Purpose. The justification of the new equation of friction of flexible bodies, which confirm the concepts of friction of bodies during operation of transport machines with flexible tie body. Methods.A comparison of the known concepts of the friction of bodies, the influencing factors, and the solutions of the Euler problem of the sliding of a flexible body along a fixed block. Originality. For the first time it is established that the new equation of friction of flexible bodies: -includes the frictional force and the normal reaction between the bodies, which are linearly connected; -corresponds to the equilibrium conditions of the mechanical system; -coincides with the law of friction of bodies of Coulomb, which is common. Practical implications.New scientific knowledge widens the idea of the friction of bodies. They contribute to a deeper understanding of the physics of the process and the accuracy of conducting research, determine the development of technology and perfection of transport vehicles with a flexible body, increase their efficiency and operation safety.

Usually, basic traffic flows of mining enterprises are effected with the help of transportation vehicles with a flexible tractive element, i.e. belt conveyor, ground ropeway etc. Parameters of transport and operation procedures depend upon mining and geological conditions of mineral mining, technical characteristics, and operation parameters of the transportation vehicles. Objective is to substantiate a new equation of friction of flexible bodies which corresponds to classical concepts of friction of bodies. The methods are based upon the adjustment of common idea of friction of bodies; factors, working upon friction; and solutions of Euler problem on flexible body slip along the fixed block. As a result, common factors of friction of inflexible bodies, i.e. friction force and normal reaction between linearly connected bodies, have been determined; new equation of friction of flexible bodies has been substantiated. Scientific novelty has been represented by means of a new equation of friction of flexible bodies (in the indirect form) which: involves friction force and normal reaction between linearly connected bodies; corresponds to equilibrium conditions of a mechanical system; and coincides with friction law of Coulomb bodies being common one. Practical implication is in the proposed new scientific knowledge giving corrected idea of friction of flexible bodies. The knowledge improves both education level and research level stipulating technological expansion as well as upgrade of transportation vehicles with flexible body. The findings can be applied to improve both efficiency and safety of transportation vehicles with a flexible tractive element under complicated operation conditions; among other things, it concerns mining enterprises.