132 



HANDBOOK OF MECHANICAL DESIGN 



In calculating Class I springs, the procedure is similar except that the permissible 

 working stress must be based on the endurance value of the material. A tentative 

 allowable stress is assumed, and the wire diameter is calculated by following the same 

 procedure as outlined above for Class I and Class II springs. The calculated wire 

 diameter is then checked against the endurance charts as given in Figs. 249 to 253 for 

 the various materials. 



As an example of the use of the endurance charts, assume a valve spring had been 

 calculated to be made of Swedish steel wire 0.177 in. diameter and the wire calculated 

 to be stressed to 62,000 lb. per sq. in. when the valve is closed and 81,000 lb. per sq. in. 



10 20 30 40 50 



Lower Stress in Thousands of Lb. per Sq.ln. 



Fig. 253. — Allowable torsional stress range for 

 phosphor-bronze wire. 



-200 200 600 1,000 1,400 



Tefnperafure in Deg.F^ 



Fig. 254. — Value of torsional modulus of elasticity of 

 steel at various temperatures. 



when the valve is open. A check must then be made to see if this stress range is per- 

 missible. With reference to Fig. 249, from 62.0 on the lower-stress scale, representing 

 62,000 lb. per sq. in. stress, go up vertically on the chart to the curve representing the 

 next larger wire diameter, namely, 0.1920. The maximum stress allowable as read 

 from the scale on the left of the chart is 83.0, or 83,000 lb. per sq. in. Since this is 

 greater than 81,000, the given stress range is therefore safe. 



NATURAL FREQUENCY 



Springs must be designed so that their natural frequency of vibration will not be 

 close to their frequency of deflection in operation, in order to avoid resonance and 

 resulting high stresses. If their natural frequency is sufficiently high to escape 

 resonance with any harmonic below the twentieth order, resonance will be avoided. 

 This wiU be assured if 



250d VG/(D - d)W 



equals or exceeds 20 



Deflection cycles per minute 



The order of harmonic as calculated by this equation should be as much above 

 20 as possible. The order of harmonic, for a given spring material, decreases with 

 the difference between the coil diameter and the diameter of the wire and is inversely 



