A single-row, deep-groove ball bearing number 6308 is subjected to the following set of loads for the given times:

Question

Condition [latex]F_i[/latex] Time
1 650 lb 30 min
2 750 lb 10 min
3 250 lb 20 min

This cycle of 60 min is repeated continuously throughout the life of the bearing. The shaft carried by the bearing rotates at 600 rpm. Estimate the total life of the bearing.

Accepted Answer

Using Equation (14-11), we have

[latex]F_m=\left(\frac{\sum_i{(F_i)^PN_t}^{I/P} }{N} ight) [/latex] (14-11a)

[latex]F_m=\left(\frac{30(650)^3 + 10(750)^3 + 20(250)^3}{30 + 1 0 + 20} ight)^{1/3}=597 [/latex] lb

Now use Equation (14-12):

[latex]L=\left(\frac{C}{F_m} ight)^P [/latex] (14-12a)

From Table 14-3, for the 6308 bearing, we find that C = 7050 lb. Then

TABLE 14-3 Bearing selection data for single-row, deep-groove, Conrad-type ball bearings
A. Series 6200.
Bearing number	Nominal bearing dimensions							Preferred shoulder diameter		Bearing weight	Basic static load rating. [latex]C_o[/latex]	Basic dynamic load rating. c
	d		D		B		r*	Shaft	Housing
	mm	in	mm	in	mm	in	in	in	in	lb	lb	lb
6200 6201 6102 6203	10 12 15 17	0.3937 0.4724 0.5906 0.6693	30 32 35 40	1.1811 1.2598 1.3780 1.5748	9 10 11 12	0.3543 0.3937 0.4331 0.4724	0.024 0.024 0.024 0.024	0.500 0.578 0.703 0.787	0.984 1.063 1.181 1.380	0.07 0.08 0.10 0.14	520 675 790 1010	885 1180 1320 1660
6204 6205 6206 6207	20 25 30 35	0.7874 0.9843 1.1811 1.3780	47 52 62 72	1.8504 2.0472 2.4409 2.8346	14 15 16 17	0.5512 0.5906 0.6299 0.6693	0.039 0.039 0.039 0.039	0.969 1.172 1.406 1.614	1.614 1.811 2.205 2.559	0.23 0.29 0.44 0.64	1400 1610 2320 3150	2210 1430 3350 4450
6208 6209 6210 6211	40 45 50 55	1.5748 1.7717 1 .9685 2.1654	80 85 90 100	3.1496 3.3465 3.5433 3.9370	18 19 20 21	0.7087 0.7480 0.7874 0.8268	0.039 0.039 0.039 0.059	1.811 2.008 2.205 2.441	2.874 3.071 3.268 3.602	0.82 0.89 1.02 1.36	3650 4150 4650 5850	5050 5650 6050 7500
6212 6213 6214 6215	60 65 70 75	2.3622 2.5591 2.7559 2.9528	110 120 125 1.30	4.3307 4.7244 4.9213 5.1181	22 23 2425	0.8661 0.9055 0.9449 0.9843	0.059 0.059 0.059 0.059	2.717 2.913 3.110 3.307	3.996 4.390 4.587 4.783	1.73 2.18 2.31 2.64	7250 8000 8800 9700	9050 9900 10800 11400
6216 6217 6218 6219	80 85 90 95	3.1496 3.3465 3.5433 3,7402	140 150 160 170	5.5118 5.9055 6.2992 6.6929	26 28 30 32	1.0236 1.1024 1.1811 1.2598	0.079 0.079 0.079 0.079	3.504 3.740 3.937 4.213	5.118 5.512 5.906 6.220	3.09 3.97 4.74 5.73	10500 12300 14200 16300	12600 14600 16600 18800
6220 6221 6222 6224	100 105 110 120	3.9370 4.1339 4.3307 4.7233	180 190 200 215	7.0866 7.4803 7.8740 8.4646	34 36 38 40	1.3386 1.4173 1.4961 1.5748	0.079 0.079 0.079 0.079	4.409 4.606 4.803 5.197	6.614 7.008 7.402 7.992	6.94 8.15 9.59 11.4	18600 20900 23400 26200	21100 23000 24900 26900

