experimental research on cage dynamic characteristics of

Mechanics & Industry 20, 204 (2019)© AFM, EDP Sciences 2019https://doi.org/10.1051/meca/2019007

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Experimental research on cage dynamic characteristics of angularcontact ball bearingQingqing Li1, Xiaoyang Chen1,*, Tao Zhang1, Shijin Chen1, and Jiaming Gu2

1 Department of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, PR China2 Shanghai Tian An Bearing Co. Ltd, Shanghai 201108, PR China

* e-mail: x

Received: 7 August 2018 / Accepted: 25 January 2019

Abstract. The dynamic performance and life of the precise bearing, even abnormal operation and early failureare affected directly by the complex and unstable motion of the cage. Based on the cage dynamic performancetest device with controllable motion of inner and outer rings, respectively, the dynamic characteristics of thecage were studied under different rotating speeds and loads, while inner ring rotated with outer ring fixed andinner–outer rings rotated reversely. Then the trajectory of the cagemass center was drawn through experimentalstudy. The three-dimensional space motions of cage reveal that, when only inner ring rotates, the trajectories ofcage mass center are approximately circular under axial load, and the amplitude of the axial displacement raiseswith the increase of the rotation speeds. With the increase of radial loads, the cage mass center trajectories areshaking from a circle to a small area on the side of the bearing center. When the inner–outer rings rotate in theopposite direction, the rotation speed of the cage is greatly reduced, and the mass center trajectories of the cageoscillate irregularly on side of the bearing center. As the relative rotation speed of rings increases, the axialdisplacement fluctuation enlarges. With the increase of the radial loads, the axial fluctuation decreases.

Keywords: Angular contact ball bearings / dynamic characteristic / cage whirl / test rig

1 Introduction

With the development of aerospace and equipmentmanufacturing, angular contact ball bearings are theessential components of aero engines and precisionmachinetools, their accuracy, longevity, and reliability are criticalto the entire equipment. The cage is the main researchobject of the dynamic characteristics of the rolling bearing.The instability of the cage will cause the friction torque ofthe bearing to fluctuate, the friction and wear will beincreased, thus the whistling will occur, even the cage willbreak, which will cause bearing failure or spindle bearingjam and catastrophic consequences [1–3]. Since 1960s,people began to notice the dynamic performance of high-speed rolling bearings and mainly studied the stability ofthe cage.

Due to the special position of the cage in the bearing andthe transient nature of the force, the current motionanalysis is mainly based on a dynamic model. On the onehand, the equations of motion are established based on thegeometric structure and the motion relationship betweenthe bearings to obtain the movement law of the parts. On

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the other hand, a general dynamics analysis software isused to establish a model based on the parameters of thebearing, set the working conditions to analyze and solve,then the post-processing software is used to extract themotion characteristics of each part. Gupta [4–6] estab-lished a complete dynamics model of all bearing parts,which can simulate the transient motion characteristics ofbearing parts, in addition, ADORE, a dynamic analysisprogram for rolling bearings that considers factors such asgeometry, lubrication, cage structure, and materials, wasdeveloped, and the effect of load and speed on the masscenter movement of the cage was experimentally investi-gated to verify the simulation results of the ADOREprogram. Gentle and Pasdari [7] found that the frictionbetween the ball and the cage, the torque generated by thecage rotation, the temperature of the bearing, the lubricantcontent and viscosity, and the structural dimensions of thecage have an effect on the stability of the cage throughexperiments. Kingsbury [8,9] used the ratio of the angularvelocity of the cage mass center to the ball revolution speedas a criterion for determining the stability of the bearing,proposed the eddy model of the angular contact ballbearing, measured and identified different types of cagewhirling, and divided it into stability and instability.Stevens [10] studied the influence of the instability of the

