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SRSTI 55.43.03; 73.31.41.
Balgabekov Toleu Kunzholovich
Candidate of Technical Sciences,
head of the department «Transport Engineering and Technology»,
S. Seifullin Kazakh Agrotechnical University,
Nur-Sultan, 010000, Republic of Kazakhstan,
e-mail: tdi_kstu@mail.ru
Shontayev Djamanbai Salykovich
Candidate of Technical Sciences,
head of the department «Transport Engineering and Technology»,
S. Seifullin Kazakh Agrotechnical University,
Nur-Sultan, 010000, Republic of Kazakhstan,
e-mail: dshontaev@mail.ru
Kongkybayeva Arailym Niyazbekqyzy
master of Science, Senior Lecturer,
the department «Transport Engineering and Technology»,
S. Seifullin Kazakh Agrotechnical University,
Nur-Sultan, 010000, Republic of Kazakhstan,
e-mail: arai_janaarka@mail.ru
SHOCK RESEARCH IN SELF-PROPELLED CONCRETE MIXERS (SPC)
The article presents studies of the shock process of the mechanical part of (SPC), which are impacted, their strength is determined by the reaction to shock. This characteristic is determined either by the displacement of the mixer relative to, or the magnitude of the dynamic loads. Key words: research, impact wear, concrete mixer, load, hit, mechanical system.
INTRODUCTION
The linear passive damped mechanical system of the SPC exhibits certain transients with certain frequencies and attenuation rates after excitation. The Laplace transform of the reaction of the mechanical system of the SBS increases indefinitely, when I approaches the complex frequency, including the attenuation rate and the angular attenuation rate and the angular, of any of these transients. Thus, it is necessary to describe the mechanical system of the SPC by means of its transition characteristic as a variable with a steady-state characteristic.
MAIN PART
In contrast to vibrations, the mechanical impact of the SPC against a single obstacle has a relatively short duration and either ends abruptly or quickly goes out. Its most significant representation without the aid of a complex frequency should be interpreted as an extreme case of steady-state periodic oscillations described by the equation (1).
a - criminal frequency, rad/s;
fa - corresponding frequency, Hertz, Euler's relation has the form:
¿febMs ) = t - 4,} + J simoun t - Qa >
or:
(2)
fcfl^i-flrl = eusCt^i - 0„) 4 jiJn((^f - fta)
(3)
If all /"■, are harmonic components (those are multiple of some fundamental frequency), the resulting waveform is repeated all the time.
The equation (3) and (4) express the complex function of time of a unit vector rotating in the complex plane, counterclockwise rotation direction.
The complex exponential function is used for theoretical analyzes instead of simpler and the introduction of complex numbers provides a simple way to express the change in phase and amplitude of the oscillation during the solution process.
Replacing in expression (1) the summation by continuous integration over the entire frequency range:
where is the Fourier spectrum or the Fourier transform:
(4)
It is a complex function of the frequency, including the phase angle . The complex exponential function in the integrand of equation (4.70) must be considered as a mathematical test, introduced during the study to indicate the required frequency.
If f is the mobility of the transfer of a mechanical system from an excitation point to a point of interest to us, then it should characteristically be represented in the following form:
(6)
where ЫП = У(/}Р(/).
It should be noted that the main method of calculating the response to a shock, very close to the method of calculating periodic oscillations, it consists in the transition from the time domain to the frequency one, followed by the inverse transformation to the time domain. Consequently, value Vif)] Fourier transforms must be taken as a criterion for the danger of periodic oscillations [2].
Calculations are made in complex numbers, which, if necessary, are converted into real numbers.
A more perfect approach to considering the theory of ABS impact on a single obstacle is such an approach, when the integration of expression (7) is limited to positive time, and jw is replaced by i, which allows us to have the real part expressing the decay rate to obtain the Laplace transform:
The restriction of the integration domain is equivalent to the assumption that the shock acceleration is zero in the case of negative time to prove general theorems.
The linear passive damped mechanical system of the SBS exhibits certain transients with certain frequencies and attenuation rates after excitation. The Laplace transform of the reaction of the SPC mechanical system increases infinitely when iapproaches the complex frequency, including the attenuation rate and the angular attenuation rate and the angular, of any of these transient processes. Thus, it is necessary to describe the SBS mechanical system by means of its transient response as a variable with a steady state characteristic.
Control systems, such as active depreciation systems, during the first test may exhibit an exponentially increasing (up to the limits of linearity) at one or more complex frequencies. Consequently, Laplace transform is the basis for the theory of stability of a control system, butin shock and vibration technology, shock absorption systems are used only when necessary, because they consume power, are expensive, and for satisfactory operation they need to be adapted using relatively complex technical methods. Consequently, shock theory is limited mainly to the effects of excitation of passive systems [3].
