Purpose. To develop a synergetic model and, on its basis, a theory of wave abrasive-fatigue wear of rubber lining in the ball mills; to confirm fidelity of the analytical model by industrial test results. Methodology. A comprehensive approach was used, which included analytical studies and extensive industrial tests of different ball mills. findings. On the basis of the designed synergetic model and the Polya-Velikanov equations, mathematical equations were formulated, with the help of which it

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... is possible to describe a pattern of wave abrasive-fatigue wear of rubber lining; on the basis of the theory of deterministic chaos, key regularities were identified in the wave motion of inputs inside the tube of the mill; correctness of the analytical model was confirmed by results of industrial tests, which are presented herein. Originality. An original synergetic model was developed and, on its basis, a theory of the wave abrasive-fatigue wear of rubber lining in the ball mills was created. Key regularities of wave motion of inputs inside the tube of the mill were identified. Practical value. On the basis of analytical calculations, the Wave-type rubber linings were designed and implemented, which are currently competitive at the world market. On the basis of the lining, a new energy-and resource-saving technology of mineral disintegration in the ball-tube ore-grinding mills was created and implemented into industry.