Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions
The aim of this work is to optimize the geometric form of additional plastic working elements of shock absorbers for various cases of impact loading. A finite element model of plastic element was used to evaluate the stressed state generated in cases of coupling of heavy freight trains with various...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2002
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| Назва видання: | Проблемы прочности |
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| Цитувати: | Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions / A. Boiko // Проблемы прочности. — 2002. — № 3. — С. 134-140. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-468012016-04-14T10:40:06Z Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions Boiko, A. Научно-технический раздел The aim of this work is to optimize the geometric form of additional plastic working elements of shock absorbers for various cases of impact loading. A finite element model of plastic element was used to evaluate the stressed state generated in cases of coupling of heavy freight trains with various types of mandrel. Numerical simulation results show that application of plastic working element with convex generating line of mandrel is optimal for damping shock loads and minimize damage during collisions. Проведена оптимизация геометрической формы дополнительного пластичного рабочего элемента для различных случаев ударного нагружения. Для оценки усилий сцепления тяжелых грузовых составов с разными видами амортизатора использовали конечноэлементную модель пластичного элемента. Эксперименты, включающие математическое моделирование, показали, что пластичные рабочие элементы с выпуклой образующей являются наиболее эффективными при столкновениях. Проведено оптнмізацію геометричної форми додаткового пластичного робочого елемента для різних випадків ударного навантаження. Для оцінки зусиль зчеплення важких вантажних потягів із різними видами амортизаторів використовували скінченноелементу модель пластичного елемента. Експерименти, до складу яких входило математичне моделювання, показали, що пластичні робочі елементи з опуклою твірною є найбільш ефективними при зіткненнях. 2002 Article Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions / A. Boiko // Проблемы прочности. — 2002. — № 3. — С. 134-140. — Бібліогр.: 5 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/46801 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Boiko, A. Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions Проблемы прочности |
| description |
The aim of this work is to optimize the geometric form of additional plastic working elements of shock absorbers for various cases of impact loading. A finite element model of plastic element was used to evaluate the stressed state generated in cases of coupling of heavy freight trains with various types of mandrel. Numerical simulation results show that application of plastic working element with convex generating line of mandrel is optimal for damping shock loads and minimize damage during collisions. |
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Article |
| author |
Boiko, A. |
| author_facet |
Boiko, A. |
| author_sort |
Boiko, A. |
| title |
Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions |
| title_short |
Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions |
| title_full |
Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions |
| title_fullStr |
Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions |
| title_full_unstemmed |
Energy Absorption Optimization of Multiaction Plastic Working Element of Vehicle Systems under Emergency Impact Loading Conditions |
| title_sort |
energy absorption optimization of multiaction plastic working element of vehicle systems under emergency impact loading conditions |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2002 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/46801 |
| citation_txt |
Energy Absorption Optimization of Multiaction Plastic Working
Element of Vehicle Systems under Emergency Impact Loading
Conditions / A. Boiko // Проблемы прочности. — 2002. — № 3. — С. 134-140. — Бібліогр.: 5 назв. — англ. |
| series |
Проблемы прочности |
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AT boikoa energyabsorptionoptimizationofmultiactionplasticworkingelementofvehiclesystemsunderemergencyimpactloadingconditions |
| first_indexed |
2025-07-04T06:18:46Z |
| last_indexed |
2025-07-04T06:18:46Z |
| _version_ |
1836696135000915968 |
| fulltext |
UDC 539.4
Energy Absorption Optimization of Multiaction Plastic Working
Element of Vehicle Systems under Emergency Impact Loading
Conditions
A. Boiko
Institute of Mechanics, Riga Technical University, Riga, Latvia
УДК 539.4
Оптимизация пластичного рабочего элемента многоразового
дей стви я в усл ов и я х авар и й н ого удар н ого н агруж ения
транспортных средств
А. Бойко
Институт механики, Рижский технический университет, Рига, Латвия
Проведена оптимизация геометрической формы дополнительного пластичного рабочего
элемента для различных случаев ударного нагружения. Для оценки усилий сцепления тяже
лых грузовых составов с разными видами амортизатора использовали конечноэлементную
модель пластичного элемента. Эксперименты, включающие математическое моделирова
ние, показали, что пластичные рабочие элементы с выпуклой образующей являются наи
более эффективными при столкновениях.
