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CIRP Annals - Manufacturing Technology 64 (2015) 377–380

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A defect-driven diagnostic method for machine tool spindles

Gregory W. Vogl *, M.A. Donmez

Engineering Laboratory, National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, MD 20899-8220, USA

Submitted by J. Peters (1), Leuven, Flanders, Belgium

1. Introduction

Unexpected failure of machine tool spindle bearings will resultin production loss. Hence, condition monitoring for spindles playsan important role in improving productivity [1]. Yet there iscurrently no universally accepted method for determining themachine tool spindle condition. The vibrations of the spindlehousing have been analyzed for machine acceptance purposes.However, resulting diagnostic methods are insufficient since themeasured vibrations are often not clearly related to bearingdamage. Therefore, a robust method to detect bearing faults earlyand avoid expensive repairs and machine downtime is needed.

One simple approach for diagnosing the spindle condition is tocompare the root-mean-square (RMS) vibration of the spindlehousing to threshold values [2]. More intricate approaches use thehigh-frequency resonance technique [3], envelope spectrumanalysis [4], wavelet transforms [5], neural networks [6],synchronous sampling [7], auto-correlation analysis [8], modaldecomposition [9], fractals and kurtosis [10].

A significant problem with all methods is that spindle diagnosescan be corrupted by system dynamics. The rotor excitation istransformed by system dynamics to yield the vibration data;vibration is a convolution of spindle dynamics and excitation frombearings. Resonances can adversely affect spindle conditionmetrics [2], and metrics based on vibration data may depend onspindle speed [11], even though spindle damage is not speed-dependent. For example, Fig. 1 shows that the long term spindle

condition (LTSC) metric from ISO/TR 17243-1 [2] rates a nspindle, with only 510 h of operation time and excelperformance, as a ‘C’ and ‘not suitable for long term operatio

2. Method for estimating spindle condition

Ideally, only the bearing defect geometry should be usedestimate the spindle condition. Therefore, measured data musused to separate system dynamics from defect geometry. In

case, a metric could be devised that depends only upon beadefects and is hence truly representative of the spindle condit

Fig. 2 shows a methodology for estimating spindle conditbased on the separation of spindle dynamics and defe

A R T I C L E I N F O

Keywords:

Spindle

Condition monitoring

Vibration

Machine tools

A B S T R A C T

Simple vibration-based metrics are, in many cases, insufficient to diagnose machine tool spindle condi

These metrics couple defect-based motion with spindle dynamics; diagnostics should be defect-drive

new method and spindle condition estimation device (SCED) were developed to acquire data an

separate system dynamics from defect geometry. Based on this method, a spindle condition metric rel

only on defect geometry is proposed. Application of the SCED on various milling and turning spindles sh

that the new approach is robust for diagnosing the machine tool spindle condition.

� 2015 C

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Contents lists available at ScienceDirect

CIRP Annals - Manufacturing Technology

journal homepage: http: / /ees.elsevier.com/cirp/default .asp

2 4 6 8 10 12 14 16 18 200

BA

Fig. 1. Example of dubious spindle condition metric.

Fig. 2. NIST methodology for estimating spindle condition based on separation of

system dynamics and bearing defect geometry.

* Corresponding author.

E-mail address: gvogl@nist.gov (G.W. Vogl).

http://dx.doi.org/10.1016/j.cirp.2015.04.103

0007-8506/� 2015 CIRP.

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G.W. Vogl, M.A. Donmez / CIRP Annals - Manufacturing Technology 64 (2015) 377–380378

section outlines the method, while later sections describe its

Data collection

s seen in Fig. 2, the first step of the new spindle conditionation method is to collect data on the spindle housing.

3(a) shows a spindle condition estimation device (SCED)ted for this purpose. The device attaches to spindle housingsa magnetic base. A solenoid with a force sensor is used foracts, yielding a frequency response function (FRF) through useorce and acceleration data. Two accelerometers of varyingitivity and range allow for robust collection of vibration data.een in Fig. 3(b)–(d), the device can be used on milling anding spindles in various configurations.

he SCED with instrumentation and custom software are usedata acquisition at a sampling rate of fs = 51 200 Hz. First, ten

acts are performed with no rotor motion and repeatableimum force (�200 N). Then, accelerometer data are collectedvarious spindle speeds, from 1200 rpm (20 Hz) up to thedle’s maximum speed, e.g., spindle speeds from 1200 rpm to

rpm with a 100 rpm interval. For statistical purposes, tens (Nr = 10) are conducted for each spindle speed.

Equation of motion

efects in the spindle bearings affect the rigid-body componente rotor motion. For any spindle speed, the motion of the point P

the rotor (see Fig. 2) can be described in the cycles perlution (CPR) domain as r(CPR), where CPR is defined as

¼ f(1)

where an overbar denotes the discrete Fourier transform (DFT) andG[f] is the dynamics transfer function relating force excitation toresulting velocity. For sufficiently small frequencies, G[f] isapproximated as

G½ f � ¼ meff v3 FRF½ f � (3)

where meff is an effective mass based on spindle configuration,v = 2pf, and FRF[f] is the measured FRF that relates vibrationdisplacement (derived from measured acceleration) to appliedforce. The method uses Eq. (2) to solve for both the spindle defectfunction, r̄½CPR�, in the CPR domain and the dynamics transferfunction, G[f], in the frequency domain. The natural logarithm ofeach side of Eq. (2) separates the unknowns G[f] and r̄½CPR�:

lnjv̄j ¼ lnjGj þ lnjr̄j (4)

A linear system of equations can be created by utilizing data forall spindle speeds. To this end, the velocity data should be used in

lnjv̄i;nj ¼ lnjG½ f i;n�j þ lnjr̄nj (5)

for the ith spindle speed and the nth CPR value. This processrequires the same CPR values, regardless of spindle speed, achievedwhen the record length Ni is approximately

Ni ¼ 2 round1

2

f s

f sp;i DCPR

!(6)

where round(x) rounds x to its nearest integer, fsp,i is the ith spindlespeed, and DCPR is the desired CPR resolution. The resolution DCPR

should be small enough to successfully separate the spindle defectfrequency components, e.g., DCPR = 0.05.

