A single-row, deep-groove ball bearing number 6208 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 (14-10), we have
[latex]F_{m}=\left(\frac{\Sigma_{i}\left(F_{i} ight)^{p} N_{i}}{N} ight)^{1 / p}[/latex] (14–10a)

[latex]F_{m}=\left(\frac{30(650)^{3}+10(750)^{3}+20(250)^{3}}{30+10+20} ight)^{1 / 3}=597 \mathrm{lb}[/latex]
Now use Equation (14-11):
[latex]L=\left(\frac{C}{F_{m}} ight)^{p}[/latex] (14–11a)
From Table 14-3, for the 6208 bearing, we find that [latex]C=6902 \mathrm{lb}[/latex]. Then
[latex]L=\left(\frac{6902}{597} ight)^{3}=1545 ext { million rev }[/latex]
At a rotational speed of [latex]600 \mathrm{rpm}[/latex], the number of hours of life would be
[latex]L=\frac{1545 imes 10^{6} \mathrm{rev}}{1} \cdot \frac{\min }{600 \mathrm{rev}} \cdot \frac{\mathrm{h}}{60 \mathrm{~min}}=42917 \mathrm{~h}[/latex]

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

TABLE 14–3 Dimensions for Single Row, Deep-groove Ball Bearings
Bearing number	Nominal bearing dimensions						Basic load ratings				Maximum fillet radius [latex]r_{max}^1[/latex]		Minimum shaft shoulder diameter, S		Maximum housing shoulder diameter, H		Bearing mass
Bearing number	Bore, d		Outside dia., D		Width, B		Static, [latex]C_o[/latex]		Dynamic, C		Maximum fillet radius [latex]r_{max}^1[/latex]		Minimum shaft shoulder diameter, S		Maximum housing shoulder diameter, H		Bearing mass
	mm	in	mm	in	mm	in	kN	[latex]lb_f[/latex]	kN	[latex]lb_f[/latex]	mm	in	mm	in	mm	in	kg	[latex]lb_m[/latex]
6000	10	0.3937	26	1.0236	8	0.315	1.96	441	4.62	1039	0.3	0.012	12	0.472	24	0.945	0.019	0.042
6200	10	0.3937	30	1.1811	9	0.3543	2.36	531	5.07	1140	0.6	0.024	14	0.551	26	1.024	0.032	0.071
6300	10	0.3937	36	1.3780	11	0.4331	8.06	1812	3.4	764	0.6	0.024	14	0.551	31	1.220	0.053	0.117
6001	12	0.4724	28	1.1024	8	0.315	2.36	531	5.07	1140	0.3	0.012	14	0.551	26	1.024	0.022	0.049
6201	12	0.4724	32	1.2598	10	0.3937	3.1	697	6.89	1549	0.6	0.024	16	0.63	28	1.102	0.037	0.082
6301	12	0.4724	37	1.4567	12	0.4724	4.15	933	9.75	2192	1.0	0.039	17	0.669	32	1.260	0.060	0.132
6002	15	0.5906	32	1.2598	9	0.3543	2.85	641	5.59	1257	0.3	0.012	17	0.669	30	1.181	0.030	0.066
6202	15	0.5906	35	1.378	11	0.4331	3.75	843	7.8	1754	0.6	0.024	19	0.748	31	1.220	0.045	0.099
6302	15	0.5906	42	1.6535	13	0.5118	5.4	1214	11.4	2563	1.0	0.039	20	0.787	37	1.457	0.082	0.181
6003	17	0.6693	35	1.378	10	0.3937	3.25	731	6.05	1360	0.3	0.012	19	0.748	33	1.299	0.039	0.086
6203	17	0.6693	40	1.5748	12	0.4724	4.75	1068	9.56	2149	0.6	0.024	21	0.827	36	1.417	0.065	0.143
6303	17	0.6693	47	1.8504	14	0.5512	6.55	1473	13.5	3035	1.0	0.039	22	0.866	42	1.654	0.120	0.265
6004	20	0.7874	42	1.6535	12	0.4724	5	1124	9.36	2104	0.6	0.024	24	0.945	38	1.496	0.069	0.152
6204	20	0.7874	47	1.8504	14	0.5512	6.55	1473	12.7	2855	1.0	0.039	25	0.984	42	1.654	0.110	0.243
6304	20	0.7874	52	2.0472	15	0.5906	7.8	1754	15.9	3575	1.0	0.039	27	1.063	45	1.772	0.140	0.309
6005	25	0.9843	47	1.8504	12	0.4724	6.55	1473	11.2	2518	0.6	0.024	29	1.142	43	1.693	0.080	0.176
