An 02-series single-row deep-groove ball bearing with a 65-mm bore (see Tables 11–1 and 11–2 for specifications) is loaded with a 3-kN axial load and a 7-kN radial load. The outer ring rotates at 500 rev/min.
(a) Determine the equivalent radial load that will be experienced by this particular bearing.
(b) Determine whether this bearing should be expected to carry this load with a 95 percent reliability for 10 kh.

Question

Accepted Answer

(a) [latex]F_{a}=3 kN , F_{r}=7 kN , n_{D}=500 rev / min , V=1.2[/latex]

From Table 11-2, with a 65 mm bore, [latex]C_{0}=34.0 kN[/latex] .

[latex]F_{a} / C_{0}=3 / 34=0.088[/latex]

From Table 11-1, [latex]0.28 \leq e \leq 3.0[/latex].

[latex]\frac{F_{a}}{V F_{r}}=\frac{3}{(1.2)(7)}=0.357[/latex]

Since this is greater than e, interpolating Table 11-1 with [latex]F_{a} / C_{0}=0.088[/latex] , we obtain [latex]X_{2}=0.56 ext { and } Y_{2}=1.53[/latex] .

Eq. (11-9):

[latex]\begin{aligned}&F_{e}=X_{i} V F_{r}+Y_{i} F_{a}=(0.56)(1.2)(7)+(1.53)(3)=9.29 kN \&F_{e}>F_{r} ext { so use } F_{e} .\end{aligned}[/latex]

(b) Use Eq. (11-7) to determine the necessary rated load the bearing should have to carry the equivalent radial load for the desired life and reliability. Use the Weibull parameters for Manufacturer 2 on p. 608.

[latex]x_{D}=\frac{L_{D}}{L_{R}}=\frac{10000(500)(60)}{10^{6}}=300[/latex]

Eq. (11-7):

[latex]\begin{aligned}C_{10} &=a_{f} F_{D}\left[\frac{x_{D}}{x_{0}+\left( heta-x_{0} ight)\left(1-R_{D} ight)^{1 / b}} ight]^{1 / a} \C_{10} &=(1)(9.29)\left[\frac{300}{0.02+(4.459-0.02)(1-0.95)^{1 / 1.483}} ight]^{1 / 3} \&=73.4 kN\end{aligned}[/latex]

From Table 11-2, the 65 mm bearing is rated for 55.9 kN, which is less than the necessary rating to meet the specifications. This bearing should not be expected to meet the load, life, and reliability goals.

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Eq. (11-7): [latex]C_{10} \doteq a_{f} F_{D}\left[\frac{x_{D}}{x_{0}+\left( heta-x_{0} ight)\left(1-R_{D} ight)^{1 / b}} ight]^{1 / a} \quad R \geq 0.90[/latex]

Eq. (11-9): [latex]F_{e}=X_{i} V F_{r}+Y_{i} F_{a}[/latex]

Table 11–1 Equivalent Radial Load Factors for Ball Bearings	[latex]F_{a} / C_{0}[/latex]	e	[latex]F_{a} /\left( VF _{r} ight) \leq e[/latex]		[latex]F_{a} /\left( VF _{r} ight)>e[/latex]
	[latex]F_{a} / C_{0}[/latex]	e	[latex]X_{1}[/latex]	[latex]Y _{ 1 }[/latex]	[latex]X_{2}[/latex]	[latex]Y _{ 2 }[/latex]
	0.014*	0.13	1.00	0	0.56	2.30
	0.021	0.21	1.00	0	0.56	2.15
	0.028	0.22	1.00	0	0.56	1.99
	0.042	0.24	1.00	0	0.56	1.85
	0.056	0.26	1.00	0	0.56	1.71
	0.070	0.27	1.00	0	0.56	1.63
	0.084	0.28	1.00	0	0.56	1.55
	0.110	0.30	1.00	0	0.56	1.45
	0.17	0.34	1.00	0	0.56	1.31
	0.28	0.38	1.00	0	0.56	1.15
	0.42	0.42	1.00	0	0.56	1.04
	0.56	0.44	1.00	0	0.56	1.00
	*Use 0.014 if [latex]F_{a} / C_{0}<0.014[/latex].

Table 11–2 Dimensions and Load Ratings for Single-Row 02-Series Deep-Groove and Angular-Contact Ball Bearings	Bore, mm	OD, mm	Width, m m	Fillet Radius, mm	shoulder Diameter, mm		Load Ratings, kN
					shoulder Diameter, mm		Deep Groove		Angular Contact
					[latex]d _{ s }[/latex]	[latex]d _{ H }[/latex]	[latex]C_{10}[/latex]	[latex]C_{0}[/latex]	[latex]C_{10}[/latex]	[latex]C_{0}[/latex]
	10	30	9	0.6	12.5	27	5.07	2.24	4.94	2.12
	12	32	10	0.6	14.5	28	6.89	3.10	7.02	3.05
	15	35	11	0.6	17.5	31	7.80	3.55	8.06	3.65
	17	40	12	0.6	19.5	34	9.56	4.50	9.95	4.75
	20	47	14	1.0	25	41	12.7	6.20	13.3	6.55
	25	52	15	1.0	30	47	14.0	6.95	14.8	7.65
	30	62	16	1.0	35	55	19.5	10.0	20.3	11.0
	35	72	17	1.0	41	65	25.5	13.7	27.0	15.0
	40	80	18	1.0	46	72	30.7	16.6	31.9	18.6
	45	85	19	1.0	52	77	33.2	18.6	35.8	21.2
	50	90	20	1.0	56	82	35.1	19.6	37.7	22.8
	55	100	21	1.5	63	90	43.6	25.0	46.2	28.5
	60	110	22	1.5	70	99	47.5	28.0	55.9	35.5
	65	120	23	1.5	74	109	55.9	34.0	63.7	41.5
	70	125	24	1.5	79	114	61.8	37.5	68.9	45.5
	75	130	25	1.5	86	119	66.3	40.5	71.5	49.0
	80	140	26	2.0	93	127	70.2	45.0	80.6	55.0
	85	150	28	2.0	99	136	83.2	53.0	90.4	63.0
	90	160	30	2.0	104	146	95.6	62.0	106	73.5
	95	170	32	2.0	110	156	108	69.5	121	85.0

Question 11.20: An 02-series single-row deep-groove ball bearing with a 65-m...

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