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SPRINGS 149 



SEMIELLIPTIC LAMINATED SPRINGS 



The chart on the facing page will facilitate the design of a semielliptic spring having 

 graduated leaves of rectangular cross section. The chart is a graphical solution of 

 the following formulas : 



_ 2/ X d2E 

 ^ - KXU ^^^^ 



12 



where R = rate of deflection, in lb. load per in. L = full length of spring, in in. 



deflection W = width of leaves, in in. 



E = modulus of elasticity, 28,000,000 llr. T = thickness of leaves, in in. 



per sq. in. I = moment of inertia 



K = constant for semielliptic springs = 

 0.9 



The accompanying example shows how to use the chart. By starting with the 

 desired rate of deflection, R = 1,200 lb. per in. deflection, read straight up to the 

 length of spring, L = 55 in. Cross horizontally to the hne representing the number of 

 leaves, 6 leaves, then vertically to the hne in the upper section of the chart correspond- 

 ing to the width of the spring, "PF = 5 in. From this point, trace horizontally to the 

 parabohc curve. The figure, 0.4375 in., directly above this last intersection, desig- 

 nates the thickness of each leaf in the spring. The spring has 1,200 lb. per in. rate of 

 deflection, is 55 in. from eye to eye, has six leaves 5 in. wide, and each leaf is 0.4375 in. 

 thick. 



To find the safe load on the spring after the other values have been estabhshed 



from the chart, 



„ 4.DET ^ SL' 



^ - -Jj- or i^ - 1^ 



where S = unit fiber stress, in lb. per sq. in. T = thickness of leaves, in in. 



D = total amount of deflection, in in. L = full length of spring, in in. 



E = modulus of elasticity 



The allowable working fiber stress will vary with the material used. Usually 

 one-third of the elastic Umit may be considered a safe working stress. For example, 

 if the elastic hmit is 180,000 lb. per sq. in., the safe unit stress will be 60,000 lb. per 

 sq. in. By substituting this latter value for S in the formula, the amount of deflection 

 D can then be solved. D multiplied by R (rate of deflection in pounds per inch) wifl 

 give the fuU load capacity of the spring. In practice, the spring may be stressed to 

 two-thirds of the elastic limit, but only under an occasional emergency load on the 

 spring. 



