Determination of Inductance of Vehicle Electromagnet in Magnetic Levitation Transprort System
Objective. Of the work consists in receiving new analytic expressions for determination of inductance of vehicular electromagnets of transport levitation systems. Methods. The key feature of calculation model of onboard coils in accordance with their inductance on the example of squared electromagnets lies an assumption about a smallness of the size «heights» in comparison with its other geometrical sizes. There is also an assumption that thickness of a skin layer of the conductor significantly surpasses cross sectional size of the wire making the coil. The single-turn coil is considered, inductance of an actual electromagnet is accepted proportional to a square of the number of turns. When calculating inductance the dimensionless quantities are used. As an absolute, a quarter of perimeter of the coil on the centerline is chosen. The condition of obtaining the approximate formula for calculation of inductance of the flat rectangular coil is the small thickness of a winding in comparison with the geometrical sizes of the coil. Results. Accurate analytical expression for inductance of a «thin» source of squareshaped magnetic field as the algebraic sum of elementary functions has been received. Results of a numerical analysis show dependence of the relative inductance of the square-shaped flat coil on thickness relation to its minimum size. Influence of «elongation» of the coil (relation of length to width) is investigated. It is noted that inductance decreases with decrease of «elongation», and also with increase in the relation of thickness to the minimum size. Practical importance. The approximate formula for calculation of value of inductance has been obtained. Its uncertainty does not exceed 14 % in the areas of changes of all geometrical parameters of an electromagnet is output. Borders of practical application of the received analytic expressions at the accepted assumptions have been set. The received expressions are fairly simple structurally and are easily programmed