By studying this curve, it will be possible to find equivalent forces and, based on the comparative estimation, develop design recommendations for choosing the graph’s efficient shape. Trapezoidal and parabola graphs are most common. This research determines the equivalent force at a trapezoidal velocity graph.
Methods of research. The analytic calculation takes into account that the trapezoidal graph allows many velocities and accelerations not only at different, but also at constant values of the rise and travel time, whereas the parabola velocity graph does not. It greatly widens the possibilities for efficient dynamic modes selection. The non-isosceles property of a trapezoidal widens the possibilities still greater. The indicated properties of the trapezoidal graph were taken into account when deriving the estimated dependencies.
Research result. The kinematics of the mine winder vessel with a trapezoidal velocity graph is analyzed. Formulas have been obtained that allow to determine the root-mean-square and equivalent effort, suited for feasibility estimation a trapezoidal graph, without preliminary calculation a n d graphs of velocity, acceleration and force.
Conclusions. The trapezoidal velocity graph provides the possibility of a large choice of energetically expedient dynamic modes, since these modes depend not only on the frequency of operations, but also on graph’s degree of incompleteness and asymmetry coefficient. The kinematic and force dependencies obtained analytically make it possible to make a reasonable choice of the velocity graph when designing a mine winder.
Keywords: mine winder; equivalent force; root mean square force; hoisting speed; velocity graph; trapezoidal graph; velocity graph asymmetry.

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