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Question 15.7: A single-row deep groove ball bearing No. 6002 is subjected ...

A single-row deep groove ball bearing No. 6002 is subjected to an axial thrust of 1000 N and a radial load of 2200 N. Find the expected life that 50% of the bearings will complete under this condition.

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\text { Given } F_{a}=1000 N \quad F_{r}=2200 N .

Bearing = No. 6002
Step I X and Y factors
Referring to Table 15.5, the capacities of bearing No. 6002 are,

Table 15.5 Dimensions and static and dynamic load capacities of single-row deep groove ball bearings

Designation Basic load
ratings (N)		 Principal
dimensions (mm)
C_{0} C B D d
61800 630 1480 5 19 10
6000 1960 4620 8 26
6200 2240 5070 9 30
6300 3750 8060 11 35
61801 695 1430 5 21
6001 2240 5070 8 28
6201 3100 6890 10 32
6301 4650 9750 12 37
61802 815 1560 5 24 15
6002 2500 5590 9 32
6202 3550 7800 11 35
6302 5400 11400 13 42
61803 930 1680 5 26 17
6003 2800 6050 10 35
6202 4500 9560 12 40
6303 6550 13500 14 47
6403 11800 22900 17 62
61804 1500 2700 7 32 20
16404 3400 7020 8 42
6004 4500 9360 12 42
6204 6200 12700 14 47
6304 7800 15900 15 52
6404 16600 30700 19 72
61805 1960 3120 7 37 25
16005 4000 7610 8 47
6005 5600 11200 12 47
6205 6950 14000 15 52
6305 11400 22500 17 62
6405 19600 35800 21 80
61806 2080 3120 7 42 30
16006 5850 11200 9 55
6006 6800 13300 13 55
6206 10000 19500 16 62
6306 14600 28100 19 72
6406 24000 43600 23 90
61807 3000 4030 7 47 35
16007 6950 12400 9 62
6007 8500 15900 14 62
6207 13700 25500 17 72
6307 18000 33200 21 80
6407 31000 55300 25 100
61808 3350 4160 7 52 40
16008 7800 13300 9 68
6008 9300 16800 15 68
6208 16600 30700 18 80
6308 22400 41000 23 90
6408 36500 63700 27 110
61809 3800 6050 7 58 45
16009 9300 15600 10 75
6009 12200 21200 16 75
6209 19600 33200 19 85
6309 30000 52700 25 100
6409 45500 76100 29 120
61810 4250 6240 7 65 50
16010 10000 16300 10 80
6010 13200 21600 16 80
6210 19600 35100 20 90
6310 36000 61800 27 110
6410 5200 87100 31 130
61811 5600 8320 9 72 55
16011 12200 19500 11 90
6011 17000 28100 18 90
6211 25000 43600 21 100
6311 41500 71500 29 120
6411 63000 99500 33 140
61812 6100 8710 10 78 60
16012 13200 19900 11 95
6012 18300 29600 18 95
6212 28000 47500 22 110
6312 48000 81900 31 130
6412 69500 108000 35 150
61813 8300 11700 10 85 65
16013 14600 21200 11 100
6013 19600 30700 18 100
6213 34000 55900 23 120
6313 56000 92300 33 140
6413 78000 119000 37 160
61814 9150 12100 10 90 70
16014 19000 28100 13 110
6014 24500 37700 20 110
6214 37500 61800 24 125
6314 63000 104000 35 150
6414 104000 143000 42 180
61815 9800 12500 10 95 75
10615 20000 28600 13 115
6015 26000 39700 20 115
6215 40500 66300 25 130
6315 72000 112000 37 160
6415 114000 1530000 45 190
C_{o}=2500 N \text { and } C=5590 N

\text { Also, } \quad F_{a}=1000 N \quad F_{r}=2200 N .

\left(\frac{F_{a}}{F_{r}}\right)=\left(\frac{1000}{2200}\right)=0.455 .

\text { and } \quad\left(\frac{F_{a}}{C_{o}}\right)=\left(\frac{1000}{2500}\right)=0.4 .

Referring to Table 15.4,

Table 15.4 X and Y factors for single-row deep groove ball bearings

e \left(\frac{F_{a}}{F_{r}}\right)>e \left(\frac{F_{a}}{F_{r}}\right) \leq e \left(\frac{F_{a}}{C_{0}}\right)
Y X Y X
0.22 2.0 0.56 0 1

0.025
0.24 1.8 0.56 0 1 0.040
0.27 1.6 0.56 0 1 0.070
0.31 1.4 0.56 0 1 0.130
0.37 1.2 0.56 0 1 0.250
0.44 1.0 0.56 0 1 0.500

\left(\frac{F_{a}}{F_{r}}\right)>e .

The value of Y is obtained by linear interpolation.

Y=1.2-\frac{(1.2-1.0)}{(0.5-0.25)} \times(0.4-0.25)=1.08 \text { and } .

X = 0.56

\text { Step II Bearing life }\left(L_{10}\right) .

P=X F_{r}+Y F_{a}=0.56(2200)+1.08(1000) .

= 2312 N
From Eq. (15.7),

C=P\left(L_{10}\right)^{1 / 3}             (15.7).

C=P\left(L_{10}\right)^{1 / 3} \quad 5590=2312\left(L_{10}\right)^{1 / 3} .

\therefore \quad L_{10}=14.13 \text { million rev. }

\text { Step III Bearing life }\left(L_{50}\right).

It can be proved that the life \left(L_{50}\right) , which 50% of the bearings will complete or exceed, is approximately five times the life \left(L_{10}\right) which 90% of the bearings will complete or exceed.
Therefore

L_{50}=5 L_{10}=5(14.13)=70.65 \text { million rev. }

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