Question: a vertical shaft made from aisi 1040 cold drawn steel...
A vertical shaft, made from AISI 1040 cold drawn
steel, carries pulleys. A schematic of the shaft is shown in a
horizontal position for convenience of plotting axial diagrams. The
tensile forces in the belts under operating conditions are shown.
Also, the shaft carries an axial compressive load of 6.2 kN. The
torque/power is transmitted between each pulley and the shaft by a
key fitted in a sled-runner keyseat type.
The steps listed below will ultimately lead you to the computation of the maximum shear stress using the equation
T_max= maximum shear stress at the same point where σ and T occur
σ= tensile or compressive stress creates by various loads
T= shear stress creates by various loads
Direct Compression stress and deformation
1. Using reasonable design assumptions, propose a diameter for the shaft based on direct normal stress. Be sure to state your safety factor and reasons for picking that factor.
2. Determine the stress concentration factor K_t for a sled-runner keyseat (same as in bending).
3. Using the stress concentration factor K_t just determined, adjust your recommendation for shaft diameter.
4. Based on your recommended diameter, compute the deformation δ_c due to force P.
Torsional shear stress and deformation
5. Compute the torque T_B and T_C due to tensile forces in the belts at point B and C, respectively.
6. Draw the torque diagram to show the level of torque in all segments of the shaft.
7. Based on your recommended diameter found in step 4 above, compute the nominal torsional stress T_Bnom and T_Cnom on the outer surface of the shaft for cross sections passing through points B and C due to the torque T_B and T_C.
8. Compute the angle of twist θ_BC of the cross section passing through B with respect to that passing through point C.
9. Determine the stress concentration factor K_t, in torsion, for a sled-runner keyseat.
10. Using the stress concentration factor K_t just determined, calculate the shear stresses T_B and T_C on the outer surface of the shaft for cross sections passing through points B and C, respectively.
11. If necessary, adjust your recommended diameter to allow for the direct shear stress. Reiterate the calculations for σ, δ_c, and T_B.
12. Determine the force F that the shaft exerts on the key
13. Suggest the dimensions (length, width, and height) of the key if it was made of steel. ( there are many possible solutions)
Are the values of the deformation δ_c due to the compressive force P, and the angle of twist θ_BC acceptable for a power transmission shaft such as the one under consideration? Why?
What considerations and standards did you use to determine safety factors?