RU2849649C2 - Method of feeding material into working space of crushing-grinding machine - Google Patents

Abstract

FIELD: crushing or grinding of various materials.

SUBSTANCE: invention relates to grinders. Disclosed is a method of feeding material to gripper rotor blades of crushing-grinding machine, including its movement on distributing device along steepest descent line.

EFFECT: uniform and efficient feed of raw stock, higher quality of finished product, power savings.

1 cl, 7 dwg

Description

The invention relates to devices for crushing materials and can be used for a more uniform and efficient supply of raw materials to the acceleration-impact rotor of a crushing and grinding machine.

A method for feeding material into a grinder is known, which includes its movement along a distribution device along the line of the fastest descent [USSR A.s. No. 1727894, B02C 13/16, 23.04.93, Bulletin No. 15. Rotor mill].

The disadvantage of this method is the low efficiency of uniform distribution of the material over the conical surface and the low speed of its movement along the cone generatrix.

A method is known for feeding material into the working chamber of a crushing and grinding machine through a loading hopper equipped with a box with a rolling surface for moving the initial product, which sets the line of the fastest descent [RU 2546228 C1, 10.04.2015].

The disadvantage of this method is that it cannot be applied to a crushing and grinding machine, which is based on the principle of distributing material in a rotor by a rotating distribution device and ejecting the material from the rotor by blades onto impact surfaces.

The technical task of the invention is to increase the efficiency of the method and the speed of material capture by rotor blades, in which, thanks to a new theoretical mathematical justification, better conditions for material capture by rotor blades are achieved.

The stated task is achieved by the fact that in the method of feeding the material to the grip of the rotor blades of the crushing and grinding machine, including its movement along the distribution device, along the line of the steepest descent, the absolute value of the speed of movement of the material along the distribution device is specified by a system of equations:

where V is the speed of movement of the material along the generating surface;

ϕ is the angle between the velocity vector and the direction of gravity;

g - acceleration of gravity;

k is a constant coefficient of friction;

u - optimal control;

Fig. 1 shows the kinematic diagram of the crushing and grinding machine; Fig. 2 - the conical profile of the distribution device; Fig. 3 - the proposed profile of the distribution device; Fig. 4 - a diagram of the forces acting on a material point of mass m; Fig. 5 - a graphical dependence of the trajectory of movement of a material point of the material at k = 0.1; Fig. 6 - a change in the speed of a material point of the material at k = 0.1; Fig. 7 - a calculation diagram of the movement of a material particle along a straight inclined surface.

The essence of the method is as follows.

The material is poured into the receiving opening of the crushing and grinding machine through the loading branch 5, fixed on the housing 1. Entering the rotating distribution device 7, the material, under the action of centrifugal force and gravity, slides down and is captured by blades 4, installed on the rotor rotating with the help of shaft 3.

When the material moves along the rotating distribution device, a high speed of material ejection from the rotor is ensured.

Having reached the end of the blades 4, the material is thrown onto the impact surface 2, where it is crushed under the action of the kinetic energy accumulated during acceleration.

The finished product is removed from the working space of the crushing and grinding machine through the unloading device 6.

Since energy consumption increases quadratically with increasing rotor angular frequency, leading to higher product costs, it is necessary to create conditions for increasing the material's ejection velocity from the accelerating blade without increasing its rotational speed. This can be achieved by improving the material's capture by the rotor blade, while maintaining all other geometric and kinematic parameters constant. Increasing particle velocity and streamlining its direction are possible by modifying the conical shape of the distribution device (Fig. 2, Fig. 3).

This is achieved by the fact that the absolute value of the speed of movement of the material along the distribution device is specified by a system of equations:

where V is the speed of movement of the material along the generating surface;

ϕ is the angle between the velocity vector and the direction of gravity;

g - acceleration of gravity;

k is a constant coefficient of friction;

u - optimal control;

The given mathematical dependencies were obtained as follows.

Consider the sliding of a material point with constant mass, moving along a curved surface under the action of gravity. This point is acted upon by the dry friction force F _S and the support reaction component N, in a direction perpendicular to the velocity vector V (Fig. 4).

The equations of motion of the material point under consideration have the form:

where ϕ is the angle between the velocity vector and the direction of gravity.

The magnitude of the dry friction force is determined using Coulomb's law F _S =k⋅|N|, where k is the constant coefficient of friction.

After the necessary transformations, the system of equations of motion (1) will look as follows:

where u is the optimal control defined by:

where ψ is a parameter determined by the expression:

The system of differential equations (2) is solved as a Cauchy problem with initial conditions:

For calculations, the friction coefficient k=0.1 was adopted.

For the numerical solution of the system of differential equations of motion of a material point, the 4th order Runge-Kutta method was used.

The trajectory of motion of a material point obtained as a result of calculations is shown in Fig. 5. The change in the velocity of the point over time is shown in Fig. 6.

On the graph of the change in velocity (Fig. 6), the extremum is observed at t=0.268 s. Calculations show that for this moment in time, the velocity of the material is V=1.419 m/s, the angle of inclination of the velocity vector ϕ=75.23°, and the coordinates of the material point are z _max =-0.148 m, x _max =0.185 m.

Now let us compare the obtained results with the motion of the same material point along a straight inclined surface, as shown in Fig. 7. Let us compose a differential equation for the motion of a material point along a straight inclined surface with a constant angle of inclination under the action of gravity mg, dry friction force F _S and support reaction N, in projection onto the axis As, coinciding with the direction of movement along the inclined line.

As a result of double integration of equation (6) with the initial position of the material particle at point A and with the initial velocity of the particle V _A =0, the velocity of the material point is determined by the expression:

and the law of its motion:

Hence, the time it takes for the particle to reach point B will be t _max = 0.297 s. When the particle reaches point B, its speed will be 1.594 m/s. The angle of inclination of the surface ϕ = 51.35°.

To determine the efficiency of the proposed distribution device profile, we compare the projections of the particle velocities at point B onto the Ox axis.

With the proposed profile with a conical profile The difference is 9.26%.

Thus, as a result of calculations and comparison of two centrifugal impact crusher inlet section profiles, it was found that the proposed profile increases the particle velocity of the crushed material by 9.26%, thereby enhancing crushing efficiency. Furthermore, the proposed profile brings the particle velocity vector approaching the rotating blades 31.74% closer to the particle's natural radial trajectory.

Consequently, the use of the proposed profile of the distribution device allows for an increase in the impact speed of the material on the impact surface, leading to a more efficient grinding process.

The proposed method, due to a more uniform and efficient feed of material to the rotor blades of a crushing and grinding machine, improves the quality of the finished product and reduces energy costs for the destruction process.

Claims (9)

A method for feeding material to the rotor blades of a crushing and grinding machine, including its movement along a distribution device along the line of steepest descent, characterized in that the absolute value of the speed of movement of the material along the distribution device is specified by a system of equations: where V is the speed of movement of the material along the generating surface; ϕ is the angle between the velocity vector and the direction of gravity; g - acceleration of gravity; k is a constant coefficient of friction; u - optimal control;