6205	25	0.9843	52	2.0472	15	0.5906	7.8	1754	14	3147	1.0	0.039	30	1.181	47	1.850	0.130	0.287
6305	25	0.9843	62	2.4409	17	0.6693	11.6	2608	22.5	5058	1.0	0.039	32	1.26	55	2.165	0.230	0.507
6006	30	1.811	55	2.1654	13	0.5118	8.3	1866	13.3	2990	1.0	0.039	35	1.378	50	1.969	0.160	0.353
6206	30	1.811	62	2.4409	16	0.6299	11.2	2518	19.5	4384	1.0	0.039	35	1.378	57	2.244	0.200	0.441
6306	30	1.811	72	2.8346	19	0.748	16	3597	28.1	6317	1.0	0.039	37	1.457	65	2.559	0.350	0.772
6007	35	1.3780	62	2.4409	14	0.5512	10.2	2293	15.9	3575	1.0	0.039	40	1.575	57	2.244	0.160	0.353
6207	35	1.3780	72	2.8346	17	0.6693	15.3	3440	25.5	5733	1.0	0.039	42	1.654	65	2.559	0.290	0.639
6307	35	1.3780	80	3.1496	21	0.8268	19	4272	33.2	7464	1.5	0.059	43	1.693	72	2.835	0.460	1.014
6008	40	1.5748	68	2.6772	15	0.5906	11.6	2608	16.8	3777	1.0	0.039	45	1.772	63	2.480	0.190	0.419
6208	40	1.5748	80	3.1496	18	0.7087	19	4272	30.7	6902	1.0	0.039	47	1.85	73	2.874	0.370	0.816
6308	40	1.5748	90	3.5433	23	0.9055	24	5396	41	9218	1.5	0.059	48	1.89	82	3.228	0.630	1.389
6009	45	1.7717	75	2.9528	16	0.6299	14.6	3282	20.8	4676	1.0	0.039	50	1.969	70	2.756	0.250	0.551
6209	45	1.7717	85	3.3465	19	0.748	21.6	4856	33.2	7464	1.0	0.039	52	2.047	78	3.071	0.410	0.904
6309	45	1.7717	100	3.937	25	0.9843	31.5	7082	52.7	11848	1.5	0.059	53	2.087	92	3.622	0.830	1.830
6010	50	1.9685	80	3.1496	16	0.6299	16	3597	21.6	4856	1.0	0.039	55	2.165	75	2.953	0.260	0.573
6210	50	1.9685	90	3.5433	20	0.7874	23.2	5216	35.1	7891	1.0	0.039	57	2.244	83	3.268	0.460	1.014
6310	50	1.9685	110	4.3307	27	1.063	38	5843	61.8	13894	2.0	0.079	59	2.323	101	3.976	1.050	2.315
6011	55	2.1654	90	3.5433	18	0.7087	21.2	4766	28.1	6317	1.0	0.039	62	2.441	83	3.268	0.390	0.860
6211	55	2.1654	100	3.9307	21	0.8268	29	6520	43.6	9802	1.5	0.059	63	2.48	92	3.622	0.610	1.345
6311	55	2.1654	120	4.7244	29	1.1417	45	10117	71.5	16075	2.0	0.079	64	2.52	111	4.370	1.350	2.977
6012	60	2.3622	95	3.7402	18	0.7087	23.2	5216	29.6	6655	1.0	0.039	67	2.638	88	3.465	0.420	0.926
6212	60	2.3622	110	4.3307	22	0.8661	32.5	7307	47.5	10679	1.5	0.059	68	2.677	102	4.016	0.780	1.720
6312	60	2.3622	130	5.1181	31	1.2205	52	11691	81.9	18413	2.0	0.079	71	2.795	119	4.685	1.700	3.749
6013	65	2.5591	100	3.937	18	0.7087	25	5621	30.7	6902	1.0	0.039	72	2.835	93	3.661	0.440	0.970
6213	65	2.5591	120	4.7244	23	0.9055	40.5	9105	55.9	12567	1.5	0.059	73	2.874	112	4.409	0.990	2.183
6313	65	2.5591	140	5.5118	33	1.2992	60	13489	92.3	20751	2.0	0.079	76	2.992	129	5.079	2.100	4.631
6014	70	2.7559	110	4.3307	20	0.7874	31	6969	37.7	8476	1.0	0.039	77	3.031	103	4.055	0.600	1.323
6214	70	2.7559	125	4.9213	24	0.9449	45	10117	60.5	13602	1.5	0.059	78	3.071	117	4.606	1.050	2.315
6314	70	2.7559	150	5.9055	35	1.378	68	15288	104	23381	2.0	0.079	81	3.189	139	5.472	2.500	5.513
6015	75	2.9528	115	4.5276	20	0.7874	33.5	7531	39.7	8925	1.0	0.039	82	3.228	108	4.252	0.640	1.411
6215	75	2.9528	130	5.1181	25	0.9843	49	11016	66.3	14906	1.5	0.059	83	3.268	122	4.803	1.200	2.646
