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Printer European Article Number 13 in Software ROLLING-CONTACT BEARINGS 18.16

ROLLING-CONTACT BEARINGS 18.16
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BEARINGS AND LUBRICATION
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FIGURE 18.17 Equivalent radial load when load varies periodically with angular position.
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fi = ni = Fi = a=
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fraction of revolution at load Fi application or design factor ith equivalent radial load applicable exponent 3 for ball bearings and 10 3 for roller bearings
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Example 5. A four-step loading cycle is applied to a ball bearing. For one-tenth of the time, the speed is 1000 rpm, Fr = 800 lb, and Fa = 400 lb; for two-tenths of the time, the speed is 1200 rpm, Fr = 1000 lb, and Fa = 500 lb; for three-tenths of the time, the speed is 1500 rpm, Fr = 1500 lb, and Fa = 700 lb; for four-tenths of the time, the speed is 800 rpm, Fr = 1100 lb, and Fa = 500 lb. For this shallow-angle, angular-contact ball bearing, X1 = 1, Y1 = 1.25, X2 = 0.45, Y2 = 1.2, and V = 1. This loading cycle is also depicted in Fig. 18.18.
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FIGURE 18.18 Loading cycle: one-tenth of time at 1000 rpm, Fr = 800, Fa = 400; two-tenths of time at 1200 rpm, Fr = 1000, Fa = 500; three-tenths of time at 1500 rpm, Fr = 1500, Fa = 700; four-tenths of time at 800 rpm, Fr = 1100, Fa = 500; X1 = 1, Y1 = 1.25, X2 = 0.45, Y2 = 1.2, V = 1.
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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TABLE 18.5 Tabulation for Example 5
18.17 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
ROLLING-CONTACT BEARINGS 18.18
BEARINGS AND LUBRICATION
The first step in the solution is to create Table 18.5. The equivalent radial load is Feq = [0.090(1430)3 + 0.216(2031)3 + 0.405(2969)3 + 0.288(2588)3]1/3 = 2604 lb Without the use of design factors, the equivalent radial load is Feq = [0.090(1300)3 + 0.216(1625)3 + 0.405(2375)3 + 0.288(1725)3]1/3 = 2002 lb The overall design factor is 2604/2002, or 1.30. If this sequence were common in a machinery application, a bearing manufacturer might recommend an application factor of 1.30 for this particular application.
18.8 MISALIGNMENT
The inner ring of a rolling-contact bearing is tightly fitted to the shaft, and the axis of rotation is oriented, as is the shaft centerline. The outer ring is held by some form of housing, and its axis is oriented as demanded by the housing. As the shaft deflects under load, these two axes lie at an angle to each other. This misalignment for very small angles is accommodated in slack, and no adverse life consequences are exhibited. As soon as the slack is exhausted, the intended deflection is resisted and the bearing experiences unintended loading. Life is reduced below prediction levels. A shaft design which is too limber does not fail, but bearings are replaced with much greater frequency. It is too easy to be critical of bearings when the problem lies in the shaft design. Figure 18.19 shows the dramatic fractional life reduction owing to misalignment in line-contact bearings [18.4]. If there is misalignment, it should not exceed 0.001 radian (rad) in cylindrical and tapered-roller bearings, 0.0087 rad for spherical ball bearings, or about 0.004 rad for
FIGURE 18.19 Fractional bearing life to be expected as a function of misalignment in line-contact bearings. (From Ref. [18.4], Fig. 11.)
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
ROLLING-CONTACT BEARINGS 18.19
ROLLING-CONTACT BEARINGS
deep-groove ball bearings. Self-aligning ball or spherical roller bearings are more tolerant of misalignment. The bibliography of Ref. [18.4] is extensive on this subject.
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