. The Bell System technical journal . ojected area. (Rg is conveniently expressed in terms of the ratio (R^/(Rg .SLOW KKLEASE RELAY DESIGN 201 given by the equation: ; = 2«0 + 2i) (14) in which 6\^ = x/A, the vahie of 6\o which would apply it the . were infinite, and both mating plane. On .substituting thisexpression for (Rg in (13), there is obtained the following e(]uation forthe pull at a domed pole face: F = StA mo (R 27r/?(Râ 1 + 2ir72«, (15) The right hand side of (14), and the expression given by (15) for theratio of F to <p^/(STrA) are both functions of a si
. The Bell System technical journal . ojected area. (Rg is conveniently expressed in terms of the ratio (R^/(Rg .SLOW KKLEASE RELAY DESIGN 201 given by the equation: ; = 2«0 + 2i) (14) in which 6\^ = x/A, the vahie of 6\o which would apply it the . were infinite, and both mating plane. On .substituting thisexpression for (Rg in (13), there is obtained the following e(]uation forthe pull at a domed pole face: F = StA mo (R 27r/?(Râ 1 + 2ir72«, (15) The right hand side of (14), and the expression given by (15) for theratio of F to <p^/(STrA) are both functions of a single dimcnsionlessparameter: R(R^ . These two ratios are plotted against this parameter inFig. 10. These curves show how the reluctance and pull values compare Fore < a small , r = R sine = Re h = Ri\ - Rd^cos e) = â Gap Rel uctance - r -Iwr X dr X + h -f JO 2wRmeRe ^+2 = 2wR ( 1 + -~ ) Let: (Râ = - = (R,(R. A iriaR)^ = 2TR6{Jn 1 + 27r/?(R^ / Pull for Flux <p V^ d(R(; Sir dx ^ d(S{.GSir/t d(Râ _ J^ X l^-V X - 27r7?( .Jl x+h A-77(a;R) + 27r7?(Râ Fig. 9 â Reluctance and pull of a domed i)ole face. 202 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 with those for a gap of the same separation and projected area, but withplane pole faces (a dome of infinite radius). Ampere Turn Sensitivity The effect of the relation between F and ^p on the release time cannotbe conveniently deduced from (6), which involves both the term in 2,which varies with 9?, and the reluctance (Ry, which also enters the pullrelation. If the pull is expressed in terms of ;T, however, (9) shows thatthe time varies inversely with 3^, and is .substantially independent of thereluctance, provided z is in the usual range from 2 to 6. It follows thatmaximum release time can be obtained for a given load if the \alue of 5 8 ® a. - / %J X \ A-7r(«:Kj-(RqIGap reluctance F : PULL FOR FLUX <fi \ \ \ _ \ k\ - w \ \ \\, \ \ P 877A \^^2
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