ASME Vibration Analysis Bearing

8/6/2019 ASME Vibration Analysis Bearing

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Brian T. Holm-HansenResearch Assistant,

Student Mem. ASME

Robert X. GaoAssociate Professor,

Mem. ASME,

e-mail: [email protected]

Department of Mechanicaland Industrial Engineering,

University of Massachusetts,

Amherst, MA 01003

Vibration Analysis of aSensor-Integrated Ball BearingThis paper presents an analysis of the vibrational behavior of a deep groove ball bearingwith a structurally integrated force sensor. The miniaturized force sensor, accommodatedwithin a slot on the bearings outer ring, provides on-line condition monitoring capabilityto the bearing. Analytical and finite element models were developed to predict the sensor

output due to bearing dynamic load and rotational speed variations. Experimental studieswere conducted on a ball bearing to validate the analytical and numerical solutions.Good agreement was found between the model-predicted sensor outputs and the experi-mental results. The findings validated the approach of integrated-sensing for on-linebearing condition monitoring. S0739-37170000203-8

Introduction

Rolling element bearings are widely used as low friction joints

between rotating machine components. Since the rotational mo-

tion is often a significant function of the overall system, such as

wheels on a train, rollers in a paper mill, or a rotor on a helicopter,

proper functioning of a bearing over its designed life cycle is of

vital importance to ensure product quality, prevent machine dam-age or even loss of human life 1. However, because of faultyinstallation, inappropriate lubrication, overloading, and other un-

predictable adverse conditions, premature and sudden failures of

individual bearings often occur in real-world applications 2,3.For improved bearing health and safety monitoring, the research

community has been investigating a wide range of topics related

to bearing structural design, dynamics, tribology, fault detection,

identification, and signal processing techniques 4 7. Varioussensing and measurement technologies have been developed for

improved monitoring of bearing operational parameters. Typical

representatives include acoustic emission meters, fiber optic moni-

tors, and vibration spectrum analyzers 810. To measure bear-ing vibrations, eddy current-based displacement sensors have been

developed that can be mounted through or to the side of a bearing

cap to monitor radial or axial shaft motion with respect to thebearing 11. Other types of bearing vibration sensors make use ofvelocity, acceleration, temperature, or spectral energy information

1216. While these efforts have considerably advanced thestate-of-the-art of bearing condition monitoring, few of them have

been widely used for practical, on-line applications. The need for

an effective, reliable, and on-line bearing fault detection technique

is evidenced by an emergency Airworthiness Directive AD re-cently issued by the Federal Aviation Administration FAA, re-quiring visual inspections to detect and replace faulty bearings

on several Boeing 777 aircraft engines 2. This situation clearlyindicates the need for developing an integrated bearing condition

monitoring and self-diagnostic technique for on-line, in-process

applications.

A new technique has been developed that involves the direct

structural integration of sensing elements e.g., force, temperature,and acoustic emission sensors and telemetric data communicationelectronics into the bearing environment to provide self-

diagnostic capabilities 17,18. During bearing operation, thesensing elements continuously measure the real-time fluctuationsof the bearing load variations. If predetermined threshold valuesrepresenting critical bearing operational parameters are exceeded,

an alarm signal will be triggered which is then transmitted out ofthe integrated sensor by a wireless link to the machine control

system for corresponding actions. The major advantage of thistechnique over the previous efforts is the close vicinity of the faultdetection mechanism to the fault source. The resulting shortersignal transmission path leads to quicker fault localization. In ad-dition, the sensors will be less vulnerable to background noise anddistortion of fault characteristics. The advancement of miniatur-ization technologies in recent years, including hybrid, surface

mount, and MEMS microelectromechanical systems technolo-gies, has made it possible to design and package a millimeter-sized sensor module and have it embedded directly into the outerring of a bearing. Complemented by wireless data communicationand advanced signal processing techniques such as wavelet19,20 and neural-fuzzy logic 21, the miniaturized sensor mod-ule can be functionally expanded to a telemetric probe that notonly enables on-line bearing condition monitoring, but is also ap-plicable for the diagnosis and prognosis of other manufacturingequipment and systems.

