Tumbling mills describe a class of mechanical systems defined by a cylindrical chamber filled with balls and/or rock that rotates around its own longitudinal axis. This class of mechanical systems is used to grind to a desired quality different material in at least three industries: mining, cement and metal powders industries (ore, clinker and metal powder). These tumbling mills range in size from small 1 ft diameter lab mills to a 40 ft diameter semi-autogenous industrial mill and are composed

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... of three main interactive and interdependent elements: the mill shell, liners/lifters and charge. These three elements work together to impact energy to the mill charge through the rotational motion of the mill shell. As with any mechanical system, the natural frequency of that system is essentially dictated by its mass and stiffness. In the case of a tumbling mill, a rotating system, the natural frequency of a given mill, as seen by a stationary observer, is also a function of the rotation speed. The aim of this paper The consequence for a rotating mill, and for that matter any rotating system, is that if the natural frequency of the mill should happen to match the operating rotating speed of the mill, resonance of the mill will occur. The objective of this paper is to explore the effect of mill diameter, length on mill natural frequencies as well as outline further work.