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The mechanism of forced transverse vibrations of the leading chain of special chain drives functioning in the machinery and equipment of the oil and gas industry is investigated. The total angular displacements in shaft-sleeve pairs, which are critical in the wear of the joints of chains and of the chain as a whole are determined. The calculations presented are of particular practical importance and make it possible to estimate and minimize the additional wear of a chain in a drive loop with internal gearing. Recommendations intended to improve the design of chain drives with internal gearing to realize greater useful life are given. Keywords: chain drive, internal chain gearing, sprocket, bush roller chain, transverse vibrations, oil and gas equipment.A chain drive with internal gearing [1-3] consists of a drive sprocket 1 with external teeth, a driven sprocket 2 with internal teeth, a driving roller chain 6, guide rollers 4 and 5, and buses 3 that support engagement of the chain 6 with the internal teeth of the driven sprocket 2 (Fig. 1).The fabrication of a drive sprocket (with external teeth) and of a driven sprocket (with internal teeth) is achieved on the basis of a patented technique [4,5]. In addition to the working (drive) strand S 1 and the idler strand S 2 (as in a traditional chain drive), a chain drive with internal gearing additionally contains two short strands S 3 and S 4 between the roller and the bus. The advantages of traditional chain drives are preserved, for example, the absence of slippage of the chain along the sprocket teeth, low forces acting on the shaft, and high efficiency.The drawbacks of chain drives with internal gearing (which are inherent to chain drives of the usual design) include high noise level, dynamic loads caused by internal factors typical of chain drives, and the variability of the instantaneous speeds of the chain and the driven sprocket.One of the most important problems that arise in the design of chain drives with internal gearing involves the calculation of the transverse vibrations of the drive strand of the drive, since the drive strand undergoes the maximal load in the course of operation of the drive.The specific nature of a chain drive lies in the fact that its normal operation is accompanied by cyclic disturbances, such as the hexagonal feature of the sprockets (position of the links of the chain in the form of faces of a polyhedron) and their eccentricity, and the impact of the joints of the chain and the teeth of the drive sprocket at the initial moment of gearing.Erosion of a drive roller chain in a working drive occurs continuously as the links travel along the drive loop. An increment in the average step of the chain Δt occurs as a consequence of the relative angular displacements in the joint, both

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A probabilistic method of predicting the life of chain transmissions from the wear of the roller drive chain is proposed.