To accommodate the sensor module within the bearing struc-ture, the outer ring of the bearing needs to be modified. The stress-strain relationship and structural implications of such a modifica-tion have been studied to provide a design framework 22. Ofequal importance are the dynamic implications associated with the

sensor integration. Since a bearings vibrational characteristics areaffected by its structural modifications, the dynamic response un-der varying loads and rotational speeds needs to be analyzed andexperimentally verified. This study, together with the bearingstructural analysis, provides guidelines for the design and imple-

Contributed by the Manufacturing Engineering Division for publication in the

JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 1998; re-

vised January 2000. Associate Technical Editor. K. W. Wang. Fig. 1 A sensor-integrated smart ball bearing

384 Vol. 122, OCTOBER 2000 Copyright 2000 by ASME Transactions of the ASME


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mentation of a sensor-integrated smart bearing that is capableof monitoring and assessing its own health condition during op-eration. A schematic of such a smart bearing is shown in Fig. 1, inwhich the boundary conditions for the bearing structure are alsoillustrated. These conditions will be used in this paper to present avibration analysis of an outer ring-modified ball bearing.

Structural Defect-Induced Vibration

In this section, the form of a defect signal is discussed. Severalmathematical expressions related to the mechanics of rolling ele-ment bearings are introduced. These expressions are of fundamen-tal importance to the development of a bearing vibration model.While a conventional condition monitoring system is essentially aseparated data recorder and analyzer, the integrated sensor modulestudied here is an integral part of the modified bearing structure.

An analytical model for predicting the vibration spectrum of aconventional rolling element bearing having a point defect on itsinner ring was developed by 23. This model was experimentallyverified by NASA researchers using nonlinear signal analysistechniques 24. For the analysis, the defect frequency of a bear-ing fd is defined as the frequency at which the rolling elementsimpact a structural defect on the ring surface race-way. At eachimpact, an impulsive input is applied to the bearing structure. Themagnitude of the input is proportional to the load carried by the

rolling elements, which is a function of the geometry of the bear-ing. For the presented study, a commercially available deepgroove ball bearing model 6220 was analyzed. Relevant geom-etry and dimensions are shown in Fig. 2.

Generally, the load distribution on a rolling element bearing,shown schematically in Fig. 3, is given by:

qqmax 1 12 1cos

n

for ll

0 elsewhere

(1)

where qmax represents the maximum load and is the load distri-bution factor 25. In a bearing with nominal diametral clearance,qmax can be approximated by:

qmax5Fr

Z cos (2)

where Fr is the applied radial load, Z is the number of rollingelements, and is the mounted contact angle variations in clear-ance and load are discussed later. The value of the exponent n inEq. 1 depends on the type of bearings involved. For roller bear-ings, n3/2 and for ball bearings, n10/9. The load distribution

limiting angle l in Eq. 1 is a function of the load distributionfactor . If a bearing has positive diametral clearance, meaningthat the diameter of the rolling elements does not exceed the spacebetween the inner and outer rings, then 00.5 and 0l90 deg. Here the angle l is given by:

lcos1 12 (3)

To make the present analysis independent of the radial load, Eq.1 was normalized:

q nq

qmax(4)

Assuming that the outer ring of the bearing is fixed as illustratedin Fig. 1 and the inner ring rotates at a frequency fi , as is seen inmany applications, then the frequency fd at which an inner ring

defect passes over a rolling element can be determined by:

fdfi

2 1 Z (5)

where db cos /dm is dependent on the bearing geometry, andZ is the number of rolling elements. An evaluation of eight dif-ferent deep groove ball bearings with bore diameters in the rangeof 75mmd110 mm has shown that the ratio fd /fi , given byEq. 5, is approximately equal to a constant of six. Therefore, fora bearing whose outer ring is fixed, a defect on the inner ringsurface would pass over a rolling element at about six times theshaft rotation frequency. For the presented study, the outer ring of