Ключевые слова: моделирование расширения трубы, пластичный элемент,
оптимизация амортизатора, аварийное нагружение.
The problem of effective damping of multiple impact loads in the heavy
freight trains still remains to be solved. Extreme dynamic longitudinal forces are
capable of causing significant damages of the rolling-stock, track and cargo.
Results of research on longitudinal dynamics of a train are important for
designing the rolling-stock and braking equipment, and also for selecting the
safest driving mode and forming the freight trains. Several additional plastic
shock absorber designs, capable to prevent destruction of railway car, have been
proposed [1, 2]. However, such devices have a single-use functionality which is
inappropriate in the case of repeated collisions. The design of the additional
multiaction plastic shock absorber capable of functioning several times in a short
interval of time is proposed in [3]. The proposed structure [3] of a coupling
between the railway cars includes additional multiaction plastic shock absorbers
with “mandrel - deformable tube” working elements.
1. The Research Problem. At present the finite element method (FEM) is a
common engineering method for calculation of structural strength of vehicle
systems [4]. The plastic deformation behavior of working element has been
analyzed by simulation of a thick-walled tube under shock loading conditions that
characterize collisions of heavy freight trains. The stressed state is assumed to be
two-dimensional with the maximal stress a ̂ , where a p is axial compressive
© A. BOIKO, 2002
134 ISSN 0556-171X. Проблемы прочности, 2002, № 3
Energy Absorption Optimization
stress, and o ̂ is circumferential tensile stress. The following plasticity condition
(Eq. 1) is applied
where o s o is the extrapolated yield stress, D is the modulus of hardening, and
ln(R/R o) is general tangential tensile strain.
All tests were performed by the finite element method (FEM) using the
ANSYS software package [5]. FEM mesh contains plastic, dry friction,
viscoplastic and solid elements. The criterion of optimization is the increase of
energy absorption. Parameters of optimization are the following geometrical
parameters of the working element: cone angle a, values of the tube expansion
(RdK — Rdo), heights of cylindrical surfaces of mandrel (hK - working and h0 -
directional), tube thickness S and radius of curvature of cone RAD. Constraints
of optimization are the value of the yield stress Gt of a tube material in the center
of plastic deformation, and the allowable value of the tensile strength, under
condition that the plastic element works without formation of cracks in the wall of
the deformable tube. Insofar as the problem is axisymmetric, calculation was
carried out only for one half of the element section relative to the axis of
symmetry, thus minimizing the time of calculations and making the task simpler.
The FEM model is represented in Fig. 1. The properties of deformable tube 2 are
described by a finite element with viscoelastic hardening properties. For the
description of this element the isotropic and bilinear isotropic hardening materials
are satisfactory. The mandrel properties are described by a solid-state finite element. The contact between the surfaces of the mandrel and deformable tube is
simulated by 3-nodal element with Coulomb friction, as shown in Figs. 2 and 3.
The aim of numeric simulation was optimization of mandrel generating line
form and dimensions by way of varying the form of friction surfaces. Simulation
of the tube expansion process by indentation of mandrel with weight M (weight
of the railway car) into a tube of a smaller diameter was carried out for various
°<p = ° S 0 + D l n ( R r 0 )j (1)
Fig. 1. Initial position o f the FE M model.
Fig. 2. Schem e o f the contact elem ent.
Fig. 3. Schem e o f the contact forces w ith Coulom b friction.Fig. 1
ISSN 0556-171X. npoôëeuu npouuocmu, 2002, № 3 135
A. Boiko
initial speeds of loading (Fig. 1). The complete transitional dynamic analysis for
plastic elements was used in the ANSYS processor.
As a result of the analysis of the properties of a plastic working element
installed on the emergency absorbing device, it is necessary to obtain: the
distributions of the stresses in a wall of deformable tube for various loading
speeds; modes of metal yielding with no cracks in the tube wall. For this purpose,
the accelerations and efforts values that were transmitted to the freight car during
the operation of a plastic element at collisions were determined.