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2 Q. Li et al.: Mechanics & Industry 20, 204 (2019)

angular contact ball bearing cage on the frictional torquethrough experiments about different lubricant and cagegeometrical parameters. Boesiger et al. [11] experimentallystudied the influencing factors of cage instability, andanalyzed the relationship between cage whirl frequencies.Makoto [12] analyzed the effects of working temperature,viscosity of lubricant, preload, rotational acceleration, andcage unbalance on the cage movement through tests, andstudied the vibration and movement of ceramic ballbearing cages for spindles of machine tools. Kazuo et al. [13]adopted a method of widening the test bearing cage toinstall sensors in the axial and radial directions to measurethe trajectory of the cage. The influence of the vibrationand lubrication parameters of the cage on the cage whirlingwas studied. The test scheme requires complicatedinstallation of the sensor and requires additional changingthe cage structure. Huang [14] proposed to record the radialvibration of the cage by using two laser sensors, andintroduced the orbits of cage mass center. But its test speedwas low and changed the outer ring by cutting grooves.Wen et al. [15] and Han et al. [16] developed cage dynamicperformance testing machines for different bearing sizesand operating conditions, and studied the effects of load,speed, and cage unbalance mass on cage center motion.Abele et al. [17] and Yang et al. [18] used high-speedcameras to continuously take pictures of running bearings.According to the marker points on the cage, the rotationalspeed and centroid trajectory of the cage can be obtainedthrough image processing algorithms. Palladino et al. [19]used the same photographic method to analyze the effect ofdifferent clearance ratios and axial forces on the stability ofthe cage. This method can accurately measure themovement of the cage in the radial plane without makingany changes to the cage, but only measure the radialmotions of the cage at the same time.

In summary, because of the complex movement of thebearing cage in space, its motion measurement is difficult,the existing research on the dynamic characteristics ofthe cage mainly focuses on the dynamic model of the cage,the failure mode, and the centroid trajectory. Due to thelimitation of motor or spindle speed and samplingfrequency of the displacement sensor, the rotational speedof the tested bearing cannot be higher, and the radialdisplacement measurement of the cage needs to changethe bearing structure, while there are few experimentalstudies on the non-contact measurement of the dynamicperformance of the cage without changing the bearingstructure.

Therefore, in view of the deficiencies of the current cagedynamic characteristics testing machine, a new type ofhigh-speed angular contact ball bearing cage dynamicperformance test rig is developed by our research group, therotational speed of the inner and outer rings of the bearingare controlled by two motors, at the same time, therotational speed of the cage is reduced by the inner–outerrings rotated reversely, and the axial and radial displace-ments of the cage are simultaneously measured by thevertically arranged laser line displacement sensors, then acentroid trajectory of the cage is drawn, thereby theresearch on cage dynamic characteristics can be realized byusing the experiment apparatus.

2 Experimental rig and method

2.1 Test rig

A test rig is specially developed to measure the cagedynamic characteristics of a ball bearing in threedimensions, and different conditions are analyzed, suchas the rotation speed, external radial load, and the rotatedring.

The bearing test rig is shown in Figure 1, the testbearing’s gravity is along the axial direction, whichconsists the drive, transmission, load device, andmeasuring mechanisms. One motor is connected to theinner ring of the bearing through the shaft 1 andcoupling, the other motor drives the outer ring of thetested bearing through the shaft 2, the friction wheel 2and loading wheel. The loading wheel and the frictionwheel 1 installed in the outer ring of the test bearing formfriction drive system, the radial load is applied to thebearing by the friction wheel 1, which is pressed by thespring and is arranged in a triangle shape in Figure 2.The tested bearing is an angular contact ball bearingmounted in pairs and the axial load is adjusted throughthe spacers. Located at the outer end of the test bearing,perpendicular laser sensors applied to measure the axialand radial displacements of the cage center as shown inFigure 2. During the test, by adjusting the rotation speedof two motors, on the one hand, the inner and outer ringsof the tested bearing can be rotated in the reversedirection to obtain higher relative rotation speeds,meanwhile, the rotating speed of the cage reducedgreatly and can be measured more easily; on the otherhand, it is also possible to fix one ring and rotate theother ring to study the motion characteristics of thecage. Without modification of the bearing, the cagemovements in three dimensions are measured simulta-neously.

2.2 The calibration and measurement of test

During assembling, to make sure the motor and bearinghouse are mounted on the same base, the dial gauge is usedto test the radial variation when the drive shaft rotates.The centering of the drive shaft and the spindle is fine-tuned through the set screws. This ensures that the axis ofthe motor spindle is aligned with the axis of the bearingsupport. It is also necessary to ensure that there is nodeviation between the two bearings axes and the frictionwheel so as to achieve stable transmission motion. The axisof the two mutually perpendicular laser line displacementsensors in the measuring device is aligned with the axis ofthe tested bearing so as to measure the axial and radialdisplacement of the cage at different positions of the testedbearing.

