325-tut-10-shaft fatigue

325-tut-10-shaft fatigue - MECH 325 Machine Elements...

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Unformatted text preview: MECH 325 Machine Elements Tutorial 10 – Fatigue Analysis of Shafts 1. Adapted from Shigley, Problem 6‐11 (8 Ed.) (To be demonstrated by the TA) Bearing reactions R1 and R2 are exerted on the shaft shown in the figure. The shaft rotates at 1150 rev/min and supports a 10‐kip (10,000 lbf) bending force. Determine whether a shaft made of 1095 HR steel (Sut = 120 kpsi, Sy = 66 kpsi) with d = 2 is suitable for a life of 3 minutes with a design safety factor of nd = 1.6. The surfaces are machined. th 2. Adapted from Shigley, Problem 7‐1 (8th and 9th Eds.) A shaft is loaded in bending an torsion such that Ma = 600 lbf∙in, Ta = 400 lbf∙in, Mm = 500 lbf∙in, and Tm = 300 lbf∙in. For the shaft, Su = 100 kpsi and Sy = 80 kpsi, and a fully corrected endurance limit of Se = 30 kpsi is assumed. Let Kf = 2.2 and Kfs = 1.8. Use a design factor of 2.0. Part 1 – To be done by students a. Determine the alternating and midrange von Mises stresses (σa’ and σm’) for this problem. Part 2 – To be demonstrated by TA b. Use the distortion‐Energy Gerber criterion to find the minimum acceptable diameter of the shaft. Part 3 – To be done by students c. Use the Distortion‐Energy Elliptic criterion to find the minimum shaft diameter d. Use the Distortion‐Energy Soderberg criterion to find the minimum shaft diameter e. Use the Distortion‐Energy Goodman criterion to find the minimum shaft diameter 3. Adapted from Shigley, Problem 7‐3 (8th and 9th Eds.) (To be completed at home.) The rotating solid steel shaft is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 6‐in pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA = 3000 lbf∙in. The shaft is machined from steel with Sy = 60 kpsi and Sut = 80 kpsi. Assume sharp fillet radii (1 mm) at the bearing shoulders when estimating stress concentration factors. Using a factor of safety of 2.5, show that the minimum allowable diameter of the 10 in section of the shaft is: a. d = 1.700 in when based a static yield analysis using the distortion energy theory (see Tutorial 8) b. d = 2.138 in when based on a fatigue‐failure analysis with the Distortion‐ Energy ASME Elliptic Criterion. ...
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