2. Model Validation. For validation of the accuracy of the created finite
element model in ANSYS [5] (ANSYS software package, version 5.6) a
comparison with the results of a working test at static loading was carried out.
The calculations were made for a reduced model. The experiment was carried out
with a deformable tube (sizes 20 X 1.3 X115 mm), manufactured of steel (Steel 5),
slowly loaded by a mandrel (material Steel 6) of a large diameter (values of tube
expansion RdK — Rdo = 1.2 mm). The mandrel obliquity angle was presumed to be a = 20° with the cone-generating line in the form of a straight line RAD = oo,
tube thickness S = 1.3 mm (Fig. 4).
F , N
4000
3600
. 744E+07 3200
. 411E+08
. 748E+08 2600
. 109E+09
. 142E+09 2400
. 176B+09 2000
.210E+09
.243E+09 1600
.277E+09
.311E+09 1200
800
400
A -1 0 2, m
Fig. 4. The equivalent stress (a) and expansion effort vs w orking stroke o f m andrel (b).
The results of n tests of the experiment, performed using the initial data
described above, are shown in Fig. 4. In the process of pipe expansion, the effort
P = 3560 N with a deviation ±182N (~5%) is obtained. A comparison of the
results of calculation by FEM program ANSYS and the experiment results has
confirmed the accuracy of the model (Table 1). The effects of a smooth decrease
in the effort during the initial phase of deformation (bending of a free end of tube
Fig. 4b), with the following increase in the effort and subsequent formation of a
steady center of deformation characteristic for the process of tube expansion
(Fig. 5) are reflected perfectly in the model.
The numeric simulation of a plastic working element by the ANSYS
software package shows a deviation of 1.4% in relation to the result of the
experiment, which satisfies the research problem requirements.
136 ISSN 0556-171X. npoôëeubi npounocmu, 2002, N 3
Energy Absorption Optimization
T a b l e 1
Experimental and Numeric Simulation Results
C om pared param eter E xperim ental result
(Steel 5)
A N SY S
(dashed line in Fig. 4)
Relative deviation,
%
Expansion effort F 3560±182 N 3610 N + 1 .4
T a b l e 2
Characteristics of Full-Scale Plastic Element
Properties o f m aterial
[Steel 30KhGS (m andrel), Steel 20K h (tube)]
M echanical Geom etric
M = 84 -103 kg w eight o f the ra ilw ay car Rd0 = 0.026 m RdK = 0.031 m
p = 0.15 friction coefficient h0 = 0.010 m hK = 0.005 m
Gt = 600 M Pa yield stress S = 0.022 m thickness o f tube
ETAN = 0.01 G Pa tangent m odulus а II 3 О о cone angle o f m andrel
EXXd = 198 G Pa elastic m odulus o f m andrel x = 1 — 5 m /s initial velocity
EXXp = 200 G Pa elastic m odulus o f tube Am = 0 2 m m axim um w orking stroke
o f p lastic elem ent.3
Ö
=Pr Poisson’s ratio
DENS = 7850 k g /m 3 m aterial density
Fig. 5. Schem e o f variations o f the expansion effort F from w orking stroke
3. Dynamic Calculation of a Full-Scale Construction.
calculation of plastic working element full-scale construction and optimization of
the mandrel dimensions allowed us to obtain the optimal characteristics of the
plastic element. The parameters of deformable tube for a plastic element
(preferable length and materials) are determined in Table 2.
In the above calculations, a 4-axle open wagon with a mass of 84 • 10 kg
was accepted as the basic type of railway car.
A o f m andrel.
The dynamic
ISSN Ü556-171X. Проблемыг прочности, 2ÜÜ2, N З 137
A. Boiko
The dynamic behavior of a plastic working element (mandrel 1 - deformable
tube 2) for various loading speeds was investigated (see Fig. 6). As a result of the
numeric simulation, the influence of the loading speed on the working element
characteristics was determined, and the effects of yield stress increase and
temporary resistance were revealed.
F -10“2, N
Fig. 6. Expansion effort vs working stroke of mandrel (Vi ~ 1 m/s, Vi = 2 m/s, • ••> V5 = 5 m/s).
