Mathematical model of the vibratory mill body movement with biharmonic oscillations

Abstract

Vibratory mills are widely used in various industries such as construction, mining, chemical, energy ones in order to obtain powders with the size of a particle less than 5 microns. Vibratory mills with harmonic oscillations of a cylindrical body are most widely used in world practice. The disadvantage of such mills is the presence of stagnant zones in the central part of the load which reach 40% of the total mass of milling bodies. This significantly reduces the efficiency of the grinding process. In recent years, vibratory mills with two drives have been used. The body of these mills makes biharmonic vibrations; as a result, the volume of stagnant zones decreases to 15–20%. We have proposed a new design of a vibratory mill equipped with two imbalanced vibration drives, the axes of which are shifted in different directions from the horizontal axis of the mill, passing through the center of mass of the oscillating system. This article discusses the method that allows one to calculate the trajectory of the mill body in polar coordinates. This method is contemplated for the first time. The resulting equation of the motion trajectory of the vibromill body takes into account: the geometrical parameters of the cylindrical body; body weight and load; weight of imbalances; eccentricities of imbalances; imbalance angular velocity; the forces created by imbalances; imbalance offset angles; spring stiffness and damping coefficient.