Algebraic dual-energy thermal analysis with application to variable reluctance motor design

The algebraic dual-energy method has been successfully employed in the calculation of static resistances, capacitances and inductances, yielding fast and accurate solutions. This paper extends the method to the thermal analysis and modeling of variable reluctance motors. Based on the analogy that exists between steady-state heat conduction and electrostatics, the existence of upper and lower thermal "energy" bounds is discussed and their analytic derivation is presented. The method is applied to the analysis of a simplified variable reluctance motor geometry and the p-convergence of the problem is discussed in detail. In addition, the problem of bounding the temperature at a point as opposed to bounding the "energy" of the whole system is addressed. A new algorithm is presented that employs the results of the algebraic dual-energy method to estimate the hot spot within the variable reluctance motor geometry. The results obtained are compared to finite element predictions.