Thermal Analysis of a Small D-C Motor; Part I. Dimensional Analysis of Combined Thermal and Electrical Processes [includes discussion]

A research program has been underway to study systematically small rotating electric machinery from the combined viewpoints of thermal and electrical processes. This paper is limited to the application of dimensional analysis to the detailed thermal and electrical processes occurring in the steady-state operation of a small d-c shunt-wound motor. Part II1 presents the numerous measurements of temperature distribution in the rotor and stator of such a motor made with the aid of 130 thermocouples and will correlate the experimental results in terms of dimensionless groups obtained with the aid of the dimensional analysis. Dimensional analysis was applied to this case of extremely complex and interrelated thermal and electrical processes and yielded a final single unknown functional relation between the important thermal and electrical parameters for the case of geometrically similar machines made from materials with identical electrical, magnetic, and thermal properties. The dimensionless groups which arose from this dimensional analysis were found to be of great value in planning the experimental test program and in correlating the experimental results. The dimensional analysis gave, however, no information as to the nature of the desired function relating the various dimensionless groups. The dimensional analysis was checked for the limiting case of zero internal flow of cooling air by a process of actually deriving the desired function predicted by dimensional analysis. This derivation combined equations for the electric circuit with the equations for the thermal circuit.