Mathematical Modeling of The Weight of Grain Straw during Conveying in Vertical Conveying Reaper Windrow

Abstract Analyzing the total weight of cut straws inside the conveyor is important in a vertical conveyor reapers machines to optimize the supply energy into the lugged belt conveyor system. This weight was mathematically modeled by considering the working mechanism of vertical conveyor reapers machines, corelating feeding rate of cut straws from cutter to conveyor and conveying rates of lugged belt conveyor. Then the mathematical model for total weight was defined by determining numbers of cut straws in front of each cutters or knives. The defined equation shows that the feed rate of cut straws into the conveyor is in arithmetic sequence fashion with equal initial value and common difference. The total weight of cut straws equation is an arithmetic series with positive common difference. The equation also shows that the numbers of cut straws in the conveyor increased in arithmetic progression when the numbers of cutters or knives increased. In general, the weight of cut straws in conveyor depends on mass of straw, gravitational acceleration, numbers of cutters or knives, forward speed of reaper, spacing of lugs, angular speed of conveyor pulley, diameter of conveyor pulley and diameter of straw.