For obtaining the optimal working characteristics (maximal contact surface,
maximal expansion effort, and minimal equivalent stress) of the plastic element,
we have also performed the optimization by variation of the value of RAD - form
of friction surface of a mandrel: convex, straight or concave generating line of a
cone. The respective results are represented in Fig. 7a-c.
a b c
Fig. 7. The equivalent stress ae of plastic working element for different forms of the cone
generating line of mandrel: (a) straight line, (b) concave line, (c) convex line. Speed of loading -
x = 3.05 m/s. [(a) ae = 0.665 • 109 N (tube), ae = 1.160 -109 N (mandrel); (b) ae = 0.647-109 N
(tube), ae = 1.400-109 N (mandrel); (c) ae = 0.626-109 N (tube), ae = 1.010-109 N (mandrel).]
During the optimization it was discovered that for RAD = °o expansion
effort insignificantly exceeds the effort for convex surface only in the end of
working stroke of mandrel (Fig. 8). The use of a concave surface of mandrel
(Figs. 7b and 8) gives the maximal expansion effort F = 90-104 N, but the stress
in mandrel reaches the limiting values for the chosen material (steel 30KhGS).
138 ISSN 0556-171X. npoôëeubi npounocmu, 2002, № 3
Energy Absorption Optimization
F -10“ 2 , N
Fig. 8. C alculation o f expansion effort vs w orking stroke o f m andrel for different form s o f cone
generating line: ( / ) RAD = oo; (2) RAD = 0.04 m; (3) RAD = 0.04 m, x = 3.05 m/s.
Thus, concave friction surface of mandrel requires a more durable (expensive)
brand of steel to be used.
Therefore, mandrel form with a convex friction surface RAD = 0.04 m (Figs.
7c and 8) is accepted as closest to the optimum from the point of view of maximal
energy absorption of a plastic element. The expansion effort F = 74-104 N at
working stroke Д= 0.0831 m is insignificantly less than at RAD = o (F =
= 74-104 N, Д = 0.0939 m), but the contact surface length is maximal (Fig. 7c),
while the equivalent stress is minimal and does not reach its allowable value.
Conclusions. As a result of the optimization, the energy absorption of a
plastic element has been brought to the maximum by improvement of mandrel
geometry, namely: the forms of cone friction surface, cone angle, values of tube
expansion, and heights of cylindrical surfaces of mandrel. The effects of
interaction of dry friction, elastic and solid elements are revealed. Comparison of
numerical results and experimental results shows the satisfactory accuracy of
calculation. Mandrel form with a convex friction surface (RAD = 0.04 m) is
calculated as closest to the optimum from the point of view of maximal energy
absorption of a plastic element for this case.
Numerical simulation and optimization of a plastic working element
significantly increases the accuracy of a new comprehensive coupling model by
way of including the emergency multiaction plastic shock absorbers. The model
of plastic element can be used for the construction of a complex model of
longitudinal dynamics of heavy trains.
Р е з ю м е
Проведено оптнмізацію геометричної форми додаткового пластичного робо
чого елемента для різних випадків ударного навантаження. Для оцінки
зусиль зчеплення важких вантажних потягів із різними видами аморти-
ISSN 0556-171X. Проблемы прочности, 2002, № 3 139
A. Boiko
заторів використовували скінченноелементу модель пластичного елемента.
Експерименти, до складу яких входило математичне моделювання, пока
зали, що пластичні робочі елементи з опуклою твірною є найбільш ефек
тивними при зіткненнях.
1. Automatische Mittelpufferkupplung, European Patent Application No. 0608531
of 13.12.93.
2. Central Buffer Coupling, Patent Application GB No. 2173755 of 10.04.85.
3. A. Boiko, Research of Shock Processes and Substantiation of Ways to
Increase Railway Car Safety at Collisions [in Russian], Master’s Degree Thesis, Riga Technical University (1997).
4. F. Cook and S. Mark, “Multibody dynamic simulation of the rail impact
test,” in: Proc. of the Society for Computer Simulation, Int. Summer
Computer Simulation Conference (1997).
5. The ANSYS User’s Manual, Vol. 4, Theory, Release 5.6 (2000).
R eceived 14. 11. 2001
140 ISSN 0556-171X. Проблеми прочности, 2002, № 3
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