INTERNAL TEMPERATURES OF RELAY WINDINGS 143 



from the inner and outer surfaces of the coil. If the heat flow is wholly- 

 radial, all the heat supplied must pass through one or the other of these 

 surfaces. The division of the heat between the two paths is determined by 

 the radius r' of maximum temperature. The rate of heat flow to the core 

 is therefore the rate of heat supply per unit volume Q, multiplied by the 

 volume of the coil inside the radius r\ or tt {r'^ — r\) per unit length of coil. 

 Similarly, the rate of heat flow through the outer surface per unit length of 

 coilisg.TT {r\ - /2). 



It is therefore formally possible to determine the heat division by measur- 

 ing the temperature distribution, and reading the radius of maximum tem- 

 perature directly from it. When this is done it is found that the tempera- 

 ture gradient is comparatively flat in the vicinity of the maximum, and 

 that it is therefore difficult to measure r' directly. An indirect determination 

 of the radius / may be made, however, by determining the maximum 

 temperature T' and the temperatures Ti and T2 at radii ri and r^ respectively. 

 Expressions for Ti and Ti are obtained from equation (4) by letting r = ri 

 in the one case and ^2 in the other. Then from these two expressions: 



--^' i + 2iogp-(p;- 



Knowing Ji, Ti, T\ and the radii ri and ^2, r' may be evaluated by nu- 

 merical or graphical solution of equation (7). This solution is facilitated by 

 the use of a table or plot of the function F (X) = 1 + log X^ - X^. The 

 numerator of the right hand side of equation (7) is Y {ri/r'), and the de- 

 nominator is Y ir^lr'). 



A convenient procedure for determining the temperature distribution 

 within a coil is to measure the resistance changes in different layers, tapping 

 the coil between these layers. If there is more than one layer between taps, 

 the resistance change measures the mean temperature of the layers included. 



For an accurate determination of the gradient, it is convenient to make 

 the resistance measurements on a comparative basis, as by use of the 

 bridge circuit shown in Fig. 1. Here the terminals marked and 6 are the 

 inner and outer ends of the winding, while terminals 1 to 5 denote taps 

 at intermediate layers. With the key i^ in Position 2, the bridge circuit may 

 be balanced to establish the resistance between terminals and 3, for 

 example, relative to that between terminals 3 and 6. The resistance of the 

 whole winding may be determined with sufficient accuracy (about one per 

 cent) by voltmeter-ammeter readings made with K in Position 1. With 

 this known, the resistance of the layers between taps, and hence the tem- 

 perature differences, can be computed from the bridge readings. 



