<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The paper provided describes a mathematical model of calibration process of fruit-stone culture seeds of cherry, sweet cherry, cherry-plum, apricot and almond using flat sieves with impact shock ball cleaners oscillating in the horizontal plane. It has been defined that the mathematical expectation of time of knocking out the fruit-stone from the sieve opening <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ata-2021-0020_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>T</mi><mo>⌢</mo></mover></math>
<tex-math>\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over T}</tex-math>
</alternatives>
</inline-formula> is the minimum value of ratio of average time of complete ball motion cycle in space under sieve to the probability of knocking out the stone by a ball with the kinetic energy level of 2 Mj. The dependences of energy distribution density of ball on impact on the sieve have been obtained, based on which the intervals of ball cleaner parameters have been determined, i.e. the ball diameter <italic>D</italic> belongs to the interval 25–35 mm; the space height <italic>H</italic> under sorting sieve belongs to the interval 1.2<italic>D</italic>–1.4<italic>D</italic> mm; the value range for distance between rods <italic>t</italic> belongs to the interval 0.5<italic>D</italic>–0.7<italic>D</italic> mm. Using the method of golden section, the following parameters of ball cleaner were obtained: <italic>D</italic> = 33 mm, <italic>t</italic> = 23 mm, <italic>H</italic> = 40 mm. The parameters obtained provide mathematical expectation of time of knocking out the fruit-stone from the sieve opening <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ata-2021-0020_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>T</mi><mo>⌢</mo></mover></math>
<tex-math>\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over T}</tex-math>
</alternatives>
</inline-formula> = 0.03 s. Consequently, the average ball velocity <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ata-2021-0020_eq_003.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>v</mi><mo>⌢</mo></mover></math>
<tex-math>\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over  v}</tex-math>
</alternatives>
</inline-formula> is = 0.4 m∙s<sup>-1</sup>, and the average ball path is <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ata-2021-0020_eq_004.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>L</mi><mo>⌢</mo></mover></math>
<tex-math>\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over  L}</tex-math>
</alternatives>
</inline-formula> = 0.006 m.</p>
</abstract>

The paper provided describes a mathematical model of calibration process of fruit-stone culture seeds of cherry, sweet cherry, cherry-plum, apricot and almond using flat sieves with impact shock ball cleaners oscillating in the horizontal plane. It has been defined that the mathematical expectation of time of knocking out the fruit-stone from the sieve opening 


T⌢
\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over T}

 is the minimum value of ratio of average time of complete ball motion cycle in space under sieve to the probability of knocking out the stone by a ball with the kinetic energy level of 2 Mj. The dependences of energy distribution density of ball on impact on the sieve have been obtained, based on which the intervals of ball cleaner parameters have been determined, i.e. the ball diameter D belongs to the interval 25–35 mm; the space height H under sorting sieve belongs to the interval 1.2D–1.4D mm; the value range for distance between rods t belongs to the interval 0.5D–0.7D mm. Using the method of golden section, the following parameters of ball cleaner were obtained: D = 33 mm, t = 23 mm, H = 40 mm. The parameters obtained provide mathematical expectation of time of knocking out the fruit-stone from the sieve opening 


T⌢
\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over T}

 = 0.03 s. Consequently, the average ball velocity 


v⌢
\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over  v}

 is = 0.4 m∙s-1, and the average ball path is 


L⌢
\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over  L}

 = 0.006 m.

Mathematical Modelling of the Fruit-Stone Culture Seeds Calibration Process Using Flat Sieves

Dmytriy Motornyi Tavria State Agrotechnological University

Kharkiv Petro Vasylenko National Technical University of Agriculture

Slovak University of Agriculture in Nitra

Acta Technologica Agriculturae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The paper provided describes a mathematical model of calibration process of fruit-stone culture seeds of cherry, sweet cherry, cherry-plum, apricot and almond...

Mathematical Modelling of the Fruit-Stone Culture Seeds Calibration Process Using Flat Sieves

Pubblicato online: 10 ago 2021

Pagine: 119 - 123

DOI: https://doi.org/10.2478/ata-2021-0020

Parole chiave
sieve ball cleaners, distribution density, kinetic energy, mathematical expectation

© 2021 Oleksandr Karaiev et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mathematical Modelling of the Fruit-Stone Culture Seeds Calibration Process Using Flat Sieves

Pubblicato online: 10 ago 2021

Pagine: 119 - 123

DOI: https://doi.org/10.2478/ata-2021-0020

Parole chiavesieve ball cleaners, distribution density, kinetic energy, mathematical expectation

© 2021 Oleksandr Karaiev et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Parole chiave
sieve ball cleaners, distribution density, kinetic energy, mathematical expectation