Research Article Failure Diagnosis System for a Ball-Screw ...

Research ArticleFailure Diagnosis System for a Ball-Screw byUsing Vibration Signals

Won Gi Lee1 Jin Woo Lee1 Min Sung Hong1 Sung-Ho Nam2

YongHo Jeon1 and Moon G Lee1

1Department of Mechanical Engineering Ajou University San 5 Woncheon-dong Yeongtong-gu Suwon 443-749 Republic of Korea2Korea Institute of Industrial Technology (KITECH) 1271-18 Sa-3-dong Sangrok-gu Ansan 426-791 Republic of Korea

Correspondence should be addressed to Moon G Lee moonguleeajouackr

Received 1 April 2015 Accepted 21 June 2015

Academic Editor Carlo Trigona

Copyright copy 2015 Won Gi Lee et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Recently in order to reduce high maintenance costs and to increase operating ratio in manufacturing systems condition-basedmaintenance (CBM) has been developed CBM is carried out with indicators which show equipmentrsquos faults and performancedeterioration In this study indicator signal acquisition and conditionmonitoring are applied to a ball-screw-driven stage Althoughball-screw is a typical linearly reciprocating part and is widely used in industry it has not gained attention to be diagnosed comparedto rotating parts such as motor pump and bearing First the vibration-based monitoring method which uses vibration signal tomonitor the condition of a machine is proposed SecondWavelet transform is used to analyze the defect signals in time-frequencydomain Finally the failure diagnosis system is developed using the analysis and then its performance is evaluated Using thesystem we estimated the severity of failure and detect the defect positionThe low defect frequency (asymp587Hz) is spread all over thetime in the Wavelet-filtered signal with low frequency range Its amplitude reflects the progress of defect The defect position wasfound in the signal with high frequency range (768sim1536Hz) It was detected from the interval between abrupt changes of signal

1 Introduction

Todayrsquos manufacturing systems have become gradually auto-mated for the purposes of productivity improvement and costsavings So the production facilities are to be operated for 24hours However the full ramp-up of automated productionlines with high operating ratio has also caused variousmechanical failures and accordingly increased economiclosses Generally about 15 to 40 of entire production costsare consumed for equipment maintenance and 30 of themaintenance costs are lost for unnecessary or improper job[1]

Recently in order to save high maintenance costs and toincrease manufacturing systemrsquos operating ratio condition-basedmaintenance (CBM)method has been developed [2 3]Unlike traditional maintenance that needs to be carried outon a regular time basis the CBM detects any system defectearly and identifies the cause of failure efficiently throughuse of indicator signals that reflect the actual operation

condition of systems and accordingly reduces unnecessarycosts and maintenance efforts [4 5] In order to realize theCBM method effectively it is needed to identify the physicaland structural characteristics of equipment to select theappropriate indicator signals that show the status of facilitiesand to evaluate the condition of them For this processaccurate analysis of equipment pieces and their failuresappropriatemonitoring of indicator signals correct diagnosisof defect signals and proper alarm of the condition arerequired

Research to enhance maintenance efficiency has longbeen conducted for diverse mechanical elements and mod-ules Maslach [6] monitored and analyzed the condition ofa lubricated bearing one of the representative mechanicalelements and Spoerre [7] applied the analysis to discover andclassify bearing failuresMoreover Schoen et al [8] identifieddefects in motor bearings through use of current signalsin motors and Autar [9] implemented an expert system todiagnose the condition and failure of diesel engines

Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 435870 9 pageshttpdxdoiorg1011552015435870

2 Shock and Vibration

Most research has been conducted on rotating elementssuch as engines turbines motors gears shaft or com-pressors for which it is easy to measure and treat signalsRecently research on linearly reciprocating modules thatcreates nonperiodical signals with abrupt change is alsomak-ing meaningful headway However since studies on linearlyreciprocating components have been limited to engines orcompressors further research needs to be directed at diverselinearly reciprocating modules

In this study a defect detection and diagnosis methodwas proposed for the ball-screw-driven stage a representativelinearly reciprocating mechanical module and a failurediagnosis system was designed and applied through theuse of CBM For this process firstly normal and defectfrequencies were derived from the common failure of theball-screw Second a vibration signal acquisition modulewas implemented in the diagnosis system The normal anddefect signals were obtained and then the derivation wasinvestigated Also the amplitude change of defect signal wasfound according to the progress of failure Third we appliedWavelet transformation to the signal so that the systemidentifies the defect frequencies and estimates their progressThe system is stand-alone and PC-based one so that it canbe applied to various manufacturing equipment pieces orfacilities

