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MATHEMATICAL MODEL FOR QUASI-STATIC CALCULATION OF CONICAL RUBBER-METAL ELEMENTS OF HIGH-SPEED ELECTRIC TRAINS
Khromova Galina Alekseevna1 Kamalov Ikram Saidakbarovich2 Tukhtaev Behruz Ulugbek ugli3
xdoctor tech. sciences, professor 2acting docent,
3master's student of the Department of "Electric rolling stock", State Transport University, Uzbekistan, Tashkent https://doi.org/10.5281/zenodo.11064255
ABSTRACT
ARTICLE INFO
The article presents a mathematical model for quasi-static calculation of conical rubber-metal elements of a highspeed electric rolling stock, as well as an experimentally obtained relationship between the deflection of conical shock absorbers of electric trains from various grades of rubber.
Received: 18th April 2024 Accepted: 24th April 2024 Online: 25th April 2024
KEYWORDS High-speed electric trains, conical rubber-metal elements, the rational dimensions of parts of rubber-metal elements at increased speeds.
When creating chassis for high-speed electric rolling stock, it is necessary to set and solve the tasks of ensuring safety, smoothness, and reducing vibrations at high speeds in a new way [1].
The solution to these problems is a properly designed suspension of vehicles using various types of dampers based on rubber-metal elements, a pneumatic spring and hydraulic vibration dampers, which leads to an increase in the smoothness of the rolling stock and an improvement in the strength and elastic-dissipative properties of the suspension in order to reduce dynamic effects on the track and transported goods [1,2,3]. The main reliability requirement for rubber-metal elements is that their durability should ensure the absence of failures during the assigned service life and assigned life [1,4,5].
In spring suspension of electric locomotives and electric trains, most often used are not cylindrical, but conical rubber-metal shock absorbers that experience torsion twisting during operation [3]. These shock absorbers have rectangular sections enclosed between two support surfaces and experience simultaneous compression and shear deformations (Figure 1). The rigidity of such a shock absorber depends on the angle of inclination of the base plates
P.
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Figure 1. Design scheme for rectangular shock absorbers enclosed between two inclined support surfaces.
The stiffness of the conical shock absorber can be determined by the formula in accordance with scientific articles [4,5]
2F^(Ep sin2 ß+G^cos2 ß)
^KÂ —
(1)
The calculated modulus of elasticity of the EP depending on the shape factor is determined in the same way as in uniaxial compression. The factor n is taken equal to 1, and f mm - according to the graphs shown in Figures 2 and 3, depending on the rubber grade and the load value P, kN.
h
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70,00
P, kN 0,00
50,00
40,00
30,00
20,00
10,00
0,00
... II III
0,00
4,00
8,00
9,00
10,00 12,00 16,00 f, mm
Figure 2. Dependence of deflection of conical shock absorbers of electric trains from different rubber grades f, mm on load P, kN:
m m
- Row 1 - rubber grade 2959 B; - Row 2 - rubber grade 2959;
■ ■
- Row 3 - rubber grade 3068 H; - Row 3 - rubber grade 8075 H.
The form factor in this case is determined by the formula
(2)
FF — ——
Fb 2(a+b)h
Cone shock absorbers (Figure 3) under the action of the force P in the direction of the Z axis also experience joint deformation of shear and compression and can be calculated by formula (1). Here, the form factor for determining the calculated modulus of elasticity can be
approximately found by formulas (2) and (3) in accordance with scientific articles [4,5]
m(Rc+rc)
FF —
(3)
2n (Rc+rcyS '
where Rc,rc are the average radii of the larger and smaller bases of the cone, respectively.
P, kN
P, kN
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Л кН
0 4 8 12 16 f}b
4 8 12 16 / 0196
1 i Г)
&ili ■V-
20'
I 1
H0-&у 295 <)j f
> f У
/ /
/ /
/ /
/у
8 12 [o f
л.: '
a)
6)
mm
Figure 3. Dependence of deflection of conical shock absorbers of electric trains from different rubber grades on load and shape.
A rubber-metal element is considered to be designed correctly if it meets the following requirements: deformation stiffness corresponds to the design one, stresses are evenly distributed throughout the element, thermal stress, taking into account dissipative heating, is below the permissible level for this rubber grade, residual deformations after full unloading of the element are minimal and durability under certain operating conditions of the element is within the specified limits [4,5,8,9,10].
A prerequisite for the correct design of elastic elements is knowledge of the specific conditions of their operation, which allows you to choose rubber with the necessary properties. In addition, the designer must have a clear understanding of the technology of manufacturing rubber elements, the effect on their properties of rubber components, vulcanization mode, mold design, geometric dimensions of the rubber part, etc. [4 ^ 10].
References:
1. Simon Iwnicki. Handbook of Railway Vehicle Dynamics.2006. Taylor & Francis Group. -527 p.
2. Резиновые амортизаторы в локомотивах. / И.П. Ситковский, В.И.Маевский, https://lokomo.ru/podvizhnoy-sostav/polimernye-materialy-na-zarubezhnyh-zhd/Page-34.html
3. Кононов В.Е. Резиновые амортизаторы в экипажной части локомотивов: Учебное пособие. - М.РГОТУПС, 2002.-147 с.
Innovative Academy Research Support Center UIF = 8.1 | SJIF = 7.899 www.in-academy.uz
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7. Khromova G.A., Kamalov I.S., Makhmadalieva M.A. Improved method of calculating the rational dimensions of parts of hydraulic vibrations dampers of electric trains at high speeds // «Eurasian Journal of Academic Research»: International scientific journal (ISSN: 21812020), Volume 2 Issue 12, November 2022, p. 1096-1100. https://doi.org/10.5281/zenodo.7386499
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