Different forms of the shock spectrum should be defined differently, either as typical characteristics of the mechanical equipment of the SBS, or as an indirect description of the excitation. The impact spectrum in the mechanical system of the SBS should be distinguished as non-damped or damped depending on the amount of damping, allowed in the resonator, and as positive, negative or mixed depending on the direction in which the maximum characteristic is determined. The shock spectrum may be initial (false false significant), residual and maximum, depending on the period of time in which the maximum characteristic differs (during the pulse, after it or it is unlimited). The undamped residual impact spectrum, which is identical for positive and negative stresses, is related to the Fourier transform at the same frequency through:
so that it can be considered the main measure of excitation of even complex mechanical systems.
The impact spectrum should be attributed to maximum acceleration, but the undamped residual impact spectrum becomes transformed by dividing by. At low frequencies, where the movement is more significant, this can be done using the inclined lines of the coordinate grid in the spectral graph.
L(it) = j^Vi^-'Vt
(7)
-
(8)
The final saw tooth maximum vibrational shape that is observed with the relative smoothness of its spectra is a means of achieving a given minimum shock spectrum [5].
In contrast to the Fourier transform, the undamped residual impact spectrum does not contain phase information.
Like shock, random oscillations should be considered as the limiting case of expression (1) with an infinite number of small sinusoids in random dependences in the frequency domain. Or many infinitely small strokes that occur arbitrarily in the time domain. They can be predicted and briefly described only statistically. Nevertheless, any of these points of view leads to the same basic description and gives the same hazard criterion. The first point of view leads to a less abstract development of concepts about the spectrum, while the second is probably closer to the practical sources of random oscillations or random time functions in general.
Any sample of a limited duration of random oscillations must be approximated, and by the side of its duration using equation (1), a limited number of sinusoids.
The term «pure random oscillation» should refer to a spectral function that is constant in magnitude within a significant frequency domain and refers to the spectral function of acceleration, force, or any other suitable random variable. To go from acceleration to displacement to the density of the spectral function, it is necessary to divide it intomore precisely, it is necessary to determine the sample of the density of the spectral function at a frequency f for a sample of duration T observed over the frequency band B centered at f, i.e.
AV^&Ti-^Sfl^ (9)
The density of the spectral function for random oscillations, which persists throughout the entire time, is determined from the following expression:
4.1(f) = ^im ano({ M. l ! (10)
Provided that T increase faster than B decreases. Thus, the number of spectral lines within B increases infinitely, it w(f) remains a continuous function of frequency.
For steady random fluctuations fc>[/)is the average value relative to which the score changes. For any fixed T and B standard deviation u/v{f ,R, T). divided by defined as follows:
Being partly dependent on the characteristics of the selectivity curve and methods of averaging time [15]. Any rating ai[f), made on the basis of a limited sample, especially at low frequencies, is a compromise between resolution (мало еВ) and statistical value.
If the complex subordinate ability or transfer mobility of a linear mechanical system isy(/), then the characteristic of the spectral function corresponding to the excitation, expressed as follows:
= MWJ (12)
and the full root mean square acceleration can be obtained by integrating it and determining the square root value. Therefore, any calculation of the reaction of a linear mechanical ABS system to random excitations includes the same data on the ABS system as periodic oscillation and shock, but the data on the gear ratio is used a little differently [4].
When considering a sample of random vibrations of an ABS mechanical system as the sum of impacts, the Fourier transform should be used, which gives a different definition for the estimation of the spectral function:
*m \r(f)M (i3)
where f'\ f ) - conversion Fourier, including [1,3] averaging the squared value within the frequency band B.
It should be noted that the expression (13) consistent with expression (10), and allows you to get similar results (B) with statistics for any sample of limited duration. Phase dependencies for any sample of limited duration. The frequency dependences of the phase in the general case do not matter for random oscillations.
When designing the mechanical part of SPC, including a rotating mixer, which are impacted, their strength is determined by the reaction to shock. This characteristic is determined either by the displacement of the mixer relative to the chassis, or the magnitude of the dynamic loads perceived by the ABC mechanical system, and also the mixer can be determined by the time dependence of the impact parameters by known calculation methods. It should be noted that using methods of converting the results of measurements of impact characteristics, a direct relationship can be found between the shock and the reaction of the SPC and mixer designs (3).
Drawing 1 - The design scheme of the mechanical system of ABS at impact
To develop a design, we will present the SPC mechanical system in the form of a simplified model. The design scheme of the mechanical system of the SPC is shown in Figure 1, which consists of a rotary mixer (upper weight ), chassis-based SBS (lower weight ) Depending on the purpose of the study, certain characteristics of the reaction of the model should be known: when calculating the mixer - for this you need to know the law of movement of the chassis; chassis movement is an excitation for the mixer: when calculating the chassis - for this it is necessary to know its displacements. Every mass, i.e.H, with lumped parameters has one degree of freedom, and the weightless, than weight. Consequently, little influence on the mass movement of the chassis of the ABC mixer. The impact motion of the chassis mass is the input impact motion with respect to the mixer. Choosing the necessary data processing method, information on the reaction of the mechanical system of the SPC then impact, needed to calculate the SPC elements, we obtain on the basis of changes in the motion parameters of the SPC mechanical system in time [6].
