. The Bell System technical journal . ed stress-strain curve shown by the heavy lines ofFig. 7(a). The stress distribution across any section of the wire whilewound on the winding arbor will be as shown by the heavy lines ofFig. 7(b) where Syp is the yield-point stress, the maximum stress thatthe material will sustain. The moment, across the section, requiredto produce this bending is fft/2Shydy (21) h/2 where h is the width of the wire at any point of y distance from theneutral axis and 5 is the stress at the same point. If the spring isreleased, it expands to a radius R\ in which condition t
. The Bell System technical journal . ed stress-strain curve shown by the heavy lines ofFig. 7(a). The stress distribution across any section of the wire whilewound on the winding arbor will be as shown by the heavy lines ofFig. 7(b) where Syp is the yield-point stress, the maximum stress thatthe material will sustain. The moment, across the section, requiredto produce this bending is fft/2Shydy (21) h/2 where h is the width of the wire at any point of y distance from theneutral axis and 5 is the stress at the same point. If the spring isreleased, it expands to a radius R\ in which condition the external andthe internal moments are both zero. It is now possible by applyingthe same moment as was given by equation (21) to reduce the radiusof curvature again to Rq but without causing additional plastic added stress distribution produced by this second bending musttherefore follow a straight line as shown by 52-52, which togetherwith the residual stresses in the relaxed condition (radius R^ must THE SPRING CLUTCH 735. Q. > . 1 L ^^ V^ x: ^^^ Q. .- i 736 BELL SYSTEM TECHNICAL JOURNAL equal the distribution Syp-Syp resulting from the original formingoperation. Therefore the stress distribution in the relaxed condition(radius R\) must be the difference between Syp-Syp and S1-S2. or asindicated in Fig. 7(c). The value of ^2 is of course so determined thatthe moment as specified by equation (21) is the same for the dotted-line as for the solid-line stress distribution. The value of Sr = S2 — Syp is relatively easy to determine forrectangular and round wire on the basis of the straight-line stress-straincharacteristic if the bending has been sufficiently severe to have causedplastic flow almost to the neutral axis. The moment given by theactual stress distribution will then differ but little from that obtainedby equation (21) with 5 replaced by Syp, a constant. The values of 5corresponding to the distribution are given by 5 = 2S2ylh. (22) For a r
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