Calculation of the Parameters of a Mathematical Model of an Electric Hybrid Stepper Motor Based on the Analysis of the Magneto Static Field Pattern

The article presents a solution to the problem of calculating the parameters of a mathematical model of an electric hybrid stepper motor based on an analysis of the picture of its magnetostatic field. The main disadvantage of such an engine described. Is the mid-frequency resonance, which occurs due to the coincidence of the natural frequency of the rotor with the frequency of the supply voltage pulses. The necessity of taking this factor into account when designing a discrete electric drive system based on the executive motor of this type by calculating the values of resonant frequencies and using them in developing the drive control algorithm is shown. The task of developing a mathematical model of the engine is formulated, which allows to analyze the influence of its design parameters on the spectrum of resonant frequencies. The method of calculating the parameters of a given mathematical model is formed. The variants of the mathematical description of this electric machine are considered and the selection of its known mathematical model is made based on the equivalent electric circuit. The numerical calculation of the spatial pattern of the magnetostatic field of the electric motor is performed. Based on the analysis of the calculation results, a system of assumptions has been formed to develop an equivalent magnetic circuit of an electrical machine. An equivalent magnetic circuit and the corresponding system of equations has been developed. Formed a system of equations of a mathematical model based on the equivalent circuits of the electric and magnetic circuits.On the basis of the obtained system of equations, a simulation model of a discrete electric drive was developed in the Simulink software package. Using the obtained simulation model, the calculation of transients on the angle of rotation of the rotor and the electromagnetic moment is carried out and the influence of one of the design parameters on the natural frequency of the rotor is analyzed. Based on the simulation results, it is shown that with an increase in the air gap height of a hybrid stepper motor, the resulting electromagnetic moment decreases, and the natural oscillation frequency of the rotor decreases, and the frequency at which medium-frequency resonance occurs also decreases. This mathematical model can be used at the stage of the correct calculation of the selected engine, since allows you to analyze the effect of a specific design parameter of the machine — in particular the size of the air gap on the natural frequency of the rotor, and, consequently, on the spectrum of the resonant frequencies of a discrete electric drive.

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