Bringing data in the form of a reaction of the mechanical system of the SPC mixer.
The design of the reaction value must be used to study some properties of the impact by analyzing the properties of the mechanical system of the SPC and the mixer. Then we connect the values of the maximum reactions with these properties. The considered representation of the impact has the following differences from the representation of the impact in the form of the Fourier spectrum:
- the Fourier spectrum allows you to determine the impact through the amplitudes and phase relations of its frequency components, and the reaction spectrum describes only the impact of the impact on the design of the mechanical system of the SPC and the mixer based on the maximum values of the corresponding reactions;
- the change during impact cannot be determined on the basis of the maximum reaction values of the mechanical system of the SPC and the mixer subjected to impact, those. calculation of maximum reaction values is an irreversible action. The Fourier spectrum is determined on the basis of changes in time and vice versa [7].
By limiting the analysis to the reaction of a linear SPC system with lumped parameters, having one step in the presence of viscous friction, hereinafter referred to as a simple mixer design (figurel), has two parameters on which the reaction depends: natural frequency and damping coefficient.
If there are only two parameters, we can get an idea of the maximum reactions of many simple designs based on the impact measurement. This process is called bringing data into the reaction area and is applied directly to the system, which has one degree of freedom.; it is applicable to some extent when combining natural vibrations to determine the response of a linear system, which with more than one degree of freedom. The conditions of a particular application determine the magnitude of errors arising from alignment [9-11].
CONCLUSIONS
1) Established, that with step or pulsed excitation of SBS or the mixer most important is the maximum reaction value. Two types of maximum deviation values are characteristic of SBS: one of them is the resulting amplitude of the reaction - the amplitude of the free oscillations of the SPC relative to the final position after hitting a single obstacle ; the other maximum represents the largest reaction value from the impact r, which has the same sign as excitement.
2) The greatest relative displacement is equal to the amplitude of free vibrations,which explains the discontinuities, which appear in the spectra of the largest relative reactions.
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Material received on 16.12.19.
Балгабеков Толеу Кунжолович
t.f.k., доцент, мецгеруш^ «Келжтж техника жэне технологиялары» кафедрасы,
С. Сейфуллин атындаFы ^азак агротехникалык университетi,
Нур-Султан к., 010000, ^азакстан Республикасы,
e-mail: tdi_kstu@mail.ru.
Шонтаев Джаманбай Салыкович
т^.к., аFа окытушы, «Келiктiк техника жэне технологиялары» кафедрасы, С. Сейфуллин атындаFы ^азак агротехникалык университетi, Нур-Султан к., 010000, ^азакстан Республикасы, e-mail: dshontaev@mail.ru Коццыбаева Арайлым Ниязбекцызы
магистр, «Келжтж техника жэне технологиялары» кафедрасы, С. Сейфуллин атындаFы ^азак агротехникалык университетi, Нур-Султан к., 010000, ^азакстан Республикасы, e-mail: arai_janaarka@mail.ru Материал баспаFа 16.12.19.тYстi.
Эзд1г1нен жYретiн бетонараластыргыштыц (ЭЖБА) соккы процесш зерттеу
Мацалада вздшнен журетш бетонараластыргыштыц механикалъщ бвлштц сткту процесШц зерттеулерi келтiрiлген, эсер emedi, олардыц бержтш соццыга реакциямен аныцталады. Бул сипаттама араластыреыштыц ауытцуымен де аныцталадынемесе динамикалыц жуктемелердщ мвлшерi.
Кiлттi свздер: зерттеу, соццы тозуы, бетонараластыргыш, салмац, соццы, механикалыц жуйе.
Балгабеков Толеу Кунжолович
к.т.наук., доцент, заведующий кафедрой «Транспортная техника и технологии», Казахский агротехнический университет имени С. Сейфуллина, г. Нур-Султан, 010000, Республика Казахстан, e-mail: tdi_kstu@mail.ru Шонтаев Джаманбай Салыкович
к.т.н., ст. преподаватель, кафедра «Транспортная техника и технологии», Казахский агротехнический университет имени С. Сейфуллина, г. Нур-Султан, 010000, Республика Казахстан, e-mail: dshontaev@mail.ru
Крццыбаева Арайлым Ниязбекцызы
магистр, кафедра «Транспортная техника и технологии», Казахский агротехнический университет имени С. Сейфуллина, г. Нур-Султан, 010000, Республика Казахстан, e-mail: arai_janaarka@mail.ru Материал поступил в редакцию 16.12.19.
Исследования ударного процесса в самоходных бетоносмесителях (СБС)
В статье приведены исследования ударного процесса механической части СБС, которые подвергаются ударному воздействию, прочность их определяется по реакции на удар. Данная характеристика определяется либо смещением смесителя относительно того, либо величиной динамических нагрузок.
Ключевые слова: исследование, ударный износ, бетоносмеситель, нагрузки, удар, механическая система.
