Computer aided analysis of ball burnishing process
The finite element model analysis of a rigid sphere indentation into a half-space is created and investigated as a part of comprehensive study of a ball burnishing process. The model shows good fidelity of the material elastic behavior by the Hertz contact theory. The elasticplastic behavior of the...
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irk-123456789-1125422017-01-23T03:03:49Z Computer aided analysis of ball burnishing process Storozh, Y. Lyutak, I. Storozh, B. Vasylyk, O. Yatsyshyn, M. Pasyeka, M. Приложения. Опыт разработки и внедрения The finite element model analysis of a rigid sphere indentation into a half-space is created and investigated as a part of comprehensive study of a ball burnishing process. The model shows good fidelity of the material elastic behavior by the Hertz contact theory. The elasticplastic behavior of the material with a power dependence of the isotropic strain strengthening is studied. Parameters for the further ball burnishing research are recommended. В межах аналізу процесів обкочування кулькою створено і досліджено скінченно-елементну модель вдавлювання жорсткої сфери в півпростір. Модель свідчить про високу точність відтворення пружної поведінки матеріалу за теорією Герца. Вивчено пружно-пластичну поведінку матеріалу зі степеневою залежністю ізотропного деформаційного зміцнення. Обґрунтовано рекомендації щодо вибору параметрів дослідження процесу обкочування кульками. В рамках анализа процессов обкатывания шариком создана и исследована конечно-элементная модель вдавливания жесткой сферы в полупространство. Модель свидетельствует о высокой точности воспроизведения упругости материала по теории Герца. Изучено упруго-пластичное поведение материала со степенной зависимостью изотропного деформационного усиления. Обоснованы рекомендации выбора параметров исследования процесса обкатывания шариком. 2015 Article Computer aided analysis of ball burnishing process / Y. Storozh, I. Lyutak, B. Storozh, O. Vasylyk, M. Yatsyshyn, M. Pasyeka // Управляющие системы и машины. — 2015. — № 5. — С. 61–65. — Бібліогр.: 13 назв. — англ. 0130-5395 http://dspace.nbuv.gov.ua/handle/123456789/112542 004.942 en Управляющие системы и машины Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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Приложения. Опыт разработки и внедрения Приложения. Опыт разработки и внедрения |
| spellingShingle |
Приложения. Опыт разработки и внедрения Приложения. Опыт разработки и внедрения Storozh, Y. Lyutak, I. Storozh, B. Vasylyk, O. Yatsyshyn, M. Pasyeka, M. Computer aided analysis of ball burnishing process Управляющие системы и машины |
| description |
The finite element model analysis of a rigid sphere indentation into a half-space is created and investigated as a part of comprehensive study of a ball burnishing process. The model shows good fidelity of the material elastic behavior by the Hertz contact theory. The elasticplastic behavior of the material with a power dependence of the isotropic strain strengthening is studied. Parameters for the further ball burnishing research are recommended. |
| format |
Article |
| author |
Storozh, Y. Lyutak, I. Storozh, B. Vasylyk, O. Yatsyshyn, M. Pasyeka, M. |
| author_facet |
Storozh, Y. Lyutak, I. Storozh, B. Vasylyk, O. Yatsyshyn, M. Pasyeka, M. |
| author_sort |
Storozh, Y. |
| title |
Computer aided analysis of ball burnishing process |
| title_short |
Computer aided analysis of ball burnishing process |
| title_full |
Computer aided analysis of ball burnishing process |
| title_fullStr |
Computer aided analysis of ball burnishing process |
| title_full_unstemmed |
Computer aided analysis of ball burnishing process |
| title_sort |
computer aided analysis of ball burnishing process |
| publisher |
Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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2015 |
| topic_facet |
Приложения. Опыт разработки и внедрения |
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http://dspace.nbuv.gov.ua/handle/123456789/112542 |
| citation_txt |
Computer aided analysis of ball burnishing process / Y. Storozh, I. Lyutak, B. Storozh, O. Vasylyk, M. Yatsyshyn, M. Pasyeka // Управляющие системы и машины. — 2015. — № 5. — С. 61–65. — Бібліогр.: 13 назв. — англ. |
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Управляющие системы и машины |
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УСиМ, 2015, № 5 61
Приложения. Опыт разработки и внедрения
UDC 004.942
Y. Storozh, I. Lyutak, B. Storozh, O. Vasylyk, M. Yatsyshyn, M. Pasyeka
Computer aided analysis of ball burnishing process
В рамках анализа процессов обкатывания шариком создана и исследована конечно-элементная модель вдавливания жесткой
сферы в полупространство. Модель свидетельствует о высокой точности воспроизведения упругости материала по теории
Герца. Изучено упруго-пластичное поведение материала со степенной зависимостью изотропного деформационного усиления.