2 Defect Frequencies of Ball-Screw

Most mechanical systems generate vibration signals whenthey are operated signals which offer diverse and plentifulinformation on the condition of systems In particular whenthe system runs continuously that is in steady state thevarious frequency components of vibration signals repre-sent different characteristics pertinent to each mechanicalcomponent and the amplitude of frequency componentsvaries according to the condition of system operation [10]In this study vibration was selected as indicator signals todetect and diagnose the defects of ball-screw In additiondefect frequencies were derived for main failure modes anda vibration monitoring method was presented using thefrequencies

21 Failure of Ball-Screw As shown in Figure 1 the ball-screwconsists of steel balls screw shaft nuts seals and tube Thesteel balls between the nuts and screw shaft roll so that thenut moves linearly along the screw shaft when the shaft isrotated by an actuating motor [11] Usually the nut carriesexternal loadTherefore while the steel balls are rotated by theactuation under the external load and friction the grooves inthe screw shaft are under repeated compressive stress whichcauses fatigue in the screw shaft and then various failuresdetected in the ball-screw

Autar identified that defects such as fatigue fractures andstrains aremostly found in the parts that are subject to rollingfriction and that the defects occurring in screw shafts andsteel balls represent major failure modes [9] Figure 2 showsflaking a representative fatigue fracture where the surface ofgrooves is exfoliated by the repeated compressive stress

A B

C

D

E

A steel ballB screw shaftC nut

D sealE tube

Figure 1 Structure of ball-screw

Flacking

Figure 2 Example of fatigue failure flacking

22 Defect Frequencies Fatigue fractures the major defectof the ball-screw start with local small defects but finallybreak themechanicalmodule During the progress the defectsignal is distorted more from the normal After a smalldefect occurs on the surface of the screw shaft which isin contact with the steel balls shocks take place regularlyand periodically whenever the steel balls pass through thefaults The period of the shocks varies according to thelocation of the defects in the components of the ball-screwFor this reason different defect frequencies occur for eachcomponent Harris and McCool [12] detected defects inrolling bearing by use of these defect frequencies

In this study we propose a new method to derive defectfrequencies from the relative speed of components of the ball-screw through use of the findings of Harris and McCool andby assuming the ball-screw as a rolling bearing The balls arerotating revolving and sliding in the inner and outer racesThe inner race is male screw nut and outer one is female nutWhen the balls pass along the gap between the inner andouter races themotion generates each typical vibrationMoredetails can be found in Harris and McCool [12]

If Harris method is applied the defect frequencies arededuced considering the nut as an outer ring and the screwas an inner ring as follows When the contact angle made bythe ball nuts and screw shaft is 120572 the pitch diameter of balls

Shock and Vibration 3

ne

B B

A A

v e

ni

vmv i

Nut

Nut

Screw

Screw

120572

Lp

dmDi de

Figure 3 Modeling ball-screw based on rolling bearing

is 119889119898 the diameter of each ball is119863

119908 the rotational speeds of

external and internal races are 119899119890and 119899

119894 and the number of

balls is z the defect frequencies are derived as shown in (1) to(3) from Figure 3 For the speed of rotation the nut does nothave any speed (119899

119890= 0) but the screw rotates (119899

119894= 119899) Each

defect frequency is ball pass frequencies of shaft (BPFS) ballpass frequency of nut (BPFN) and ball spin frequency (BSF)Among the frequencies the BPFS shown in (1) constitutes themajor vibration signal because it has the largest amplitudeand mostly appears in low frequency domain Note that therotations speeds are in rpm and the frequencies are in Hz

BPFS = 1120119911119899(1+

119863119908

119889119898

cos120572) (1)

BPFN = 1120119911119899(1minus

119863119908

119889119898

cos120572) (2)

BSF = 1120119899

119889119898

119863119908

(1minus119863119908

119889119898

cos120572)(1+119863119908

119889119898

cos120572) (3)

However the findings of the above three equations arestill not for ball-screw but rotational rolling bearings Sincedefect frequencies of the ball-screw are required to be newlyderived we introduced the effective pitch diameter of ball119889

1015840

119898instead of the pitch diameter of ball 119889

119898and the effective

number of balls 1199111015840 instead of the number of balls 119911 They aredrawn from (4) from Figure 4

119889

1015840

119898= (119871119901

2+ (120587119863

119887)

2)

12

119911

1015840

=

119889

1015840

119898

119863119908

(4)

