ESTIMATION AND CONTUOL OF OI'KKATE TIMI'; OF UKLAVS 



19 



changos rapidly, iHiuation (3) is (■()iitr()lliii<j;, with F coiTcspoiHliiig to a 

 more nearly constant vahio of </?. 



.\[ETIIODS OF SOLUTION 



Formally, the expression for ^p given by combining (3) and (5) may be 

 substituted in (2), eliminating (p and giving a third order non-linear dif- 

 ferential equation in x and /. Xo analytical solution to this equation is 

 known, even for the idealized case of a linear load curve. Specific solutions 

 may be obtained by means of computing devices, but there are too many 

 l)arameters imoKed to prepare a useful library of specific solutions that 

 would serve as a general treatment. 



Approximate analytical solutions can be obtained l)y a step by step 

 process, starting from the initial stage of flux development with the 

 armature at rest. These solutions are relatively simple in form and ap- 

 plication, and provide an analytical statement of the relations betw^een 

 performance and design parameters, from which conclusions can be 

 drawn as to design features and operating conditions favoring a desired 



'■■■-.--L,-x —*■ X, 



F'ig. 4 — Load and i)ull iclal ions in tlic o])ciation ol' an elect roina}i;net 



