The influence of moment load on the ball bearing stiffness
Akira ITO
Research Lab., IHI Corporation, JAPAN
1. INTRODUCTION
In designing the rotor system, accurate prediction
of rolling bearing stiffness is important to avoid
resonant vibration. Rolling bearing stiffness can be
estimated by Jones’ theory [1]. According to the
theory, tilt between inner and outer ring reduce
bearing stiffness. Some studies about stiffness
reduction in the case of fixed tilt are reported [2, 3].
Generally, rolling bearing is initially set without
tilt. Even this case, angular contact ball bearing with
axial and radial load have varied ball contact angle
and moment is occurred inside bearing. It is
estimated that inner and outer ring tilt and bearing
stiffness is reduced. In this study, the influence of
moment by combined load on bearing stiffness is
focused.
2. CALCULATION
Moment by combined load produces tilt of
bearing. First, Influence of tilt on the bearing
stiffness is estimated by quasi-static analysis based
on Jones’ theory. Two typical conditions are
supposed here. One is A) tilt constrained and the
other is B) tilt free (Fig. 1). In the case of A),
rotational axis of outer and inner ring are kept
parallel. In the case of B), outer ring can tilt until
moment load becomes zero. Table 1 shows analysis
conditions.
3. EXPERIMENT
Actual bearing stiffness was measured by
experiment. Test rig is shown in Fig.2. Two test
bearings are set on both end of a shaft. Shaft
deflection is measured by two displacement sensors.
Test condition is same as the analysis (table.1).
4. RESULTS AND DISCUSSION
Calculated and experimental results are shown in
Fig.3. There are several folds difference in the
stiffness between the calculated results of case A)
and B). It means that tilt motion affects the stiffness
significantly. Experimental stiffness is between the
calculated results of case A) and B).
In this experiment, inner and outer ring were set
without tilt. In fact the outer ring tilts, however, due
to the elastic deformation. Because the combined
load results in non-constant ball contact angle, so
that some tilt moment would occurs. Calculated
distribution of contact angle, contact force and
moment load in tilt constrained condition is shown
in Fig.4, 5. This moment is the reason why actual
bearing stiffness is softer than the tilt constrained
analytic result.
5. SUMMARY
Angular contact bearing stiffness with combined
load is softer than analytic stiffness without tilt.
Even inner and outer ring is set without tilt, moment
by combined load produce inner and outer ring tilt
so that bearing stiffness is reduced. Considering
influence of combined load is one of key point to
predict bearing radial stiffness with good accuracy.
REFFERENCE
[1] Jones, A. Burton, et al., New departure
engineering data: analysis of stresses and deflections
Vol.1 (1946), 43.
[2] Butner, M. F., ASME Rotating Machinery and
Vehicle Dynamics, DE-Vol.35 (1991) 155.
[3] Bugra H. E., John M. V., Journal of propulsion
and power, Vol.40, No.4 (2004) 634.
(A) tilt constrained
(B) tilt free
Fig. 3 Bearing radial displacement
Fig. 1 Image of outer ring tilt
Vertical axis: (radial displacement) / (bearing internal clearance)
Table 1 Analysis / test condition
Unit
Value
Bearing type
#7008A
Axial force, Fa
N
1000
Radial force, Fr
N
0～2000
Rotating speed, n
rpm
4000
Fig. 4 Contact condition between ball and outer race
Fa=1000 N, Fr=2000 N, n=4000 rpm
Test bearing
(#7008A)
(Tilt constrained)
Hydraulic
cylinder
Radial force
Axial force
Displacement
sensor
Driving
motor
Fig. 2 Section image of test rig
Fig. 5 Moment between outer and inner ring
Fa=1000 N, n=4000 rpm
(Tilt constrained)