Обоснованы рекомендации выбора параметров исследования процесса обкатывания шариком.
Ключевые слова: конечно-элементный анализ, обкатывание шариками, упруго-пластичная деформация, упрочнение, конеч-
но-элементная модель.
The finite element model analysis of a rigid sphere indentation into a half-space is created and investigated as a part of comprehensive
study of a ball burnishing process. The model shows good fidelity of the material elastic behavior by the Hertz contact theory. The elas-
tic-plastic behavior of the material with a power dependence of the isotropic strain strengthening is studied. Parameters for the further
ball burnishing research are recommended.
Keywords: finite element analysis, burnishing, elastic-plastic deformation, strengthening, finite element model.
В межах аналізу процесів обкочування кулькою створено і досліджено скінченно-елементну модель вдавлювання жорсткої
сфери в півпростір. Модель свідчить про високу точність відтворення пружної поведінки матеріалу за теорією Герца. Вивчено
пружно-пластичну поведінку матеріалу зі степеневою залежністю ізотропного деформаційного зміцнення. Обґрунтовано ре-
комендації щодо вибору параметрів дослідження процесу обкочування кульками.
Ключові слова: скінчено-елементний аналіз, обкочування кульками, пружно-пластична деформація, зміцнення, скінченно-
елементна модель.
Introduction. Burnishing is a cold working process
in which plastic deformation occurs by applying a
pressure through a ball or roller on the metallic sur-
faces. It is a finishing and strengthening process.
Improvements in surface finish, surface hardness,
wear resistance, fatigue resistance, yield and tensile
strength, and corrosion resistance can be achieved
by applying this process [1–3]. In addition, burnish-
ing is a highly efficient, technological, and saving-
cost process. It can be combined with cutting.
Therefore, it is widely used in today’s manufactur-
ing industry for finishing enhanced machine parts.
However, despite more than 50-year period of
the burnishing industrial application, numerous
studying, and its seeming simplicity, till now there
are not enough reliable engineering methods for
predicting the surface layer quality suitable for
manufacturing process planning to produce prod-
ucts with predetermined properties. An empirical
nature most of conventional studies on experimen-
tal determining a relationship between burnishing
process parameters and treated part properties di-
rectly [1–3] or by evaluating their surface layer
quality [4–10] has a significant drawback: unsuit-
ability of their results for practical applications in
other conditions, that is, for designing new manu-
facturing processes. More promising approach is
to develop analytical techniques of technological
support in obtaining given service properties of
parts worked out by Smeljansky V.M. [11]. It is
based not on external relations of the burnishing
parameters but on internal regularities and mecha-
nisms of the surface layer formation in the center
of plastic deformation formed on the theoretical
basis of continuum mechanics. However, the sim-
plification underlying the analytical dependence
of plastic deformation (neglecting the presence in
the processed material not only plastic but also
elastic deformation the volume of which exceeds
that of the plastic deformation) causing lack of
sufficient predictive power of this approach.
A number of foreign and domestic publications
in recent years (see e.g. [4–6, 8–10]) are devoted
to the research of some phenomena to improve the
surface quality due to a local elastic-plastic de-
formation by numerical methods, including finite-
element (FE) analysis. This method of continuum
mechanics also has reliable theoretical justifica-
62 УСиМ, 2015, № 5
tion. Although the FE simulation results are not in
sufficiently good agreement with the experimental
data, this approach is valuable for understanding
the material elastic-plastic behavior in the part
surface layers. Obviously, we can solve the urgent
problem of engineering techniques for the bur-
nishing prediction by using high-quality numerical
models and comprehensive approach to their study.
