TECHNICAL PAPER

Study on Measurement of Dynamic Performance of Ball Bearing*1
for Auto-tensioner
A. NAKASE T. MIZUNO

L. LOUIn this paper, the authors have developed a method for the measurement of dynamic performance of ball bearings
using a high-speed camera and image processing. The dynamic performance of a ball bearing used in a car autotensioner have been investigated as an example. The positions of the balls of the bearing have been measured using
a ring light reflected on the balls. The positions of the cage and outer ring have been measured using the markers
set upon them. The reaction between the balls and cage as well as the deformation of the pocket prongs while thebearing rotated were observed. It was found that bearing oscillation had a significant effect on the ball lead andlag as well as the deformation of the pocket prongs. It was also found that the ball lead and lag as well as thedeformation of the pocket prongs varied significantly in the non-load zone. It can be assumed that these factors
have a significant effect on the fatigue life of the cage.
Key Words: ball bearing, dynamic performance measurement, deformation of cage, ball lead and lag, slip of ballrevolution, auto-tensioner bearing

1. Introduction
Various engine accessories are used in automobiles andthese are driven by the rotational force of the crankshaft
transmitted by the accessory belt. Figure 1 shows thelayout of engine accessories. The auto-tensioner serves
the purpose of absorbing sudden changes in belt tension
and is an essential component in increasing accessory belt
1)
reliability and reducing noise . Meanwhile, enhancing
engine output and torque to improve vehicle running
performance creates greater rotational speed fluctuationof the crankshaft which drives electronic accessories.
Fluctuation in rotational speed causes accessory belttension to fluctuate also and the auto-tensioner to2)oscillate . For this reason, auto-tensioner bearings
must be capable of performing in the severe operating
conditions of oscillation and load fluctuation (rotational
fluctuation).
The bearing comprises of only four components, theinner ring, outer ring, balls and cage, however its motion
mechanism is extremely complex. The optimal designof the bearing relies heavily on clarifying the dynamic
performance of the balls and cage during rotation, andthis has been the subject of research for many long3)
years . The ball dynamic performances including ball
*1 This paper was written based on Journal of Japanese Society of
Tribologists Volume 61, No. 2 (2016) p. 120-126

JTEKT ENGINEERING JOURNAL English Edition No. 1014E (2017)

Fan

Auto-tensioner
Alternator

Water pumpAuto-tensioner
Crank shaft

Air conditioner
compressor

Fig. 1 Example of engine accessory layout

rotation, have been measured through magnetizing
the ball and using coils or hall elements4)-6). The balls
revolution measurement has been carried out using a7)high-speed camera . The dynamic performance of the8)-10)
cage has been also measured using proximity sensors .
However, these methods only measured the performanceof either the balls or cage in isolation and did not makeit possible to ascertain the motion of the balls and cagein relation to each other. The force acting on the cage iscreated as a result of the relative motion of the balls andcage therefore, in order to consider the reason for stressacting on the cage, it is important that the relative motionof the balls and cage be ascertained. It has been suggested
that the stress that acts on a cage can be measured

39−Study on Measurement of Dynamic Performance of Ball Bearing for Auto-tensioner−by rotating the inner ring and outer ring in opposite
directions, stopping the rotation of the cage and attaching11)
a strain gauge to the cage , however this differs to theactual operating environment in several ways, including
no centrifugal force being placed on the ball. Anothermethod that has been suggested for many years is toattach a strain gauge to the cage, and receive signals from12)-14). However, thisthe strain gauge through a slip ring
method meant it was also difficult to recreate the actual
operating environment due to concerns of the effect ofnoise and rotational speed limitations. In this research,a high-speed camera and image processing were used
to establish a measurement technology to visualize thedynamic performance of a ball bearing during rotation.
The example of a ball bearing for an auto-tensioner used
in a car accessory belt was used to observe the change inball bearing dynamic performance over time and the effectof bearing oscillation. The motion of the balls relative tothe cage (the ball lead and lag) and the deformation of thecage pocket prongs, which is used to estimate the stressacting on the cage, have been measured quantitatively.