Fig. 2 Geometry and dimensions of a deep groove ball bear-ing

Fig. 3 Load distribution in a radially loaded ball bearing

Journal of Vibration and Acoustics OCTOBER 2000, Vol. 122 385


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a type 6220 ball bearing whose geometrical parameters are shownin Fig. 2, was structurally modified 26. Since the bore of thisbearing is 100 mm, the analysis presented is applicable to variousdeep groove ball bearings with a bore diameter in the range of75mmd110 mm. Using the given parameters, the ratio ofbearing defect frequency fd to bearing rotational frequency fi iscalculated as fd /fi5.86 from Eq. 5, and l84 deg from Eq.3. While a rolling element would pass over a point defect on the

inner ring approximately 6 times for each inner ring revolutionassuming a fixed outer ring, a defect impulse occurs only whenthe rolling element and defect collide within the load zone i.e.,when ll. This means that the number of defect im-pulses per inner ring revolution can be approximated by:

Ni l180 fd

fi (6)

From Eq. 6, the test bearing will experience Ni3 defect im-pulses per revolution. Since the maximum load q max occurs at 0, as shown in Fig. 3, an impact between a rolling element andan inner ring defect at this location will produce a large impulseand accordingly, a large sensor output. Impacts occurring at

0 will produce smaller sensor outputs. This is demonstrated bythe simulated sensor output s( t) in Fig. 4, which shows the bear-ing response to scaled defect impulses over 7 inner ring revolu-tions note that the effect of lubrication is not considered in thepresented analysis. The large sensor output shown at t0 iscaused by an impact at 0. The variation in magnitude of theimpulses over successive bearing rotations is caused by the factthat one rotation of the inner ring does not necessarily advance therolling elements by an integer multiple of 2/Z. The angle be-tween impacts d is determined by the product of the rate atwhich the inner ring rotates (2fi), as well as the period betweenimpacts i.e., 1/fd , with fd given by Eq. 5, which in turn isrelated to the geometry of the bearing. Specifically, the resultingangle between impacts is given by d2/Z2/1 . For thebearing analyzed, 7 revolutions of the inner ring are required be-

fore the group of impulses is repeated i.e., before another impactoccurs at 0. The resulting vibration spectrum S(f ), as shownin Fig. 5, is a series of pulses occurring at integer multiples of fi .The pulses vary in magnitude with local maxima at integer mul-tiples of fd . The main lobes of the spectrum are located at n fd(n0,1,2, . . . ). As discussed previously, for an inner ringfrequency of fi1.0 Hz i.e., 60 rpm bearing rotational speed andusing Eq. 5, the defect frequency is fd5.86 Hz. Since the ratiofd /fi is constant for deep groove ball bearings with a bore in therange of 75 to 110 mm, each bearing in this dimensional rangewould have a vibration spectrum similar to that shown Fig. 5.Therefore, Fig. 5 presents a predicted, theoretical vibration spec-trum for ball bearings within the specified range, each having an

inner ring defect. Collectively, Figs. 4 and 5 present the antici-pated defect signals in the time and frequency domains that theintegrated sensor module must detect.

The above-presented analysis was based on a deep groove ballbearing with positive diametral clearance and a radial load. Theseassumptions were used to determine the magnitude and timing ofimpacts between a defect and the rolling elements. A change indiametral clearance would change the domain and range of theload distribution, and hence the magnitude of the impacts. How-

ever, the basic pattern of defect signal would remain the same.This is because the basic mechanism behind a defect signal re-mains the same: it is a sequence of impacts caused by an irregu-larity on the rolling element/raceway interface. This mechanism ispresent, even when the defect is located on a rolling elementinstead of on the raceway. It further applies to the situation whenan axial load is added to the loading condition, although the spe-cifics of the defect signal shape will vary. Furthermore, changingfrom a ball bearing to a roller bearing would not change the basicshape of a defect signal, as Eq. 1 applies to both roller and ballbearings.

Structural Model of the Outer Ring

To monitor load and vibration within the bearing structure, apiezoelectric sensor is embedded into a slot cut through the outerring. The sensor has solid contact with both the top of the slot andthe bearing housing. Each time a rolling element passes over theslot, the sensor generates an electrical charge output that is pro-portional to the load applied to the bearing, Fr . Since the outerring is structurally supported by the bearing housing, it can beassumed to be rigid. The piezoelectric sensor can be modeled as aspring with a stiffness constant k that is related to its materialcomposition. As shown in Fig. 6, the section of the bearing outerring where the slot is cut can be modeled as a beam of varyingcross-section, with a spring support at the midpoint. To establishthe structural model, boundary conditions must first be assigned.Since the ends of the beam are solidly connected to the surround-ing bearing structure, which is directly supported by a rigid hous-ing, clamped boundary conditions are considered appropriate.This model is shown in Fig. 7. Furthermore, the segment of the

ring encompassed by the slot subtends an angle of 2 sin1(L/D)2max12 deg. The difference in ring thickness between thecenter and the end of the slot is determined by:

