Purpose. To improve the energy characteristics of mine winder acceleration in the process of lifting the final load by optimizing and investigating the results which have been obtained with energy and dynamic indicators. Methodology. In order to optimize the acceleration of a mine winder, a class of continuously differentiated basis functions was used. They included the free parameters, of the variational problem were obtained. By using the numerical integration of differential equations, an analysis of the results with energy and dynamic indicators has been performed. Findings. It has been established that the mine winder motion laws, which have been obtained in the research, allow eliminating the oscillations of its elements (load and coupling halves) at the end of acceleration mode. In addition, during the acceleration, undesirable maximal dynamic loads in the rope, coupling, and drive are significantly reduced, as well as an insignificant decrease in undesirable root-mean-square values of energy and dynamic indicators of the lifting machine can be observed. It has been proved that the numerical values of the energy and dynamic indicators of the machine movement significantly depend on the characteristics of its motion during acceleration. Originality. The formulation of the optimization problem was performed, where the nonlinear integral functional was chosen as a criterion. It was established that the variational approach does not allow obtaining the exact solution of the problem. In order to find approximate solutions of the problem, we obtained five basis functions that contained free parameters. Besides that, for the synthesis of basis functions, the specified boundary conditions were used. They allowed reducing the undesirable dynamic indicators of the mine winder significantly. The obtained approximate (quasi-optimal) solutions to the variational problem were investigated according to a complex of energy and dynamic indicators. A rational basis function was established. It is simple and satisfies the requirement of sufficient accuracy of solving the optimization problem. Practical value. The optimal mode of mine winder acceleration, which has been obtained in the work, might be implemented with the help of controlled electric drive of direct or alternating current, which allows increasing the efficiency of a mine winder in terms of energy and dynamic indicators.

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