LJ-G015K, the trigger interval is 3.8ms, the effectiveaxial displacement is 15±2.3mm, and the effective rangeof the laser line is equally distributed 800 points of invalidand effective points, with an interval of 0.01mm, axialrepetitive accuracy is 0.2 and 2.5 mm in radial. Under theeffective axial distance, the data on the laser line changed

Fig. 2. Loading and measurement method.

Fig. 1. Bearing test rig.

Q. Li et al.: Mechanics & Industry 20, 204 (2019) 3

with the motion of measured subject, as the number ofinvalid and effective data collected by the software on thecomputer, thus the displacement can be obtained fromdata extraction.

In order to record the movement of the cage effectively,so adjusting the position of the laser sensors to ensure thatthemovement of the cage is within the effective range of thesensors. Therefore, based on the cage outer diameter and as

the reference, the effective measurement boundary of thesensor is larger than the cage outer diameter by 2–3mm.And the intersection of two laser lines is collinear withbearing center line.

In addition, for the calibration of the laser sensors, twoperpendicular laser lines are irradiated on the cage shownin Figure 2a. Changing the position of the cage fromposition 1 to 2 in Figure 3: move 0.618mm vertically and

Fig. 3. 3D measurement method and calibration of the laser sensor.

Table 1. Geometrical parameters of an angular contact ball bearing 7220C.

Parameters Value Parameters Value

Ball diameter 25.4 mm Cage inner diameter 128 mmBearing outside diameter 180 mm Cage outer diameter 145 mmBearing inside diameter 100 mm Pocket clearance 0.6 mmInitial contact angle 15 deg Cage width 31 mmInner curvature radius 13.210 mm Number of balls 14Outer curvature radius 13.221 mm Cage guiding land diametric clearance 2 mm

Table 2. Experimental conditions.

Rotated ring Speed (r/min) Radial load (N)

1st IRR 500�2000 0�1502nd IOR 500�2000 0�150


1.38mm horizontally. Set position 1 as the reference andrecord it, extracting and calculating the number of invaliddata of position 1(N1) and 2(N2). It turned out that0.605mm from XZ1 to XZ2 in axial, and 1.34mm from d1 tod2 in radial. The same way of calibration to another sensor.From the data, it can also be seen that the error betweenthe actual calibration data and the software display data islittle for the test bearing.

With two sensors arranged vertically, the radial motioncan be collected. One collects the axial (XZ) and verticalradial displacement (Z), the other collects the axial (XY)and horizontal radial displacement (Y), axial motionadopts the average value recorded by the sensors, so thelaser sensors can effectively record the three-dimensionalmotions of the cage center at the same time.

3 Experimental condition and bearingspecimen

This experiment adopts the laser line displacement sensorfor data acquisition, taking into account the size and

installation position of the sensor itself, angular contactball bearings 7220C are designed as test bearing. Thegeometrical parameters are listed in Table 1. In addition,the cage is made of cloth Bakelite, the inner, outer ring, andball material is GCr15 high temperature bearing steel. Thecage is inner ring guidance, and axial preload 100N isapplied by the adjusting spacer. In order to analyze thecage characteristics under different conditions and providecontrast, the study mainly focused on the cage mass centermotion under different cases of the inner ring rotated withfixed outer ring (IRR) and inner and outer rings rotatedreversely (IOR), as shown in Table 2.

4 Results and analysis

The movement of the cage mass center is affected by therotating speed, load and the impact of collision and frictionwith the ring and the rolling element. Therefore, the effectof the rotation speed and the external radial load on cagemass center whirl motion is studied. The Y and Zdisplacements represent the displacement of the cage masscenter in the radial plane, respectively, and the Xdisplacement is the axial motion, as shown in Figure 2.

4.1 Inner ring rotated with outer ring fixed

The trajectories of the cage mass center and axial motiondisplacements in the first case listed in Table 2 areillustrated in Figures 4 and 5.

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mecal psidZ

ni=500r/min

-1 0 1

-1

0

1

Y displacement (mm))

mm(

tnemecalpsid

Z

ni=500r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mecalpsidZ

ni=500r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

meca lps idZ

ni=1000r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mecalpsidZ

ni=1000r/min

-1 0 1

-1

0

1


mm(

tnemecalpsi d

Z

ni=1000r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mecal psidZ

ni=2000r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mecalpsidZ

ni=2000r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mec alp sidZ

ni=2000r/min

Fr = 0 N Fr = 50 N Fr = 150 N

Fig. 4. The trajectories of cage mass center under different radial loads.


