Generalised Hertz — Hunt — Crossley Collision Model

Borovin, G K; Lapshin, V V

doi:10.18698/1812-3368-2018-6-18-30

Cited by 3 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Переходом до нової змінної 2 y x   рівнянню (24), на початку руху, коли 0 x  , 0 x   , надаємо вигляд:…”

unclassified

“…Крім того, в [21] виведено компактні асимптотичні формули, які з похибкою меншою 1 % виражають цю спеціальну функцію через елементарні функції. Графік та деякі властивості функції Ламберта наведено також в [22,23,24]…”

unclassified

See 1 more Smart Citation

Dissipative Oscillators’ Power Characteristic Non-Symmetry Dynamic Effect

Olshanskiy¹,

Olshanskiy²

2021

MMTT

View full text Add to dashboard Cite

The features of motion of a non-linear oscillator under the instantaneous force pulse loading are studied. The elastic characteristic of the oscillator is given by a polygonal chain consisting of two linear segments. The focus of the paper is on the influence of the dissipative forces on the possibility of occurrence of the elastic characteristic non-symmetry dynamic effect, studied previously without taking into account the influence of these forces. Four types of drag forces are considered, namely linear viscous friction, Coulomb dry friction, position friction, and quadratic viscous resistance. For the cases of linear viscous friction and Coulomb dry friction the analytical solutions of the differential equation of oscillations are found by the fitting method and the formulae for computing the swings are derived. The conditions on the parameters of the problem are determined for which the elastic characteristic non-symmetry dynamic effect occurs in the system. The conditions for the effect to occur in the system with the position friction are derived from the energy relations without solving the differential equation of motion. In the case of quadratic viscous friction the first integral of the differential equation of motion is given by the Lambert function of either positive or negative argument depending on the value of the initial velocity. The elastic characteristic non-symmetry dynamic effect is shown to occur for small initial velocities, whereas it is absent from the system when the initial velocities are sufficiently large. The values of the Lambert function are proposed to be computed by either linear interpolation of the known data or approximation of the Lambert function by elementary functions using asymptotic formulae which approximation error is less than 1%. The theoretical study presented in the paper is followed up by computational examples. The results of the computations by the formulae proposed in the paper are shown to be in perfect agreement with the results of numerical integration of the differential equation of motion of the oscillator using a computer.

show abstract

“…Переходом до нової змінної 2 y x   рівнянню (24), на початку руху, коли 0 x  , 0 x   , надаємо вигляд:…”

unclassified

Dissipative Oscillators’ Power Characteristic Non-Symmetry Dynamic Effect

Olshanskiy¹,

Olshanskiy²

2021

MMTT

View full text Add to dashboard Cite

show abstract

Shock Impulse Model when Compacting a Coal Load for Coke Production

Doronin,

Zelenov,

Reizmunt

et al. 2023

System Analysis &Amp; Mathematical Modeling

View full text Add to dashboard Cite

Currently, the reserves of coking coals necessary for the production of high-quality coke are significantly reduced. One of the promising technologies for the preparation of raw materials for the production of coke is the ramming of coal charge: by increasing its density, the requirements for the quality of the initial coals are reduced and it becomes possible to widely use, along with coking, and coal of the worst quality. Determination of the characteristics of the ramming technology and equipment is carried out mainly empirically, which does not guarantee the receipt of scientifically based effective technical solutions during their development. One of the key characteristics of the coal charge ramming process is the impact energy and the shock pulse parameters corresponding to it — they determine both the density of the coal charge and the dynamic effects on the load-bearing structures of the equipment. The latter, in turn, determines the operability of the equipment, expressed in terms of strength, stability and durability. Experimental analysis and development of a mathematical model of the shock pulse during ramming of coal charge are aimed at providing information for the design and calculation process, significantly reducing the level of uncertainty in the development of ramming equipment and technology. It is shown that the shock pulse is well approximated by a sine half-wave. For a hammer with certain geometric and mass characteristics, and the corresponding impact energy, the intervals of change in the duration and peak value of the impact pulse force, as well as the relationship between these characteristics, are determined. They are an information base for expert evaluation of the characteristics of the shock pulse when the coal charge ramming energy changes.

show abstract

Oscillations of a Pulse Loaded Oscillator With a Square Resistance in the Composition of the Dissipative Force

Olshanskiy¹,

Slipchenko²,

Твердохліб³

et al. 2021

Vibrations in Engineering and Technology

View full text Add to dashboard Cite

The unsteady oscillations of a dissipative oscillator caused by an instantaneous impulse of the force are described. The case is considered when the dissipative force consists of quadratic viscous resistance and dry friction, and the theoretical results are generalized to the case of the sum of three forces. The third is the force of positional friction. Formulas for calculating the ranges of oscillations have been constructed In this case, the Lambert function of negative and positive arguments is used. It is a tabulated special function. Its value can also be calculated using its known approximations in elementary functions. It is shown that, due to the action of the dissipative force, the process of post-pulse oscillations consists of a finite number of cycles and is limited in time. This is due to the presence of dry friction among the resistance components. Examples of calculations that illustrate the possibilities of the stated theory are given. In order to check the reliability of the derived calculation formulas, numerical computer integration of the differential equation of motion was also carried out. The convergence of the numerical results obtained by two different methods is shown. Thus, it has been confirmed that with the help of analytical solutions it is possible to find the extreme displacements of the oscillator without numerically solving its nonlinear differential equation of motion. Using Lambert function and the first integral of the equation of motion made it possible to derive precise calculation formulas for determining the range of oscillations caused by the pulsed load of the oscillator. The derived formulas are suitable for calculating the value of the instantaneous impulse applied to the oscillator, which refers to the inverse problems of mechanics. Thus, by measuring the maximum displacement of the oscillator, it is possible to identify the initial velocity or instantaneous impulse applied to the oscillator. The performed numerical computer integration of the output differential equation confirmed the adequacy of the obtained analytical solutions, which concern not only direct, but also inverse problems of dynamics.

show abstract

Generalised Hertz — Hunt — Crossley Collision Model

Cited by 3 publications

References 0 publications

Dissipative Oscillators’ Power Characteristic Non-Symmetry Dynamic Effect

Dissipative Oscillators’ Power Characteristic Non-Symmetry Dynamic Effect

Shock Impulse Model when Compacting a Coal Load for Coke Production

Oscillations of a Pulse Loaded Oscillator With a Square Resistance in the Composition of the Dissipative Force

Contact Info

Product

Resources

About