Abstract
The semidirect drive cutting transmission system of coal cutters is prone to unstable torsional vibration when the resistance values of its driving permanent magnet synchronous motor (PMSM) are affected by changes in temperatures and tough conditions. Besides, the system has the properties of complex electromechanically coupling such as the coupling between electrical parameters and mechanical parameters. Therefore, in this study, the nonlinear torsional vibration equation was established on the basis of the Lagrange-Maxwell theory. Moreover, in light of the nonlinear dynamic bifurcation theory, the system stability was analyzed by taking the resistance value of power motor as the bifurcation parameter. In addition, the influence of subcritical bifurcation on the torsional vibration was studied by investigating the necessary and sufficient conditions for dynamic Hopf bifurcation and classifying the bifurcation types. At last, in order to suppress destabilizing oscillation induced by Hopf bifurcation, the nonlinear feedback controller was constructed, with the introduction of feedback from the motor velocity as well as the selection of voltage value on the q shaft as the controlled variable. Meanwhile, the three-order normal form and controlling parameters of the system were obtained with the aid of the multiple scales method and the harmonic balance method. In this way, the Hopf bifurcation point was transferred to control the stability of Hopf bifurcation and the amplitude of limit cycle, thus guaranteeing reliable and safe operation of the system. The numerical simulation results indicate that the designed controller boosts an ideal controlling effect.
Highlights
When the tail drum of the permanent magnet semidirect drive cutting transmission system in the coal cutters cuts coals and rocks, due to the uneven intensity of the coal seam, the brittle caving of the coal rock mass, and hard parcels existing, the loads on the drum exhibit the characteristics of randomness, major fluctuations, great impact, etc. [1,2,3]
The cutting transmission system of permanent magnet semidirect drive in coal cutters, which consists of a permanent magnet synchronous motor (PMSM), a speed reducer, cutting drums, and other components, is a typical electromechanical coupling system [4,5,6]
The electromechanical coupling transmission system of coal cutters under the coupling effect of electrical parameters and mechanical parameters is studied, where the dynamic model of its nonlinear coupling torsional vibration is established with reference to the LagrangeMaxwell equation
Summary
When the tail drum of the permanent magnet semidirect drive cutting transmission system in the coal cutters cuts coals and rocks, due to the uneven intensity of the coal seam, the brittle caving of the coal rock mass, and hard parcels existing, the loads on the drum exhibit the characteristics of randomness, major fluctuations, great impact, etc. [1,2,3]. It is essential to study electromechanical coupling dynamics of the semidirect drive cutting transmission system in coal cutters and the mechanism of torsional vibrations; the dynamics of the system will be further optimized. The influence of the electromagnetic stiffness and the damping coefficient on the electromechanical system was generated by Tomasz Szolc et al [29], where the rotating machine under dynamic coupling effect was modeled Concerning those electromechanical coupling system of rolling mills with nonlinear friction force, the dynamic equation of its torsional vibration was set up by Liu et al [30] through the adoption of electromechanical analytical dynamic method. The electromechanical coupling transmission system of coal cutters under the coupling effect of electrical parameters and mechanical parameters is studied, where the dynamic model of its nonlinear coupling torsional vibration is established with reference to the LagrangeMaxwell equation. The methods of multiple scales and harmonic balance are employed to obtain the third-order normal form for the system and its controlling parameters, by which the bifurcation point is transferred, enhancing the system stability and decreasing the limit cycle amplitudes
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