THE SPRING CLUTCH 737 



on the clutch arbor. The line ^o-vSo shows the stresses added by this 

 expansion where ^o is given by equation (20). The sum of these 

 stresses and those shown in Fig. 7(c) gives the total stresses as shown 

 by the solid line of Fig. 7(d). If now a load be put on the clutch a 

 uniform stress Sl will be added but this stress for even relatively light 

 loads may be sufficient to cause the total stress on the inner fibers to 

 exceed the yield point as is indicated in Fig. 7(e). The inner fibers are 

 consequently stretched and when the load is released and the spring 

 taken from the arbor it will be found that the center turns of the spring 

 have expanded. Even with the spring on the arbor if the clutch is 

 turned in the free direction it will be noticed that these center turns 

 raise off the arbor. It was shown in the paragraphs on the clutch 

 torque in the free direction that the torque did not increase appreciably 

 after the first few turns. This can be explained by the fact that as 

 soon as the outward radial force due to the compression along the wire 

 is equal to the initial inward radial force of the spring on the arbor the 

 friction on these turns vanishes. The value of the compression will be 

 fixed by a relatively few end turns. Hence if the inward force of some 

 of the center turns decreases due to their stretching this compression 

 will be sufficient to expand the turns to clear the arbor. If Sl is still 

 further increased the stretch will be sufficient to cause the diameter 

 of the center turns to exceed the arbor diameter even when no torque 

 is applied in the free direction. 



Since the yield point of metals decreases at higher temperature it is 

 possible to produce a spring having lower residual stresses by the 

 proper heat-treatment. If the wire is wound on an arbor and then 

 heated, additional plastic flow takes place since the maximum stress 

 that can be sustained at the high temperature is that shown in Fig. 7(a) 

 as the high-temperature yield point. If the spring is then cooled and 

 released the expansion will not be as great as for the untreated spring. 

 The residual stresses will again be given by equation (23) or (24) where 

 Syp is taken as the lowest yield point reached in the temperature cycle. 

 In Fig. 8, (a), (b), and (c) show the stresses in the heat-treated specimen 

 corresponding to those shown in Fig. 7, (c), (d), and (e), for the un- 

 treated spring. Figure 8(c) shows that for the same load stress as for 

 Fig. 7(e) no permanent deformation has taken place. It is of course 

 important that the strain-relieving temperature should not go high 

 enough to lower permanently the strength of the material. This 

 limit ^ for phosphor bronze is about 320" C. 



To determine the stress-temperature characteristics of 18-8 stainless 



1 "Better Instrument Springs," Robert W. Carson, Trans. A.I.E.E., vol. 52, 

 September, 1933, p. 869. 