1

2 dmdb dmdb

2L2 (7)

Using the parameters given in Fig. 2, the difference in ring thick-ness was calculated to be 0.55 mm. Since max6 deg is themaximum angle at which the bearing load q() is applied, andthe thickness difference is less than 18 percent of the thinnestsection of the ring calculated as (D2hdmdb)/23.2 mm), the modified section of the outer ring can be simpli-

Fig. 4 Bearing response to defect impulses over 7 revolutionsof the inner ring

Fig. 5 Frequency spectrum of the bearing vibration due to aninner ring defect

386 Vol. 122, OCTOBER 2000 Transactions of the ASME


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fied to that of a beam with a constant cross-section and a verticallyapplied load, as shown in Fig. 8. The bearing load q() is deter-mined by Eq. 1, and the location a where the load is applied isrelated to by the expression:

a1

2 dmdbsin (8)

When aL /2, the deflection of the sensor is given by:

caL/2

4qa 2 4a3L

192EIkL 3(9)

where E is the elastic modulus of the outer ring material, I is the

area moment of inertia of the cross-section of the modified ring,and kY33A/l is the stiffness of the piezoelectric sensor. Thecross-sectional area of the sensor is defined as A, the height is l,and the elastic modulus of the piezoelectric material is Y33 .

When aL /2, the sensor deflection is given by:

caL/2

4qLa 2L4a

192EIkL 3(10)

This translates into a load on the sensor as:

Rs33Ac

l(11)

As a result, the electrical charge produced by the sensor is:

Qd33Rs (12)

where d33 is the charge constant of the piezoelectric material.Using a charge amplifier with a gain G, the voltage output pro-duced by the embedded sensor is:

VGQGd33Y33Ac

l

(13)

This voltage output is then a direct measure of the outer ringdeflection due to a specific bearing load. Conversely, from thesensor voltage output, the load applied to the bearing can be de-termined to identify overloading conditions. Thus, the embeddedsensor module can be used in principle for both diagnostic andprognostic purposes.

For an inner ring frequency of fi11.7 Hz corresponding to abearing speed of 700 rpm, Eq. 13 produces the results as plottedin Fig. 9. Each pulse represents a rolling element passing overthe sensor module. The width of each pulse is determined by the

Fig. 6 Loads on the modified section of the outer ring

Fig. 7 Model of the modified bearing outer ring Fig. 8 Simplified model of the bearing outer ring



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length of the slot, i.e., the length of the beam in Fig. 8. Thesepulses are relatively long in duration when compared to thosecaused by a bearing structural defect, as shown in Fig. 4. The highfrequency nature of the defect-induced signals is characteristic indistinguishing them from normal load pulses caused by the

rolling elements passing over the sensor module.If the curvature of the modified bearing outer ring is not ne-

glected for the analysis, then the moment of inertia of the outerring cross-section at each individual location is a function of therolling element position a. The thinnest and thickest sections ofthe modified outer ring shown in Fig. 10 are determined as:

h1D

2h dmdb

2

4a 2 (14)

and

h 2D

2hD 1

2

4a2 (15)

Upon analysis of the outer ring geometry, the moment of inertia of

the cross-section where the slot is cut, is derived as:

lx1

3wh 2

32w g h2h 1 516

2

3h22 23

8h 1h2 16 h 12

(16)

where h1 and h 2 are given by Eqs. 14 and 15, respectively.The centroid of the cross-section is located at:

y c3wh 2

2wg h 2h1 34 h 24h 1

6wh 23wg h 2h1. (17)

and the area of the cross-section is:

Acwh 21

2wg h 2h1, (18)

