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

Abstract

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.