Question

Question Four (a) A steel ring of 300 mm and 200 mm external and internal diameters res solid steel shaft. The interference is arranged such that the radial pressure between the mating surfaces will not fall below 30 MN/m2 whilst the assembly rotates in service. If the maximum circumferential stress on the inner surface of the ring is limited to 240MN/m2, and there is no relative slip between the shaft and the ring, determine the maximum speed at which the assembly can be rotated. Take density of steel, p 7470 kg/m', v 0.3, E- 208 GPa (9 Marks). pectively is shrunk onto a (b) A 10 m Hollow shaft with 60 mm and 30 mm external and internal diameters respectively, is subjected to a torque 1300 Nm. With a Modulus of rigidity of 90 GPa, determine () the polar second moment of area (U)(i) shear stress () and (ii) the angle of twist (0) (8 Marks).

please make it easy to understand

Answer 1

Ans A

For rotating solid disk, stress at radius r

ро?r? - (3 + v) о,— А -

Where

A and B are constants

External radius = external dia/2 = 300/2 = 150 mm x 1m/1000mm

= 0.15 m

At external radius at r = 0.15 m , radial stress = 0

Poisson's ratio v = 0.3

Density = 7470 kg/m3

В 0 %3D А — 0.152 3.3 - рою (0.15)2 8

........ Eq1

And at r = 0.10 m

Radial Stress = - 30 MN/m2

3.3 "ро (0.1)? B --30 x 106 = A - 0.12 8

......... Eq2

From. Eq1 - Eq2

3.3 30 x 10° — В(100 — 44.4) -pа? (0.0225- 0.01) 8 30 x 106 B 0.0125 x 7470 3.3 x 55.6 8 x 55.6 B 0.54 x 106 +0.693w2

From eq2

0.0lo2 3.3 x 7470 x 1060.6932)+ 30 x 106 100(0.54 x A 54 x 10069.3w2 +30.8w2 30 x 106 24 x 106100.1w2

Max circumferential stress = 240 MN/m2

B OH= A +. (13) 8 (0.54 x 1000.693w2) 1.9 x 7470 x 8 0.012 (24 x 106100.lw2) + 240 x 10 0.12 78 x 106 169.3«2 - 17.7a2 240 x 106

162 x 106 2 151.7

w^2 = maximum speed = 1.07 x 10^6

w = 1034.4 rad/s