The moment of inertia about the centroid is then:

l 013

wh 232wg h 2h1 5

16

23 h22 23

8 h1h2

16h1

2wh 2 12 w g h2h 1y c2 (19)

where y c is given by Eq. 17.Assuming that the curvature of the nonprismatic beam shown in

Fig. 7 is determined by the moment of inertia and bending mo-ment at a, then

d2y

da 2

1

E

M a

Io a (20)

where a is a function of as given in Eq. 8. The slope anddeflection are then given by:

a dy

da

1

E0a M a

Io a daC1 (21)

y a 0

a

a daC2 (22)

where C1 and C2 are constants of integration determined by theboundary conditions. With the moment of inertia Io given by Eq.19 and h1 , h2 and y c given by Eqs. 14, 15 and 17, respec-tively, the outer ring structural model becomes mathematicallyquite complex the problem is statically indeterminate when com-pared to the simple model given by Eq. 13. To reduce the com-putational load while maintaining the specific features of the bear-ing structure, a finite element FE model was developed tocalculate the outer ring deflection y (a) and slope (a).

Finite Element Model of the Outer Ring

Technically, the complete bearing structure can be modeled us-ing a complex three-dimensional finite element model. However,by observing the nature of the boundary conditions and loads onthe outer ring, it was determined that the FE modeling processcould be greatly simplified by making use of the symmetry of thesystem. With respect to the boundary conditions, the surfaces ofthe bearings outer ring are fixed as indicated in Fig. 1. The loadson the bearing structure are applied to the outer ring through smallellipsoidal contact areas between the rolling elements and theouter ring groove. Assuming a pure radial load, the maximum of

Fig. 9 Sensor output predicted by the simplified model

Fig. 10 Cross-section of the modified outer ring



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the resulting Hertzian stress distribution is located at the base ofthe outer ring groove. Since this stress distribution is symmetricabout the plane which divides the outer ring through the base ofthe groove, the strain normal to this plane, x , is zero. Takingadvantage of this feature, the FE model was constructed usingfour-node quadrilateral plane strain elements. A diagram of thistype of element is shown in Fig. 11. The shape functions are:

u1

4 u l 1s 1tuJ 1s 1tuK 1s 1t

uL 1s 1tu 1 1s2 u2 1t

2 (23)

and

v

1

4v l 1s 1tvJ 1s 1tvK 1s 1t

vL 1s 1tv1 1s2v2 1t

2 (24)

where u and v are the displacements along the z and y directions,

respectively. Shown in Fig. 12 is the mesh of plane-strain ele-

ments used to model the bearing. For the steel outer ring, struc-tural elements were used. Considering the electro-mechanical in-teraction associated with the piezoelectric sensor, coupled-fieldelements were used for sensor output analysis. The constitutiveequations for the piezoceramic material are:

TD C e

e T SE (25)

where T is a stress vector, D is an electric flux density vector, C is an elasticity matrix, e is the piezoelectric matrix, isthe dielectric matrix, S is a strain vector, and E is an electricfield vector. The shape function for the electric field variable isanalogous to Eq. 23. The steel and piezoceramic material prop-

erties are given in Table 1.For both the simplified and true-geometry outer ring structural

models presented above, the output of the embedded load sensorwas assumed to be due only to a rolling element passing directlyover the slot. However, for the finite element analysis, the effectof all loaded rolling elements was taken into account. All therolling elements were modeled as compressive forces acting onthe outer ring. The magnitude of each force was calculated by Eq.

1, and the location was determined by calculating the position ofeach rolling element based on the rotational speed of the innerring. In Fig. 13, the sensor output predicted by the finite elementmodel and that by the simplified beam model are compared. Sincethe FE model considered the effect of adjacent rolling elementsthat were not located directly over the slot, an increase of thewidth of each sensor output pulse was observed from the FE

model. This means that the load sensor begins to respond to arolling element before it actually runs over the slot. Due to thestructural rigidity of the bearing, the actual difference between theFE and simplified analytical beam models is very small, especiallyin terms of the maximal signal amplitude 2 percent. Theagreement between these models verify the assumptions that wereused to derive the simplified beam model. While either model canbe used to analyze the sensor output of the bearing, the simplifiedbeam model is a better design tool, since the bearing and sensorparameters are stated explicitly in Eqs. 9, 10, and 13. Forexample, these equations can be used to design an embedded sen-sor with an output range that satisfies requirements of the dataacquisition hardware of other supporting electronics.

