The differential equations of movement along the concave profile of the grate, consisting of three broken lines, are integrated on Maple 9.5 under initial conditions, using separate functions, and graphs of the dependence of movement and speed over time are presented. The graphs show the patterns of change in displacement and speed at different angles, friction coefficient of seeds along grate with a broken line of a concave profile.How to cite this paper: Sharipov, K., Akhmedxodjayev, K., Tojiboyev, M. and Sarimsakov, O. (2020) The Mathematical Model of Seed Movement on a Concave Profile Rib. Engineering, 12,[216][217][218][219][220][221][222][223][224][225][226][227]

Improving the efficiency of the process of separating fiber from cotton seeds by improving the working chamber of the gin is one of the important issues. The main way to increase the efficiency of sawn gin is to increase the fiber content in the mass of seeds in the working chamber with a uniform decrease in its density. This can be achieved by using grates with a concave working surface, which serves to move the seeds away from the rotating saws and accelerate the release of bare seeds from the working chamber. The article discusses the movement of seeds on the concave surface of the grate and determines the rational parameters of their working part. The article explores the proposed grate model, consisting of four geometric shapes, provides an analytical analysis of the geometric types. The dependence of the location of the last rectilinear part of the general contour on the shape of its convexity and concavity is determined. Cotton seeds move along the contour in the form of a stream. We assume that the thickness of the flow along the contour is constant and equal. We compose a unique equation of the flow in each section of the circuit. To determine the state of the flow, we denote its velocity, density and pressure in each section, respectively. Let us determine the flow motion along the contour with respect to the arc.

The differential equation, obtained as a result of the theoretical study of the movement of the bare seed on the surface of the grate of the saw gin, made it possible to determine the trajectory of the movement of the seed. The rib is one of the main working bodies of the saw gin. It serves for the free passage of the saw blades through it into the working chamber, for the withdrawal of the fiber caught on the saw teeth after separating it from the seed. A number of studies have been carried out to improve the working elements of the saw gin. The purpose of the research is to create the possibility of timely withdrawal of bare seeds from the working chamber of the saw gin by creating a concavity on the working surface of the grate. The use of the Euler equation for the movement of bare cotton seed along the grate contour, taking into account its speed V, density ρ , pressure P, made it possible to obtain a graph of seed distribution along the grate contour. An experimental 30-saw gin was developed and manufactured, the research carried out on it allowed to determine the rational parameters of new grates, which are recommended for introduction into production. The dependence of the location of the rectilinear part of the general contour on the shape of its convexity and concavity is determined. Based on the above equations, using separate functions, we present the view of the grate profile in the coordinate system modeled on the MAPLE-17 program.