Determine which coil (top or bottom, or one in the middle) deflects to zero pitch first as the force is increased.

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1. A conical compression spring is made from 3-mm diameter steel wire and has an active coil diameter that varies from 25 mm at the top to 50 mm at the bottom. The pitch (distance between coils) is throughout. There are four active coils. A force is applied to compress the spring and the stress always remains in the elastic range.

a. Determine which coil (top or bottom, or one in the middle) deflects to zero pitch first as the force is increased.

b. Determine the force corresponding to the deflection identified in part (a). In other words, determine the force causing displacement of 8 mm.

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Estimate the maximum stress in the wire at critical point B.

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1.A round wire helical-coil tension spring has end loops of the type shown in Figures 14.7(a) and (b). The wire diameter of the spring is 0.042 inch, and the mean coil radius is 0.28 inch. Pertinent end-loop dimensions are riA 0.25 inch and riB 0.094 inch. An applied axial static tension force of F 5.0 lb is to be applied to the spring.

a. Estimate the maximum stress in the wire at critical point A.

b. Estimate the maximum stress in the wire at critical point B.

c. If the spring wire is ASTM A227 material, and a safety factor of 1.25 is desired, would the stresses at critical points A and B be acceptable?

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Calculate the axial force required to deflect the nested spring assembly a distance of 25 mm.

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1. Two steel, helical-coil compression springs are to be nested around a common axial centerline. The outer spring is to have an inside diameter of 38 mm, a standard wire diameter of 2.8 mm, and 10 active coils. The inner spring is to have an outside diameter of 32 mm, a standard wire diameter of 2.2 mm, and 13 active coils. Both springs are to have the same free length. Do the following:

a. Calculate the spring rate of each spring.

b. Calculate the axial force required to deflect the nested spring assembly a distance of 25 mm. c. Identify the most highly stressed spring when the assembly is a deflected 25-mm spring.

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Find a standard wire diameter and corresponding mean coil radius that will meet the desired specifications.

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1.A helical-coil compression spring is to be designed for a special application in which the spring is to be initially assembled in the mechanism with a preload of 10 N, and exert a force of 50 N when it is compressed an additional 140 mm. Tentatively, it has been decided to use music wire, to use closed ends, and to use the smallest standard wire diameter that will give a satisfactory performance. Also, it is desired to provide a clash allowance of approximately 10 percent of the maximum operating deflection. a. Find a standard wire diameter and corresponding mean coil radius that will meet the desired specifications. b. Find the solid height of the spring. c. Find the free height of the spring.

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Determine the maximum applied axial load that could be supported by the spring without initiating yielding in the wire.

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1. A proposed helical-coil compression spring is to be wound from standard unpeened music wire of 0.038-inch diameter, into a spring with outer coil diameter of inch and12 total turns from end-of-wire to end-of-wire. The ends are to be closed. Do the following:

a. Estimate torsional yield strength of the music wire.

b. Determine the maximum applied axial load that could be supported by the spring without initiating yielding in the wire.

c. Determine the spring rate of this spring.

d. Determine the deflection that would be produced if the incipient yielding load calculated in (b) above were applied to the spring.

e. Calculate the solid height of the spring.

f. If no permanent change in free height of the spring can be tolerated, determine the free height that should be specified so that when the spring is compressed to solid height and then released, the free height remains unchanged.

g. Determine the maximum operating deflection that should be recommended for this spring if no preload is anticipated. h. Determine whether buckling of this spring might be a potential problem.

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