The diagrams that follow show the mechanical linkage in a pipe organ. The organist presses down on the pedal with his or her foot, which in turn pulls the vertical tracker down, rotates the roller, and pulls the horizontal tracker sideways. While the mechanism is being actuated, the tension in the trackers rises from zero to approximately 1 kgf. The roller arms were made from aluminum alloy rod 4.75 mm in diameter. The end of the rod was turned down to a diameter of 4 mm to fit the hole in the roller, and was riveted over to hold it in place. The turning had been done with a sharp-ended lathe tool, which produced a sharp corner. A fatigue crack had initiated at this sharp corner, and led to the failure of the mechanism after only 2 years in service.
a. Why did the fatigue crack form at the sharp corner?
b. Where around the sharp corner did the fatigue crack initiate?
c. How would you modify the design to increase the fatigue life?
d. What other material would you choose to increase the fatigue life?
Schematic of the mechanical action in the region of the failed components (not to scale). The vertical tracker and the rocker are both made from light wood, and their weight can be neglected in the loading calculations
Fatigue fractures occurred at a sharp change of section in the roller arms. To scale—dimensions in mm. The maximum bending stress in the reduced section of the roller arm is given by the standard equation
Using this equation, calculate (a) the stress amplitude and (b) the mean stress of the stress cycle. Given that the true fracture stress of the alloy is 250 MN m–2, estimate (c) the stress amplitude that would produce the same fatigue life under conditions of zero mean stress.
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