The aim of this paper is to find out regularities of
the elastic-plastic behavior of the plane part material
during the indentation by a rigid sphere through cre-
ating and studying the FE model, which is a stage of
the burnishing process complex research.
The object of the study has been selected due to
the followings. Elastic behavior of the materials dur-
ing the indentation by a spherical indenter investi-
gated correctly by means of elasticity theory. There-
fore, it is expected that it will provide a reliable es-
timation of the model quality for its size, boundary
conditions, requirements to the FE size, and the way
of the load and restriction applying. It is also sug-
gested that the revealed regularities of stresses and
plastic flow during the indentation strengthening
will serve as a reliable information base for making
up a FE model for revealing peculiarities of similar
phenomena in ball burnishing processes and solving
the problem of their prediction.
Building a model and its verification. Study
techniques
It is efficient to simulate the process with the 2D
axisymmetrical model in which the sphere is mod-
eled by its thin part adjacent to the contact and the
material to be studied by a thick circular plate
(Fig. 1). The plate dimensions are many times larger
than the largest expected contact. So, in accordance
with the Saint-Venant principle, it can be rightly as-
sumed that the restrictions do not affect the stress-
strain state of the plate investigated area. The load-
ing is applied by sphere vertical displacement y and
indentation force P is defined as the plate reaction at
its fixed edges. Such a way of loading provides: an
absolute rigidity of the spherical surface, uniquely
determines the contact shape, and enables more ac-
curate comparisons of the simulation results with the
theoretical data. In addition, the finite elements in-
side the sphere are practically removed from the
analysis saving the calculation time. Contact radius
a is determined as x coordinate of the last plate ele-
ment node pressed by the sphere.
It is known, the less the finite element sizes the
higher the FE analysis accuracy but the greater the
finite element number, the desired computational
resources and time. It has been found by previous
studies that about 1% difference between the theo-
retical data and the simulation results in stress can be
achieved if the finite elements size in the plate area
adjacent to the contact does not exceed 0,003 mm.
In this case, the lowest accuracy (up to 10%) was
observed in a detecting contact size a and a location
of the plastically deformed areas. Based on the ex-
ploratory studies, it was worked out a reasonable
mesh model that includes a small area of the plate
with small mesh sizes (0,0025 mm) in places where
a significant plastic deformation is expected and
element sizes of the rest part is very much larger. In
order to significantly enhance the simulation accu-
racy in detecting the contact and plastically de-
formed areas, element sizes along the expected con-
tact and the contact symmetry axis were gradually
decreased in 2–10 times. So the finest mesh was
created near the expected contact center.
Fig. 1A fine meshed part of the model
The model allows studying the elastic-plastic
behavior of any material. Here are the results for
the case when the plate material is carbon steel 45
(similar to AISI 1045) with modulus of elasticity,
Poisson's ratio and yield strength, respectively
2·105 MPa, 0,3, and 350 MPa with a power de-
pendence of isotropic strain strengthening [12]
0,48350(1 0, 239 )pl ,
where ε is a degree of deformation, %.
УСиМ, 2015, № 5 63
The study showed not only the actual parame-
ters such as indentation force P, radius a, and con-
tact area S, sphere displacement y, etc., but also the
dimensionless normalized ones (marked with *)
with respect to the corresponding values of the same
parameters at the moment the plate material is in
the very beginning of a plastic flow (marked кр):
P*=P/Pкр, S*=S/Sкр, y*=y/yкр. The normalized
parameters allow to make many simulating results
to be invariant to the model geometrical and me-
chanical particular parameters.
Since the plate material while indenting the
sphere expected to be in a complex stress state,
the condition of a plastic flow in the material ac-
cording to the von Mises criterion is
2 2 21
1 2 2 3 3 12 (( ) ( ) ( )кр , (1)
where σi, (i=1, 2, 3) is the principal stresses in a
complex stress state; σkr is a yield stress of the ma-
terial in a simple tension.