Because the equation has cos120572 in the case that the contactangle of the grooves of balls and the screw shaft is not 0∘ thedefect frequencies are not the value of integer times of therotational speed This makes it easy to analyze frequenciesand diagnose defects because the defect vibration frequencies

Dw

Ball

120587Db

middot middotmiddot

Lp

Screw

Db

d998400

m

Figure 4 Effective pitch diameter and number of balls of ball-screwwhen considering it a rolling bearing

are distinguished from the vibration frequency by the shaftrotation and its high harmonics

3 Data Acquisition and Defect Signals

We collected normal and defect vibration signals of the ball-screw-driven stage identified the defect frequencies from afailure mode presented in Section 2 and analyzed vibrationsignals Also it is investigated how the progress of defect isreflected on the amplitude of signal

31 Experimental Setup In order to analyze the normal anddefect signals of the ball-screw-driven stage an experimentalapparatus was set up as shown in Figure 5 The stage consistsof ACmotor ball-screw stage and LM (linear motion) guideIts size was one-tenth of the actual ball-screw system that iswidely used in CNC machine tools and automation systemsMajor specifications of the ball-screw-driven stage are shownin Table 1

In order to measure and analyze the vibration signals ofthe test rig a monitoring system was implemented as shownin Figure 6 and Table 1

The vibration signals of the ball-screw are measuredwith an accelerometer mounted on the nuts while the stage


Table 1 Specifications of ball-screw-driven stage

Components Specifications Value Model (maker)

Stage Repeatability plusmn002mm LP200-SC-600L-70-H-S (LPK)Stroke 600mm

Motor Rated rotating speed 3000 rpm HF-KP73 (Mitsubishi)Input source 3 phases (60Hz)

Ball-screw

Lead 20mm

HTR 2020A (ISSOKU)Circuit 15 turns

Diameter of ball centers 21mmDiameter of balls 3969mmContact angle 45∘

Stage

LM guide

Screw

Motor

Nut

Figure 5 Ball-screw-driven stage

reciprocates a travel of 267mm at a speed of 133mms and anacceleration of 5000mms2 In order to simulate the defectsignals coming from the flaked screw shaft as shown inFigure 7 holes with a diameter of 3mmwere punched on theball groove with a carbide drill to simulate the defects

32 Normal Signal Analysis The vibration signals thatoccurred when the ball-screw-driven stage is reciprocatingwithout defect were analyzed in the frequency domain Asshown in Figure 8 60 and 120Hz were the dominant compo-nents in low frequency range This is because of the electricalcurrent and its harmonics in the motor In the followinganalysis the 60Hz component was filtered to clarify the otherfrequency components Considering the specifications of theaccelerometer the frequency component less than 10Hz hasno meaningful information

33 Defect Signal Analysis The defect frequency derivedfrom the flaking of screw shaft used for this study is derivedfrom (1) as follows

defect frequency = 1120119911

1015840

119899(1+119863119908

1198891015840

119898

cos120572)

= 0147119899

(5)

Figure 9 shows the change of defect frequency in Hzaccording to the rotational speed of the motor 119899 in rpmThe numbers in the left are rotational speeds and the peaksindicated by arrow are the defect frequencies which indicatesthat the defect frequencies from (5) took place as predictedThe major electrical noise of frequency 60Hz has been cutoff but its second harmonic 120Hz was not filtered out Itappeared as a peak at 120Hz in the graphs

Then the relation of defect frequency with the number ofdefective holes was analyzed As shown in Figure 10 ampli-tude of the defect frequency tends to be larger when the defectgets worse which makes it easier to detect and diagnose thedefects through defect frequencies and amplitude in steadystate

It has been known that the fatigue strength is satu-rated after large number of rotations [13] If the weakenedstrength is synchronized with the progress of fatigue it willresult in large vibration amplitude In the experiments thesimulated defect drilled hole on screw is mimicking theflacking fatigue The progress of fatigue was modeled as thenumber of holes Therefore the saturation stands to reasonin Figure 10 In the fault estimation of failure diagnosissystem the saturation can be taken into account whenconsidering logarithmic scale of the amplitude progress inSection 5


LabVIEW2010

software

Servo driver

AD converter

Signalanalyzer

Power supplyAccelerometer

Figure 6 Condition monitoring system with data acquisition sensor and analyzing SW

Figure 7 Simulated defects (indicated by an arrow)

4 Time-Frequency Domain Analysisfor Ball-Screw

The defects occurring in the ball-screw generate excessiveabnormal signals such as shock signals when the nuts passthrough a local defective part This abrupt change can bedetected in time domainThe defect signals from continuousball-defect interaction can be shown up in frequency domainanalysis as in Section 3Therefore we indicated the timewhenthe defect signal occurred aswell as its frequency componentsby use of a time-frequency domain analysis discrete Wavelettransform [12] as in Figure 11

