Unformatted text preview: MECH 325 Machine Elements
Tutorial 12 – Shaft Speed 1. Adapted from Shigley, 9 Ed., Problem 7‐28 (8th Ed., 7‐14). A 1‐in diameter uniform steel shaft is 24 in long between bearings. The unit weight of steel is 0.282 lbf/in3 and the modulus of elasticity is 30.0 Mpsi. Part 1 – To be demonstrated by the TA a. Determine the lowest critical speed of the shaft Part 2 – To be done by the students b. What new shaft diameter would be required to double the critical speed of the shaft c. What is the critical speed for a half‐scale version of the original shaft? 2. Adapted from Shigley, 9th Ed., Problem 7‐31 (8th Ed., 7‐17). (To be done by the students) What is the possible range of critical speed for a hollow shaft with uniform diameter (expressed as a ratio to the critical speed of a solid shaft of the same diameter)? 3. Adapted from Shigley, 9th Ed., Problem 7‐32 (8th Ed., 7‐18). The shaft shown in the figure carries a 20‐lbf gear on the left and a 35‐lbf gear on the right. Deflection analysis for the various loading conditions is shown below. Consider the portions of the shaft between the bearing centres and neglected the reduced diameter for the bearings. Assume the shaft is made of steel with unit weight of 0.282 lbf/in3. Shaft Deflection Analysis Results Location Due to gear weights Due to shaft weight 2 in 1.153×10‐5 9.287×10‐6 4.5 in 2.227×10‐5 1.716×10‐5 ‐ 5 12.5 in 2.040×10 1.249×10‐5 14 in 1.106×10‐5 9.344×10‐6 th Part 1 – To be demonstrated by the TA a. Use Rayleigh’s Method to estimate the first critical speed due to the loads (neglect the shaft) Part 2 – To be done by the students b. Use Rayleigh’s Method to estimate the shaft critical speed without the loads c. Use Dunkerley’s Method to estimate the critical speed of the shaft with loads 4. Adapted from Shigley, Example 7‐6 (8th and 9th Eds.) (To be done by students.) A steel shaft has a diameter of 2 in. The shaft rotates at 600 rev/min and transmits 5 hp through a gear. a. What size cup‐point setscrew would be required to hold the gear. Note: a safety factor of 4 is a typical minimum for a setscrew subjected to dynamic loading. b. Select an appropriate size gib‐head key to hold the gear if the power transmitted is increased to 40 hp (assume the key is made of steel with yield strength of 70 kpsi). A safety factor of 2.5 is desired. Use the distortion‐energy theory to select a key (note that under distortion‐energy, the shear yield strength is Ssy = 0.577Sy). Table 7‐4 (setscrew holding power) Table 7‐6 (Standard key dimensions) ...
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 Fall '10
 PeteOstafichuk
 Critical speed

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