DOC PREVIEW
CU-Boulder ASEN 5519 - VIBRATIONAL ANALYSIS OF A BALL BEARING

This preview shows page 1-2-16-17-18-34-35 out of 35 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 35 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 35 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 35 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 35 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 35 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 35 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 35 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 35 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

VIBRATIONAL ANALYSIS OF A BALL BEARINGRohini KesavanASEN 5519: Fluid-Structure InteractionOVERVIEWn Introductionn Structural Defect Induced Vibrationn Structural Model of the outer ringn Finite Element Model of the outer ringn Results Comparisonn Conclusion n Future WorkINTRODUCTION§ The project presents an analysis of the vibrational behavior of a deep groove ball bearing with a structurally integrated force sensor§ The miniaturized force sensor, accommodated within a slot on the bearing’s outer ring provides on-line conditioning monitoring capability to the bearing§ Analytical and finite element models are developed to predict the sensor output due to the bearing dynamic load and rotational speed variationSENSOR-INTEGRATED SMART BALL BEARINGGEOMETRY OF A DEEP GROOVE BALL BEARINGD-Outer Diameterdb-Ball Diameterdm-Pitch Diameterw-Raceway widthL-Slot lengthψ-Limiting angled -Bore DiameterLoad distribution on a rolling element bearing is given bywhere n= 3/2 for roller bearingsn=10/9 for ball bearingsFr– Applied radial Load Z – Number of rolling elementsa- Mounted contact anglenqq )]cos1(211[)(maxψεψ −−=αcos5maxZFqr=STRUCTURAL MODEL OF THE OUTER RINGn A piezoelectric sensor is embedded into a slot cut through the outer ring to monitor load and vibration within the bearing structuren The piezoelectric sensor is modeled as a spring with stiffness k that is related to its material compositionn Clamped boundary conditions are considered appropriate since the ends of the beam are solidly connected to the surrounding bearing structureLOADS ON MODIFIED SECTION OF THE OUTER RINGSIMPLIFIED MODEL OF THE BEARING OUTER RINGThe bearing load is determined by Eq. in slide 6 and the location ‘a’ where the load is applied is related to by the expressionwhen a<L/2, the deflection of the sensor is given bywhen a>L/2, the sensor deflection is given bywhere k= - Elastic Modulus of the piezoelectric material.)sin()(21ψbmdda +=322/192)34(4kLEILaqaLa−−=≤δ)(ψq322/192)4()(4kLEIaLaLqLa−−−=>δIA33γ33γThis translates into a load on the sensor as The electrical charge produced by the sensor is Q =Using a charge amplifier with a gain G, the voltage output produced by the embedded sensor is V= GQ =This voltage output is a direct measure of the outer ring deflection due to a specific bearing load. Conversely, from the sensor voltage output, the load applied to the bearing can be determined to identify overloading conditionslARsδγ33=sRd33lAGdδγ3333BEAM MODELBENDING MOMENT DIAGRAMSHEAR FORCE DIAGRAMMODE SHAPES 1MODE SHAPE 2Variation of amplitude against excitation frequency when an harmonic load is appliedFINITE ELEMENT MODEL OF THE OUTER RINGn Technically the complete bearing structure can be modeled using a complex three-dimensional FE model.n However, by observing the nature of the boundary conditions and loads on the outer ring, it was determined that the FE model could be simplified by using symmetry of the systemn Loads on the bearing structure are applied to the outer ring through small ellipsoidal contact areas between the rolling elements and the outer ring groove§Assuming a pure radial force, the resulting Hertzian stress distribution is located at the base of the groove§Since the stress distribution is symmetric about the plane which divides the outer ring through the base of the groove, the strain normal to the plane ex, is zero§The FE model was constructed using a four-node quadrilateral plain strain element.)1()1()]1)(1()1)(1()1)(1()1)(1([41)1()1()]1)(1()1)(1()1)(1()1)(1([4122212221tvsvtsvtsvtsvtsvvtusutsutsutsutsuuLKJILKJI−+−++−++++−++−−=−+−++−++++−++−−=where u and v are the displacements along z and y directions.Finite Element Model of the modified outer ringGEOMETRIC MODEL OF THE OUTER RINGOUTER RING WITH BOUNDARY CONDITIONSMODE SHAPE 1MODE SHAPE 2MODE SHAPE 3FREQUENCY VS. DISPLACEMENT PLOTFREQUENCY VS. VOLTAGE PLOTSCHEMATICS OF THE BEARING TEST BED•Inner ring of the bearing is mounted on a shaft and secured withan end cap. The outer ring is secured with a flat ring•With the shaft mounted in the chuck of a lathe a threaded rod isinserted through a frame, screwed into the top of the housing and secured with a nut•Turning a nut at the top of the rod compressed a calibrated spring and applied a radial load to the bearing•The free end of the shaft is supported with a live center, and the lathe was used to spin the shaft at various rotational speeds while the housing remained fixed•Data from the embedded sensor was recorded using a computer which was equipped with a data acquisition systemPREDICTED AND EXPERIMENTAL SENSOR OUTPUTS• The difference between the predicted sensor output and experimental output is due to two reasons.1,Unlike the sensor output predicted by the FE model, the experimental data did not reach exactly the zero output line dueto vibrational noise, which was observed from the machine environment during the experiments.2, In the FE model, the housing was assumed to be infinitely rigid. However, the experimental housing has a certain degree offlexibility since it was made of aluminum which is an elastic material.CONCLUSIONn The structural integration of a load sensor into the outer ring of a rolling element bearing provides an effective means for assessing the time varying load conditions within the bearing structuren The project emphasizes the importance of combined time and frequency domain analysis of the sensor signal to accurately assess the conditions of the bearingFUTURE WORKn Comparing analytical and FE results with experimental datan Improving on the beam model by adding more elementsn Developing advanced and efficient signal processing techniques using wavelet transformation and neural-fuzzy networksn Developing monitoring systems to provide early defect warning capabilities to a wide range of rolling element bearingsReferencesn Brian T. Holm, Robert X. Gao, “Vibrational Analysis of a Sensor-Integrated Ball bearing”, Vol.122, October 2000, ASMEn Brown, P.J., “Condition Monitoring of Rolling Element Bearing”, Noise Control Vibrat. Insul.8, No.2, pp 41-44n Berggren, J.C.1988, “Diagnosing Faults in Rolling Element Bearings, Part I: Assessing Bearing condition”, Vibrations, 4, No. 1, pp 5-13n Tandon N., Nakra B.C, 1990, “Defect Detection in Rolling Element Bearings by Acoustic Emission Method” , J. Acoustic Emiss.9, No.1, pp


View Full Document

CU-Boulder ASEN 5519 - VIBRATIONAL ANALYSIS OF A BALL BEARING

Documents in this Course
Lecture

Lecture

13 pages

Load more
Download VIBRATIONAL ANALYSIS OF A BALL BEARING
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view VIBRATIONAL ANALYSIS OF A BALL BEARING and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view VIBRATIONAL ANALYSIS OF A BALL BEARING 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?