Machinery's Handbook, 31st Edition
Spring Design
317
Open Ends Not Ground, Right Hand Helix
Closed Ends Not Ground, Right Hand Helix
Closed Ends Not Ground, Left Hand Helix
Open Ends Not Ground, Left Hand Helix
Fig. 12. Types of Helical Compression Spring Ends Spring design formulas: Table 3 gives formulas for compression spring dimensional characteristics, and Table 4 gives design formulas for compression and extension springs. Curvature correction: In addition to the stress obtained from the formulas for load or deflection, there is a direct shearing stress and an increased stress on the inside of the section due to curvature. Therefore, the stress obtained by the usual formulas should be multiplied by a factor K taken from the curve in Fig. 13. The corrected stress thus obtained is used only for comparison with the allowable working stress (fatigue strength) curves to determine if it is a safe stress and should not be used in formulas for deflection. The curva ture correction factor K is for compression and extension springs made from round wire. For square wire reduce the K value by approximately 4 percent. Design procedure: The limiting dimensions of a spring are often determined by the available space in the product or assembly in which it is to be used. The loads and deflec tions on a spring may also be known or can be estimated, but the wire size and number of coils are usually unknown. Design can be carried out with the aid of the tabular data that appears later in this section (see Table 5, which is a simple method, or by calculation alone using the formulas in Table 3 and Table 4. Example: A compression spring with closed and ground ends is to be made from ASTM A229 high carbon steel wire, as shown in Fig. 14. Determine the wire size and number of coils. Method 1, using table: Referring to Table 5, starting on page 321 , locate the spring out side diameter ( 13 ∕ 16 inches, from Fig. 14 on page 319 ) in the left-hand column. Note from the drawing that the spring load is 36 pounds. Move to the right in the table to the figure nearest this value, which is 41.7 pounds. This is somewhat above the required value but safe. Immediately above the load value, the deflection f is given, which in this instance is 0.1594 inch. This is the deflection of one coil under a load of 41.7 pounds with an uncor- rected torsional stress S of 100,000 pounds per square inch for ASTM A229 oil-tempered MB steel. For other spring materials, see the footnotes to Table 5. Moving vertically in Table 5 from the load entry, the wire diameter is found to be 0.0915 inch. The remaining spring design calculations are completed as follows: Step 1: The stress with a load of 36 pounds is obtained by proportion, as follows: The 36 pound load is 86.3 percent of the 41.7 pound load; therefore, the stress S at 36 pounds = 0.863 3 100,000 = 86,300 pounds per square inch.
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