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Question 14.2: Allowable Load of a Helical Compression Spring A helical com......

Allowable Load of a Helical Compression Spring

A helical compression spring for mechanical device is subjected to an axial load P . Determine:

a. The yield strength in the shear of the wire.

b. The allowable load P corresponding to yielding.

Design Decisions: Use a 0.0625 in. music wire. The mean diameter of the helix is D =0.5 in. A safety factor of 1.5 is applied due to uncertainty about the yielding.

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The spring index is C=D / d=0.5 / 0.0625=8 .

a. Through the use of Equation (14.12) and Table 14.2, we have

S_{u s}=A d^b           (14.12)

S_u=A d^b=186\left(0.0625^{-0.163}\right)=292  ksi

Then, by Table 14.3, S_{y s}=0.4(292)=117  ksi .

b. The allowable load is obtained by applying Equation (14.6) as

\tau_t=K_s \frac{8 P D}{\pi d^3}=K_s \frac{8 P C}{\pi d^2}             (14.6)

P_{\text {all }}=\frac{\tau_{\text {all }} \pi d^2}{8 K_s C}

where

\tau_{ all }=\frac{S_{y s}}{n}=\frac{117}{1.5}=78  ksi

K_s=1+\frac{0.615}{8}=1.077        (from Equation (14.7))

K_s=1+\frac{0.61 .5}{C}        (14.7)

Hence,

P_{\text {all }}=\frac{\pi(78,000)(0.0625)^2}{8(1.077)(8)}=13.9  lb

TABLE 14.2
Coefficients and Exponents for Equation (14.12)
A
Material ASTM No. b MPa ksi
Hard-drawn wire A227 −0.201 1510 237
Music wire A228 −0.163 2060 186
Oil-tempered wire A229 −0 193 1610 146
Chrome-vanadium wire A232 −0.155 1790 173
Chrome-silicon wire A401 −0 091 1960 218
Source: Associated Spring-Barnes Group, Design Handbook, Associated Spring-Barnes Group, Bristol, CN, 1987.

 

TABLE 14.3
Approximate Strength Ratios of Some
Common Spring Materials
Material S_{y s} / S_u S_{e s}^{\prime} / S_u
Hard-drawn wire 0.42 0.21
Music wire 0.40 0.23
Oil-tempered wire 0.45 0.22
Chrome-vanadium wire 0.52 0.20
Chrome-silicon wire 0.52 0.20
Source: Associated Spring-Barnes Group, Design Handbook, Associated Spring-Barnes Group, Bristol, CN, 1987.
Notes: S_{y s} , yield strength in shear; S_u, ultimate strength in tension; S_{e s}^{\prime} , endurance limit (or strength) in shear.

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