Пошук двочастотних режимів руху двомасної вібромашини з віброзбудником у вигляді пасивного автобалансира

We analytically investigated dynamics of the vibratory machine with rectilinear translational motion of platforms and a vibration exciter in the form of a ball, a roller, or a pendulum auto-balancer.The existence of steady-state motion modes of the vibratory machine was established, which are close to the dual-frequency regimes. Under these motions, loads in the auto-balancer create constant imbalance, cannot catch up with the rotor, and get stuck at a certain frequency. In this way, loads serve as the first vibration exciter, inducing vibrations with the frequency at which loads get stuck. The second vibration exciter is formed by the unbalanced mass on the casing of the auto-balancer. The mass rotates at rotor speed and excites faster vibrations of this frequency. The auto-balancer excites almost perfect dual-frequency vibrations. Deviations from the dual-frequency law are proportional to the ratio of loads’ mass to the mass of the entire machine, and do not exceed 2 %.A dual-frequency vibratory machine has two oscillation eigenfrequencies. Loads can get stuck only at speeds close to the eigenfrequencies of vibratory machine's oscillations, or to the rotor rotation frequency.The vibratory machine has always one, and only one, frequency at which loads get stuck, which is slightly lower than the rotor speed.At low rotor speeds, there is only one frequency at which loads get stuck.In the case of small viscous resistance forces in the supports, at an increase in the rotor speed, the quantity of frequencies at which loads get stuck in a vibratory machine increases, first, to 3, then to 5. In this case, new frequencies at which loads get stuck:– occur in pairs in the vicinity of each eigenfrequency of the vibratory machine's oscillations;– one of the frequencies is slightly lower, while the other is slightly higher, than the eigenfrequency of vibratory machine's oscillations.Arbitrary viscous resistance forces in the supports may interfere with the emergence of new frequencies at which loads get stuck. That is why, in the most general case, the quantity of such frequencies can be 1, 3, or 5, depending on the rotor speed and the magnitudes of viscous resistance forces in supports.Аналитически найдены двухчастотные режимы движения двухмассной вибромашины с прямолинейным поступательным движением платформ и вибровозбудителем в виде шарового, роликового или маятникового автобалансира. С применением метода малого параметра найдены законы двухчастотных вибраций платформ и получено уравнение для поиска частот застревания грузов в автобалансире. Оценены величины составляющих, не учтенных в законах двухчастотных вибрацийАналітично знайдені двочастотні режими руху двомасной вібромашини з прямолінійним поступальним рухом платформ і віброзбудником у вигляді кульового, роликового або маятникового автобалансира. Із застосуванням методу малого параметра знайдені закони двочастотних вібрацій платформ і отримано рівняння для пошуку частот застрявання вантажів в автобалансирі. Оцінені величини складових, не врахованих в законах двочастотних вібраці

Parameter optimization of the centrifugal juicer with the ball auto-balancer under the impulse change of an unbalance by 3D modeling

