Modeling the motion and mass quantity of fruit by rotating sizing machines

Abstract

This paper analyzes theoretically the motion and mass quantity of eight fruit types, roundish in shape, along rotating sizing machines. Mathematical model of the motion of fruit on the rotating disc is solved in spherical coordinate system which is tied to the disc. The exact solution is simplified introducing assumptions that are do not significantly affect the accuracy of the solution. Starting from differential equation of fruit motion on a rotating disk of the sizing machine, all forces acting on fruit were determined as well as velocities and time necessary for fruit to reach the disk rim if found in some upper position on the cone. Mass quantity analysis comprised sized fruit mass and weight capacity. New empirical coefficients were introduced: extent ratio, feed ratio and distribution ratio. The results obtained for the adopted values ke = 0.7, kf = 1, kd = 0.5 coincide approximately with those reported to date for fruit mass quantity rate on sizing machines. It was found that mass quantity rates vary considerably, depending on fruit diameter and mass. Fruit numbers mass quantity ranges from 8949 crops/h for apple to 40,157 crops/h for deep frozen raspberry. Mass quantity varies from 229.1 kg/h for cherry to 2054.7 kg/h for apple.

Keywords

• fruit sizing
• fruit motion
• mass quantity