Mathematical Modeling of Mechanical Forces and Power Balance in Electromechanical Energy Converter

Abstract

This article proposes a calculation method for mechanical (electromagnetic) forces arising in an electromechanical energy converter acting on current circuits in a magnetic field, or on capacitor plates in an electric one. Transformations were performed on the basis of the principle of possible displacements involving the apparatus of partial derivatives. It was found that the power converted into mechanical power is partially spent on changing the energy of the electromagnetic field, and the remaining power, determined by the co-energy, is converted into mechanical power. Expressions for the mechanical (electromagnetic) forces were obtained based on the power balance. The reliability of the obtained results was compared with the known results. Of these, one can observe the well-known 50/50 principle, which states that only part of the power associated with the movement of the circuits is converted into mechanical power, while the rest is intended for changing the energy of the magnetic field.

Keywords

• mathematical modeling
• differential equations
• partial differential equations
• electromechanical energy conversion
• energy
• co-energy