The optimization of the parameters of the centrifugal juicer with the ball auto-balancer under the impulse change of the sieve unbalance at cruising velocity is conducted by 3D modeling. The dependence of the duration of the transition processes on the main parameters of the juicer and the auto-balancer is studied.Using the example of a two-ball auto-balancer, the impulse changes of an unbalance, which are the most unfavorable for the duration of transition processes, are found: the turn of the unbalance vector around the rotation axis of the rotor by 90° or 180°. In this, the balls pass the longest distance along the running track.The following is established.1. The proposed in previous works methods of optimizing the parameters of machines with an auto-balancer for minimization of the duration of transition processes are also efficient under the impulse change of an unbalance at cruising velocity.2. The previously obtained results are confirmed, namely:a) the increase of the number of the balls in the auto-balancer leads to the decrease of the duration of transition process; this is explained by the fact, that:– when there are more than two balls in the auto-balancer, the multi-parameter family of the steady motions appears in the rotor machine;– under the change of an unbalance, the balls make the transition between the two nearest steady motions;b) the decrease of the running track radius leads to the decrease of the duration of transition processes; this is due to the fact, that the running track becomes more filled and the balls need to move less between auto-balancing positions;c) the dependence of the optimal values of the parameters of the centrifugal juicer and the auto-balancer on the magnitude of an unbalance is revealed. The dependence is significant only for the two-ball auto-balancer and weakens with the increase of the number of the balls in the auto-balancer;d) the use of the two-ball auto-balancer, both in practice and for theoretical and experimental studies of the duration of transition processes in auto-balancing of machines, is inexpedient.3. It is established that at the centrifugal juicer run-up with the fixed unbalance and under the impulse change of its unbalance at cruising velocity:– the trends in the influence of the running track radius of an auto-balancer and the number of the balls on the duration of transition processes are identical;– the optimal values of the main parameters of the auto-balancer and the centrifugal juicer coincide, except for the coefficient of viscous resistance forces of the relative motion of the balls;– the optimal values of the coefficient of viscous resistance forces of the relative motion of the balls at run-up are less than the corresponding values under the impulse change of an unbalance by 50 %.3D-моделированием проведена оптимизация параметров центробежной соковыжималки с шаровым автобалансиром при импульсном изменении неуравновешенности сита. Показана работоспособность ранее предложенной методики оптимизации. Подтверждено, что увеличение количества шаров в автобалансире и уменьшение радиуса беговой дорожки шаров ускоряет наступление автобалансировки. Выявлена неэффективность использования двухшаровых автобалансиров для исследования продолжительности переходных процессов при автобалансировке роторных машин3D-моделюванням проведена оптимізація параметрів відцентрової сокодавки з кульовим автобалансиром при імпульсній зміні незрівноваженості сита. Показана ефективність раніше запропонованої методики оптимізації. Підтверджено, що збільшення кількості куль в автобалансирі та зменшення радіусу бігової доріжки куль пришвидшує настання автобалансування. Виявлена неефективність використання двохкульових автобалансирів для дослідження тривалості перехідних процесів при автобалансуванні роторних маши

Дослідження особливостей балансування гнучких двоопорних роторів двома пасивними автобалансирами, розміщеними біля опор

A discrete N­mass model of a flexible double­support rotor with two passive automatic balancers of pendulum, ball or roller type was constructed. Automatic balancers are placed near supports. The system of differential equations, which describes the motion of a rotor machine, is obtained.The primary (sustained) motions of a system as the motions, in which automatic balancers eliminated displacements of a rotor in supports, were found. It is shown that on the primary motions, the total imbalances of a rotor and AB, reduced to two correction planes (supports), equal zero.It was proposed to examine the stability (of the family) of sustained motions by generalized coordinates, which set the displacement of a rotor in the supports and by dynamic variables that equal total imbalances of a rotor and AB in two correction planes. We obtained differential equations, which describe the change in these variables that describe the process of self­balancing.By the analysis of differential equations of the motion of a system it was established that:– on the primary motions, AB eliminate rotor deflections and vibrations in elastic viscous supports, but do not remove shaft deflections in non­supporting points;– on the primary motions elastic viscous supports are conditionally converted into hinge supports;– shaft deflections in non­supporting points and the primary motions change with the change in angular speed of rotation of the rotor;– primary motions exist at a certain distance of the speed of rotation of the rotor from the critical speeds of flexible rotor rotation with the hinge supports instead of elastic viscous supports;– at the speeds of rotation of a rotor shaft close to any of these speeds, the conditions of existence of the primary motions are disrupted because shaft deflections theoretically grow to infinity and the balancing capacity of AB is not sufficient for the compensation for the imbalances of the rotor;– in practice these deflections are limited and, therefore, proper selection of the balancing capacity of AB can ensure existence of primary motions at all speeds of rotation of rotor.Построена дискретная многомассовая модель гибкого ротора на двух податливых опорах с двумя пассивными автобалансирами, расположенными возле опор. Получены две системы дифференциальных уравнений, описывающие, соответственно, движение роторной машины в целом и процесс автобалансировки. Найдены основные установившиеся движения (на которых автобалансиры устраняют прогибы ротора в опорах), установлены условия их существованияПобудована дискретна багатомасова модель гнучкого ротора на двох податливих опорах з двома пасивними автобалансирами, розташованими біля опор. Отримані дві системи диференціальних рівнянь, що, відповідно, описують рух роторної машини в цілому і процес автобалансування. Знайдені основні усталені рухи (на яких автобалансири усувають переміщення ротора в опорах), встановлені умови їх існуванн

Пошук умов настання автобалансування у рамках плоскої моделі ротора на анізотропних пружно-в'язких опорах