For more effective analysis we used the DaubechiesWavelet (db14) function which is similar to the impulsesignals in discrete Wavelet transform In addition we ana-lyzed the signals from levels 1 to 9 to restrict the frequencyanalysis domain of the obtained signals into integer numbersFigure 11 shows only detailed graphs of levels 1 2 and 5 wheredefect signals experience a more drastic change than normalsignals when the defect occurs

The result can be an indicator that detects the location ofdefects Since the defect is located in the center of the screwthe nut passes through the defective point at 1 and 3 secondsThus defect vibrations occur at those times as shown in thegraphs of levels 1 and 2 The high frequencies by the shockoccurring from the defect position are in the range from 384to 768Hz and from 768 to 1536Hz

Also the amplitude can be an estimator of the defectprogress The continuous defect frequency BPFS is dis-tributed around 587Hzwhen themotor rotates with 399 rpmin the ball-screw stage The graph of level 5 (48sim96Hz)confirms that the component occurs over the whole timerange with a certain magnitude of amplitude which tends tobe changed by the progress of defect

5 Failure Diagnosis System

A PC-based ball-screw failure diagnosis system was designedby applying the analysis of defect frequencies based onWavelet transform to detect and diagnose the defects ofa ball-screw through the developed vibration monitoringmethodThe system is of stand-alone type therefore it can beapplied to any equipment after modification of the diagnosisalgorithm

It has an accelerometer 356A16 from PCB Piezotronicsa data acquisition PXI-4472 from National Instruments(NI) and a signal analyzer PXI-88187 from NI The systemwas applied to a ball-screw-driven stage with motor HF-KP73 fromMitsubishi ball-screwwith the simulated defectsHTR 2020A from ISSOKU and linear motion (LM) guidemechanism LP200-SC-600L-70-H-S from LPK

51 Failure Diagnosis Algorithm As shown in Figure 12 thefailure diagnosis system consists of signal acquisition signal


1

05

0

minus05

minus1

minus15

Acce

lera

tion

(g)

0 1 2 3 4 5

Time (s)

(a)

00004

00003

00002

00001

0

Am

plitu

de

0 20 40 60 80 100 120 140

Frequency (Hz)

(b)

Figure 8 Frequency domain analysis of normal signal

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

477 rpm 677 rpm

877 rpm

Figure 9 Defect frequency variation according to the rotating speed change of motor the frequencies are indicated by arrows

800E minus 04

600E minus 04

400E minus 04

200E minus 04

000E + 00

Am

plitu

de

1 2 3

Number of defect holes

Figure 10 Defect amplitude variations according to the defect progress


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signalAc

cele

ratio

n (g

)Ac

cele

ratio

n (g

)

2

1

0

minus1

minus2

2

1

0

minus1

minus2

Defect signal

(a) Detail (level 1 768sim1536Hz)

0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

1

05

0

minus05

minus1

minus15

1

05

0

minus05

minus1

minus15

(b) Detail (level 2 384sim768Hz)

0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

06

04

02

0

minus02

minus04

minus06

06

04

02

0

minus02

minus04

minus06

(c) Detail (level 5 48sim96Hz)

Figure 11 Wavelet transform of normal and defect signals for one reciprocation of ball-screws during 4 s when the defect is at the center ofscrew shaft

filtering fault diagnosis and saving modules In particularthe delivered data is filtered using discreteWavelet transformThe filtering module plays a role of band-pass filter for therange that includes the defect frequenciesThe algorithmwasimplemented in a PC using graphic user interface (GUI) toolLabVIEW 2010

Figure 13 displays the interface screen of the developedfailure diagnosis system It monitors a certain frequencyrange of current condition It also shows whether there isan initial defect and diagnoses defects by presenting a faultprogress rate

52 Failure Detection Test Results We carried out a flakingfailure diagnosis test for the ball-screw by using the designed

failure diagnosis system The vibration signals of the ball-screw-driven stage which is under flaking failure werecollected during test The failure diagnosis test results areshown in Figure 13

The diagnosis of the flacking fatigue failure is performedunder assumption that the weakened strength is synchro-nized with the progress of fatigue and this will result inlarge vibration Taking into account the logarithmic progressof failure the amplitude of normal signal was set as a minvalue and the amplitude of the maximum tolerable flakingwas set as a max value The amplitude in between the twowas interpolated and then its progress was presented aspercentage value The result showed that approximately 65of flaking failure has been progressed in Figure 13 It may


