 40 % and 20 % to 30 %, 
respectively (Fig. 10). 
It was found that at values d < 0.62, the 
damageability of AA5056 alloy reaches a critical lev 
ω > 0.3, which, according to the recommendations 
[16], is unacceptable for critical products. In this 
case, the stamping of the APWBET in one operation 
is impossible, and in the technological process, 
it is necessary to provide an additional transition 
of preliminary profiling - the upsetting of the end 
thickening of the cylindrical billet with subsequent 
annealing and the final dimensions are formed at the 
second operation (Fig. 11).
Fig. 9.  Assessment of the damageability of the material
Fig. 10.  Damageability of the material when stamping the APWBET

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)5-6, 223-230
229 The Double-Sided Upsetting of the End Thickenings on Rod Blanks 
Fig. 11.  Schematic diagram of the forging of the APWBET  
from the profile billet
Fig. 12.  Determining the number of stamping operations  
(material - AA5056)
When using a preformed billet with a diameter of 
the thickened part d
1
 = 19 mm and length l = 25 mm, 
the damageability of the material at the final stamping 
operation is reduced, not exceeding the value  
ω = 0.25, which meets the requirements for products 
of the critical application.
Fig. 12 presents a diagram for determining 
the number of necessary forming operations when 
stamping the APWBET. The area of the diagram 
below each curve, corresponding to the coefficient 
of friction μ, at given d and R are characterized by 
the values of damageability ω > 0.3, which means the 
necessity of the operation of preliminary profiling of 
the workpiece. In this case, the stamping is performed 
in two transitions. The area of the diagram over the 
above curves corresponds to the permissible values of 
damageability ω ≤ 0.3, which means that it is possible 
to obtain the product in one stamping operation.
Thus, with the given ratios of geometric 
parameters and the degree of deformation, the 
APWBET can be produced in one stamping operation 
with values of the degree of plasticity resource 
utilization acceptable for critical parts. When stamping 
the end thickenings of large diameter, it is necessary to 
use pre-profiling of the middle part of the APWBET to 
ensure rational kinematics of the flow of the deformed 
material and to reduce the damageability. 
5  CONCLUSIONS
1. The stamping axisymmetric parts with end 
thickenings from a bar of continuous cross-section 
was proposed, expanding the technological 
capabilities of cold stamping of small, precise 
parts of complex shapes, providing increased 
productivity and reduced material losses.
2. As a result of modelling the stamping of solid 
APWBET from a cylindrical billet, we come to 
the conclusion that the factors influencing force 
modes of APWBET stamping are the geometric 
parameters of the tool and the billet: the radius 
of curvature of the die cavity R, the radius of 
curvature of the punch projection r, initial d and 
final D diameters of the blank, and also friction 
conditions at the contact boundaries of the tool 
and billet, characterized by friction coefficient 
μ. By doing so, a quantitative assessment of 
the influence of these parameters within the 
investigated range is given.
3. The assessment of the damageability of the blank 
material in dangerous points has been carried 
out. Thus, we establish the ranges of deformation 
degree and product geometry changes, at which 
the stamping of solid APWBET can be performed 
for one and two form-modifying operations.
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