THE SPRING CLUTCH 733 



validity of the equation and then by determining Hmiting values for the 

 coefficient of friction, to use this equation as a design relation, especially 

 if only a minimum torque limit is set. Measurements of the slipping 

 torque, as a function of the number of turns, were made on the same 

 dial clutch that was used for checking the free torque. 



This slipping torque was not steady as was the case in the free direc- 

 tion but varied as much as ± 20 per cent. An average value was taken 

 in each case. An uncertainty also existed regarding the number of 

 turns engaging the rotating arbor. Since the crossover from one arbor 

 to the other requires practically one whole turn, slight differences in the 

 arbor diameters may result in a gain or loss of almost half a turn. In 

 addition to these factors there was an end effect due to the fact that 

 the free end of the spring wire was cut off square rather than beveled 

 but this factor although calculable was neglected in view of the other 

 uncertainties. The results of these measurements are shown in Fig. 6. 



From equation (8) it can be seen that for large values of N the plot 

 of T' versus N will be a straight line provided /z is independent of the 

 force between the spring and the arbor. The slope of this straight 

 line when multiplied by the proper constant, which can be shown to be 

 0.368, gives the coefficient of friction. For the experimental points 

 shown in Fig. 6 this value of /i is 0.165. Using this value of m in 

 equation (6) the calculated curve was plotted. Considering the un- 

 certainties involved the calculated and measured curves are in good 

 agreement. 



The dotted curve of Fig. 6 shows the effect of lubricating the clutch 

 with a light machine oil. This resulted in only a small decrease of the 

 coefficient of friction. The curve shown by the dashes illustrates the 

 effect of lubricating a clutch with spermaceti. The coefficient was no 

 longer a constant but decreased with an increase in load. 



Spring Stresses 



In determining the load that a spring clutch will withstand, first 

 without stretching which will result in backlash, and second without 

 breaking, initial as well as load stresses must be considered. The 

 initial stresses are made up of the residual stresses due to forming the 

 spring, plus the stresses due to expanding the spring to fit the arbor, 

 that is from an inner radius Vi to an inner radius r^. 



Of these limiting load values the easiest to calculate is the torque 

 required to break the spring. This is given by the product of the 

 radius of the spring and the breaking strength of the spring wire. 

 Loads much smaller than this value would stretch some of the fibers 

 of the spring, especially those in which a high initial stress already 



