Mathematical Model of the Dynamic Action of the Controlled Vibration Exciter on the Processed Medium of Mixer with Toroidal Working Container

Abstract

Vibration mixers are technological machines that are meant for mixing of different processed medium. A driving force in such machines is realizing by oscillation exciter. In this article, the constructive scheme of the vibration mixer is introduced. Such a mixer has the toroidal working container and is equipped with controlled mechanical centrifugal unbalanced exciters of oscillations with a vertically located unbalanced shaft. The work principle of one of the possible configurations in this exciter is considered and provided. One inflexible and two mobile unbalances are strengthen on its unbalanced shaft. The mobile unbalances by means of independent external action, that is caused by mechanism for managing of mobile unbalances, have an opportunity to change synchronously its positions on the unbalanced shaft directly in time of mixer’s work. The centrifugal inertia forces of inflexible and mobile unbalances make the dynamic wrench that consists of the main vector  and the main moment  and rotates with unbalanced shaft. It is determined that the value of the main vector  and the main moment  evaluate the dynamic action of this vibration exciter to the mixer’s working container. The mathematical model of the dynamic action of oscillator exciter on the processed medium of mixer with the toroidal working container is received. Depending on the value of turn angle of mobile unbalances from its starting positions exciter: a) staying in the dynamic balance state; b) is generating the translation force field; c) generates the wrench force field of this or that direction. These opportunities of controlled vibration exciter firmly provide anfractuous circulative motion of the processed medium on the volume of the mixer’s working container. Using of controlled exciter also leaves out the transfers through intermediate resonance frequencies. As its starting and stopping happen in a dynamic balance state, so it leaves out the possibility of manifestation of the “Sommerfeld’s effect†that is harmful for the driven motor, improves the constructive availability of the vibration mixer and increases its efficiency and life duration.