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ELECTRICAL ENGINEERING
ANALYSIS OF MECHANICAL AND ELECTRICAL VIBRATIONS IN THE ENGINES OF MILITARY AND COMBAT VEHICLES ON THE BASIS OF DIFFERENTIAL EQUATIONS
Jahongir Ulashov
PhD,
Associate Professor of the Department of Natural and Scientific Sciences, Chirchik Higher Tank Command and Engineering School,
Uzbekistan, Chirchik
Nemadullo Makhmudov
PhD,
Professor of the Department of Natural Sciences, Academy of Sciences of the Armed Forces of the Republic of Uzbekistan,
Uzbekistan, Chirchik
Gafurjan Tuganov
Associate Professor, Head of the Department of Aviation Equipment, Military Aviation Institute of the Republic of Uzbekistan,
Uzbekistan, Tashkent
Inomdzhon Makhmudov
Student, Academic Lyceum, Samarkand State University named after Sh.Rashidov,
Uzbekistan, Samrkand
АНАЛИЗ МЕХАНИЧЕСКИХ И ЭЛЕКТРИЧЕСКИХ КОЛЕБАНИЙ В ДВИГАТЕЛЯХ ВОЕННЫХ И БОЕВЫХ МАШИН НА ОСНОВЕ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ
Джахонгир Зайниддинович Улашов
канд. физ.-мат. наук, PhD, Доцент кафедры естественных и научных наук, Чирчикское высшее танковое командно-инженерное училище,
Узбекистан, г. Чирчик
Немадулло Ахматович Махмудов
канд. физ.-мат. наук, профессор кафедры естественных наук Академии наук вооруженных сил Республики Узбекистан, Узбекистан, г. Чирчик
Туганов Гафурджан Шокирович
доц., начальник кафедры Авиационного оборудования, Военный авиационный институт Республики Узбекистан,
Узбекистан, г. Ташкент
Махмудов Иномджон Немадуллаевич
студент, Академический лицей,
Самаркандский государственный университет имени Ш.Рашидова,
Узбекистан, г. Самрканд
Библиографическое описание: ANALYSIS OF MECHANICAL AND ELECTRICAL VIBRATIONS IN THE ENGINES OF MILITARY AND COMBAT VEHICLES ON THE BASISOF DIFFERENTIAL EQUATIONS // Universum: технические науки : электрон. научн. журн. Ulashov J.Z. [и др.]. 2025. 1(130). URL: https://7universum.com/ru/tech/ar-chive/item/18906
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UNIVERSUM:
ТЕХНИЧЕСКИЕ НАУКИ_январь. 2025 г.
ABSTRACT
This article discusses the solution of one of the current problems of mechanical and electrical vibrations that occur in military and special equipment, using the section of mathematics of differential equations. The article presents a simple diagram of an electric circuit and gives a solution to the second derivative of current with respect to time with the right-hand side of the invariant coefficient of the second order using special differential equations.
АННОТАЦИЯ
В данной статье рассматривается решение одной из актуальных проблем механических и электрических вибраций, возникающих в военной и специальной технике, средствами раздела математики дифференциальных уравнений. В статье приведена простая схема электрической цепи и дано решение второй производной тока по времени с правой частью инвариантного коэффициента второго порядка с помощью специальных дифференциальных уравнений.
Ключевые слова: колебание, уравнение, дифференциальное уравнение, постоянный коэффициент.
Keywords: oscillation, equation, differential equation, constant coefficient.
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It is known from the laws of mechanical motion that the vibration of a rigid body with mass can be free or forced. Free vibration equations are characterized by damping and consist of a homogeneous differential equation. Usually, in internal combustion engines, continuous oscillations are formed that are not necessarily damped. The reason for this is that external force periodically affects the system. In internal combustion engines, as a result of the explosion of fuel, mechanical vibrations (vibrations) are generated, and it is natural for
electric vibrations to be generated in the electric circuit and electric motor (generator)[1]. Mechanical forced vibrations are represented by second-order inhomogene-ous special differential equations with constant coefficients. Forced vibration is generated under the influence of an external force and its general formula is given in the form (1).
d2 x dx
m—- + X--+ kx = f(t)
at2 at ' v '
(1)
where m- the mass of the body (object) (kg), x- is the function representing the law of motion, the deviation of the points on the surface of the engine from a certain position (m),
k- uniformity (stiffness) of the elastic system, A - proportionality coefficient,
This differential equation is derived from Newton's second law, one of the fundamental laws of dynamics[2]. Any moving object comes under the influence of this law. In turn, the rotational vibration of the flywheel on the axis is also expressed by equation (1). Only, xinstead of the law
f(t) - external force or driving force, - acceleration of the system,
d2x
—- system speed.
of motion^, the angle of rotation of the flywheel (rad), instead of the massm, the moment of inertia of the flywheel is replaced I (kg ■ m2), instead of the torquek, the angular velocity wof the axis is replaced, and as a result, the following equation (2) is formed.
ida2+xdft + «<p = m
(2)
Equation (2) is called a special form equation with a second-order constant coefficient on the right side. In addition, it is possible to analyze the mechanical vibrations (vibrations) occurring in alternating synchronous three-phase generators (including asynchronous motors) using equation (1).
One of the factors (physical process) that causes the most damage to the techniques is vibration. The factors that
create it are mechanical and electrical vibrations. We use the differential equations branch of mathematics to bring the mechanical or electrical vibrations in this phenomenon to the limit of human knowledge. Suppose a non-branched alternating current circuit connected in series is given (Fig. 1).
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ЛД1 i лл
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январь, 2025 г.