When the condition is inner ring rotated with fixedouter ring, the trajectories of the cage mass center areillustrated in Figure 4 and axial motion in Figure 5, inwhich the rotating speeds are 500 (ni = 500, no=0) r/min,1000 (ni = 1000, no=0) r/min, and 2000 (ni = 2000, no=0)r/min under different radial loads, ni and no are therotation speed of inner and outer rings, respectively, andprocessing the axial motion into difference betweenXmax,Xmin and standard deviation. It is shown that thetrajectories of the cage mass center are similar to a circle,and the whirl radius of the cage motions is equal to the

guiding radius clearance. On increasing the rotatingspeeds, given that the limitation of the samplingfrequency of the laser sensor, the data collected in onerevolution of the cage are reduced to form a polygonalcentroid trajectory, and the axial movement amplitude isincreased from 0.2755mm in 500 r/min to 0.4455mm in2000 r/min under axial load. The test bearing is innerrace guidance, higher rotating speeds of inner ring bringout greater speed of cage, the centrifugal force of the cageincreased under the rotation motion, larger interactionforces such as contact and collision interaction between

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

ni=500r/min

dis

pla

cem

ent(

mm

)X

Time(s)

Xmax- Xmin= 0.2755mm

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

ni=500r/min


dis

pla

cem

ent(

mm

)X

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

ni=500r/min


dis

pla

cem

ent(

mm

)X

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3

0.4Xmax- Xmin= 0.322mm

ni=1000r/min

dis

pla

cem

ent(

mm

)X

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

ni=1000r/min


dis

pla

cem

ent(

mm

)X

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

ni=1000r/min


dis

pla

cem

ent(

mm

)X

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


ni=2000r/min

dis

pla

cem

ent(

mm

)X

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

ni=2000r/min


dis

pla

cem

ent(

mm

)X

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

ni=2000r/min


dis

pla

cem

ent(

mm

)X

Time(s)

Fr = 0 N Fr = 50 N Fr = 150 N

Fig. 5. The axial displacements of cage mass center under different radial loads.


cage and balls and between cage and inner ring generate,so the range by cage center area of whirl trajectories andthe fluctuation by difference of axial displacementenlarged.

Indicating that the increment of radial loads can bringtrajectories of cage mass center from regular to irregular,and the whirl radii of cage motions are diminished to form

the patterns at one side of the bearing center, which isconsistent with the experimental investigation in Wenet al. [15], and it is also consistent with observation that thecage is biased to one side during the test, and the variationof axial fluctuation range is smaller. As is known that theincreasing external radial loads can make the contact loadsbetween balls and rings become unevenly distributed,

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mec alp sidZ

n=622 r/minni=378 r/min, no= -244 r/min

-1 0 1

-1

0

1


mm(

tnemec alpsi d

Z

n=614r/minni=357r/min, no= -257r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

meca lpsi dZ

n=617 r/min ni=359 r/min, no= -258 r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mecal ps idZ

n=1004 r/minni=590 r/min, no= -414 r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tnemecalp sid

Z


-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

meca lpsidZ


-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mec alpsidZ

n=1835r/minni=1092r/min, no= -743 r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mecalp sidZ

n=2007r/minni=1175 r/min, no= -832 r/min

-1 0 1

-1

0

1

Y displacement (mm)

)m

m(tne

mecalpsidZ


Fr = 0 N Fr = 50 N Fr = 150 N

Fig. 6. The trajectories of cage mass center under different radial loads.


uneven load distribution will differentiate the tractionforces of balls, to which lead the speed fluctuation of balls.On accounting of the speed of balls vary constantly, thefrequency of collision between the cage pocket and balls willenhance, the resultant force of cage changes over and overagain at the same time. It brings out the complicated andirregular whirl trajectories and the decrease of whirl radii ofcage motion.

4.2 Inner and outer rings rotated in opposite direction

The trajectories of the cage mass center and axial motiondisplacements in the second case listed in Table 2 areillustrated in Figures 6 and 7.