Fig. 11 Four-node quadrilateral plane strain element withparametric coordinates s and t

Fig. 12 Finite element model of the modified outer ring

Table 1 Material properties used for modeling the bearing vi-brations



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Results Comparison

To further verify the theoretical results obtained from the ana-lytical and FE models, an experimental investigation was con-ducted using the test bearing shown in Fig. 2. A bearing test bedwas designed and fabricated for the experiments, as shown in Fig.

14. The inner ring of the modified bearing was mounted on a 100mm shaft and secured with an end cap. A flat ring was used tosecure the outer ring in a housing. With the shaft mounted in thechuck of an industrial lathe, a threaded rod was inserted through aframe, screwed into the top of the housing and secured with a nut.The frame was supported by the lathe. Turning a nut at the top ofthe rod compressed a calibrated spring and applied a radial load tothe bearing. With the spring stiffness constant ks (lb/in ) and thenumber of threads per inch on the rod Nt known, the spring de-flection, and therefore the magnitude of radial load, were deter-mined. The free end of the shaft was supported with a live center,and the lathe was used to spin the shaft at various rotationalspeeds while the housing remained fixed. Data from the embeddedsensor was recorded using a 166 MHz laptop computer, whichwas equipped with a PCMCIA-based data acquisition system.

The cross-sectional area of the piezoelectric sensor was A41.4 mm2 and the height was l2.5 mm. The sensor was madeout of type PXE-5 piezoceramic. The corresponding materialproperties are given in Table 1. The frequency at which the rollingelements pass over the slot where the sensor is located is given by:

fd0fi

2 1 Z (26)

where fi is the shaft frequency, Z10 is the number of rollingelements, and is defined by db cos /dm . For a typical ex-perimental run with a lathe setting of 700 rpm, fi11.7 Hz, re-sulting in fd68.5 Hz, as per Eq. 5, and fd048.5 Hz. Since

Z10, the rolling elements in this bearing are each separated by36 deg. The corresponding arc length is 36 deg/180 degD/256.5 mm which is approximately three times the length L of theslot. The experimental results are shown in Fig. 15. A comparisonwith the predicted results from the FE and simplified analyticalmodels shows that the theoretical and experimental studies are ingood agreement. To quantify this observation, the root-mean-square RMS error erms was evaluated:

erm s VexpVFE2/N (27)where Vexp is the sensor output recorded from the experiment, VFEis the sensor output predicted by the finite element model, and N

is the number of data points recorded. From the data plotted inFig. 15, the value of e rm s is calculated as e rm s0.54 Volts, whichis less than 17 percent of the maximum recorded sensor output.This error is attributed to two reasons. First, unlike the sensoroutput predicted by the FE model, the experimental data did not

Fig. 13 Sensor output predicted by finite element model and simplified analytical model

Fig. 14 Schematics of the bearing test bed



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reach exactly the zero output line due to vibrational noise, whichwas observed from the machine environment during the experi-ments. Because of the high sensitivity of the piezoelectric sensor,the structure-borne vibration of the machine was contained in thesensor output. Secondly, in the FE model, the housing was as-sumed to be infinitely rigid and in solid contact with the outer

ring. However, the experimental housing has a certain degree offlexibility since it was made of aluminum which is an elasticmaterial. The output of the sensor is affected by this flexibilitybecause the sensor is a structural link between the top of the outerring slot and the housing. The largest error between the measuredand predicted sensor outputs occurs when a rolling element islocated near the edge of the slot i.e., the location of a rollingelement is approximately max. This confirms that the embeddedsensor actually starts responding to a rolling element load beforethe rolling element itself is exactly over the slot. The smallesterrors occur either when a rolling element passes over the centerof the slot i.e., when the sensor output is dominated by the rollingelement load or when the rolling elements are located as far as

possible from the slot i.e., when the sensor output is dominatedby noise from structure borne vibration. This agreement betweenthe analytical, FE, and experimental techniques further verifies the

simplified beam model as an accurate and efficient design tool.

