Calculation of the throwing angle of a fertilizer centrifugal device as functions of random coordinates of feeding point

Vasiliy Chernovolov,Lyudmila Kravchenko,Vladimir Litvinov,Alla Nikitina,D. Rudoy,S. Ignateva

doi:10.1051/e3sconf/202017505016

Vasiliy Chernovolov, Lyudmila Kravchenko + Show 4 more

Open Access

https://doi.org/10.1051/e3sconf/202017505016

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Abstract

Liquid fertilizers fed into centrifugal device are spread along angle and radius of feed under action of blades. This article describes how to calculate throwing angular characteristics using Mathcad. The package consists of four programs. Program Mf is intended for calculation of probability density of supply point coordinates under assumption of bivariant normal distribution of system r, γ, which are specified in the form of vectors. The result of the calculation is displayed as matrix Mf. The program Mα calculates the throwing angle for all combinations r, γ.. To calculate the throwing angle, the method of solving differential equations of particle movement along the blade of the device with input data was used: Radius of the disk R, angular speed ω, coefficient of friction of fertilizers on the blade f. The program Ms extracts from the matrix Mf elements Corresponding to a throw angle less than a given number A. The program F (A) sums the elements of the matrix Ms. We obtained the values of the throw angle distribution function by multiplying the resulting sum by the intervals of vectors r and γ. The calculated throwing angle distribution function is approximated by the standard normal distribution function.

Highlights

Сentrifugal devices for distribution of mineral fertilizers are widely used because of their simplicity, high productivity, and easy loading
The throwing angle α (Figure 1) relative to the line of motion is determined by the formula where λ – an angular coordinate of the feed point of the particle, θ is the angle between the absolute velocity and the radius vector of the particle, ωt1 is the angle of descent of the particle, i.e. the angular sliding of the particle in absolute motion until it leaves the shovel
The method for calculating the distribution function of the throwing angle of fertilizers by a centrifugal device as a function of the random coordinates of feed points was verified by a numerical illustration

Summary

Introduction

Сentrifugal devices for distribution of mineral fertilizers are widely used because of their simplicity, high productivity, and easy loading. Flowing fertilizers fed to the distributing device get a spread in the angle and radius of the feed under the impact of the shovels. Programs for calculating the throwing angle should be updated so that the throwing angle is determined as a function of two random arguments – the polar coordinates of the feed points. Where λ – an angular coordinate of the feed point of the particle, θ is the angle between the absolute velocity and the radius vector of the particle, ωt is the angle of descent of the particle, i.e. the angular sliding of the particle in absolute motion until it leaves the shovel. Fertilizer feed to any point of the spiral provides a set constant value of the angle α. Let us consider the application of the method for calculating the throwing angle for a device with radial shovels

Algorithm for calculating

Conclusions