Tesis

560

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition

III. Design of Mechanical Elements

11. Rolling−Contact Bearings

© The McGraw−Hill Companies, 2008

Rolling-Contact Bearings

559

11–6

Combined Radial and Thrust Loading
A ball bearing is capable of resisting radial loading and a thrust loading. Furthermore, these can be combined. Consider Fa and Frto be the axial thrust and radial loads, respectively, and Fe to be the equivalent radial load that does the same damage as the combined radial and thrust loads together. A rotation factor V is defined such that V = 1 when the inner ring rotates and V = 1.2 when the outer ring rotates. Two dimensionless groups can now be formed: Fe /V F r and Fa /V F r . When these two dimensionless groups areplotted as in Fig. 11–6, the data fall in a gentle curve that is well approximated by two straight-line segments. The abscissa e is defined by the intersection of the two lines. The equations for the two lines shown in Fig. 11–6 are Fe =1 V Fr when Fa ≤e V Fr when Fa >e V Fr
(11–8a) (11–8b)

Fa Fe = X +Y V Fr V Fr

where, as shown, X is the ordinate intercept and Y is the slope of the line for Fa/V F r > e. It is common to express Eqs. (11–8a) and (11–8b) as a single equation, Fe = X i V F r + Yi Fa
(11–9)

where i = 1 when Fa /V F r ≤ e and i = 2 when Fa /V F r > e. Table 11–1 lists values of X 1 , Y1 , X 2 , and Y2 as a function of e, which in turn is a function of Fa /C0 , where C0 is the bearing static load catalog rating. In these equations, the rotation factor V is intended tocorrect for the rotatingring conditions. The factor of 1.2 for outer-ring rotation is simply an acknowledgment that the fatigue life is reduced under these conditions. Self-aligning bearings are an exception: they have V = 1 for rotation of either ring. The X and Y factors in Eqs. (11–8a) and (11–8b) depend upon the geometry of the bearing, including the number of balls and the ball diameter. TheABMA Figure 11–6
The relationship of dimensionless group Fe/(VFr) and Fa/(VFr) and the straightline segments representing the data.
F e VF r

1

Slope Y X

F a VF r 0 e

Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition

III. Design of Mechanical Elements

11. Rolling−Contact Bearings

© The McGraw−Hill Companies, 2008

561

560

Mechanical EngineeringDesign

Table 11–1 Equivalent Radial Load Factors for Ball Bearings
Fa /C0 0.014* 0.021 0.028 0.042 0.056 0.070 0.084 0.110 0.17 0.28 0.42
0.56
∗ Use

Fa /(VFr) e 0.19 0.21 0.22 0.24 0.26 0.27 0.28 0.30 0.34 0.38 0.42
0.44

e Y1 0 0 0 0 0 0 0 0 0 0 0
0

Fa /(VFr) X2 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.56
0.56

e Y2 2.30 2.15 1.99 1.85 1.71 1.63 1.55 1.45 1.31 1.151.04
1.00

X1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.00

0.014 if Fa C0

0.014.

Figure 11–7
The basic ABMA plan for boundary dimensions. These apply to ball bearings, straight roller bearings, and spherical roller bearings, but not to inchseries ball bearings or tapered roller bearings. The contour of the corner is not specified. It may be rounded or chamfered, but itmust be small enough to clear the fillet radius specified in the standards.

Width series 4 Diameter 3 series 2 1 0

0

1

2 r

3

00 02 03 04

10 12

13

20

22

23

30

31

32

Dimension series Bore

r

recommendations are based on the ratio of the thrust component Fa to the basic static load rating C0 and a variable reference value e. The static load rating C0 istabulated, along with the basic dynamic load rating C 10, in many of the bearing manufacturers’ publications; see Table 11–2, for example. Since straight or cylindrical roller bearings will take no axial load, or very little, the Y factor is always zero. The ABMA has established standard boundary dimensions for bearings, which define the bearing bore, the outside diameter (OD), the width, and the...