performance of the bearing during rotation is captured
using a high-speed camera and the markers placed on theouter ring and cage are tracked using image processing.
The marker positions obtained through tracking are
expressed by camera coordinates (whereby the horizontal
and vertical directions of the image have been establishedas the X axis and Y axis, unit: pixels), then this isconverted into coordinates where the X axis and Y axis
have been taken on the bearing radial plane (bearing
coordinates, unit: mm). The bearing coordinates will be
fixed and therefore not subject to change due to bearing
rotation. The dynamic performance of the ball bearing
during rotation is observed from the relative positions of
the markers after the aforementioned conversion had been
made.
Cage marker

Outer ring markerxy

Putting markers on the bearing

Pocket prong end face marker
Pocket prong
interval d p
Taking video by a high-speed camera

Pocket prong end face marker

d bc

Tracing the markers by
an image processing technology

BallCage marker

Cage marker

Fig. 3 Markers on sample bearing

2. 2 Measurement Method
Transforming
camera coordinate system tobearing coordinate system

Analyzing the bearing
dynamic performanceFig. 2 Measurement process of bearing dynamic performance

2. Measurement Methods and Conditions
2. 1 Measurement Process
Figure 2 shows the process used to measure thedynamic performance of a ball bearing. Markers
are placed on the outer ring and cage, the dynamic

40

Figure 3 shows the bearing used in the measurement.
A circular marker is attached to the outer ring and cage inorder to calculate rotational speed. Moreover, the change
in the interval between the marker attached to the cagepillar and balls (d bc ) was used to calculate the motion of
the balls relative to the cage. Pocket prong deformationis measured by putting markers on the end faces of thecage’s pocket prong and observing the change in theprong end face interval (d p ). Placing markers on theouter ring and cage does not affect bearing dynamic
performance however the ball dynamic performance
would be affected if the same marker was used on theballs. Consequently, an original approach of measurement
based on the reflection of a ring-shaped light wasestablished in order to calculate ball positions. As shownin Fig. 4, a ring-shaped light was used and the camera and

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−Study on Measurement of Dynamic Performance of Ball Bearing for Auto-tensioner−

light were set up on the central axis in a coaxial direction.
As a result, the reflection of the ring-shaped light (lightring) appears close to the center of all ball positions. Thisis shown in Fig. 5. As Fig. 6 (a) shows, the spot lightcannot be positioned symmetrical to the bearing center,
therefore the light reflecting from the ball appears closer
to the position where the spot light is located. Therefore,
if the ball revolves, the reflective light moves in relation
to the ball and it becomes difficult to calculate the ballposition from the reflective light. By using a ring-shaped
light as shown in Fig. 6 (b), the light ring will appear
symmetrical to the bearing center regardless of ballrevolution. By tracking the positional change of this lightring, it is possible to determine ball positions. However,in reality, it is difficult to capture images by positioninga camera, ring-shaped light and bearing on the same axis
and, in the case of the subject of measurement for thispaper, i.e., the auto-tensioner bearing, oscillation is alsoa factor and it is extremely difficult to align the centersof the camera and light with the center of the bearing,then maintain this state. In order to solve this problem,the below correction method has been devised. Figure 7
shows the process for determining ball positions while
Fig. 8 shows the concept of ball position correction.
First, the center coordinates (the circle center of lightrings, C1) were calculated by circle approximation using
all ball light ring centers R1, R2, … Rz (where z = No. ofballs). Next, the center of the bearing (inner ring) was
calculated as C2 and the difference between C1 and C2 was
calculated. This difference is considered to be the amount,the center of ring light needs to be displaced relative tothe bearing center. Therefore the corrected positions foreach ball, B1, B2, … Bz , were calculated.
Spot light

Ring light

CameraCamera(a) Spot light

Fig. 6 Difference between spot light and ring light

Calculating the light ring center
positions on balls (R1 〜 R7)

Ring light

Bearing
View A

View A

Central axis

Light source

Calculating the bearing center (C2)

Calculating the circle center oflight rings (C1) by a circle fitting
Calculating the difference ( r ) between the bearing center (C2)and the circle center of light rings (C1)

Calculating the ball positions (B1 〜 B7) using r , R1 〜 R7

Fig. 7 Process for determining ball positions

R1

R7
R6

R3

C1

B1

B7

R2

R5

High-speed camera(b) Ring light

C2
C1

B2

B6

B3
B5

R4
Correction
value rB4

Correction
value rR1 〜 R7 ：Light ring positions (Before correction)
C1 ：Circle center of light rings
C2 ：Bearing center
B1 〜 B7 ：Ball positions (After correction)

