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ARTICLE INFO
MODERNIZATION OF THE DESIGN OF THE COIL SPRING OF THE AXLE SUSPENSION OF HIGH-SPEED ELECTRIC
TRAINS
Khromova Galina Alekseevna1 Kamalov Ikram Saidakbarovich2 Omonov Shokhzhakhon Alisher ugli3
xdoctor tech. sciences, professor, 2associate professor, 3master's student of the Department of "Electric rolling stock", State Transport University, Uzbekistan, Tashkent https://doi.org/10.5281/zenodo.14799706
ABSTRACT
Received: 24th January 2025 Accepted: 30th January 2025 Online: 31st January 2025
KEYWORDS Electric rolling stock, highspeed electric train, axle box spring suspension, coil springs, vibrations, stressstrain state, calculation method for dynamic strength of coil springs, algorithm, program,
MATHCAD 15.
The article presents a mathematical model and a developed algorithm for numerical studies on the selection of rational parameters of a modernized coil spring for axle box spring suspension of high-speed electric trains, the design of which is protected by patent of the Republic of Uzbekistan for invention No. IAP 05219 [1].
МОДЕРНИЗАЦИЯ КОНСТРУКЦИИ ВИНТОВОИ ПРУЖИНЫ БУКСОВОГО ПОДВЕШИВАНИЯ ВЫСОКОСКОРОСТНЫХ ЭЛЕКТРОПОЕЗДОВ
Хромова Галина Алексеевна1 Камалов Икрам Саидакбарович2 Омонов Шохжахон Алишер угли3
^доктор технических наук, профессор, 2доцент,
3магистрант кафедры "Электроподвижной состав," Ташкентский государственный транспортный университет, Узбекистан https://doi.org/10.5281/zenodo.14799706
ARTICLE INFO
ABSTRACT
Received: 24th January 2025 Accepted: 30th January 2025 Online: 31st January 2025 KEYWORDS
Электроподвижной состав, высокоскоростной электропоезд, буксовое рессорное подвешивание, винтовые пружины,
В статье представлены математическая модель и разработанный алгоритм численных исследований по выбору рациональных параметров модернизированной винтовой пружины для буксового рессорного подвешивания высокоскоростных электропоездов, конструкция которой защищена патентом Республики Узбекистан на изобретение No IAP 05219 [1 ].
вибрации, напряженно-деформированное
состояние, расчета прочности пружин,
метод динамической
винтовых алгоритм,
программа, MATHCAD15.
The spring suspension system of electric rolling stock is one of the critical components of mechanical equipment, since its design and characteristics directly determine the safety of movement, smoothness of the ride and reliability of other components of the sprung part. The main tasks in creating new designs of spring suspension of electric trains, as well as modernization of existing ones, are expansion of functional capabilities, increase in reliability, strength and durability [2,3,4].
Research has been conducted and is being conducted on this topic by leading scientists worldwide such as S.A. Brebbia (Wessex Institute of Technology, UK), G.M. Carlomagno (University of Naples di Napoli, Italy), A. Varvani-Farahani (Ryerson University, Canada), S.K. Chakrabarti (USA), S. Hernandez (University of La Coruna, Spain), S.-H. Nishida (Saga University, Japan). Authoritative scientific schools and prominent scientists in the CIS countries from MIIT, PGUPS, MAI, VNIIZhT, JSC VNIKTI, JSC Russian Railways, etc. worked on these issues. A significant contribution to solving many complex problems and checking theoretical conclusions related to the study of the processes of oscillations of the spring suspension of the rolling stock was made by the Russian Research Institute of Railway Transport (CNII MPS) and the Russian Research Institute of Railcar Building (NIIV), where along with theoretical studies, a large number of experimental studies (bench and full-scale ones) were conducted [2,3,4]. In Uzbekistan, the academician of the Academy of Sciences of the Republic of Uzbekistan, professor, doctor of technical sciences Glushchenko A.D., professors Fayzibaev Sh.S., Khromova G.A., Shermukhamedov A.A., Adylova Z.G., Rakhimov R. V., Ruzmetov Ya. O., Khamidov O. R., Radjibaev D. O. and their students studied the problems of optimizing the systems of spring suspension of rolling stock [5^8].
However, in the existing calculation methods, the curvilinearity of surfaces, impulse contact processes that occur during the operation of the spring suspension of ground vehicles, the complexity of the dynamic loading pattern, and the volumetric configuration of systems have not been taken into account so far.
To derive the equations of spatial oscillations of a cylindrical elastic rod bent along a helix with a variable radius of curvature of the coils, we used the results obtained in [5^8] and the following assumptions.
1. The boundary element is taken as a single coil of a cylindrical elastic rod bent along a helix with a fixed radius of curvature (Fig. 1). N is the number of boundary elements (depending on the spatial configuration of the spring element); it is connected into a single dynamic system using boundary conditions.
We used the calculation scheme shown in Fig. 2 (for axle box spring suspension of highspeed electric trains) [by patent of the Republic of Uzbekistan for invention No. IAP 05219 [1].
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2. One coil is described by a curvilinear coordinate system (Fig. 1), characterized by distance I to fix the location of a particular section, measured along the length of a helical line bent along the radius Rs in plane Y I, passing through the centers of gravity of these sections.
The parameters of the sections of the spring coil (Fig. 1) are taken into account according to
- cross-sectional area Fs =
- mass intensity M1 spring coil material.
ndl^p
redf
and i1 mass moment of inertia, where p is the density of the
redf
equatorial Ix = Iy = and polar I0 = Ix + Iy = = moments of inertia of the
32
cross-sectional area of the spring coil,
- modulus of elasticity of the first E and the second G kinds of the coil material.
