Mechanical Systems Lab – Homework #6
Fall 2024
Note that homework#6 is graded as half of a lab report.
Reading materials: “Prediction of fatigue failure” from J. A. Collins, Design of machine
elements and machines, section 5.6 (Pages 241 to 281).
Problem 1 - Analysis: [40 pts]
A 230 mm by 230 mm square bar is subjected to an axial cyclic force that ranges from 9000
kN (tension) to -6000 kN (compression). The material is a steel-alloy with hot-rolled finish,
ultimate tensile strength of 600 MPa and yield strength of 300 MPa. The part is subjected
to an operating environment where temperatures reach a maximum of 500oC. How many
cycles of operation could be expected from this part if a reliability level of 99% is desired?
Use the following set of equations to calculate the necessary knockdown factors, note that
kld and ktmp are in addition o the other k’s in Collins Table 5.3.
•Load factor (kld ): Most published fatigue strength data are for rotating bending tests
using specimens of circular cross-section. There is a consistent difference between the
results from rotations and axial fatigues testing. For that reason:
kld = 0.7 if instead, axial loading,
kld = 1.0 if bending.
•Size factor (ksz ): Test specimens are usually small (0.3 in dia.). If the part is larger,
correction factor must be included due to the fact that larger parts fail at lower stresses
due to higher probability of a flaw being present in the higher stressed volume. Also,
if instead the part has rectangular cross-section (b×h) then an equivalent circular
diameter needs to be calculated. For that reason, in millimeters, we have:
dequiv =r0.05 ×b×h
0.0766 ,and (dequiv ≤8mm, ksz = 1,
8mm < dequiv ≤250 mm, ksz = 1.189d−0.097
equiv
•Surface finish factor (ksr ): Test specimens are often polished to a mirror finish to
preclude surface imperfections acting as stress raisers. Rougher finishes will negatively
impact the fatigue strength of the part. For that reason, using the equation proposed
by Shigley and Mischke,
ksr =A(Sut)b,if ksr >1→1.
Surface finish A [MPa] b
Ground 1.58 -0.085
Machined 4.41 -0.265
Hot-rolled 57.7 -0.718
As-forged 272 -0.995
Table 1: Coefficients for Shigley and Mischke surface-factor equation.
1