Signalacquisition

FilteringDWT

RPM

Fault diagnosis

Signalanalysis

Faultidentification

(alarming)

Faultestimation

Save

Filetxt

Figure 12 Scheme of failure diagnosis system

Figure 13 GUI and result of flaking failure diagnosis

require verification by experts because the estimation isbased on the intuition of designers

6 Conclusion

In this research a condition monitoring method was devel-oped by using a diagnosis system to detect and warn offailures in ball-screw-driven stage (Table 2) The system usesvibration as an indicator signal A new analysis model isproposed to identify defect frequencies in ball-screw whenit is operated continuously that is in steady state Moreovertime-frequency analysis was carried out based on Wavelettransformation to detect the change of signal not only insteady state but also in transient condition As a result thefollowing can be drawn

(1) The defect frequencies in steady state can be derivedby modeling ball-screw as rolling bearing using rel-ative speeds rotational speed diameter and contactangle of each component The frequencies are notinteger times of the rotational speed of ball-screw sothat they are easily distinguished from the harmonicsof the speed Because there is the larger amplitude ofthe defect vibration for more defects it is effective toestimate the defect progress

(2) In this study defect frequencies are derived by assum-ing the ball-screw as a rolling bearing Through useof the findings we can detect both progression andoccurrence time of failure in linearly reciprocatingmechanical module

(3) Wavelet transform shows the defect vibration clearlyIn low frequency range the defect frequency 587Hzappeared The amplitude of the frequency is used asestimator of the failure progress In high frequencyrange 768sim1536Hz we were able to locate the defectposition from the signalrsquos abrupt change

(4) Together with the identified frequency and Wavelettransform we developed a failure diagnosis system Itcan detect the defect and show the failure progress Itwas set up in PC with stand-alone scheme thereforeit can be applied easily to various equipment pieces

Nomenclature

120572 Contact angle119863119887 Pitch diameter of ball of screw119863119894 Diameter of screw groove119863119908 Diameter of ball119889119890 Diameter of nut groove119889119898 Pitch diameter of ball119889

1015840

119898 Effective pitch diameter of ball119871119901 Lead of screw119899119890 Rotational speed of nut119899119894 Rotational speed of screw

V119890 Tangential linear speed of nut

V119894 Tangential linear speed of screw

V119898 Tangential linear speed of ball at its pitch circle119911 Number of balls119911

1015840 Effective number of balls


Table 2 Specifications of condition monitoring system

Equipment Specifications Value Model (maker)

Accelerometer Frequency range 05ndash5000Hz 356A16 (PCB Piezotronics)Voltage sensitivity 100mVg

AD converterResolution 24 bits

PXI-4472 (National Instruments)Sampling rate 1024 kSsecInput range plusmn10V

Signal analyzer LabVIEW software (Ver 2010) PXI-8187 (National Instruments)

Conflict of Interests

The authors declared no conflict of interests regarding publi-cation of the paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) Grant funded by the Korea government(MSIP) (no 2014R1A2A1A10052344)

References

[1] T WiremanWorld Class Maintenance Management IndustrialPress New York NY USA 1990

[2] A Ellis and A Byron ldquoCondition based maintenancerdquo TheJethro Project vol 10 pp 1ndash5 2008

[3] A K S JardineD Lin andD Banjevic ldquoA review onmachinerydiagnostics and prognostics implementing condition-basedmaintenancerdquoMechanical Systems and Signal Processing vol 20no 7 pp 1483ndash1510 2006

[4] R K Mobley An Introduction to Predictive MaintenanceButterworth-Heinemann New York NY USA 2nd edition1989

[5] F P Garcıa Marquez A M Tobias J M Pinar Perez and MPapaelias ldquoCondition monitoring of wind turbines techniquesand methodsrdquo Renewable Energy vol 46 pp 169ndash178 2012

[6] J K Maslach ldquoFerrographic analysis of grease-lubricated sys-tems an analysis of greases in roller bearingsrdquo LubricationEngineering vol 52 no 9 pp 662ndash666 1996

[7] J K Spoerre ldquoApplication of the cascade correlation algorithm(CCA) to bearing fault classification problemsrdquo Computers inIndustry vol 32 no 3 pp 295ndash304 1997

[8] R R Schoen T G Habetler F Kamran and R G BartheldldquoMotor bearing damage detection using stator current moni-toringrdquo IEEE Transactions on Industry Applications vol 31 no6 pp 1274ndash1279 1995

