Answer to Question #121747 in Civil and Environmental Engineering for Ayush

Question

A bearing with 70 mm shaft in a 70.5 mm sleeve 150 mm long, the uniformed clearance space
is filled with SAE 45 lubricating oil at 350C.
Calculate the rate at which heat is generated at the journal bearing when the bearing shaft
rotates at 250 rpm. Show the answer in kN-m/s, J/s and hp.

Answer 1

Given data;

Diameter of bearing (D) = 70 mm

Diameter of sleeve (D_S) = 70.5 mm

Length of bearing (L) = 150 mm

SAE 45 oil at 35⁰ C

Rotational speed (N) = 250 rpm

Calculate radial clearance between the sleeve and the journal bearing

h = (D_s - D)/2

h = (70.5-70)/2

h = 0.25 mm

Calculate dynamic viscosity of the SAE oil at 35 degree celsius

u = 0.1232 pa s

velocity of shaft

v = (3.14*DN)/60

v = 3.14(70*10^-3)(250)/60

v = 0.91629 m/s

Assuming the linear velocity profile of the oil within the gap between the shaft and sleeve, the shear stress can be calculated as

tau (t) = u v/h

t = (0.1232 pa s) (0.91629/0.25*10^-3)

t = 451.55 pa

Shear force, F = t*a = t*3.14*D*L

F = 451.55*3.14*0.07*0.15

F = 14.895N

Torque, T = F*D/2

T = 14.895*0.07/2

T = 0.521N.m

Rate of heat generated , p = 2*3.14NT/60

p = 2*3.14*250*0.521/60

P = 13.6397 J/s = 0.0136397 kN-m/s = 0.01829114 hp