In this work, we consider methods for analytical construction of the profile of rotor blades mixer, as well as mathematical modeling of their work on moving and mixing bulk material on a conveyor to increase process efficiency mixing raw materials and optimizing its operating costs. In addition to increasing the effectiveness of the mixing process and lower operating costs, the goal of implementation the proposed methods is the consciousness of production with the least possible errors that would meet modern technical requirements and be adapted to consumer tasks. In this regard, the aim of this work was to determine rational parameters and geometric characteristics of the profile of the rotor mixer blades contributing to improving the quality of mixing the metallurgical charge transported on a conveyor belt. To achieve the goal by modeling, which is a key method of the fourth concept industrial revolution, using the developed mathematical model analyzed the movement of a particle of material along a conveyor belt with its subsequent interaction with the blades of the working body of the rotary mixer.

The article presents the movement kinematics of the modular bar element of a dynamically active polymer sieve of a vibrating screen. On the basis of analytical methods, the mathematical model was obtained, which makes it possible to determine the law and trajectory of the modular bar element movement depending on its geometric characteristics, physico-mechanical properties of the polymer material, the regime and technological parameters of the vibrating screen. The results of this research show that in the working frequency range of the vibrating screen grate, modular bar element of the dynamically active sieve moves along the trajectories, the envelope of which is represented by Cassini’s ovals, which along with the generation of the amplitude component in the horizontal and vertical directions allows one to obtain the selfcleaning effect of the sowing surface.

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