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MEGN 481 HW 6

Due 10-29-15 prior to test

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Use the following values in the problem: d=1.75”, l=14”, a=4”, b=10”, P1=750 lbf, P2=325 lbf, Tmin=0 ft-lb, Tmax=2000 ft-lb (magical sin wave input), the shaft is steel having σUTS=108 ksi and σy=62 ksi. The torque is being transmitted into the shaft at gear with P1 and out of the shaft at gear with P2. The gear at P2 has a 10” diameter and weighs 10 lbf while the gear at P1 has a 5” diameter and weighs 5lbf. Both gears have a width of 2” (assume simple disk if necessary), are made of steel, and have σUTS=108 ksi and σy=62 ksi. All FoS need to be at least 2 for all problems.

1. If the key located at the gear with P2 is steel with σUTS=88 ksi and σy=52 ksi determine the size of key (base x height x length) necessary to give a FoS of at least 2 against both shear and bearing failure.

2. Determine the amount of diametral interference needed to provide a suitable interference fit at the gear with P1 such that a key would not be necessary for that gear.

3. Rather than a key located at gear with P2, design a suitable spline for the shaft-gear connection. Specifically, determine dp and l.

4. Find the shaft whirl and torsional critical frequencies of the shaft shown above. The rotational speed is 1725 rpm. You can assume that the gears are simple disks in this problem.