132 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



design variables to obtain maximum speed. In particular, it has been 

 shown that for a given relay, with a specified load and power input, a 

 winding can be selected to minimize the operate time. Aside from this, 

 the relations show that for a given relay, the operate time depends only 

 upon the load and travel and the power input, varying inversely as the 

 latter at low levels of power input, and inversely as its cube root at 

 high levels. 



Further conclusions can be drawn from these relations mth reference 

 to development studies of relays and other electromagnets. The spring 

 load and travel may be considered as fixed requirements, so far as the 

 magnet design is concerned. The available power may be fixed by circuit 

 considerations, or it may be related to the design by a requirement 

 that the winding dissipate this power in the holding interval, a condition 

 that imposes a minimum size on the coil and the magnet structure. 

 Subject to this and some other limitations, there is a design choice of 

 the dimensions and configuration which determine the magnetic circuit 

 constants, the mass of the armature, and the eddy current conductance. 



The preceding discussion has shown that, with an optimum choice of 

 pole face area, the magnetic characteristics affect the time only with 

 respect to the leakage factor, the ratio of leakage to useful flux. This 

 factor may be reduced by using a "tight" magnetic circuit, but if this 

 is done the factor tends to vary directly as the length of the magnetic 

 path and inversely as the separation of the core and return members in 

 relation to their cross sections. The leakage may be minimized by using 

 a square outline for the magnetic path. The optimum speed magnet 

 then has a specific configuration in which all dimensions are fixed in re- 

 lation to the cross section of the magnetic members. This dimension then 

 determines the mass of the armature. 



For this optimum configuration, the power, the spring load, the mass, 

 and the travel determine a level of pull which minimizes the operate 

 time. This pull requires a certain armature cross section if saturation is 

 to be avoided, as the effective pole face area is fixed in relation to the 

 cross section. If the resulting armature mass is minor compared with the 

 mass of the load, the operate time attainable varies with the cube root 

 of the applied power, as in the cases discussed above. 



With increased power, however, the optimum pull and armature cross 

 section increase, and must eventually reach a level where the armature 

 mass becomes the dominant portion of the mass term. As this condition 

 is approached, any increase in power is offset by an increase in armature 

 mass, such that a lower limit is imposed on the operate time proportional 

 to the travel, corresponding to an upper Umit to the average armature 



