The thermal time constants of dynamo-electric machines

Considering the thermal behavior of a dynamo-electric machine intended for continuous service, its acceptance tests require, at present, only a limiting temperature elevation under a continuous rated load. For the intelligent operation of a machine after it has been put in service, additional information is desirable concerning its thermal behavior under changes of load. This subsidiary thermal information concerning a machine with a continuous rating may consist of (1) its final temperature rise under some steady load other than its rated load, such as either 75 per cent or 125 per cent of the rated load, and (2) its thermal time constant. The thermal time constant of a machine, assumed as conforming strictly to an exponential law of temperature rise above a constant ambient temperature, after being transferred suddenly from one steady load to another, is taken as the time required to attain 1 – ∊^–1 or 63.2 per cent of the final temperature change. This may be called the exponential thermal time constant. This is a fundamentally scientific quantity; but is very awkward to remember or to explain to a person not well versed in the mathematical theory of the subject. It is recommended in the paper that for all practical engineering work, a new time constant called the binary time constant be used. It would correspond to the “Period,” or “Half-value period,” already used in the Science of Radio-activity and in measurements of Radio active decay. A binary time constant is that time in which a machine, assumed as conforming to an exponential law of temperature change, after being suddenly transferred from one steady load to another, attains one half of the final temperature change (50 per cent). In two binary time constants, it will then attain ¾ (75 per cent) of the final temperature change, in three of them ⅞ths (87.5) and, so on. This is an easy relation to remember and explain. A bina- y thermal time constant may be taken, for practical purposes, as 70 per cent of the classical exponential time constant. It is more strictly 69.32 per cent. Although dynamo machines do not rigidly follow an exponential law of temperature change, for reasons discussed, yet for many purposes the deviation therefrom may be ignored. It is recommended that the binary time constant of all such machines may be adopted, where practical, for industrial use. In rotating machines, there are two thermal time constants, the constant-loss time constant, and the variable-loss time constant. The latter, expressed as a binary constant, is the practical one presenting itself for use. The binary thermal time constant has also useful applications in correcting the final ambient temperature during a continuous-load test, when the ambient temperature has been observed to change.