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<span lang="EN-US">A program was developed in the package of symbolic transformations Maple. It provides automatic analytical transformation and derivation of formulas and plotting of the main characteristics of induction motors (IM) in a convenient form for an electrical engineer and student: torque=f(slip) T=f(s), angular speed=f(Torque) ω=f(T), angular speed=f(Current) ω=f(I), current=f(slip) I=f(s); cos(φ) and phase angle (phi) φ for stator currents and rotor currents, and magnetizing circuit, machine efficiency η=f(s) and a number of other characteristics. The calculation is based on the equivalent circuit of IM motors in its different variants: with one cage in the rotor, with two or more cages in the rotor, taking into account the skin effect in the rotor rods and without it. The user can build up the equivalent circuit to the desired configuration. The algorithm of further transformations is based on analytical obtaining of amplitude/frequency and phase/frequency characteristics in the nodes of the equivalent circuits with further calculation by power and slip. Online animation of the graphs with alternate variations of all resistances R and inductances L values of the model is provided. The article contains screenshots of important parts of the programs and illustrates the complete set of graphs.</span>

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The range of values ​​of the coefficient of resistance to movement of the chain of typical longwall armored face conveyors and the coefficient of inner viscous friction in the chain, both immersed in the moving load and during the idle run of the conveyor, is estimated. The computer model of the conveyor is built as a multi-mass elastic-viscous stretched closed chain without sag with the number of masses n = 200 and one induction drive motor located in the head of the conveyor. Using the constructed model, three-dimensional space-time dynamic characteristics of speeds and forces in the chain of the CP72 longwall armored face conveyor are obtained. Start up to rated speed v≈1 m / s and the working process is simulated with an unloaded conveyor. The spatial form of frictional self-oscillations in the model with distributed parameters is shown. The resonance frequencies and amplitudes of oscillations of the efforts in the circuit and the length of the corresponding spatial waves have been determined. It was found that at the first and second resonance frequencies, self-oscillations are not excited, since the damping effect of the electric drive is quite pronounced in this frequency band. The direct connection of vibration amplitudes with the energy efficiency of the conveyor electric drive is indicated.