6315	75	2.9528	160	6.2992	37	1.4567	76.5	17199	114	25629	2.0	0.079	86	3.386	149	5.866	3.000	6.615
6016	80	3.1496	125	4.9513	22	0.8661	40	8993	47.5	10679	1.0	0.039	87	3.425	118	4.646	0.850	1.874
6216	80	3.1496	140	5.5118	26	1.0236	55	12365	70.2	15782	2.0	0.059	89	3.504	131	5.157	1.400	3.087
6316	80	3.1496	170	6.6929	39	1.5354	86.5	19447	124	27878	2.0	0.079	91	3.583	159	6.260	3.600	7.938
6017	85	3.3465	130	5.1181	22	0.8661	43	9667	49.4	11106	1.0	0.039	92	3.622	123	4.843	0.890	1.962
6217	85	3.3465	150	5.9055	28	1.1024	64	14388	83.2	18705	2.0	0.079	94	3.701	141	5.551	1.800	3.969
6317	85	3.3465	180	7.0866	41	1.6142	96.5	21695	133	29901	2.5	0.098	98	3.858	167	6.575	4.250	9.371
6018	90	3.5433	140	5.5118	24	0.9449	50	11241	58.5	13152	1.5	0.059	98	3.858	132	5.197	1.150	2.536
6218	90	3.5433	160	6.2992	30	1.1811	73.5	16524	95.6	21493	2.0	0.079	99	3.898	151	5.945	2.150	4.741
6318	90	3.5433	190	7.4803	43	1.6929	108	24281	143	32149	2.5	0.098	103	4.055	177	6.969	4.900	10.805
6019	95	3.7402	145	5.7087	24	0.9449	54	12140	60.5	13602	1.5	0.059	103	4.055	137	5.394	1.200	2.805
6219	95	3.7402	170	6.6929	32	1.2598	81.5	18323	108	24281	2.0	0.079	106	4.173	159	6.260	2.600	5.733
6319	95	3.7402	200	7.874	45	1.7717	118	26529	153	34397	2.5	0.098	108	4.252	187	7.362	5.650	12.458
6020	100	3.9370	150	5.9055	24	0.9449	54	12140	60.5	13602	1.5	0.059	108	4.252	142	5.591	1.250	2.756
6220	100	3.9370	180	7.0866	34	1.3386	93	20908	124	27878	2.0	0.079	111	4.37	169	6.654	3.150	6.946
6320	100	3.9370	215	8.4646	47	1.8504	140	31475	174	39119	2.5	0.098	113	4.449	202	7.953	7.000	15.435
6021	105	4.1339	160	6.2992	26	1.0236	65	14726	72.8	16367	2.0	0.079	114	4.488	151	5.945	1.600	3.528
6221	105	4.1339	190	7.4803	36	1.4173	104	23381	133	29901	2.0	0.079	116	4.567	179	7.047	3.700	8.159
6321	105	4.1339	225	8.8583	49	1.9291	153	34397	182	40917	2.5	0.098	118	4.646	212	8.346	8.250	18.191
6022	110	4.3307	170	6.6929	28	1.1024	73.5	16524	81.9	18413	2.0	0.079	119	4.685	161	6.339	1.950	4.300
6222	110	4.3307	200	7.874	38	1.4961	118	26529	143	32149	2.0	0.079	121	4.764	189	7.441	4.350	9.592
6322	110	4.3307	240	9.4488	50	1.9685	180	40486	203	45638	2.5	0.098	123	4.843	227	8.937	9.550	21.058
6024	120	4.7244	180	7.0866	28	1.1024	80	17986	85.2	19155	2.0	0.079	129	5.079	171	6.732	2.050	4.520
6224	120	4.7244	215	8.4646	40	1.5748	118	26529	146	32824	2.0	0.079	131	5.157	204	8.031	5.150	11.356
6324	120	4.7244	260	10.2362	55	2.1654	186	41817	208	46763	2.5	0.098	133	5.236	247	9.724	14.500	31.973
6026	130	5.1181	200	7.874	33	1.2992	100	22482	106	23831	2.0	0.079	139	5.472	191	7.520	3.150	6.946
6226	130	5.1181	230	9.0551	40	1.5748	132	29676	156	35072	2.5	0.098	143	5.63	217	8.543	5.800	12.789
6326	130	5.1181	280	11.0236	58	2.2835	216	48561	229	51484	3.0	0.118	146	5.748	264	10.394	18.000	39.690

Question 14.6: A single-row, deep-groove ball bearing number 6208 is subjec...

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