To verify that Eq. 26 correctly gives the frequency at whichthe rolling elements pass over the slot, the spectrum of the sensor

output was calculated and plotted in Fig. 16. In the upper portion

of the figure, several important features of the normalized spec-

trum have been indicated. Two of these features are inherent char-

acteristics of systems involving rotating machinery and sensitive

electronics. The first feature is a small peak located at the shaft

speed fi11.7 Hz. This was caused by a slight imbalance of a

rotating component e.g., the lathe chuck. Second, the frequencyof the power supply for the computer and lathe motor was 60 Hz,

and electrical coupling between the power supply and the sensor

electronics produced a 60 Hz component in the sensor signal. The

most distinct feature in the spectrum is a large peak caused by the

rolling elements passing over the load sensor at the frequency fd0.

Fig. 15 Predicted and experimental sensor outputs

Fig. 16 Spectrum of the experimental data



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Evaluating Eq. 26 with the parameters given in Fig. 2 and fi11.7 Hz, the roll-over frequency is fd0

48.5 Hz, which agrees

with the experimental results shown in Fig. 16a. The harmonicsof fd0

are also very prominent features of the spectrum. According

to the vibration model described in the section Structural DefectInduced Vibration, an inner ring defect would produce a spec-trum with lobes centered at the defect frequency fd68.5 Hz, asshown in Fig. 5. The spectrum shown in Fig. 16a has whatappears to be a very small lobe at 68.5 Hz, despite the fact that thetest bearing had no inner ring defect. As stated above, the sensorsignal was contaminated with structure-borne noise. Since this

type of noise is generally uncorrelated as opposed to the vibrationcaused by a defect, the lobe at 68.5 Hz should not appear in theauto-correlation spectrum, which is shown in Fig. 16b. Indeed,the auto-spectrum has no lobe at 68.5 Hz. The main feature of theauto-spectrum is a peak at fd0

48.5 Hz, the frequency at which

the rolling elements pass over the load sensor. The harmonics offd0

are much less pronounced, as are the peaks at the shaft speed

and power supply frequency.

Conclusions

The structural integration of a load sensor into the outer ring ofa rolling element bearing provides an effective means for assess-ing the time-varying load conditions within the bearing structure.The developed beam and finite element models were able to pre-dict the output of an outer ring-embedded load sensor modulequite accurately, thus providing valuable input to the sensor de-sign. Results of the study have shown that a bearing defect pro-duces a pattern of signals which is not repeated between succes-sive revolutions of the inner ring. It has also been shown that animpact between a defect and a rolling element is a relatively highfrequency phenomena when compared to the pulse caused by arolling element passing over the sensor module. The basic shapeof the pulse is given by Eqs. 9, 10 and 13, which are notsinusoidal expressions. Thus, in the frequency domain, the loadmeasurement pulse has several harmonics that can bury the sig-nature of a defect, and with the addition of structure-borne noise,a defect might not be discovered by simply looking at the spec-trum of the sensor signal. However, it has been shown that calcu-lating the auto-correlation spectrum effectively compensates forthe effect of the load pulse harmonics and structure-born noise.

This emphasizes the importance of combined time and frequencydomain analysis of the sensor signal to accurately assess the con-dition of a bearing. With the combination of a well-designed sen-sor, an efficient signal processing algorithm and a knowledge ofbearing mechanics, the condition of a bearing can be established,as demonstrated by the analytical and experimental results fromthis study. These results have shown that an integrated sensor isable to provide effective bearing condition monitoring throughdynamic load and vibration measurement.

Future Work

Future research will focus on developing advanced and efficientsignal processing techniques using wavelet transformation andneural-fuzzy networks to relate signal features to specific bearingfaults. Also, further experimental investigations will be conducted

on an improved bearing test bed that allows for a much widerrange of operating conditions to be studied. The combined theo-retical and experimental work will establish a strong basis for thedevelopment of an integrated on-line bearing condition monitor-ing system to provide early defect warning capabilities to a widerange of rolling element bearings and manufacturing equipment.

Acknowledgment

This work was supported by the National Science Foundationunder CAREER award DMI-9624353 and by the SKF ConditionMonitoring company. The authors would like to thank Mr.Changting Wang and the College of Engineering machine shopfor their help in the experiments.

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