When the condition is inner and outer rings rotatedreversely, the trajectories of the cage mass center areshowed in Figure 6 and axial motion in Figure 7,

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=622r/min

)m

m(tne

mecalps i

dX

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=614r/min

)m

m(tne

mecalpsi

dX

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=617r/min

)m

m(tne

mec alps i

dX

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=1004r/min

)m

m(tne

mecalps i

dX

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=1014r/min

)m

m(tne

mecalp si

dX

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=1002r/min)

mm(t

nemec al

psid

X

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=1835r/min

)m

m(tne

meca lp si

dX

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=2007r/min

)m

m(tne

mecalpsi

dX

Time(s)

0 1 2 3 4-0.2

-0.1

0.0

0.1

0.2

0.3


n=2004r/min

)m

m(tne

mec alp s i

dX

Time(s)

Fr = 0 N Fr = 50 N Fr = 150 N

Fig. 7. The axial displacements of cage mass center under different radial loads.


which the actual measured relative rotating speeds (n)are marked in the picture under different radial loads,respectively. On accounting of revolution speed of cage ismostly decreased, the whirl trajectories of cage presentcomplicated patterns, which appeared swaying aroundone side of the bearing center, and with the increase ofrotation speeds, the interaction forces between cage andballs got enhanced, the axial displacement fluctuation

become large from the difference between Xmax and Xmin,about 0.143, 0.1485, and 0.2305mm under differentspeeds.

With the external radial loads increasing, the change ofcagemass center trajectories is not obvious. Due to the cagespeed reduced greatly, the resultant force on cage is small,the axial displacement fluctuates little until the higherrotation speed.

0 500 1000 1500 2000 25000.00

0.02

0.04

0.06

0.08

0.10S

tandar

d d

evia

tion

Rotation speed (r/min)

—— IRR

—— IOR

Fig. 8. The standard deviation of axial displacement in axialload.


Comparing the two conditions under three times tests,the whirl trajectories of the cage mass center vary fromwell-defined to irregular under two conditions, which onlyinner ring rotated with outer ring fixed, inner and outerrings rotated in opposite direction. By calculating thestandard deviation of axial displacement in axial loadunder different speeds of three times test work respectivelyand then fitting the standard deviation in curve, it is shownin Figure 8, the cage fluctuation in IRR is larger than thatin IOR. Because of the frequent collision between the cageand the guided ring and the frequent interaction betweenthe cage pockets and the balls, a circular centroidtrajectory is easily formed when the cage is properly highspeed. Correspondingly, the cage rotation speed is greatlyreduced to zero under the opposite direction of inner andouter rings, the revolution speed of the balls is significantlyreduced similarly, so the impact between the cage and theballs is weakened. And the cage pocket clearance is lessthan the guiding clearance, the resultant force of thecage reduces and the friction force with the ball isthe main resource, thus the cage forms a disorderedmovement pattern, and the axial displacement of the cageis smaller.

5 Conclusion

Through adequate and extensive experimental workson the bearing cage test rig, the dynamic characteristicsof cage in three dimensions with rotated inner ring–fixed outer ring (IRR) and inner–outer rings rotatedreversely (IOR) under different speeds and externalradial loads are investigated, and the conclusions aredrawn as follows:
(1) The scheme of cage dynamic characteristics in bearing
cage test rig is feasible, without modification in the testbearing, the cage motion in three-dimensional spacecan be measured by two laser sensors in verticallyarrangement.

(2)
Under axial load, a regular circle whirl trajectory isformed at the IRR condition, the cage will keep a
constant speed, and the whirl radii are equal to thecage-ring guiding radius clearance. An irregularpattern on the side of bearing center is exhibited atthe IOR condition, the cage rotation speed is closed tozero.

(3)
For only inner ring rotated (IRR), the increase in therotating speeds makes the trajectories of cage masscenter more regular and enlarges the axial motionrange; on increasing the external radial loads, thetrajectories of cage mass center transform from regularcircle patterns to irregular ones that shake on the side ofthe bearing center.
(4)
For the case of IOR, the cage mass center trajectoriesare less changed by rotational speeds and radial loads.The increasing relative rotating speeds make the axialdisplacement fluctuation enlarged; with the incrementof external radial loads, the axial fluctuation dimin-ished.
Acknowledgments. This work was carried out with financialsupport from the National twelfth five-year project of China forscience and technology under Contract D.50-0109-15-001.

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Cite this article as: Q. Li, X. Chen, T. Zhang, S. Chen, J. Gu, Experimental research on cage dynamic characteristics of angularcontact ball bearing, Mechanics & Industry 20, 204 (2019)

experimental research on cage dynamic characteristics of

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