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Machine Design Assignment on Fatigue Analysis and Stress Concentration - Prof. Kenneth E. , Assignments of Machine Design

An assignment for me 401 – machine design course, which covers topics such as fatigue analysis, stress concentration factor, and elevated temperature effects on metals. The assignment includes four problems related to these topics, requiring calculations and explanations for different materials and geometries.

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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koofers-user-qag 🇺🇸

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ME 401 – Machine Design
Spring 2009, Assignment 7
Unless otherwise stated, assume reliability of 90% and factor of safety of 1. Complete
the remaining problems on the previous assignment (problems 5, 6, 7).
1. For elevated temperatures, fatigue analysis must be conducted differently. Briefly (1
or 2 concise sentences each) describe the following:
a) How is yield strength affected by elevated temperatures? How does that affect
analysis of parts?
b) What is creep, and at what temperature does it become a concern in metals?
c) What effect does elevated temperature have on endurance limit of steel?
d) What effect does elevated temperature have on tensile strength? How does that
affect fatigue analysis? Which modification factors (k
a
, k
b
, etc.) are affected by
tensile strength and hence are affected by temperature?
2. (10 pts) The plate shown below is 0.250 inch thick, 4 inch wide, 20 inch long, with a
0.100 inch diameter hole in the middle. What is the fatigue stress concentration
factor, K
f
, due to the hole if the plate is:
a) ASTM Grade 30 Gray Cast Iron
b) 2024-T6 aluminum alloy
c) AISI 1020 cold drawn steel
d) AISI 1095 normalized steel
3. (20 pts) The plate shown below is made from plain carbon steel. It is 4 inches wide,
20 inches long, and has a 2.00 inch diameter hole in the middle. How thick must the
plate be in order to survive 10
6
stress cycles (infinite life)? Assume localized yielding
is acceptable but gross yielding is not (localized yielding is yielding near the stress
concentration, gross yielding is yielding in the bulk material away from the stress
concentration). Use a values of S
y
=120ksi and S
u
=190ksi. Consider force
fluctuations of:
a) F
max
of 20,000 pounds tension and F
min
of 8000 pounds compression
b) F
max
of 8000 pounds tension and F
min
of 20,000 pounds compression.
F (cyclic)
F
pf2

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ME 401 – Machine Design Spring 2009, Assignment 7

Unless otherwise stated, assume reliability of 90% and factor of safety of 1. Complete the remaining problems on the previous assignment (problems 5, 6, 7).

  1. For elevated temperatures, fatigue analysis must be conducted differently. Briefly ( or 2 concise sentences each) describe the following: a) How is yield strength affected by elevated temperatures? How does that affect analysis of parts? b) What is creep, and at what temperature does it become a concern in metals? c) What effect does elevated temperature have on endurance limit of steel? d) What effect does elevated temperature have on tensile strength? How does that affect fatigue analysis? Which modification factors (ka, kb, etc.) are affected by tensile strength and hence are affected by temperature?
  2. (10 pts) The plate shown below is 0.250 inch thick, 4 inch wide, 20 inch long, with a 0.100 inch diameter hole in the middle. What is the fatigue stress concentration factor, Kf, due to the hole if the plate is: a) ASTM Grade 30 Gray Cast Iron b) 2024-T6 aluminum alloy c) AISI 1020 cold drawn steel d) AISI 1095 normalized steel
  3. (20 pts) The plate shown below is made from plain carbon steel. It is 4 inches wide, 20 inches long, and has a 2.00 inch diameter hole in the middle. How thick must the plate be in order to survive 10^6 stress cycles (infinite life)? Assume localized yielding is acceptable but gross yielding is not (localized yielding is yielding near the stress concentration, gross yielding is yielding in the bulk material away from the stress concentration). Use a values of Sy=120ksi and Su=190ksi. Consider force fluctuations of: a) Fmax of 20,000 pounds tension and Fmin of 8000 pounds compression b) Fmax of 8000 pounds tension and Fmin of 20,000 pounds compression.

F (cyclic)

F

  1. (40pts) There is an off-balance rotating disk suspended at the end of the support bar as shown. Young’s modulus of the bar is 200GPa. The disk is rotating at 2000 RPM (revolutions per minute). The peak force (P 0 ) produced by the rotating disk is 20kN, and it has a mass of 500kg. The support bar has a thickness of 5mm and is 2000mm long. Based on the Transmitted Force (curve provided as a check to your own analysis) plot the nominal stress and stress near the 10 mm diameter hole as a function of plate width, w (let 0.001<w<0.1). Do not give consideration to hole for the mounting pin but do consider stress concentration for the disk’s axle. Assume AISI 1040 Annnealed.

Hint: use Fig A-15-12, and a spread sheet. The stress concentration factor is a function of width, so you have a few choices. You could enter values of Kt for 5 to 10 different widths and interpolate, or you can create a graph plotting 3 values of Kt verses w (such as for d/w= 0.15, 0.4, 0.8), plot an exponential trend line to fit these 3 points and use the equation for the trend line to determine the function describing Kt vs w. Double check to make sure the trend line agrees with Fig A-15-12.

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0. Plate width (m)

Transmitted force (N)

10 mm dia (for disk’s axle)

w

0.5w

Support bar (5mm X w X 2000mm)

Main structural frame (assume perfectly rigid and fixed in position)

Mounting bracket (assume perfectly rigid)

Support fasteners

NOT TO

SCALE

25 mm

Rollers to prevent Mounting vertical displacement pin

Width, w Details of disk axle area of support bar

Use this graph to check your own spread sheet. It will difficult to properly complete this assignment without your own correct spread sheet.