[9] R K Autar ldquoAn automated diagnostic expert system for dieselenginesrdquo Journal of Engineering for Gas Turbines and Power vol118 no 3 pp 673ndash679 1996

[10] C-S Liu Fault detection of rolling element bearings [PhDthesis] University of Washington Seattle Wash USA 2005

[11] D-S Kim S-H Lee Y-C Yoo and H-E Kim ldquoLife analysisthrough reliability test of ball screw for machine toolsrdquo inProceedings of the Fall Conference of the Korean Society ofMechanical Engineers pp 1517ndash1521 KSMTE YongpyeongRepublic of Korea November 2009 (Korean)

[12] T A Harris and J I McCool ldquoOn the accuracy of rollingbearing fatigue life predictionrdquo Journal of Tribology vol 118 no2 pp 297ndash310 1996

[13] R C Juvinall and K M MarshekMachine Component DesignJohn Wiley amp Sons Hoboken NJ USA 5th edition 2011

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DistributedSensor Networks



Most research has been conducted on rotating elementssuch as engines turbines motors gears shaft or com-pressors for which it is easy to measure and treat signalsRecently research on linearly reciprocating modules thatcreates nonperiodical signals with abrupt change is alsomak-ing meaningful headway However since studies on linearlyreciprocating components have been limited to engines orcompressors further research needs to be directed at diverselinearly reciprocating modules

In this study a defect detection and diagnosis methodwas proposed for the ball-screw-driven stage a representativelinearly reciprocating mechanical module and a failurediagnosis system was designed and applied through theuse of CBM For this process firstly normal and defectfrequencies were derived from the common failure of theball-screw Second a vibration signal acquisition modulewas implemented in the diagnosis system The normal anddefect signals were obtained and then the derivation wasinvestigated Also the amplitude change of defect signal wasfound according to the progress of failure Third we appliedWavelet transformation to the signal so that the systemidentifies the defect frequencies and estimates their progressThe system is stand-alone and PC-based one so that it canbe applied to various manufacturing equipment pieces orfacilities

2 Defect Frequencies of Ball-Screw

Most mechanical systems generate vibration signals whenthey are operated signals which offer diverse and plentifulinformation on the condition of systems In particular whenthe system runs continuously that is in steady state thevarious frequency components of vibration signals repre-sent different characteristics pertinent to each mechanicalcomponent and the amplitude of frequency componentsvaries according to the condition of system operation [10]In this study vibration was selected as indicator signals todetect and diagnose the defects of ball-screw In additiondefect frequencies were derived for main failure modes anda vibration monitoring method was presented using thefrequencies

21 Failure of Ball-Screw As shown in Figure 1 the ball-screwconsists of steel balls screw shaft nuts seals and tube Thesteel balls between the nuts and screw shaft roll so that thenut moves linearly along the screw shaft when the shaft isrotated by an actuating motor [11] Usually the nut carriesexternal loadTherefore while the steel balls are rotated by theactuation under the external load and friction the grooves inthe screw shaft are under repeated compressive stress whichcauses fatigue in the screw shaft and then various failuresdetected in the ball-screw

Autar identified that defects such as fatigue fractures andstrains aremostly found in the parts that are subject to rollingfriction and that the defects occurring in screw shafts andsteel balls represent major failure modes [9] Figure 2 showsflaking a representative fatigue fracture where the surface ofgrooves is exfoliated by the repeated compressive stress

A B

C

D

E

A steel ballB screw shaftC nut

D sealE tube

Figure 1 Structure of ball-screw

Flacking

Figure 2 Example of fatigue failure flacking

22 Defect Frequencies Fatigue fractures the major defectof the ball-screw start with local small defects but finallybreak themechanicalmodule During the progress the defectsignal is distorted more from the normal After a smalldefect occurs on the surface of the screw shaft which isin contact with the steel balls shocks take place regularlyand periodically whenever the steel balls pass through thefaults The period of the shocks varies according to thelocation of the defects in the components of the ball-screwFor this reason different defect frequencies occur for eachcomponent Harris and McCool [12] detected defects inrolling bearing by use of these defect frequencies

In this study we propose a new method to derive defectfrequencies from the relative speed of components of the ball-screw through use of the findings of Harris and McCool andby assuming the ball-screw as a rolling bearing The balls arerotating revolving and sliding in the inner and outer racesThe inner race is male screw nut and outer one is female nutWhen the balls pass along the gap between the inner andouter races themotion generates each typical vibrationMoredetails can be found in Harris and McCool [12]

