Machinery's Handbook, 31st Edition
Spring Design 327 (see Table 6.) The bending stress S b at section B should be compared with allowable stresses for torsion springs and with the elastic limit of the material in tension (See Fig. 7 through Fig. 10.) Stresses in cross-over hooks: Results of tests on springs having a normal average index show that the cross-over hooks last longer than regular hooks. These results may not occur on springs of small index or if the cross-over bend is made too sharply. In as much as both types of hooks have the same bending stress, it would appear that the fatigue life would be the same. However, the large bend radius of the regular hooks causes some torsional stresses to coincide with the bending stresses, thus explaining the earlier breakages. If sharper bends were made on the regular hooks, the life should then be the same as for cross-over hooks. Table 6. Formula for Bending Stress at Section B Type of Hook Stress in Bending
d P B
P B
d
S IDd PD 5 b 3 2 =
ID
D
D
Regular Hook
Cross-over Hook
Stresses in half hooks: The formulas for regular hooks can also be used for half hooks, be- cause the smaller bend radius allows for the increase in stress. It will therefore be observed that half hooks have the same stress in bending as regular hooks. Frequently overlooked facts by many designers are that one full hook deflects an amount equal to one half a coil and each half hook deflects an amount equal to one tenth of a coil. Allowances for these deflections should be made when designing springs. Thus, an exten sion spring, with regular full hooks and having 10 coils, will have a deflection equal to 11 coils, or 10 percent more than the calculated deflection. Extension Spring Design.— The available space in a product or assembly usually deter mines the limiting dimensions of a spring, but the wire size, number of coils, and initial tension are often unknown. Example: An extension spring is to be made from spring steel ASTM A229, with regular hooks as shown in Fig. 17. Calculate the wire size, number of coils and initial tension. Note: Allow about 20 to 25 percent of the 9 pound load for initial tension, say 2 pounds, and then design for a 7 pound load (not 9 pounds) at 5 ∕ 8 inch deflection. Also use lower stresses than for a compression spring to allow for overstretching during assembly and to obtain a safe stress on the hooks. Proceed as for compression springs, but locate a load in the tables somewhat higher than the 9 pound load. Method 1, using table: From Table 5 locate 3 ∕ 4 inch outside diameter in the left column and move to the right to locate a load P of 13.94 pounds. A deflection f of 0.212 inch appears above this figure. Moving vertically from this position to the top of the column a suitable wire diameter of 0.0625 inch is found. The remaining design calculations are completed as follows: Step 1: The stress with a load of 7 pounds is obtained as follows: The 7 pound load is 50.2 percent of the 13.94 pound load. Therefore, the stress S at 7 pounds = 0.502 percent 3 100,000 = 50,200 pounds per square inch. Step 2: The 50.2 percent figure is also used to determine the deflection per coil f : 0.502 percent 3 0.212 = 0.1062 inch.
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