Machinery's Handbook, 31st Edition
Spring Design 337 1) Select the next larger gage size, which is Number 32 (0.090 inch) from Table 14. The torque is 11.88 pound-inches, the design stress is 166,000 pounds per square inch, and the deflection is 14.9 degrees per coil. As a percentage the torque is 10 ∕ 11.88 3 100 = 84 percent. 2) The new stress is 0.84 3 166,000 = 139,440 pounds per square inch. This value is under the bottom or Severe Service curve, Fig. 7, and thus assures longer life. 3) The new deflection per coil is 0.84 3 14.97 = 12.57 degrees. Therefore, the total num ber of coils required = 90 ∕ 12.57 = 7.16 (say 7 1 ∕ 8 ). The new overall length = 8 1 ∕ 8 3 0.090 = 0.73 inch (say 3 ∕ 4 inch). A slight increase in the overall length and new arm location are thus necessary. Method 2, using formulas: When using this method, it is often necessary to solve the for mulas several times because assumptions must be made initially either for the stress or for a wire size. 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. 24): Step 1: Note from Table 13, page 334 that the wire diameter formula is: . d S T 1018 b 3 = Step 2: Referring to Fig. 7, select a trial stress, say 150,000 pounds per square inch. Step 3: Apply the trial stress, and the 10 pound-inches torque value in the wire diameter formula: . , . . . d S T 1018 150 000 10 18 10 0 000679 0 0879 inch b 3 3 3 # = = = = The nearest gauge sizes are 0.085 and 0.090 inch diameter. Note : Table 21, page 347 , can be used to avoid solving the cube root. Step 4: Select 0.085 inch wire diameter and solve the equation for the actual stress: . . . , S d T 1018 0085 10 18 10 165 764pounds per square inch b # = = = 3 3 Step 5: Calculate the number of coils from the equation, Table 13: , . , , . . ( ) N S D EdF 392 392 165 764 0 585 28 500 000 0 085 90 5 73 5 4 say 3 b # # # # = = = ° Step 6: Calculate the total stress. The spring index is 6.88, and the correction factor K is 1.13 therefore total stress = 165,764 3 1.13 = 187,313 pounds per square inch. Note : The corrected stress should not be used in any of the formulas as it does not determine the torque or the deflection. Torsion Spring Design Recommendations.— The following recommendations should be taken into account when designing torsion springs: Hand: The hand or direction of coiling should be specified and the spring designed so deflection causes the spring to wind up and to have more coils. This increase in coils and overall length should be allowed for during design. Deflecting the spring in an unwinding direction produces higher stresses and may cause early failure. When a spring is sighted down the longitudinal axis, it is “right hand” when the direction of the wire into the spring takes a clockwise direction or if the angle of the coils follows an angle similar to the threads of a standard bolt or screw, otherwise it is “left hand.” A spring must be coiled right-handed to engage the threads of a standard machine screw. Rods: Torsion springs should be supported by a rod running through the center when- ever possible. If unsupported, or if held by clamps or lugs, the spring will buckle and the torque will be reduced or unusual stresses may occur.
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