Fig. 8 Concept of correction of ball positions

Lighting
circleFig. 4 Measurement system

Fig. 5 Ring-shaped light reflected on balls

JTEKT ENGINEERING JOURNAL English Edition No. 1014E (2017)

2. 3 Measurement Conditions
As shown in Table 1, if the photographing resolutionof the high-speed camera used in this research is 1 024×1
024 pixels, the maximum filming speed is 5 400 frames/s.
The specifications of the sampling bearing are shown in
Table 2. As a result of determining the filming range withconsideration to the bearing O.D. of 52mm and autotensioner’s oscillation, the resolution of the photographed
image was approximately 0.06mm/pixel. The shutter
speed of the high-speed camera was set at 1/41 000s sothat the marker exposed to the image sensor would moveless than the resolution of the photographed image. The
configuration of the device used in this research allows a-1bearing revolution speed of 1 800 min .

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−Study on Measurement of Dynamic Performance of Ball Bearing for Auto-tensioner−

In order to verify the effectiveness of the ball position
correction method while the centers of the camera,
light and bearing were displaced away from the sameaxis, an experiment was conducted to confirm themeasurement accuracy in advance by using an XY
axis stage. This experiment system is shown in Fig. 9.
The relative positions of each bearing component do
not change, therefore the change in relative position ofeach component when the XY axis stage moved wasconsidered measurement error. The XY axis stage was
moved 10mm therefore it would be greater than the
maximum displacement after considering the central
axis displacement due to displacement when the camera,
light and bearing are set up, in addition to oscillation.
A dynamic performance measurement was performed
using an experimental device which simulated the actual
operating environment of an auto-tensioner. Figure 10
is a schematic diagram of the experiment device andthe auto-tensioner as a major component. The belt islooped on a drive pulley and an idler pulley and the autotensioner pulley pushes the belt via a spring, which inturn applies a fixed tension on the belt. The rotation of
the drive pulley passes via the belt to rotate the bearing’s
outer ring, which is attached to the auto-tensioner pulley.
By causing the rotation of the drive pulley to fluctuate, thebelt tension was changed and the auto-tension oscillation
reproduced. The bearing is subjected to a load from thebelt via the pulley. As shown in Fig. 10, the direction
receiving the belt load was made the datum (0 degree)
and the bearing rotating direction was considered theforward direction, while the ball rotating direction wasmade u. The main experimental conditions are shown in
Table 3. The difference in performance depending on thepresence/absence of oscillation was also considered bymeasuring a state without auto-tensioner oscillation while
not creating drive pulley rotational fluctuation.

CameraRing light

Bearing
XY axial stage

Fig. 9 Appearance of experimental system

Sample bearing
Auto-tensioner pulley

Auto-tensioner
Drive pulley
Oscillation

Rotating
direction

Idler pulley

Belt

u

Load zone

Belt

Belt load (u=0°)

Fig. 10 Schematic diagram of auto-tensioner

Table 3 Experimental conditions
Drive pulley rotating with oscillation

Yes, No

Initial tension of belt, N

900

Revolution speed of sample bearing, min−1

1 800

Photographing speed, frame/s

5 400

Photographing shutter speed, s

1/41 000

3. Experiment Results and Observations
3. 1 Measurement Accuracy

Table 1 Photographing conditions of experiments

Highspeed
cameraRing Light

Maximum photographing
speed, frame/s

675 000

Maximum shutter speed, s

1/2 700 000

Photographing resolution,pixel

1 024×1 024

Image scale, mm/pixel

About 0.06

Output power, W

250

Table 2 Specifications of sample bearing

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Bearing number

6304

Outer size, mm

52Cage material

Plastic

Number of balls, z

7

Figure 11 shows the measurement error for the pocketprong interval which expresses the amount of cage
pocket prong deformation, while Table 4 shows themeasurement error for the interval between the ball andthe cage marker, which is an indication of the lead andlag of the ball in relation to the cage. As can be seen from
Fig. 11, even if the XY axis stage carrying the bearing is
moved 10mm, the maximum measurement error for the
pocket prong interval was around 7 μm and the maximum
measurement error for the interval between the ball andthe cage marker was around 21 μ m. This equates toaround 3.9% of the pocket prong’s maximum deformation(180 μm). It also equates to around 7.4% of the maximum
clearance between the ball and the pocket (285 μm). The
subjects of measurement for the purpose of this research,
namely the cage pocket prong deformation and the leadand lag of the ball relative to the cage are relative values

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Outer ring

1 600
1 400
1 200
1 000
800

Measurement error, µm

0

180

360

540

720

Ball revolution angle u, deg.

