Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller

Abstract Due to increasing demand of lightweight shafts from industries, the drive systems are crucially demanded for larger inertias of motors and load machines because of control structures for the electrical equipment. The mathematical modeling of two-mass torsional vibration system consisting of motor and roller has been proposed via newly presented fractal–fractional differential operators. The dynamical model of the electromechanical coupling main drive system of rolling mill is based on total kinetic energy and potential energy on the basis of two degree-of-freedom. The fractal and fractional evolutionary differential equation containing nonlinearity have been investigated for the derivation of numerical schemes. Three types of numerical schemes say Caputo differential scheme, Caputo–Fabrizio differential scheme, and Atangana–Baleanu differential scheme have been established through Adams–Bashforth–Moulton method. In order to check the stability and effectiveness, we presented the chaotic comparison of Caputo fractal– fractional operator, Caputo–Fabrizio fractal–fractional operator, and Atangana fractal–fractional operator on the basis of dynamical embedded parameters (vibration angle, rotational speed, stiffness coefficient, load friction damping torque, and few others). Our results suggest that fractal–fractionalized model for electromechanical drive system of rolling mill has better attenuation performance and tracking behaviors in comparison with classical models.