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

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

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Question #121747

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.

Expert’s answer

Given data;Diameter of bearing (D) = 70 mmDiameter of sleeve (DS) = 70.5 mmLength of bearing (L) = 150 mmSAE 45 oil at 350 CRotational speed (N) = 250 rpmCalculate radial clearance between the sleeve and the journal bearingh = (Ds – D)/2h = (70.5-70)/2h = 0.25 mmCalculate dynamic viscosity of the SAE oil at 35 degree celsiusu = 0.1232 pa svelocity of shaftv = (3.14*DN)/60v = 3.14(70*10-3)(250)/60v = 0.91629 m/sAssuming the linear velocity profile of the oil within the gap between the shaft and sleeve, the shear stress can be calculated astau (t) = u v/ht = (0.1232 pa s) (0.91629/0.25*10-3)t = 451.55 paShear force, F = t*a = t*3.14*D*LF = 451.55*3.14*0.07*0.15F = 14.895NTorque, T = F*D/2T = 14.895*0.07/2T = 0.521N.mRate of heat generated , p = 2*3.14NT/60p = 2*3.14*250*0.521/60P = 13.6397 J/s = 0.0136397 kN-m/s = 0.01829114 hp

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