ME304 Individual Project

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:

1. Torque T (N.m)

Torque can be calculated as

= ​= 9549.29N.m

2. 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, D_s is the shaft diameter and J is the polar moment of inertia

3. 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

4. Principal stresses σp1, σp2 (N/m2) on the outer surface of the shaft

5. Von Mises stress σv (N/m²) on the outer surface of the shaft

6. 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

x^1/3= 131.366mm

Parameter	Value
Maximum torsional shear stress τ
Maximum tensile bending normal stress σ
Principal stresses σp1, σp2
Von Mises stress σv

7. 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

8. 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