The expression of the right side of equation (1)
is equivalent stress σeq or the von Mises stress.
The model quality was tested by comparing the
results of the numerical and theoretical modeling (by
the Hertz theory [13]) for normalized displacement
y* (8 points) with its variation ranges from 0,5 to 1.
An average error for maximum pressure σ3 in the
contact center was 0,25% with a standard deviation
of 0,0295. The comparison results for indentation
parameters which are independent of the sphere dis-
placement by the Hertz theory are summarized in
the table. The results confirm the high accuracy for
stresses evaluated by the FE model.
FE Simulation results and their analysis
The modeling studies have shown that the devel-
opment of the plate stress-strain state during the
sphere indentation can be divided into two stages:
1. The elastic stage which lasts from the very
beginning of the sphere indentation until gaining
the critical stress by the expression (1) in the plate
most severely stressed point. The elastic state is
observed at y*≤1 (Fig. 2,a,b);
2. The elastic-plastic stage (y*>1) happens when
the stress in any part of the plate material reaches or
exceeds the critical value and a plastic flow occurs.
The rest of the material is in an elastic state.
The elastic-plastic stage develops in three phases.
T a b l e. Comparison of the sphere indentation parameters for the
plate elastic state by the Hertz theory and the FE simulation
Comparison factor h/a στ max/σ3
σeq.мах/
στ max
σ1/σ3=σ2/σ3
The theoretical results 0,48 0,31 2 approximately
0,8
Average FE simula-
tion results R 0,480 0,309 2,00 0,796
Standard deviations Sd
of FE simulation results 0,0078 0,0002 0,00005 0,0002
Relative standard
deviations Sd/R, % 1,63 0,06 0,003 0,03
Deviations from the
theoretical results, % 0,0 0,32 0,0 approximately
0,5
Notes: h is a depth of the maximum equivalent σeq.max and shear
στ.maxstresses; σі, (і=1,2,3)is principal stresses in the contact center
а b
с d
Fig. 2. Distribution of equivalent (a) and intensity (b) stresses in
the plate (y*=1, the elastic stage), and equivalent stress (c)
and plastic deformation (d) for y*=10 (the first phase of the
elastic-plastic stage)
In the first phase (1<y*<15), the plastic material
area is completely surrounded by the material in an
elastic state (Fig. 2,c,d). The material strengthening
the flows so that the maximum equivalent stress,
stress intensity (like in the elastic stage (Fig. 2,a,b)),
and the maximum equivalent plastic strain are lo-
cated on the contact symmetry axis at the same
depth h from the contact center. The increase in rela-
tive depth h/a (maximum stresses and plastic strain
placement on the contact vertical symmetry axis
(Fig. 3)) indicates the prevailing development of
material strengthening in a depth. However, the ma-
terial plastic flow causes the stress leveling in the
radial direction both in the plate volume and in its
contact. So, the maximum contact pressure gradu-
ally shifts from the contact center to its periphery
(relative coordinate x/a of its applying increases,
64 УСиМ, 2015, № 5
see Fig. 4, plot x_Pmax_a) and the pressure dis-
tribution in the contact (coefficient K of pressure
distribution – ratio of maximum pressure Pmax in
the contact and average pressure P/S – reduces,
see Fig. 4, plot K) levels as well. Note that for the
elastic state (y*≤1), K is close to 1,5 which corre-
sponds to the contact pressure distribution by a
hemisphere; if the distribution is uniform K=1.
0 100 200 300 400 500 600 700
0.2
0.3
0.4
0.5
0.6
0.7
h/
a elast_pl
elast
y
Fig. 3. Relative location h/a of the maximum equivalent stress and
stress intensity on the contact symmetry axis versus y* for
the material states: elastic-plastic (plot «elast_pl»), idealized
elastic (plot «elast»)
0 100 200 300 400 500 600 700
0
0.5
1
1.5
2
x_Pmax_a
K
y
Fig. 4. Relative radius x/a (plot «x_Pmax_a») applying maximum
contact pressure Pmax and K versus y*
An important feature of the second phase of the
material elastic-plastic behavior (15≤y*<50) is the
critical stress yields up to the contact surface and
spreads to its center. The phase is characterized by
the followings: a practical stability and the largest
values of ratio h/a (Fig. 3), leveling off the stress
and consequently the plastic deformation along
some curve toward the edge of the plastically de-
formed contact (Fig. 5, y*=15 and 35).Their dif-
ference is less than 1%. Such behavior of the
stress-strain state is associated with leveling off
the contact pressure and increasing coordinate x/a
applying maximum pressure Pmax (see Fig. 4).
