120 THE BELL SY.^TEM TECHNICAL JOURNAL, JANUARY 1954 



operation), C,, equals or exceeds 4 ((Rl equals or exceeds 3 (Ro), and Xi/xn 

 lies in the range from 1 to 3. For 4 < Cl < 10 and 1 < .Ti/.ro < 3, 

 1.5 < Cw < 2.G. In practice therefore Cw has a value close to 2.0 for 

 most electromagnets. 



The term in V, the second term in (15), varies inversely as the power 

 I'R, while the third, or inertia term, varies as the cube root of the power. 

 Hence the second term tends to dominate at low values of PR, and the 

 third term tends to dominate at high values. For a low power input 

 therefore the operate time is controlled by the load V, and varies in- 

 ^'ersely as the power input, while for a high power input, the operate 

 tine is controlled by the inertia term, m{xi — x^)' , and varies inversely 

 as the cube root of the power. In the load controlled case, the time varies 

 directly as the load; in the mass controlled case it varies as the cube 

 root of the mass and as the two-thirds power of the travel Xi — x-i . The 

 eddy current term is very nearly a constant increment to the other two ^ 

 terms, and is therefore relatively more important, the faster the opera- 

 tion. 



PRELIMINARY TIMING ESTIMATES 



Within the limits of accuracy to which this two stage approximation 

 applies, the effect of the magnet design upon the operate time appears 

 only in Ie and Cw . If the former is neglected, the optimum value of v 

 is 0.715, and 



\ In -^ = 2.5 . 



V 1 — V 



Taking Cw as having the representative value of 2.0, (15) reduces to: 



101' /I35m(-ri - .r2)-Y (,c\ 



''^PR^\ — m — ;• ^^^^ 



This simple approximation provides rough estimates of the operate 

 times attainable with any electromagnet for a given load and power 

 input. As an illustration, consider a typical relay spring load involving 

 a travel of 40 mil-in (0.1 cm) with a level of spring force of 100 gm (lO"" 

 dynes), so that V = 10 ergs. Let the effective mass m of the moving parts 

 be 10 gm. For a steady state power input of 0.5 watts (5 X 10 ergs sec), 

 the two terms of (16) have values of 0.020 sec and 0.014 sec, respectively, 

 so that U equals 0.034 sec. For an input of 5 watts, the two terms become 

 0.002 sec and 0.007 sec, respectively, and /o equals 0.009 sec. The neg- 

 lected Ie term of (15) might amount to an increment of 0.005 sec for a 

 solid core of magnetic iron, but would be proportionally smaller for higher 



