Purpose. Development of a mathematical model of gear mesh which takes into account flexibility of a pinion support for studying the influence of lateral vibrations on gear dynamics as a whole. Methodology. The calculation model is designed using lumped-parameters method. The research on dynamics of the system is performed by methods of the theory of oscillations of two degree of freedom systems. Using the approximate method of theory of oscillations and algebra, vibrational amplitude of the system is defined. The results of numerical integration of dynamic equations are compared to the experimental data. Findings. State-of-the-art review on gear mesh models taking into account coupling effect of pinion torsional and lateral vibrations is performed. Based on the lumped-parameters method, an analytical model for calculating dynamics of gear mesh with flexible support is developed. The amplitude-frequency response of open gearing of a tumbling mill MSHRGU 4500 x 6000 is studies taking into account flexibility of a pinion shaft and bearing parts. It is shown that torsional vibrations of a pinion and lateral vibrations of a power unit have a coupling effect. The models of highly loade gearing give values of natural frequencies with a significant error. A range of possible force resonance in a power unit of tumbling mill open gearing is defined. Causes of excessive vibroactivity of mechanical systems of drives of certain mills and increasing vibroactivity when in operation are established. It is shown that amplification of vibroactivity of a tumbling mill power unit due to intermittent action of forces with gearing frequency is improbable. Rational techniques of reducing vibroactivity of existing mills due to lubrication and increasing hardness of working face of gear teeth are defined. Originality. Methods for defining resonance range of gear mesh which consider a coupling effect of pinion torsional vibrations and pinion shaft lateral vibrations are developed. Practical value. The range of possible force resonance in a power unit of tumbling mill MSHRGU 4500 - 6000 open gearing is defined.

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