Page 379 - Shigley's Mechanical Engineering Design

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354 Mechanical Engineering Design
6–57 A schematic of a clutch-testing machine is shown. The steel shaft rotates at a constant speed ω.
An axial load is applied to the shaft and is cycled from zero to P. The torque T induced by the
clutch face onto the shaft is given by
fP(D + d)
T =
4
where D and d are defined in the figure and f is the coefficient of friction of the clutch face. The
shaft is machined with S y = 120 kpsi and S ut = 145 kpsi. The theoretical stress-concentration
factors for the fillet are 3.0 and 1.8 for the axial and torsional loading, respectively.
Assume the load variation P is synchronous with shaft rotation. With f = 0.3, find the max-
6
imum allowable load P such that the shaft will survive a minimum of 10 cycles with a factor of
safety of 3. Use the modified Goodman criterion. Determine the corresponding factor of safety
guarding against yielding.

R = 0.1 in d = 1.2 in

Problem 6–57
P

Friction pad D = 6 in

6–58 For the clutch of Prob. 6–57, the external load P is cycled between 4.5 kips and 18 kips.
Assuming that the shaft is rotating synchronous with the external load cycle, estimate the num-
ber of cycles to failure. Use the modified Goodman fatigue failure criteria.
6–59 A flat leaf spring has fluctuating stress of σ max = 360 MPa and σ min = 160 MPa applied for
4
8 (10 ) cycles. If the load changes to σ max = 320 MPa and σ min =−200 MPa, how many cycles
should the spring survive? The material is AISI 1020 CD and has a fully corrected endurance
strength of S e = 175 MPa. Assume that f = 0.9.
(a) Use Miner’s method.
(b) Use Manson’s method.
6–60 A rotating-beam specimen with an endurance limit of 50 kpsi and an ultimate strength of 140 kpsi
is cycled 20 percent of the time at 95 kpsi, 50 percent at 80 kpsi, and 30 percent at 65 kpsi. Let
f = 0.8 and estimate the number of cycles to failure.
3
6–61 A machine part will be cycled at ±350 MPa for 5 (10 ) cycles. Then the loading will be changed
4
to ±260 MPa for 5 (10 ) cycles. Finally, the load will be changed to ±225 MPa. How many
cycles of operation can be expected at this stress level? For the part, S ut = 530 MPa, f = 0.9,
and has a fully corrected endurance strength of S e = 210 MPa.
(a) Use Miner’s method.
(b) Use Manson’s method.
6–62 The material properties of a machine part are S ut = 85 kpsi, f = 0.86, and a fully corrected
endurance limit of S e = 45 kpsi. The part is to be cycled at σ a = 35 kpsi and σ m = 30 kpsi