If Harris method is applied the defect frequencies arededuced considering the nut as an outer ring and the screwas an inner ring as follows When the contact angle made bythe ball nuts and screw shaft is 120572 the pitch diameter of balls


ne

B B

A A

v e

ni

vmv i

Nut

Nut

Screw

Screw

120572

Lp

dmDi de








119894= 119899) Each


BPFS = 1120119911119899(1+

119863119908

119889119898

cos120572) (1)

BPFN = 1120119911119899(1minus

119863119908

119889119898

cos120572) (2)

BSF = 1120119899

119889119898

119863119908

(1minus119863119908

119889119898

cos120572)(1+119863119908

119889119898

cos120572) (3)


1015840




119889

1015840

119898= (119871119901

2+ (120587119863

119887)

2)

12

119911

1015840

=

119889

1015840

119898

119863119908

(4)


Dw

Ball

120587Db

middot middotmiddot

Lp

Screw

Db

d998400

m













Ball-screw

Lead 20mm



Stage

LM guide

Screw

Motor

Nut






1015840

119899(1+119863119908

1198891015840

119898

cos120572)

= 0147119899

(5)





LabVIEW2010

software

Servo driver

AD converter

Signalanalyzer














1

05

0

minus05

minus1

minus15

Acce

lera

tion

(g)

0 1 2 3 4 5

Time (s)

(a)

00004

00003

00002

00001

0

Am

plitu

de

0 20 40 60 80 100 120 140

Frequency (Hz)

(b)


00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

477 rpm 677 rpm

877 rpm


800E minus 04

600E minus 04

400E minus 04

200E minus 04

000E + 00

Am

plitu

de

1 2 3




0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signalAc

cele

ratio

n (g

)Ac

cele

ratio

n (g

)

2

1

0

minus1

minus2

2

1

0

minus1

minus2

Defect signal


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

1

05

0

minus05

minus1

minus15

1

05

0

minus05

minus1

minus15


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

06

04

02

0

minus02

minus04

minus06

06

04

02

0

minus02

minus04

minus06









Signalacquisition

FilteringDWT

RPM

Fault diagnosis

Signalanalysis

Faultidentification

(alarming)

Faultestimation

Save

Filetxt




6 Conclusion






Nomenclature


1015840















Acknowledgment


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ne

B B

A A

v e

ni

vmv i

Nut

Nut

Screw

Screw

120572

Lp

dmDi de








119894= 119899) Each


BPFS = 1120119911119899(1+

119863119908

119889119898

cos120572) (1)

BPFN = 1120119911119899(1minus

119863119908

119889119898

cos120572) (2)

BSF = 1120119899

119889119898

119863119908

(1minus119863119908

119889119898

cos120572)(1+119863119908

119889119898

cos120572) (3)


1015840




119889

1015840

119898= (119871119901

2+ (120587119863

119887)

2)

12

119911

1015840

=

119889

1015840

119898

119863119908

(4)


Dw

Ball

120587Db

middot middotmiddot

Lp

Screw

Db

d998400

m













Ball-screw

Lead 20mm



Stage

LM guide

Screw

Motor

Nut






1015840

119899(1+119863119908

1198891015840

119898

cos120572)

= 0147119899

(5)





LabVIEW2010

software

Servo driver

AD converter

Signalanalyzer














1

05

0

minus05

minus1

minus15

Acce

lera

tion

(g)

0 1 2 3 4 5

Time (s)

(a)

00004

00003

00002

00001

0

Am

plitu

de

0 20 40 60 80 100 120 140

Frequency (Hz)

(b)


00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

477 rpm 677 rpm

877 rpm


800E minus 04

600E minus 04

400E minus 04

200E minus 04

000E + 00

Am

plitu

de

1 2 3




0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signalAc

cele

ratio

n (g

)Ac

cele

ratio

n (g

)

2

1

0

minus1

minus2

2

1

0

minus1

minus2

Defect signal


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

1

05

0

minus05

minus1

minus15

1

05

0

minus05

minus1

minus15


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

06

04

02

0

minus02

minus04

minus06

06

04

02

0

minus02

minus04

minus06









Signalacquisition

FilteringDWT

RPM

Fault diagnosis

Signalanalysis

Faultidentification

(alarming)

Faultestimation

Save

Filetxt




6 Conclusion






Nomenclature


1015840















Acknowledgment


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Ball-screw

Lead 20mm



Stage

LM guide

Screw

Motor

Nut






1015840

119899(1+119863119908

1198891015840

119898

cos120572)

= 0147119899

(5)