Within the framework of the planar model of the rotor mounted on anisotropic elastic-viscous supports and balanced by a passive auto-balancer, conditions for  the occurrence of auto-balancing were analytically determined.An empirical criterion for stability of the main motion was applied. It was found that depending on the forces of viscous resistance in supports, the rotor has one or three critical speeds. These speeds are between two natural frequencies of rotor oscillation in absence of resistance forces in supports. Auto-balancing, respectively, occurs when the single critical speed is exceeded or between the first and the second and above the third critical speeds.At low forces of viscous resistance, the rotor has three critical  speeds. The first and the third critical speeds coincide with two natural frequencies of rotor oscillation in absence of resistance forces in supports. The second critical  speed is between the first two. An additional (second) critical  speed appears when the auto-balancer is mounted on the rotor. In the transition of this speed the behavior of the auto-balancer changes: the auto-balancer reduces the rotor imbalance at slightly lower rotor  speeds and increases it at somewhat higher  speeds.At finite forces of viscous resistance in supports, depending on the magnitude of these forces, the rotor has one or three critical  speeds.At large forces of viscous resistance in supports, the rotor has one critical speed. Depending on the relationship between the coefficients of the forces of viscous resistance, this speed is closer to the smallest or the largest natural frequency of the rotor oscillation.The results obtained were confirmed by computational experiments. It was established that the criterion correctly describes the qualitative behavior of the rotor – auto-balancer system: it determines the number of critical speeds and the region of the auto-balancing onset. Accuracy of determining critical speeds (the boundaries of the regions of auto-balancing onset) increases with:– reduction of the auto-balancer mass with respect to the rotor mass;– an increase in forces of viscous resistance to the motion of correction weightsПрименен эмпирический критерий устойчивости основного движения. Установлено, что в зависимости от сил сопротивления в опорах у ротора одна или три критические скорости. Автобалансировка, соответственно, наступает: при превышении единственной критической скорости; между первой и второй, и над третьей критической скоростью. Оценена точность полученных результатов вычислительными экспериментамиЗастосований емпіричний критерій стійкості основного руху. Встановлено, що в залежності від сил в’язкості в опорах у ротора одна чи три критичні швидкості. Автобалансування, відповідно, настає: при перевищенні єдиної критичної швидкості; між першою і другою та над третьою критичною швидкостями. Оцінена точність отриманих результатів обчислювальними експериментам

Пошук двочастотних режимів руху одномасної вібромашини з віброзбудником у вигляді пасивного автобалансира

Dynamics of a single-mass vibratory machine with rectilinear translational motion of the platform and a vibration exciter in the form of a ball, a roller, or a pendulum auto-balancer was analytically explored.The steady-state motion modes, close to dual-frequency modes were found. At these motions, loads in the auto-balancer create constant imbalance, cannot catch up with the rotor and get stuck at a certain frequency. In this way, loads operate as the first vibration exciter, exciting vibrations at frequency of the loads getting stuck. The second vibration exciter is formed by unbalanced mass on the auto-balancer body. The mass rotates at rotor speed and excites more rapid vibrations with this frequency. It was found that despite a strong asymmetry of supports, the auto-balancer excites almost perfect dual-frequency vibrations. Deviations from the dual-frequency law are proportional to the ratio of loads’ mass to the mass of the entire machine and do not exceed 2 %.It was established that at small forces of external and internal resistance, when the loads’ mass is much smaller than the platform’s mass, etc., there are three characteristic rotor speeds. These speeds are larger than the resonance velocity of platform oscillations. At the same time:– at the rotor speeds smaller than the first characteristic speed, there is only frequency when the loads get stuck, in this case it is smaller than the resonance velocity of platform oscillations;– at the above-resonance rotor speeds, located between the first and the second characteristic speeds, there are three frequencies when the loads get stuck, among which only one is below-resonance;– at the above-resonance rotor speeds, located between the second and the third characteristic speeds, there are three frequencies of the loads getting stuck, in this case, they are all above-resonance;– at the above-resonance rotor speeds, exceeding the third characteristic speed, there is only one frequency when the loads get stuck, in addition, it is above-resonant and close to the rotor speed.Only at the rotor speeds smaller than the second characteristic speed, there always exists one, and only one, below-resonance frequency of the loads getting stuckИсследованы двухчастотные режимы движения одномассной вибромашины с прямолинейным поступательным движением платформы и вибровозбудителем в виде шарового, роликового или маятникового автобалансира. Методом малого параметра приближенно найдены частоты, на которых могут застревать грузы и соответствующие законы двухчастотных вибраций платформы. Оценены величины неучтенных в законах составляющихДосліджено двочастотні режими руху одномасної вібромашини з прямолінійним поступальним рухом платформи і віброзбудником у вигляді кульового, роликового або маятникового автобалансира. Методом малого параметра наближено знайдені частоти, на яких можуть застрявати вантажі і відповідні закони двочастотних вібрацій платформи. Оцінені величини неврахованих в законах складови