Maximum variation of pocket prong

Fig. 12 Rotational speed of outer ring and cage, revolution
speed of ball

100
Distance between ball and cage

50

Ball

1 800

Maximun clearance between ball and cage pocket
150

Cage

2 000
Revolution speed, min−1

calculated from the distances between two points within
the bearing, therefore are not affected by oscillation of the
bearing overall or camera vibration. Consequently, it isfeasible that the measurement error for a bearing during
rotation is equal to the results of this experiment. This
demonstrates that the measurement method used in thisresearch is sufficiently accurate.

0−50

3. 3 Ball Lead and Lag

Pocket prong distance

−100
−150

0

2

4

6

8

10

Movement distance of stage, mm

Fig. 11 Confirmation of measurement accuracy

Table 4 Results of measurement accuracy
Item

Pocketprong
interval

Distance between
ball and cage marker

Maximum measurement
error, mm

0.007

0.021

Maximum variation of
pocket tongue interval, mm

0.18

−

Maximum clearance between
ball and cage pocket, mm

−

0.285

Error percentage, %

3.9

7.4

It can be ascertained from Fig. 12 that there is adifference in the rotational speed of the cage and therevolution speed of the ball. This means there is leadand lag of the ball relative to the cage. Figure 13 shows
one example of the ball lead and lag relative to the cage.
The median of the distance between the ball and cage
marker was made the point where there is neither lead
nor lag. If the ball lead and lag is a positive value, the ballmoves in front of the rotational direction relative to thecage, or in other words, takes the lead. Figure 13 showsthat in a non-load zone, the ball lead and lag is repeated
and the ball moves vigorously within the pocket. Thisis considered to be due to the bond between the balls
created by the inner ring and outer ring being weaker in
the non-load zone, therefore making the balls susceptible
to bearing oscillation. Meanwhile, it can be seen that theball lead and lag changes slowly in load zones.
Load zone

3. 2 Ball Revolution Slip
Figure 12 shows one example of the rotational
speeds of the outer ring and cage due to fluctuation indrive pulley rotation, and the revolution speed of theball. Figure 12 represents two revolutions of the ball.
Furthermore, the ball revolution speed is shown for only
one of the seven balls, while the cage rotational speed isan average calculated from the seven markers place atequal intervals. Figure 12 shows that, in contrast to theouter ring rotational speed, which is synchronized withthe drive pulley rotational speed and changes with eachrevolution, the cage rotational speed and ball revolution
speed fluctuate in sync with outer ring rotational speed
however because the ball revolution speed does notchange evenly it is predicted that the ball is slipping
relative to the outer ring.

JTEKT ENGINEERING JOURNAL English Edition No. 1014E (2017)Ball lead and lag, mm

0.3
Lead

0.2
0.1
0
−0.1
−0.2
−0.3

Lag
0

180

360

540

720

Ball revolution angle u, deg.

Fig. 13 Ball lead and lag (With oscillation)

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−Study on Measurement of Dynamic Performance of Ball Bearing for Auto-tensioner−

Figure 14 provides one example of measuring thedeformation of the pocket prong. The median of thepocket prong intervals was considered as having zerodeformation. A positive value means that the pocketprong is deforming in the direction that the prong opens.
It can be seen from Fig. 14 that, at most, pocket prong
deformation is around 0.18mm. It is also obvious thatpocket prongs deform frequently in non-load zones. Thisis predicted to be due to the ball colliding with the pocket
wall in non-load zones which can easily result in fatigue
failure of the cage. While the change is not as frequent
in load zones as it is in non-load zones, the maximum
deformation is equivalent. The stress acting on the pocket
can be predicted from pocket deformation and this isconsidered to contribute to elucidation of the cage failure
mechanisms and optimal design.

when there is no bearing oscillation. It can be seen from
Fig. 17 that, compared to cases such as Fig. 14 withbearing oscillation, no oscillation means that the pocketprong deformation is extremely small, with the maximum
amount being under 0.04mm. Therefore, it is clear thatbearing oscillation has a significant effect on the pocket
deformation.
0.5

0.25
Position y, mm

3. 4 Deformation of Cage Pocket

0

−0.25
−0.5
−0.5

0.25

0.5

Fig. 15 Movement of bearing center

0.2
Open

0.1

Load zone
0.3

0
−0.1

Close
0

180

360

540

720

Ball revolution angle u, deg.

