Abstract
In electromechanics, a generalized electric machine is widely used to carry out analysis of complex processes and phenomena, synthesis of control systems, etc. Considering that in the vast majority of electric machines, the rotor has only one degree of freedom relative to the stator, mathematical models of classical generalized electric machines are based on physical models containing two pairs of orthogonal windings and one axis of rotation. At the same time, the modern development of the component base makes it possible to implement in practice and use in precision devices relatively new types of electric machines, the rotor of which has three degrees of freedom relative to the stator rather than one degree. The mathematical description of such machines, obtained, for example, on the basis of the Lagrange equation of the second kind, contains variable coefficients and is significantly more complex than classical (single-stage) machines. Therefore, there was an objective need to extend the tools of the classical generalized machine to three-stage ones. This article presents mathematical models of a generalized three-stage electric machine having two sets of three orthogonal windings to each other. These models (by analogy with the models of classical generalized machines) are obtained with mutually non-movable stator and rotor windings for two cases: when these windings rotate (that is, they are located on the rotor) and when they are stationary (that is, they are located on the stator). The obtained mathematical models no longer have variable coefficients, which greatly simplifies the process of analyzing the functioning of such machines in various modes and devices, and also allows the synthesis of interconnected motion control circuits along each of the three axes.
Keywords
electric machine, rotor, stator, winding, inductance, voltage, current, flow coupling, electromagnetic moment
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