LabVIEW2010

software

Servo driver

AD converter

Signalanalyzer














1

05

0

minus05

minus1

minus15

Acce

lera

tion

(g)

0 1 2 3 4 5

Time (s)

(a)

00004

00003

00002

00001

0

Am

plitu

de

0 20 40 60 80 100 120 140

Frequency (Hz)

(b)


00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

477 rpm 677 rpm

877 rpm


800E minus 04

600E minus 04

400E minus 04

200E minus 04

000E + 00

Am

plitu

de

1 2 3




0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signalAc

cele

ratio

n (g

)Ac

cele

ratio

n (g

)

2

1

0

minus1

minus2

2

1

0

minus1

minus2

Defect signal


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

1

05

0

minus05

minus1

minus15

1

05

0

minus05

minus1

minus15


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

06

04

02

0

minus02

minus04

minus06

06

04

02

0

minus02

minus04

minus06









Signalacquisition

FilteringDWT

RPM

Fault diagnosis

Signalanalysis

Faultidentification

(alarming)

Faultestimation

Save

Filetxt




6 Conclusion






Nomenclature


1015840















Acknowledgment


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










LabVIEW2010

software

Servo driver

AD converter

Signalanalyzer














1

05

0

minus05

minus1

minus15

Acce

lera

tion

(g)

0 1 2 3 4 5

Time (s)

(a)

00004

00003

00002

00001

0

Am

plitu

de

0 20 40 60 80 100 120 140

Frequency (Hz)

(b)


00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

477 rpm 677 rpm

877 rpm


800E minus 04

600E minus 04

400E minus 04

200E minus 04

000E + 00

Am

plitu

de

1 2 3




0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signalAc

cele

ratio

n (g

)Ac

cele

ratio

n (g

)

2

1

0

minus1

minus2

2

1

0

minus1

minus2

Defect signal


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

1

05

0

minus05

minus1

minus15

1

05

0

minus05

minus1

minus15


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

06

04

02

0

minus02

minus04

minus06

06

04

02

0

minus02

minus04

minus06









Signalacquisition

FilteringDWT

RPM

Fault diagnosis

Signalanalysis

Faultidentification

(alarming)

Faultestimation

Save

Filetxt




6 Conclusion






Nomenclature


1015840















Acknowledgment


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

05

0

minus05

minus1

minus15

Acce

lera

tion

(g)

0 1 2 3 4 5

Time (s)

(a)

00004

00003

00002

00001

0

Am

plitu

de

0 20 40 60 80 100 120 140

Frequency (Hz)

(b)


00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

00002

000015

00001

5E minus 5

0

Am

plitu

de

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

477 rpm 677 rpm

877 rpm


800E minus 04

600E minus 04

400E minus 04

200E minus 04

000E + 00

Am

plitu

de

1 2 3




0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signalAc

cele

ratio

n (g

)Ac

cele

ratio

n (g

)

2

1

0

minus1

minus2

2

1

0

minus1

minus2

Defect signal


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

1

05

0

minus05

minus1

minus15

1

05

0

minus05

minus1

minus15


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

06

04

02

0

minus02

minus04

minus06

06

04

02

0

minus02

minus04

minus06









Signalacquisition

FilteringDWT

RPM

Fault diagnosis

Signalanalysis

Faultidentification

(alarming)

Faultestimation

Save

Filetxt




6 Conclusion






Nomenclature


1015840















Acknowledgment


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signalAc

cele

ratio

n (g

)Ac

cele

ratio

n (g

)

2

1

0

minus1

minus2

2

1

0

minus1

minus2

Defect signal


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

1

05

0

minus05

minus1

minus15

1

05

0

minus05

minus1

minus15


0 05 1 15 2 25 3 35 39

Time (s)

0 05 1 15 2 25 3 35 39

Time (s)

Normal signal

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Defect signal

06

04

02

0

minus02

minus04

minus06

06

04

02

0

minus02

minus04

minus06









Signalacquisition

FilteringDWT

RPM

Fault diagnosis

Signalanalysis

Faultidentification

(alarming)

Faultestimation

Save

Filetxt




6 Conclusion






Nomenclature


1015840















Acknowledgment


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Signalacquisition

FilteringDWT

RPM

Fault diagnosis

Signalanalysis

Faultidentification

(alarming)

Faultestimation

Save

Filetxt




6 Conclusion






Nomenclature


1015840















Acknowledgment


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















Acknowledgment


References
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Failure Diagnosis System for a Ball-Screw ...

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Transcript of Research Article Failure Diagnosis System for a Ball-Screw ...