Дослідження збудження кульовим автобалансиром двохчастотних коливально-обертових вібрацій короба грохоту

The 3D model of the screen stand with the vibrational-rotational duct motion was developed. The ball-type auto-balancer, which makes it possible to create the two-frequency vibrations, is used as the vibration exciter. The main parameters, which influence the stability of the dual frequency vibrations, were defined after adjusting and testing the model. It was established that the ranges of the dual frequency vibrations are relatively large, which makes it possible to change the characteristics of vibrations with a change in the parameters from these ranges.An increase in the summary mass of the spheres increases the amplitude of slow vibrations of the duct masses in direct proportion. This increases in direct proportion the vibration energy directed toward the execution of the main technical process.An increase in the unbalanced mass on the auto-balancer case increases the amplitude of rapid vibrations of the duct masses center in direct proportion.It was established that an increase in the rotation frequency of the rotor increases the amplitude of the rapid vibration speeds of the duct in direct proportion. This increases the vibration energy directed toward the duct self-cleaning and the change through the vibrations of the mechanical properties of the workable material in proportion to the square of rotation frequency of the rotor.The simulation showed that the auto-balancer works as two separate vibration exciters. In the first one, the spheres rotate practically evenly with the resonance frequency of the duct vibrations, at this, independent of its loads, the spheres automatically adjust to this frequency, by which they excite the slow resonance duct vibrations (12 Hz) with a large amplitude. In the second one, the mass on the AB case excites the rapid duct vibrations with (any) existing non-resonant rotation frequency of the rotor.3D моделированием исследован процесс возбуждения шаровым автобалансиром бигармонических колебаний, у которых низшая частота совпадает с собственной частотой колебаний короба грохота. Найдены области изменения основных параметров, внутри которых гарантировано наступают двухчастотные вибрации, исследовано влияние основных параметров из найденных областей на характеристики двухчастотных вибраций.3D моделюванням досліджено процес збудження кульовим автобалансиром бігармонійних коливань, у котрих нижча частота співпадає з власною частотою коливань короба грохоту. Знайдені області зміни основних параметрів, всередині яких гарантовано настають двохчастотні вібрації, досліджений вплив основних параметрів зі знайдених областей на характеристики двохчастотних вібрацій

Оптимізація 3D-моделюванням параметрів відцентрової сокодавки з кульовим автобалансиром при імпульсній зміні незрівноваженості

The optimization of the parameters of the centrifugal juicer with the ball auto-balancer under the impulse change of the sieve unbalance at cruising velocity is conducted by 3D modeling. The dependence of the duration of the transition processes on the main parameters of the juicer and the auto-balancer is studied.Using the example of a two-ball auto-balancer, the impulse changes of an unbalance, which are the most unfavorable for the duration of transition processes, are found: the turn of the unbalance vector around the rotation axis of the rotor by 90° or 180°. In this, the balls pass the longest distance along the running track.The following is established.1. The proposed in previous works methods of optimizing the parameters of machines with an auto-balancer for minimization of the duration of transition processes are also efficient under the impulse change of an unbalance at cruising velocity.2. The previously obtained results are confirmed, namely:a) the increase of the number of the balls in the auto-balancer leads to the decrease of the duration of transition process; this is explained by the fact, that:– when there are more than two balls in the auto-balancer, the multi-parameter family of the steady motions appears in the rotor machine;– under the change of an unbalance, the balls make the transition between the two nearest steady motions;b) the decrease of the running track radius leads to the decrease of the duration of transition processes; this is due to the fact, that the running track becomes more filled and the balls need to move less between auto-balancing positions;c) the dependence of the optimal values of the parameters of the centrifugal juicer and the auto-balancer on the magnitude of an unbalance is revealed. The dependence is significant only for the two-ball auto-balancer and weakens with the increase of the number of the balls in the auto-balancer;d) the use of the two-ball auto-balancer, both in practice and for theoretical and experimental studies of the duration of transition processes in auto-balancing of machines, is inexpedient.3. It is established that at the centrifugal juicer run-up with the fixed unbalance and under the impulse change of its unbalance at cruising velocity:– the trends in the influence of the running track radius of an auto-balancer and the number of the balls on the duration of transition processes are identical;– the optimal values of the main parameters of the auto-balancer and the centrifugal juicer coincide, except for the coefficient of viscous resistance forces of the relative motion of the balls;– the optimal values of the coefficient of viscous resistance forces of the relative motion of the balls at run-up are less than the corresponding values under the impulse change of an unbalance by 50 %.3D-моделированием проведена оптимизация параметров центробежной соковыжималки с шаровым автобалансиром при импульсном изменении неуравновешенности сита. Показана работоспособность ранее предложенной методики оптимизации. Подтверждено, что увеличение количества шаров в автобалансире и уменьшение радиуса беговой дорожки шаров ускоряет наступление автобалансировки. Выявлена неэффективность использования двухшаровых автобалансиров для исследования продолжительности переходных процессов при автобалансировке роторных машин3D-моделюванням проведена оптимізація параметрів відцентрової сокодавки з кульовим автобалансиром при імпульсній зміні незрівноваженості сита. Показана ефективність раніше запропонованої методики оптимізації. Підтверджено, що збільшення кількості куль в автобалансирі та зменшення радіусу бігової доріжки куль пришвидшує настання автобалансування. Виявлена неефективність використання двохкульових автобалансирів для дослідження тривалості перехідних процесів при автобалансуванні роторних маши

