Question 7.1: Endurance Limit of a Torsion Bar A round torsion bar machine...
Endurance Limit of a Torsion Bar
A round torsion bar machined from steel is under reversed torsional loading. Because of the design of the ends, a fatigue stress-concentration factor Kf exists. Estimate the modified endurance limit.
Given: The diameter of the bar is d = 1⅝ in. and Kf = 1.2. The operating temperature is 500°C maximum.
Assumption: Reliability is 98%.
Design Decision: The bar is made of AISI 1050 cold-drawn steel.
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From Table B.3, we find the ultimate strength in tension as Su = 100 ksi. Then, applying Equation 7.4, the endurance limit of the test specimen is
Ses′=0.29Su=0.29(100)=29 ksi
By Equation 7.7 and Table 7.2, the surface finish factor is
Cf=ASub=2.7(100)−0.265=0.80
The reliability factor corresponding to 98% is Cr = 0.84 (Table 7.3). Using Equation 7.9, the size factor Cs = 0.85. Applying Equation 7.11,
Cs={0.850.70(13 mm<D≤50 mm)(21<D≤2in.)(D>50 mm)(D>2 in.) (7.9)
Ct=⎩⎪⎨⎪⎧1T≤450∘C1−0.0058(T−450)1−0.0032(T−840)(840∘F)450∘C<T≤550∘C840∘F<T≤1020∘F (7.11)
Ct=1−0.0058(500−450)=0.71
Hence, the endurance limit for design is found to be
Ses=CfCrCsCt(1/Kf)Ses′=(0.80)(0.84)(0.85)(0.71)(1/1.2)(29)=9.8 ksi (b)
Table 7.2 Surface Finish Factors Cf |
|||
A | |||
Surface Finish | MPa | ksi | b |
Ground | 1.58 | 1.34 | −0.085 |
Machined or cold drawn | 4.51 | 2.7 | −0.265 |
Hot rolled | 57.7 | 14.4 | −0.718 |
Forged | 272.0 | 39.9 | −0.995 |
Table 7.3 Reliability Factors |
|
Survival Rate (%) | Cr |
50 | 1.00 |
90 | 0.89 |
95 | 0.87 |
98 | 0.84 |
99 | 0.81 |
99.9 | 0.75 |
99.99 | 0.70 |