Mechanical power under harmonic influences

Abstract

The purpose of the study is to detail the types of mechanical power under harmonic oscillations. Due to the irreversibility of thermal energy, its derivative takes only positive values. At the same time, derivatives can be taken from both potential and kinetic energy. Wherein, the most interesting case is presented by harmonic oscillations, with the derivatives (instantaneous powers) necessarily being sign-changing functions, which fundamentally distinguishes them from thermal power. An analogue of kinetic energy in electrical engineering is the energy of the magnetic field of an inductor, an analogue of potential energy is the energy of the electric field of a capacitor, and an analogue of mechanical thermal energy is the thermal energy dissipated by a resistor. It is shown that during mechanical vibrations, not only a sign-positive thermal power develops, but sign-alternating reactive powers, characterizing the reversibility of the kinetic and potential energies do as well. Active power is understood as the average value of instantaneous half period power, while reactive power is an amplitude value. The total mechanical power, on the one hand, is described by the Pythagorean formula, and on the other hand, it is equal to the product of the effective values of the harmonic quantities. The peculiarity of the complex representation is that when calculating the total power, one of the multiplied vectors must be conjugate. The concept of mechanical reactive, active and apparent power is a generalization of the corresponding concepts from electrical engineering, which is a manifestation of electro-mechanical dualism. Since the drives of machines and mechanisms are predominantly electromechanical, the mechanical reactive power is transformed into the electrical reactive power of the network, degrading the quality of electricity. In this regard, the consideration of mechanical reactive power is of no small importance.