Способи балансування осесиметричного гнучкого ротора пасивними автобалансирами

The conditions for the occurrence of auto-balancing when balancing a flexible axisymmetric rotor by any number of passive auto-balancers of any type are determined. The problem is actual for the high-speed rotors working at supercritical speeds (rotors of aircraft engines, gas turbine engines of power plants, etc.).The empirical criterion for the occurrence of auto-balancing is applied. Transformations were carried out on the example of the flexible axisymmetric rotor of constant section on two rigid hinge supports. The findings are applicable to rotors with another type of fixing.It is established that auto-balancing of the rotor by n passive auto-balancers located in different correction planes is possible only if the rotor speed exceeds the n-th critical speed. The number of auto-balancers can be arbitrary. Between the critical rotor speeds, additional critical speeds appear. Auto-balancing occurs whenever the rotor passes a critical speed and disappears whenever the rotor passes an additional critical speed.If n auto-balancers are located in the n nodes of the rotor flexural (n+1)-th mode, the j·n-th additional critical rotor speed matches with the j(n+1)-th critical speed, /j=1, 2, 3,…/. When balancing the flexible rotor between the n-th and (n+1)-th critical speeds, such number and placement of auto-balancers are optimum. Auto-balancers at the same time balance the first n distributed modal unbalances and do not respond to the (n+1)-th ones.The additional critical speeds are due to the installation of the auto-balancers on the rotor. Upon transition to them, the behavior of auto-balancers changes. At slightly lower rotor speeds, the auto-balancers reduce the rotor unbalance, and at slightly higher ones – increase it.Применен эмпирический критерий наступления автобалансировки для гибкого осесимметричного ротора, балансируемого n пассивными автобалансирами любого типа. Установлено, что автобалансировка может происходить только на скоростях, превышающих n-ю критическую скорость вращения ротора. Найдены диапазоны угловых скоростей вращения ротора, на которых будет наступать автобалансировка. Предложены способы оптимальной балансировки ротораЗастосовано емпіричний критерій настання автобалансування для гнучкого осесиметричного ротора, що балансується n пасивними автобалансирами будь-якого типу. Встановлено, що автобалансування може відбуватися тільки на швидкостях, що перевищують n-ю критичну швидкість обертання ротора. Знайдено діапазони кутових швидкостей обертання ротора, на яких наступатиме автобалансування. Запропоновано способи оптимального балансування гнучкого ротор

Емпіричний критерій настання автобалансування і його застосування для осесиметричного ротора з нерухомою точкою і ізотропною пружною опорою