2Pscos X
a)
Xs (t, l)
o 4 o
b)
Fig. 1. Boundary element in the form of a single coil of a cylindrical elastic rod bent along a helix with a fixed radius of curvature: a). one model coil; b). developed view.
3. We introduce generalized coordinates that take into account:
- elastic bending deformations xs(t,£), ys(t,£) in two planes - tangent to the helix and parallel to the axis of the cylinder of radius Rs of the winding of the coil, and perpendicular to the first plane.
- elastic deformations under torsion Qs(t,l) and compression Us(t,l) relative to the longitudinal axis of the helix of the spring.
4
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Fig. 2. Calculation scheme for simulation of vibrations of cylindrical elastic rod bent along a helix (for axle box spring suspension of high-speed electric trains).
3. With the introduced assumptions, using the Ostrogradsky-Hamilton method [4], we compose the equations of oscillations for one coil of the spring along each generalized coordinate of elastic deformations. Then, using the Euler equation for elastic systems, we obtain, as a result, a system for describing the bending (in two planes), longitudinal and torsional vibrations of a cylindrical rod bent along a helix, which generally characterizes the spatial vibrations of a coil of a helical spring
d4ys ,d2ys W 2 , D . ^ , ys , WM d2ys . d4ys \ +Rs (R2 dl + dl3 ) £sEIv Ps(l) C0S(Rs) ,
d4xs , d2xs 1 . - GI0\ , 1 f,. d2xs . d4xs \
~d~x + dx ' ETX (pss - rV + ET (mi ddt2 - li Td^)
+
GL
d2Qs
dl2 R.E Ir
o
2n cos A
Ps(t)C0S(ß,
d3ys . 1 dys FsRs2 d2Us M^ d2Us
dl3
1
Rs
d2xs dl2
s dl di2
'y GIo
dl2
EIV
d 2
= 0 ,
d2 Qs 1
=--cos A
d 2
G o
sin
(Rs)^)-
(1)
(2)
(3)
(4)
1sE IX
The resulting system of differential equations allows approximate solutions for the cases when Pssinl and PscosA are constants. These solutions include functions of static xs(l),ys(l),Us(l),Qs(l) and dynamic xa(tJ),ya(tJ),Ua(tJ), Qa(tJ) components.
For numerical calculation in the MATHCAD 15 programming environment, we accept the following initial data and assumptions: 1. We accept a model of a cylindrical helical spring, characterized by a wire diameter ds, an average coil diameter Ds, a pitch between turns Ss in an unloaded state, a number of turns is, a static load Ps , a lead angle in a loaded state A.
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2. We present the initial model as a single coil with a vertical axis of symmetry and length passing through the center of gravity of the sections of the helix ls (Fig. 1, a).
3. For the accepted model of a single coil, the upper section for 1 = 0 is considered cantilever (free end), loaded with concentrated static load Ps , and the lower section for I = I s - is considered clamped.
Conclusions:
1. The proposed numerical-analytical applied method and refined methods of dynamic strength calculation (using the method of boundary elements - Boundary Element Technology) for curvilinear elements of the rolling stock of railways of a complex profile (springs, vibration dampers, cradle suspension units, spring suspension) are planned to be used in the design , operation and modernization with the extension of the useful life of locomotives.
2. The proposed methods are relevant for the Republic of Uzbekistan, and for the CIS countries, as they allow us to obtain better dynamic characteristics of ground vehicles, which determine their reliability and key performance indices.
References:
1. Глущенко А.Д., Хромова Г.А., Мохаммед Исса Махмуд Ахмад. Упругий элемент. Патент Республики Узбекистан на изобретение № IAP 05219, опубл. 28.06.2002 г., Бюл. № 3.
2. Ибрагимов М.А. Совершенствование конструкции рессорного подвешивания локомотивов. Винтовые цилиндрические пружины: монография. / М.А. Ибрагимов.-МИИТ, 2010.-127 с.
3. Branislav Titurus, Jonathan du Bois, Nick Lieven, Robert Hansford. A method for the identification of hydraulic damper characteristics from steady velocity inputs. Mechanical Systems and Signal Processing, 2010, 24, (8), pp. 2868-2887. (2010).
4. Timoshenko S. P. Strength of Materials: Part II - Advanced Theory and Problems. - СПб.: Издательство «Лань», 2002. - 672 c.
5. Khromova G. A., Mukhamedova Z. G., Yutkina I. S. Optimization of dynamic characteristics of emergency recovery rail service cars. / Monograph. ISBN 978-9943-975-966. - Tashkent: "Fan va tekhnologiya", 2016. - 253 p.
6. Khromova G., Makhamadalieva M. and Khromov S. Generalized dynamic model of hydrodynamic vibration dampener subject to viscous damping. E3S Web of Conferences, EDP Sciences 264 (2021), 05029. https://doi.org/10.1051/e3sconf/202126405029
7. Khromova G., Kamalov I. and Makhamadalieva M. Development of a methodology for solving the equations of bending vibrations of the hydro friction damper of the electric train of disk type. AIP Conference Proceedings, 2656(1) (2022). https://doi.org/10.1063/5.0108814
8. Khromova G. A., Makhamadalieva M. A. Development of a mathematical model to justify rational parameters of the spring suspension of the high-speed electric train Afrosiab. // Universum: технические науки : электрон. научн. журн. 2022. 10(103). URL: https://7universum. com/ru/tech/archive/item/14404
