Question

5. Estimate the life (in hours) of an 02-series single-row deep-groove ball bearing with a 50-mm bore working under the following condition: axial force = 4 kN, radial force = 6 kN, outer ring rotating at 360 rpm, temperature = 50 °C, light impact, reliability = 97%. (6 points)

Answer 1

The given data is

02-series single row deep groove ball bearing

bore diameter d = 50mm

Axial load F_a=4KN

Radial load F_r=6KN

Outer ring speed N=360rpm

temperature T=50^oC

Light impact

Reliability = 97%

solution:

Life in hours L_h = (L₁₀ x 10⁶ )/(60 x N)

Life in million revolutions L₁₀ = (C₁₀/P)^k

C₁₀=basic dynamic loading

C₀= basic static loading

Equivalent load P = (XVF_r + YF_a)S

values obtained from design data book:

For bore d=50mm : C₀=19.6KN, C₁₀= 35.1KN

service factor S = 1.5 for light impact

race rotation factor V=1.2 for outer ring rotation

V=1.0 for inner ring rotation

F_a/C₀ = 4/19.6 = 0.204

F_a/(V x F_r)= 4/(1.2 x 6) = 0.55

from data book , for F_a/C₀=0.2 e=0.34

therefore F_a/(V x F_r) > e

for the above condition X=0.56 , Y=1.31 obtained from design data book

by substituting the above values in the equivalent load formulae

Equivalent load P = (XVF_r + YF_a)S

P = 13.908KN

Life in hours L_h = (L₁₀ x 10⁶ )/(60 x N)

Life in million revolutions L₁₀ = (C₁₀/P)^k

L₁₀ = (35.1/13.908)³ (for ball bearings k=3)

L₁₀ = 16.074 million revolutions

Life in hours L_h = (L₁₀ x 10⁶ )/(60 x N)

L_h = (16.074x 10⁶ )/(60 x 360)

L_h = 744 hr

The reference books used are

1. Design Data Handbook by S.Md.Jalaludeen

2.Shigley's Mechanical Engineering Design, 9th Edition-McGraw-Hill