The results of the material elastic-plastic behavior
under the spherical indenter and regularities of its
strain strengthening make it possible to choose a
reasonably rational option range for further 3D FE
research of a ball burnishing process. This will fa-
cilitate the research and improve the result reliability.
Such studies should be performed in the range of
ball normalized displacement y* from 35 to 150, i.e.,
within parts of the second and third phases of the
material elastic-plastic stage.
a b
c d
Fig. 5. Distribution of equivalent stress (a,c) and plastic deforma-
tion (b,d) for the second phase of the elastic-plastic stage:
y*=15 (a,b); y*=35 (c,d)
The third phase (y*≥50) begins with the com-
pletion of the continuous plastic state formation of
the material in the contact – the critical stress
reaches its center. In this case, the contact is in-
creasing more intensively (decreasing ratio h/a,
see Fig. 3) with practically a constant rate. An
overall depth and width of the material plastically
deformed area increase significantly (Fig. 6). More-
over, it extends beyond the contact edge (y*>150,
see Fig. 7,d,e,i,j) forming a projecting collar.
0 100 200 300 400 500 600 700
0
50
100
150
Str
hn_max
hn_20%
y
Fig. 6. The material maximum strengthening (chart «Str», %), its
depth h/hkr (plot «hn_max») and depth of 20% strengthening
h20/hkr (plot «hn_20 %») at the contact symmetry axis versus y*
This range of the indenter displacement is inher-
ent in: a high level of material strengthening – from
24 to 35%, a high degree of uniformity in the dis-
tribution of the strengthened region (see Fig. 5 and
7), a significant depth and width of the plastically
deformed area is approximately equal to the con-
tact size. Furthermore, we should expect a high sta-
УСиМ, 2015, № 5 65
a b
c d
e f
Fig. 7. Distribution of equivalent stress (a,c,e) and plastic deforma-
tion (b,d,f) for the third phase of the elastic-plastic stage:
y*=50 (a,b); y*=200 (c,d); y*=700 (c,d)
bility of the process due to a small dependence h/a
from y* for this range (see Fig. 3).The upper limit of
the recommended range is selected base on the fact
that when y*>150 plastically deformed material ex-
tends beyond the contact to form a collar of plasti-
cally strengthened material. Its appearance may
cause some unwanted effects: instability of the proc-
ess and results of the material strengthening along
the feed direction through successive increasing in
the collar height and related changes in burnishing
geometry and forces; an excessive material plastic
deformation can cause its destruction; an appearance
of great waviness on machined surfaces that will
require an additional grinding operation.
Conclusions
This paper shows a feasibility of using finite element analy-
sis to study burnishing processes of the machine part surfaces.
The FE model has been created for simulating a rigid sphere
indentation in a half-space for a wide range of the sphere nor-
malized displacement. Its good quality is confirmed by the
Hertz contact theory for ball elastic indentation into a flat sur-
face. The model simulation of the material behavior with a
power dependence of isotropic strain strengthening revealed
that the stage of an elastic-plastic deformation proceeds three
phases, which differ in the stresses and strains distribution in
the volume, contact, and surfaces around it. The revealed regu-
larities helped to justify a reasonable range of the ball dis-
placement variation for further FE studying ball burnishing
processes. Such studies should be performed in the range of
ball displacement y* from 35 to 150.
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Поступила 09.04.2015
E-mail: leuro@list.ru
© Я.Б. Сторож, И.З. Лютак, Б.Д. Сторож, О.Б. Василик,
Н.Н. Яцышин, Н.С. Пасека, 2015
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|