We formulated the empirical criterion for the occurrence of auto­balancing for the rotors balanced by passive auto­balancers. The criterion is applicable for rigid and elastic rotors on ductile supports and for elastic rotors on rigid supports. The criterion is intended to answer the question if it is possible in principle, and under what conditions, to automatically balance a particular rotor n by passive auto­balancers of any type in n planes of correction. In accordance with the criterion, the possibility of applying passive auto­balancers for rotor balancing (in “zero approximation”) is determined not by the type of auto­balancers, but by rotor itself. In this case, reaction of rotor to the elementary imbalances, applied in the required planes of correction, is essential. That is why the criterion makes it possible to obtain universal conditions for the occurrence of auto­balancing, applied for any types of auto­balancers.The criterion is applied in the following sequence.1. A physical­mechanical model of rotor with elementary imbalances, located in the required planes of correction, is described.2. Differential equations of motion of the unbalanced rotor are derived.3. Steady motion of a rotor, which corresponds to the applied elementary imbalances, is searched for.4. A functional of the criterion for the occurrence of auto­balancing is built. As a rule, this is a quadratic form from elementary imbalances.5. By analysis of the functional (sign definiteness of the obtained quadratic form), conditions for the occurrence of auto­balancing are determined. The result is conditions of two types. The first ones set limitations to the mass­inertia rotor characteristics. The second ones are a range of angular speeds of rotor rotation, at which auto­balancing will occur provided the first conditions are met.The criterion is used for the axisymmetric rotor with a fixed point and isotropic elastic support. It was found that auto­balancing will occur only in the case of a long rotor, relative to the point O, independent of the number of auto­balancers (planes of correction) at the speeds, which exceed the only resonance speed of rotor rotation.Сформулирован эмпирический критерий наступления автобалансировки для ротора, уравновешиваемого пассивными автобалансирами. Критерий позволяет определять диапазоны скоростей вращения ротора, на которых наступает автобалансировка. Он применим для жестких роторов на податливых опорах и для гибких роторов при любом количестве пассивных автобалансиров любого типа. Приведен пример применения критерия для ротора с неподвижной точкойСформульовано емпіричний критерій настання автобалансування для ротора, що балансується пасивними автобалансирами. Критерій дозволяє визначати діапазони швидкостей обертання ротора, на яких настає автобалансування. Він застосовний для жорстких роторів на піддатливих опорах і для гнучких роторів при будь-якій кількості пасивних автобалансирів будь-якого типу. Наведений приклад застосування критерію для ротора з нерухомою точко

Рівняння руху вібромашин з поступальним рухом платформ і віброзбудником у вигляді пасивного автобалансира

Generalized models have been built of one-, two-, and three-mass vibration machines with a rectilinear translational motion of platforms and a vibration exciter in the form of a ball, a roller, or a pendulum auto-balancer.In the generalized model of a single-mass vibration machine, the platform relies on an elastic-viscous support with the guides enabling the platform’s rectilinear translational motion. A passive auto-balancer is installed on the platform.In the generalized models of two- and three-mass vibration machines, each platform relies on a fixed external elastic-viscous support with the platforms coupled in pairs by elastic-viscous inner supports. The guides allow the platforms to move rectilinearly translationally. A passive auto-balancer is installed on one of the platforms.We have derived differential equations of the motion of vibration machines. The equations are reduced to the form that is independent of the type of an auto-balancer.The models of particular one-, two- and three-mass vibration machines can be obtained from the generalized models by selecting a specific type of the auto-balancer.The models of particular two-mass vibration machines can also be obtained from the corresponding generalized model by rejecting one of the external elastic-viscous supports.The models of particular three-mass vibration machines can also be derived from the corresponding generalized model by rejecting:– one or two external elastic-viscous supports;– one of the three inner elastic-viscous supports;– one or two external elastic-viscous supports and one of the three inner elastic-viscous supports.The constructed models are applicable both for analytical studies into dynamics of the relevant vibration machines and for performing computational experiments.When employed in analytical studies, the models are designed to search for the established modes of a vibration machine motion, to determine conditions for their existence and stabilityПостроены обобщенные модели одно-, двух- и трехмассных вибромашин с прямолинейным поступательным движением платформ и вибровозбудителем в виде шарового, роликового или маятникового автобалансира. Выведены дифференциальные уравнения движения. Уравнения приведены к виду, не зависящему от типа автобалансира. Из обобщенных моделей можно получать частные, путем отбрасывания части внешних или внутренних упруго-вязких опорПобудовані узагальнені моделі одно-, двох- і трьохмасних вібромашин з прямолінійним поступальним рухом платформ і віброзбудником у вигляді шарового, роликового або маятникового автобалансира. Виведені диференціальні рівняння руху. Рівняння приведені до вигляду, що не залежить від типу автобалансира. З узагальнених моделей можна отримувати частині, шляхом відкидання частини зовнішніх або внутрішніх пружно-в'язких опо