Periodical solutions of forced oscillations of working part of vibration-transport machine considering the compelling load and friction force in supports
This article considers the problem of analytical definition of a type of linear flat oscillations of working part (WP) of vibration-transport machine when compelling load is periodical, considering the friction forces in supports. The feature of imitation model of the process is that the value of compelling force depends on the position of the working part, whereas the friction force in supports is constant. The switching-on of the compelling load occurs when working part is passing through the zero point, moving in positive direction of coordinate axis with the target initial speed. The direction of action of compelling force coincides with the positive direction of WP movement. The switching-off of the compelling load occurs when the working part reaches definite (target) position. The cycle of the work process consists of the three stages. At the first stage, the compelling force and the resistance force are influencing the WP. At the second stage of the movement, WP is making free oscillations with the constant resistance. During the backward movement of WP, when WP reaches the target position again, the additional springs are attached to decrease the amplitude of oscillation. As the result, there occurs the intermittent growth of the aggregate coefficient of rigidity of elastic supports of the system, and from this moment the third stage of the movement starts - the free oscillations of WP with resistance under increasing rigidity of elastic elements. The results of calculations have shown that the WP oscillation amplitude value is nearly equal to the amplitude obtained in the experiment with trial-industrial vibration-transport machine, the error is not greater than 10%.