TABLE 14-3 ( continued)
A. Series 6200. continued
Bearing number	Nominal bearing dimensions								Preferred shoulder diameter		Bearing weight	Basic static load rating. [latex]C_o[/latex]	Basic dynamic load rating. c
	d		D			B		r*	Shaft	Housing
	mm	in	mm		in	mm	in	in	in	in	lb	lb	lb
6226 6228 6230 6232	130 140 150 160	5.1181 5.5118 5.9055 6.2992	230 250 270 290		9.0551 9.8425 10.6299 11.4173	40 42 45 48	1.5748 1.6535 1.7717 1.8898	0.098 0.098 0.098 0.098	5.669 6.063 6.457 6.850	8.504 9.291 10.079 10.886	12.7 19.6 25.332.0	29100 29300 32500 35500	28700 28700 30000 32000
6234 6236 6238 6240	170 180 190 200	6.6929 7.0866 7.4803 7.8740	310 320 340 360		12.2047 12.5984 13.3858 14.1732	52 52 55 58	2.0472 2.0472 2. 1654 2.2835	0.118 0.118 0.118 0.118	7.362 7.758 8.150 8.543	11.535 11.929 12.717 13.504	38.5 41.0 50.5 61.5	43000 46500 54500 60000	36500 39000 44000 6500
B. Series 6300
6300	10	03.937		35	13.780	11	0.4331	0.024	0.563	1.181	0.12	805	1400
6301	12	04.724		37	14.567	12	04.724	0.039	0.656	1.220	0.13	990	1680
6302	15	05.906		42	16.535	13	05.118	0.039	0.781	1.417	0.18	1200	1980
6303	17	06.693		47	18.504	14	05.512	0.039	0.875	1.614	0.25	1460	2360
6304	20	0.787		52	20.472	15	05.906	0.039	1.016	1.772	0.32	1730	2760
6305	25	09.843		62	24.409	17	06.693	0.039	1.220	2.165	0.52	2370	3550
6306	30	1.1811		72	28.346	19	07.480	0.039	1.469	2.559	0.76	3150	4600
6307	35	13.780		80	31.496	21	08.268	0.059	1.688	2.795	1.01	4050	5800
6308	40	15.748		90	35.433	23	09.055	0.059	1,929	3.189	1.40	5050	7050
6309	45	1.77 17		100	39.370	25	09.843	0.059	2.126	3.583	1.84	6800	9150
6310	50	19,685		110	43.307	27	10.630	0.079	2.362	3.937	2.42	8100	10700
6311	55	2.1654		120	47244	29	11.417	0.079	2.559	4.331	2.98	9450	12300
6312	60	23.622		130	5.1181	31	12.205	0.079	2.835	4.646	3.75	11000	14100
6313	65	25.591		140	55.118	33	12.992	0.079	3.031	5.039	4.63	12600	16000
6314	70	27.559		150	59.055	35	13.780	0.079	3.228	5.433	5.51	14400	18000
6315	75	29.528		160	62992	37	14.567	0.079	3.425	5.827	6.61	16300	19600

TABLE 14-3 ( continued)
B. Series 6300. continued
Bearing number	Nom inal bearing dimensions							Preferred shoulder diameter		Bearing weight	Basic static load rating. [latex]C_o[/latex]	Basic dynamic load rating, c
								Shaft	Housing
	d		D		B		r*
	mm	in	mm	in	mm	in	in	in	in	lb	lb	lb
6316 6317 6318 6319	80 85 90 95	3. 1496 3.3465 3.5433 3.7402	170 180 190 200	6.6929 7.0866 7.4803 7.8740	39 41 43 45	1.5354 1.6 142 1.6929 1.7717	0.079 0.098 0.098 0.098	3.622 3.898 4.094 4.291	6.220 6.535 6.929 7.323	7.93 9.37 10.8 12.5	18300 20400 22500 24900	21300 22900 24700 26400
6320 6321 6322 6324	100 105 110 110	3.9370 4.1339 4.3307 4.7244	215 225 240 260	8.4646 8.8583 9.4488 10.2362	47 49 50 55	1.8504 1.9291 1.9685 2.1654	0.098 0.098 0.098 0.098	4.488 4.685 4.882 5.276	7.913 8.307 8.898 9.685	15.3 17.9 21.0 27.6	29800 32500 38000 38500	30000 31700 35500 36000
6326 6328 6330 6332	130 140 150 160	5.1181 5.51 18 5.9055 6.2992	280 300 320 340	11.0236 11.81 10 12.5984 13.3858	58 62 65 68	2.2835 2.4409 2.5591 2.6772	0.118 0.1 18 0.118 0.118	5.827 6.220 6.614 7.008	10.315 11.102 11.890 12.677	40.8 48.5 57.3 58	44500 51000 58000 58500	39500 43500 47500 48000
6334 6336 6338 6340	170 180 190 200	6.6929 7.0866 7.4803 7.8740	360 380 400 420	14.1732 14.9606 15.7480 16.5354	72 75 78 80	2.8346 2.9528 3.0709 3. 1496	0.118 0.118 0.157 0.157	7.402 7.795 8.346 8.740	13.465 14.252 14.882 15.669	84 98 112 127	73500 84000 84000 91500	56500 61500 61500 65500
Source: NSK Corporation. Ann Arbor. Ml. *Maximum fillet that corner radius will clear.

[latex]L=\left(\frac{7050}{597} ight)^3=1647 [/latex] million rev

At a rotational speed of 600 rpm, the number of hours of life would be

L=[latex]\frac{1647 imes 10^6 \ rev}{1} .\frac{min}{600 \ rev}.\frac{h}{60 \ min} =45 745 \ h [/latex]

Note that this is the same bearing used in Example Problem 14-3 which was selected to operate at least 30 000 h when carrying a steady load of 650 lb.

Question 14.6: A single-row, deep-groove ball bearing number 6308 is subjec...

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