Experimental and mathematical modelling of grain material velocity

The present article represents the next stage in the cycle of work on the research of vibrating motion of grain material. This paper contains the experimental results of the operation of a vibrating conveying machine. The investigation was carried out in three stages. The purpose of the first full-factor experiment with four varying factors was to identify factors having the least impact on the time of movement of grain material. As a result, it was found that the angle of vibration direction that has an impact on the amplitude has almost no effect on the velocity of the grain material. In the second phase of experiment carried out with three varying factors at fixed angle of vibration direction, the equation of mathematical model of time of passage of the control area has been obtained. Moreover, on the basis of previous studies, the angle of vibration direction was fixed at the position which has the greatest influence on the vibration amplitude. The third stage of the experiment was to evaluate applicability of the obtained model equation to describe movement of other grain crops with ellipsoidal grain shape. Verification of the obtained model for adequacy using Fisher's criterion showed that with 95% probability the obtained equation can be used for estimation of movement of grain material having ellipsoidal shape on vibrating surface

Modelling and calculation of stumulated oscillation for a crushing plant with vibration

The paper presents the results of the mathematical modelling of external stimuli to improve the efficiency of the removal of grain material from the grinding zone. Thus, the authors proposed to improve the evacuation conditions of the finished product from the working chamber of the crushing plant, as one of these solutions to improve the grinding process in crushers. As a result of creation of external vibrating influence. For this purpose, the calculation chart for modelling the proceeding process of the crushing plant body movement is created which takes into account weight and sizes of the crusher, weight, angular velocity of rotation and eccentric piece location, as well as rigidity of an elastic suspension on which the crusher is established. For the solution of the posed problem, we used methods of analytical mechanics, the Lagrange equation of the second kind, for the mechanical system with two degrees of freedom. As a result of calculations amplitude-frequency characteristics of mechanical system are determined. The conclusion about the choice of the angular velocity of the eccentric rotation for creation of necessary external stimulating influence on the crushing system and improvement of conditions of evacuation of a ready product from a working zone is given. The resonance frequencies of firstand second-order system vibrations and the vibrator frequency are determined to achieve resonance frequencies. Keywords: vibration, modelling, Lagrangian equations of the second kind, grinding, crushing plant