Question

2. Determine the value of the critical speed of rotation for the simply supported shaft carrying two loads at D and C as illustrated, applying. Use any method to make the determination. Given: D = 40 mm, E = 200 GPa. 600 N 300 N DI D B -0.5 m-* 1 m 1 m

Answer 1

We know that critical speed of shaft in revolutions per second (RPS) is equal to the natural frequencyof transverse vibration in Hertz.

and

To calculate the natural frequency of transverse vibration, i will use drunkley method.

Drunkley method is semi-emprical,it gives approximate result,

According to drunkley Empirical formula, + Where for 27 Di fo? tom? 2 Sg and Di = deflection in Shaft (static). 19.8) similarly 25 0.4985. 25 1 D2 0.4985 Prz = 1 n sa 4 fo2 = 0.4985 SAR pa f² (64985 .4985 Voi fo 0.4985 A tA2 Now: for the given arrangment of Shaft Ꮎo Goon to D2 DI kle 0.5m im Im Com Now we determine Static deflection in shaft using Concept of beam deflection.

1,= 2,0²2 3EIL Wheere and o'. Dia 64 distance from left End b= (2-a). Goon X •5² x 2² 3x 200x109x(1.256637x107) x2.5 moment of inertia of Shaft my co-ou)" = 1.2566 37 x 107 my Di = 3.18309 x 103 m. Similarly 300 NX (105) 2 x (132 3 x 200 X 109x (1.256637 *167)x2.5 -3 02= 3.58098 X10 0.4985 rota2 0.4985 (3.58048X10-1) + (8.183X10-3 f = 6.061 Hertr. i critical speed of shaft = 6.061 revolution Per Second N = 363.67 RPM ~ Ary

Critical speed of shaft = 363.67 RPM (revolution per minute)