Fig. 14 Deformation of pocket prong (With oscillation)

Ball lead ang lag, mm

Deformation of
pocket prong, mm

0Position x , mm

Load zone

−0.2

−0.25

Lead

0.2
0.1
0
−0.1
−0.2
−0.3

Lag
0

180

360

540

720

Ball revolution angle u, deg.

3. 5 Effect of Bearing Oscillation

44

Fig. 16 Ball lead and lag (Without oscillation)
Load zone
0.2
Deformation of
pocket prong , mm

The rotational fluctuation of the drive pulley passes
through the belt and pulley to be transmitted to thebearing outer ring and this causes the bearing to oscillate
as it rotates. Figure 15 shows one example of measuring
the trajectory of the bearing center (inner ring center).
The coordinate origin was made the average positionof the bearing center trajectory. Bearing oscillates
repeatedly while tracing an oval path in the opposite
direction to outer ring rotation. It is considered that thismovement causes inertia to work on the balls and cage,
and affect the ball lead and lag and cage deformation.
The frequency of the oval movement is consistent withthe rotational fluctuation frequency of the drive pulley.
In order to consider the difference in the ball lead andlag depending on the presence/absence of bearing
oscillation, Fig. 16 shows the ball lead and lag when
there is no rotational fluctuation, therefore no bearing
oscillation. This shows that, compared to cases such as
Fig. 13 when there is bearing oscillation, the change inthe ball lead and lag is slower. This demonstrates thatbearing oscillation has a significant effect on the ball leadand lag. Figure 17 shows the pocket prong deformation

Open
0.1
0
−0.1
−0.2

Close
0

180

360

540

720

Ball revolution angle u, deg.

Fig. 17 Deformation of pocket prong (Without oscillation)

4. Conclusion
This research has established a method to measure
the dynamic performance of a ball bearing by utilizing
a high-speed camera and image processing. Below are
the results obtained by using this method to examine aball bearing for auto-tensioner used in a car accessory
belt to consider the change over time of bearing dynamic

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−Study on Measurement of Dynamic Performance of Ball Bearing for Auto-tensioner−

performance.
(1) By utilizing the reflective light from the balls, it
was possible to measure the position of balls during
rotation, which was previously difficult to achievewith conventional measurement techniques.
(2) By tracking the positional fluctuation of the ball andouter ring markers, it was possible to measure thechanges over time in ball revolution speed and outerring rotational speed. In turn, this made it possible
to observe the slip of balls relative to the outer ring
quantitatively. If this measurement method is applied
to inner ring rotation, it would be possible to observe
the slip of balls relative to the inner ring quantitatively.
(3) By measuring the relative distance between the balland cage, it was possible to observe the lead and lag ofballs quantitatively, which reflects the ball movement
relative to the cage. An experiment showed notabledifference between movement trends in load zones
versus non-load zones. The bearing oscillation has
more effect in non-load zones, causing the lead andlag of balls to change frequently. This is considered toaffect the cage fatigue failure.
(4) Deformation of the cage pocket prong was calculated
by measuring the change in intervals between
pocket prongs. Therefore, it became possible topredict the stress acting on a pocket from pocketprong deformation. This is consdered to contributeto elucidation of the cage failure mechanisms andoptimal design.
(5) Bearing oscillation caused by rotational fluctuationof the drive pulley has a significant effect on the
bearing dynamic performance. With oscillation,
the deformation of the cage pocket prong increases
significantly. In addition, there is greater change in thelead and lag of balls relative to the cage.

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K. KAWAKITA: Measuring Method for ThreeDimensional Ball Motion in Ball-Bearings and SomeJTEKT ENGINEERING JOURNAL English Edition No. 1014E (2017)

A. NAKASE*

T. MIZUNO**

L. LOU****A n a l y s i s Tech n o l og y R & D D e p t . , R e s ea rch &Development Headquarters** P ro c e s s Te ch n o l og y R & D D e p t . , R e s e a rch &Development Headquarters*** A n a l y s i s Tech n o l og y R & D D e p t . , R e s ea rch &Development Headquarters, Doctor of Engineering

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