Machinery's Handbook, 31st Edition
320
Spring Design
. 125 86 300 1 5 103 500 Stress Solid pounds per square inch # = = , . ,
Step 6: Step 7:
. . d OD 1 00915 08125 1 79 Spring Index = − = − = Step 8: From Fig. 13 on page 319 , the curvature correction factor K = 1.185 . . .
Step 9: Total Stress at 36 pounds load = S 3 K = 86,300 3 1.185 = 102,300 pounds per square inch. This stress is below the 117,000 pounds per square inch permitted for 0.0915 inch wire shown on the middle curve in Fig. 3 on page 311 , so it is a safe working stress. Step 10: Total Stress at Solid = 103,500 3 1.185 = 122,800 pounds per square inch. This stress is also safe, as it is below the 131,000 pounds per square inch shown on the top curve of Fig. 3, and therefore the spring will not set. Method 2, using formulas: The procedure for design using formulas is as follows (the design example is the same as in Method 1, and the spring is shown in Fig. 14): Step 1: Select a safe stress S below the middle fatigue strength curve Fig. 3 on page 311 for ASTM A229 steel wire, say 90,000 pounds per square inch. Assume a mean diameter D slightly below the 13 ∕ 16 -inch O . D ., say 0.7 inch. Note that the value of G is 11,200,000 pounds per square inch (Table 20 on page 346 ). Step 2: A trial wire diameter d and other values are found by formulas from Table 4 as follows: . , . . d S PD 255 90 000 255 36 07 3 3 # # = = . . 0 000714 0 0894 inch 3 = = Note: Table 21 on page 347 can be used to avoid solving the cube root. Step 3: From Table 21 (also see the table on page 2703 ), select the nearest wire gauge size, which is 0.0915 inch diameter. Using this value, the mean diameter D = 13 ∕ 16 inch − 0.0915 = 0.721 inch. Step 4: The stress . . . . , / S d PD 0 393 0 393 0 0915 36 0 721 86 300 lb in 3 3 2 # # = = = Step 5: The number of active coils is
. 3 1416 86 300 0 721 11 200 000 00915 125 91 say 9 , . , , . . . ( 2 # # # # =
N SD GdF =
)
=
2
π
The answer is the same as before, which is to use 11 total coils of 0.0915-inch diameter wire. The total coils, solid height, etc., are determined in the same manner as in Method 1. Table of Spring Characteristics.— Table 5 gives characteristics for compression and extension springs made from ASTM A229 oil-tempered MB spring steel having a tor sional modulus of elasticity G of 11,200,000 pounds per square inch, and an uncorrected torsional stress S of 100,000 pounds per square inch. The deflection f for one coil under a load P is shown in the body of the table. The method of using these data is explained in the problems for compression and extension spring design. The table may be used for other materials by applying factors to f . The factors are given in a footnote to the table.
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