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BELL SYSTEM TECHNICAL JOURNAL 



In this case the torque increases rapidly with an increase in either 

 N or n especially for large values of Nijl. The coefificient of friction is 

 in general a rather variable factor. It is to be expected that the 

 slipping torque will also be variable, but since a lower limit can in 

 general be set for this coefficient it will always be possible to make the 

 number of turns of the spring such as to give any desired lower limit 

 of torque. 



The Radial Force on the Arbor 



One method of evaluating the force /o occurring in the torque rela- 

 tions depends on equating the potential energy of strain per unit 

 length of the wire when on the arbor to the work done in expanding 

 the spring from its free diameter to the diameter of the arbor. 



Let 



E = Young's modulus for the spring material, psi 



/ = the area moment of the wire section, in.^ 



h = the radial thickness of the wire, in. 



Ri = free radius to the neutral axis, in. 



;'i — free inner radius of the spring, in. 



Fig. 4 — Element of spring in initial and expanded condition. 



Consider the portion of spring wire shown in Fig. 4 straightened 

 out from the initial radius of curvature Ri to the radius Ro. The 



