Analysis and Synthesis of Engineering Surfaces in Bridge Manufacturing and Design - Manufacturing Systems Processes - page 21

FIGURE 1.8 Angular-contact ball bearing: geometry and forces.

TABLE 1.10 Data for Test Bearing

Parameter Value

Type Angular-contact

No. of balls 16

Ball diameter 1.40 mm

Pitch circle diameter 6.75 mm

Radial clearance 0.032 mm

Test load (axial) 1000 N

Test speed 1800 rpm

Contact deflection 0 0.0092 mm

10 9 Nm 23 Compliance factor C f

Contact angle

9.56

18.8°

The total axial force on the bearing is the sum of the axial components of the normal forces on all the
balls ( Fig. 1.8 ):

N b

P a Q j sin (1.18)

j 1

where is the contact angle. These equations are used in the calculation of axial vibration force for a

test bearing. The data for the test bearing are adapted from [71], and are shown in Table 1.10 .

Vibration Force with Synthesized Profiles
The experimental and synthesized errors from milling and grinding are superposed on the ideal profile
of the ball bearing outer race and the resulting deflection is calculated according to Eq. (1.16), i.e.,
is a contribution of the profile error. Equation 1.18 is used to calculate the axial force at various points
in time, from 0

j t ()

T 0 / N b , where T 0 is the time for one revolution of the bearing. The force pattern
will be periodic with period T 0 / N b , as the balls and the inner race are assumed to have ideal profiles. The
results for two profiles, one each from milling and grinding, are shown in Fig. 1.9 .
This figure enables the performance comparison of experimental and synthesized profiles. The com-
parisons show good agreement with respect to absolute values and range of variation for both processes
considered.

t