Motion of a Mill with Polyharmonic Vibration of the Grinding Chamber

Abstract: Fine grinding in mills of various types is of great interest today. Comparison shows that vibrational mills are best for fine grinding. Designs of vibrational mills are considered, as well as approaches to their improvement. The structure and operational principle of a mill with polyharmonic vibration of the grinding chamber are outlined. The motion of the cylindrical housing in a new mill design with polyharmonic vibration of three vibration sources for superfine grinding is mathematically described. On that basis, the center-of-mass position of the mill’s grinding chamber relative to the OX and OY coordinate axes is analytically determined. The kinetic energy and potential energy of the grinding bodies are calculated, as well as the vibrational amplitude of the charge’s center of mass relative to the OX and OY axes.