726 



BELL SYSTEM TECHNICAL JOURNAL 



It is obvious that if the driving drum be rotated in the direction to 

 wind up the spring and decrease the diameter, the spring will grip the 

 cylinders and will be capable of exerting more torque than it would in 

 the direction of rotation which tends to unwind the spring. Equations 

 are to be developed which will permit the calculation of these two 

 torque values in terms of the physical dimensions and the material 

 constants of the clutch. 



Torque of Spring Clutch in the Free Direction 

 In Fig. 3 assume that the spring is fastened to the left-hand arbor in 

 order that any slipping which may take place must occur on the driving 

 drum on the right. Assume also that the spring is so formed that the 



Fig. 3 — Diagram of spring clutch. 



inward radial force on the drum per unit length of the material is 

 constant when no torque is applied. 



Notation 

 / = length along the line of contact of the spring on the arbor, 



measured from the free end to any point, in. 

 ju = coefficient of friction between the spring and the arbor 

 ^2 = radius of the arbor, in. 

 R2 = radius to the neutral bending axis of the spring when on the 



arbor, in. 

 N == number of turns on the right-hand arbor 

 P = compression in the spring wire at any point due to the applied 



torque; this is not the stress in the material but the resultant 



force acting across the entire cross section of the wire, lb. 

 /o = radial force of spring on arbor when no torque is applied, lb. per 



in. of contact line. 