Figure 1. Unbranched The main reason for this is that alternating current i(t) is produced in synchronous generators, which are considered the primary (main) source of electricity. The above simple electric circuit consists of L- inductive coil, R- resistance, C- capacity (capacitor), E- electric driving force. The current in the electric circuiti(t), the capacitor charge q, and the voltages are respectively denoted by UR, UL andUc. Since the elements in the electric circuit are connected in series^ = UR + UL + Uc,
alternating current circuit.
the total voltage is equal to. When evaluating any complex branched electric circuit, it is evaluated by its equivalent simple electric circuit. For this reason, our main goal Ris L,C,Eto scientifically check a simple electric circuit formed by connecting the current i(t) — d-elements in series [3]. We create the following differential equation from the equality of current UL — L —, voltagees, and Uc — -.
L- + Ri+- — E (3)
dt C v '
(3) by differentiating the differential equation once linear differential equation with the following constant
with respect to time and dividing both parts of the equa- coefficients.
tion by L, we form the second-order non-homogeneous
d2i , R di , 1 1 dE ...
--+ —---\--- I = -----(4)
dt2 L dt LC L dt w
The differential equation (4) is the oscillation formula in whichR, L, Cs are fixed numbers, for conven-
c =1 1 dE
ience R — 2, L — 1, 5---= sin t by performing
the substituton, we get the following equation
\2 i'\ + 5 i = sin t (5)
(5) of the differential equation (0) = 1 va i'(0) — We find the solution of a homogeneous differential
2we find a general solution that satisfies the initial con- equation with constant coefficients of the second order
ditions. i — eXt we look for it. Taking first and second order de-
To solve the equation, first homogeneous i"t + rivatives i' — AeXti" — A2eXt 2i't + 5 i = 0 we find the general solution of i(t).
A2eXt + 2AeXt + 5eXt — 0
eXt(A2 + 2A + 5) — 0 eXt > 0,A2 + 2A + 5 — 0 A12 — -1±2i
a = -l,ß = 2
i(t) = eat(C1 cos ßt + C2 sinß t) = e-t(C1 cos 2t + C2 sin 2 t)
the private solution of the inhomogeneous part order derivatives over dan (5) and take them to the
of the differential equation is i * (t) — A sin t + differential equation.
B cos tlooking in the view[4].first on i*(t) dan t bo'yicha birinchi we take the First-Order and second-
—A sin t — B cos t + 2A cos t-2B sin t + 5A sin t + 5B cos t — sin 12A cos t + 4B cos t + 4A sin t — 2B sin t — sin t
(2A + 4B = 0 {A = 5
{4A-2B — 1 1 1
B —--
V 10 11 i * (t) — — sin t — —Cos t
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i(t) = е t(C1 cos 2t + С2 sin2 t) + —sin t — —cos t
(5) the total solution of the differential touch i = ï + i *was equal to.
1 1 -s in t — — 5 10
Using the boundary conditions CxandC2 finding the values of the constants[5].Using the boundary conditions and finding the values of the constants[6-9].
1 11
1 = C--^C. = —
1 10 1 10
i'(t) = — e t(C1cos2t + C2sin2t) + e t(—2C1cos2 t + 2C2sin2 t) +—sint ——cos t
1 29
2 = — C^ + 2C2+-^ C2= —
I 2 5 2 20
(5) the general solution of the differential touch satisfying the initial condition
II 29 1 1
i( t) = e-1(—cos 2t +—s in2 t) +-s in t--c os t (6)
v J v10 20 J 5 10 v '
is in view.
Conclusion It is possible to prevent a technical malfunction by par-
„. .. ^ , • „ , • „ r- tially replacing a specific unit, eliminating expensive re-
The idea of the study is that in the process of me- , . , . ,
placement, which increases the life of the internal com-
chanical oscillation, an electrical signal arises with
... .. ^ ^ . . f bustion engine. Modern diagnostic technology requires
which you can diagnose the technical condition of the
information for processing and solving where the ad-
engine. Predict until the engine stops completely, excluding the non-maintainability of an expensive engine.
References:
dress and location of the future problem are indicated.
1. Ulashov J.Z., Maxmudov N.A., Shavazov K.A. The role of physical and mathematical laws in diagnosing electrical equipment of military vehicles // Sustainable agriculture. - Toshkent, 2022.- Special issue. 2022.- P. 115-118.
2. Ulashov J.Z., Zoirov M.A., Odashov Z.Z.Harbiy texnikalarning elektr jihozlarini diagnostikalashda fizika-matemat-ika qonunlaridan foydalanish // - Zirhli qalqon. - Toshkent, 2022. - № 8(20) 2022.- B. 73-78.
3. Ulashov J.Z., Eshquvvatov Sh.N., Misirov Sh.Ch., Xalimov E.X., Maxmudov N.A., Turniyazov R.Q. Explanation of electric current in military vehicles according to the laws of physical and athematics // The scientific journal Universum: Technical sciences. - Moscow, 2023. - Issue: 2(107). February 2023. Part 6. - pp. 57-63.
4. Piskunov N.S. Differensial va integral hisob. 2-tom. Oliy texnika o'quv yurtlari uchun darslik. O'qituvchi nashriyoti. - Toshkent 1974.
5. Mahmudov G'.N. AvtomobiUarning elektr va elektron jihozlari. "NOSHIR" Toshkent 2011.
6. Danov B.A. Ignition control systems for automobile engines. Moscow, Hotline-Telecom, 2005
7. Electronic resource https://220volt.uz
8. Electronic resourcehttps://micromir-nn.ru
9. Electronic resourcehttps://www.joom.com/ru
