A30-mm diameter 1035 HR steel (tensile strength 500 MPa) shaft is used to transmit a steady 1 kW of power rotating at 600 rpm. For a safety factor of 3.0, calculate the magnitude of a completely reversed bending moment that can be applied to the shaft at a shoulder step where the diameter increases to 33-mm with a shoulder fillet radius of 5.25-mm. Use DE-Goodman criterion for safety under fatigue loading.

See explanation for step by step procedure towards getting answer

Explanation:

Given that

h = 30 mm

h' = 25 mm

Δh = 30 - 25 = 5 mm

Initial width = b

Final width = 1.04 b

Roll radius, r = 300 mm

Inlet velocity Vi = 77 m/min

N = 45 RPM

a)

As we know that

Δh = μ². r

μ = Coefficient of friction

r = roll radius

By putting the values

Δh = μ². r

5 = μ² x 300

μ=0.12

b)

From continuity equation

Ai Vi = Vf

Ai = Inlet area, Vi = inlet velocity

= exit area, Vf = exit velocity

b x h x Vi = 1.04 b x h' x Vf

b x 30 x 77 = 1.04 b x 25 x Vf

Vf=88.84 m/min

c)

Forward slip S given as

V = Roller speed

We know that

V=84.82 m/min

S=0.047