Problem 1 - Shaft Design

Your task is to design a shaft such as shown below. The shaft is subjected to an axial and radial load at the gear wheel's center position as indicated. A torque T is introduced from the right end of the shaft and removed at the gear wheel. The number of stepped section is given, however the length of each section and their diameters are unknown and need to be determined. Determine the length and the diameter of each section so that

a) the deflection at the gear wheel's center is smaller than 0.05".

b) the critical speed does not meet the working speed of 1600 rev/min with an error margin of 200 rev/min.

The distance between the center of the left ball bearing and the gear wheel is fixed and must be 3.5", the distance to the right bearing is variable. The shaft must be safe with a factor of safety n = 1.4. Consider the weight of the shaft, work with a material with 8.05 kg/m3 , equal to 0.00029 lbf/in3.

Determine:

• The stepped section, all diameters and length for a factor of safety n = 1.4.

• The deflection for this shaft at the center

• The critical speed for this shaft.

• Optimize your shaft for weight, the sections should not be larger than required to achieve the deflection goal of 0.05" at the gear wheel.

Note

• Consider the weight of the shaft!

• Although there is not axial load, fix the axial location of the gear wheels.

• Use one fixed mount and one floating mount for your bearings.

• The inner diameters of all gear wheels are flexible, you have to determine them.

• Omit the Marin factors, consider all of them as 1

Attachment:- material.rar