A transfer shaft (see Figure 1 and 2) in a high performance gearbox is to be designed such that the weight is minimised. The function of the transfer shaft dictates the lengths, points of load application (F = 50 ??) and bearing locations (???? and ????) leaving the only variable the diameter of the shaft. For compatibility and manufacturing purposes it has been decided that the shaft is to be machined from carbon steel (σyy = 250 MMaE = 210 GPa).
Your tasks as the Design Engineer are:
1) Draw the Free Body Diagram, Shear Force Diagram, Bending Moment Diagram and Torque Diagram of the shaft, showing magnitude and direction of forces and bending moments.
2) Determine the critical point on the shaft (location where combined maximum stress occurs), and hence calculate the principal stress, justify your answer with diagrams.
3) Determine the equivalent moment acting on the shaft and hence specify the minimum diameter required such that the Maximum normal stress theory of failure is satisfied with a safety factor of 1.5.
4) Discuss any additional assessments that you would consider in the design of this component (Do not carry out analysis) also discuss any limitations of approximating the shaft as a beam.
Note: The transfer arms and loading pins are NOT to be assessed. The shaft may be approximated as a beam of constant circular cross section with equivalent loads induced from transfer arms.
Figure 1 Transfer Shaft and Loading
Figure 2 Top View of Transfer Shaft with length dimensions (mm)The maximum principal stress at a point under normal and shear stress is:
General form of Bending stress equation:
σbending = My/I
General form of shear stress due to torsion equations:
t = Tr/j
General form of shear stress due to bending equation:
t = 4v/3A
Equivalent Moment: Me = 1/2 [M + M2 + T2]
Maximum normal stress theory of failure: If σb denote the permissible bending stress for the steel shaft:
σb = 32Me/Πd3