Movement of the Trash Inside of Fiber Material When Available Elastic Force of Clutch

In the article, the motions of the magpies inside the fibrous material are studied in the presence of an elastic bonding force and the force of dry friction. It is assumed that the volatility of raw cotton in the form of a ball hits the initial velocity about the grate, and after the impact the velocity of the center of mass of the volatility is zero. Until the moment of impact, the mote is located along the beam, which tilts to the horizon and has the same velocity with the center of the fly, and after the impact it moves along this ray. The case is considered when the coefficients of dynamic rigidity, adhesion strength and coefficient of friction depend on the temperature difference between the initial and the current, and it is assumed that these parameters decrease with increasing temperature difference. Accordingly, in the equation of motion of the mote, the sign of the speed of movement of the magpies is taken into account in the direction of the force of contact between it and the fibrous mass. Different stages of the motion of the speck along the ray are considered. On the basis of the equations obtained, the trajectories and the geometric locations of the points of location of the magpies located along the ray are established.

DOI: 10.4236/eng.2018.109042 580 Engineering ommended the optimal moisture parameters of the material and the productivity of the corresponding machine, depending on the initial contamination and moisture content of the material being processed [2] [3] [4] [5]. However, the mechanism for extracting weedy impurities from the composition of the pulp has not yet been fully disclosed, and factors that affect the coupling of trash with fibrous material have not been established. The proposed recommendations are not sufficiently substantiated (especially theoretically). Theoretically, the effect of temperature on the process of recovering impurities is not studied. The experimental data obtained in [2] [3] [4] show a significant decrease in the magnitude of the contact force between impurities and the pulp. There are still ways to increase the efficiency of the cleaning process from weeds; it is required to establish the optimum temperature and humidity condition of raw cotton.

Main Part
Let the particle of raw cotton strike with the initial speed 0 ν about the grate.
We assume that after impact the velocity of the center of mass (the seed nucleus) is zero. Prior to the impact, the mote with mass m is located along the beam, which forms an angle 0 ϕ with the horizon. Before the impact, the mote has the same speed with the core and after the impact it moves along the OM 0 beam.
Then, after the impact, the equation of motion of the speck along the ray is written as: where: τ -time, x-movement of a speck along the ray OM 0 , c 1 -dynamic stiffness; q 1 -coupling force; m-mass of trash, f 1 -coefficient of friction, between the trash and fiber.
Consider the case where the coefficient of dynamic stiffness c 1 , the adhesion force q 1 and the coefficient of friction f 1 depend on the temperature difference.
The action of the elastic force and the frictional force of the contact to determine the relative displacement of the trash along the fiber is shown in Figure 1.

Initial conditions
Equation (2) where: Equation (4) for a given temperature variation with respect to time and coordinate ζ is integrated numerically. If we assume that T = T 0 , (in the absence of temperature difference), then the coefficient of Equation (4) does not depend on time and its solution in a dimensionless form is written down where: Expression (5) describes the law of motion of a speck between fibrous spaces after impact of volatiles on the grate. In the presence of a frictional force on the part of the fibrous mass, the mote at a certain instant of time stops. Its further movement depends on the initial impact velocity.
In the process of motion, part of the initial kinetic energy If the initial velocity is insufficient, then it is possible that all the acquired potential energy of the pulp goes only to dissipation and, therefore, no further movement of the mote is possible, that is, the process does not purify the impact Further movement towards the center of the flying, as noted above, again depends on the initial speed.
From (6) we find the speed of the mote where: Inequalities (6) give Hence we obtain the condition for the velocity If condition (7) is not satisfied, then the mote is further in a state of rest.
When condition (7) is satisfied, the motion of the mote is described by equation Then the mote makes a reverse movement to the center and the depth of maximum penetration will be equal to ξ . If 20 0 ξ < it will be introduced into the depth of the ball.
In the first case we have: in the second case  To assess the effect of changes in the stiffness coefficients c 1 , f 1 and the adhesion force q 1 on temperature, experimental studies were carried out [6].
For constants f 1 and q 1 with a change in the stiffness coefficient c 1 according to Formula (1), we should write Equation (4) in the form:

Analysis of Results
As can be seen, the solutions of the equation of motion of the mote, in each stage are presented in an analytical form, which includes mechanical parameters.
Comparing the types of solutions (9) with (5) that correspond to the 1 and 2 stages of the movement, we note that the change in the stiffness factor affects the stop and mobility time values at each stage, the movement of weed impurities.  It is shown that as the temperature of the fiber increases, the amplitude of displacement of the litter increases. For example, at a fiber temperature t В = 20˚C, the amplitude of the trash displacement ends in the second stage, and at a fiber temperature t В = 50˚C on the third.

Conclusions
Thus, under impact, a part of the garbage that is on the surface of the cotton particle is removed, and some of it moves into the inside of the particle. The