Given:
- Power transmitted P = 500 kW
- Shaft rotational speed ω1 = 500.0 rpm
- Safety factor FS = 3.0
- Pitch diameter of gear 1 is dp = 250.0 mm
- Use von Mises criterion (i.e., DET)
- Neglect all the weights (because they are small compared to the applied forces)
- See the figure for the other parameters
Find:
- Torque T (N.m)
Torque can be calculated as
= = 9549.29N.m
- Maximum torsional shear stress τ (N/m2) within the shaft (resulted from T, T = P/ω1
Shaft torsional shear stress is given as
Where T is the torque, Ds is the shaft diameter and J is the polar moment of inertia
- Maximum tensile bending normal stress σ (N/m2) within the shaft (resulted from F, F = T/rp)
Bending moment M1=
Force F=
M1=
Bending moment M2= , which the maximum bending moment
=
427,753.55N/m2
- Principal stresses σp1, σp2 (N/m2) on the outer surface of the shaft
- Von Mises stress σv (N/m2) on the outer surface of the shaft
- Shaft diameter DS (m) by stress. Then produce a table showing the above stress values, from (b) to (e)
The material is AISI 4140 (Chromium-Molybdenum Steel) (Sharan & Patel, 2019).
Where is the yield strength of the material
x1/3= 131.366mm
| Parameter | Value |
| Maximum torsional shear stress τ | |
| Maximum tensile bending normal stress σ | |
| Principal stresses σp1, σp2 | |
| Von Mises stress σv |
- Shaft diameter DS (m) by displacement (i.e., deflection) with maximum displacement ratio (𝛿𝑎) allowable = 5*10-4.
To check the diameter obtained
hence unacceptable
Diameter to increase by ratio
mm
- Show possible designs
References
Sharan, G., & Patel, R. K. (2019). Optimization of cutting parameters of turning for hardness of AISI 4140 alloy steel. Materials Today: Proceedings, 18(7), 3582-3589. https://doi.org/10.1016/j.matpr.2019.07.289
