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In the above cases, we have considered intermediate supports as frictionless, and no friction of discs with the medium in which these discs are oscillating. In actual practice, we have supports and discs with friction and this produces some frictional (damping) torque on the shaft or discs. Although the rotor is rotating at a certain constant spin speed, frictions in these supports and discs give a constant damping torque. However, the torque on the shaft and discs is a function of the spin speed of the rotor. Due to relative twisting of the shaft ends during torsional oscillations, the hysteretic damping due to shaft material is present, which is a function of the rate of change of relative angular displacements. Overall effects of these frictions are much less on the torsional natural frequencies of rotor systems and for initial estimates of system dynamic characteristics it can be ignored. Torsional oscillations of the rotor with torsional dampers are considered subsequently.
Adaptive sliding mode control based on fuzzy logic for hybrid smart microgrid energy management system
Where H is an inertia constant of the turbine generator set, is the mechanical torque of the turbine, and is a damping torque. The damping torque, , represents the rotational losses of the rotating parts which consist of the magnetic losses and the mechanical losses (Kadiman 2018).