For an M number of spindle speeds and an N number of CPR

values, there are an M � N number of equations according toEq. (5). For each CPR value, the velocity, v(t), can now be processedfor use within Eq. (5). To this end, the velocity DFT, v̄r½i; CPRn�, forthe ith spindle speed and rth trial is averaged in a root-mean-square fashion over the Nr trials as

jv̄i;nj ¼1

Nr

XNr

r¼1

jv̄r½i; CPRn�j2" #1=2

(7)

Finally, a P number of unique frequencies, (f1, f2, . . ., fp), are used toapproximate Eq. (5) as

lnjv̄i;nj ¼ lnjG½ f̃i;n�j þ lnjr̄nj (8)

where f̃i;n is the closest value to fi,n within the set of frequencies.Eq. (8) yields an M � N number of equations that are linear in

the unknowns, ln|Gp| and lnjr̄nj. Because the linear system isoverdetermined, a least-squares solution exists. The variablesrelated to system dynamics and bearing defect geometry are highlycoupled for robustness. For data collected at twenty spindle speeds(M = 20), up to 60 values of r̄ relate to one G variable, and one r̄value is related to up to 20 values of G.

2.3. Least-squares formulation

The next step of the method is to create a constraint equationand solve for G[f] and r̄½CPR�. A unique least-squares solutionrequires at least one constraint. As Eq. (2) reveals, the product oftwo unknown functions is the same to within a scaling factor, a,

. (a) Spindle condition estimation device, being (b) horizontal on a vertical milling

r, (c) upright on a turning center, and (d) upside-down on a turning center.

f sp

s the spindle speed in hertz, and f is the frequency (Hz) ofrest. Hence, r(CPR) is a measure of displacement associated

bearing defects.he next step of the method is to process the velocity, v(t),ch is derived from the measured acceleration, for use within antion of motion (EOM). Note that either velocity or acceleration

be used to yield the same result. Accordingly, application ofsical mechanics yields the approximate EOM as

R�j ¼ jG½ f �jjr̄½CPR�j (2)

because ð1=aÞG½ f � � ar̄½CPR� still yields G½ f � � r̄½CPR�. FRF data isused to create the constraint equation,

XJ

j¼1

ln G j ¼XJ

j¼1

lnðmeff v3j FRF jÞ (9)

in which only the J number of points with an acceptable coefficientof variation (COV � 0.03) and frequency (100 Hz < f < 200 Hz) areused. The COV requirement ensures that only robust data is used,while the frequency requirement ensures that Eq. (3) may be used;the spindle rotor can be regarded as being fairly rigid for a

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G.W. Vogl, M.A. Donmez / CIRP Annals - Manufacturing Technology 64 (2015) 377–380 379

frequency f that is well below the fundamental frequencies of thespindle assembly from 1.2 kHz to 2.5 kHz [12].

Finally, the set of equations from Eq. (8) with the constraintEq. (9), are solved in a weighted least-squares fashion usingweights that depend on signal to noise, COV, and velocity spectrummagnitudes. The result is the unique solution of G[f] and r̄½CPR�.

2.4. Spindle defect metric

The defect function, r̄½CPR�, is used to create a spindle conditionmetric, independent of spindle speed and dynamics G[f]. A spindledefect metric function, rrms, is defined as

rrmsðCPRcrÞ ¼ 1

2

XCPRmax

CPRcr

fr̄½CPR�g2

" #1=2

(10)

where CPRmax is the maximum CPR value and CPRcr is a chosenminimum threshold. Eq. (10) is equivalent to the RMS of r(t) that ishigh-pass filtered to keep terms with sufficiently high frequencies(CPRcr � 1.5) indicative of spindle defects. Fig. 4 shows the spindlemetric function from Eq. (10) for 11 machine tool spindles, groupedas ‘new’, ‘used’, or ‘worn’ based on the total operation time. Asoperation time increases, spindle wear increases and ‘defectenergy’ moves into higher CPR values.

This trend of defect energy with operation time can be revealedusing a single defect metric,

rmetric ¼1

2

XCPRmax

CPR¼1:5

fr̄½CPR�CPRg2

" #1=2

(11)

Eq. (11) is related to the RMS velocity, vrms, of point P (see Fig. 2)associated with the rigid-body component of the rotor motion withan angular speed of V; that is, vrms ¼ rmetricV. Consequently,Eq. (11) is a measure of the spindle condition that is related tovelocity while being independent of spindle speed. Fig. 5 showsthat the spindle defect metric ranges from 0.3 mm (new spindle) to18 mm (spindle with about 16 000 h of operation time) for themachine tools utilized in Fig. 4.

T2 has a condition that is about 3 times better than Spindle T1, ethough Spindle T1 has far fewer operation hours. Howeaccording to the spindle defect metric in Eq. (11), the two spinhave basically the same condition.

Fig. 6 helps explain the differences among the ISO metric

the proposed metric. The ISO metric is generally the largest RMfiltered vibration, and as seen in Fig. 6(a) and (b), Spindle T1 hgreater vibration (and hence ISO metric) than Spindle T2. HoweFig. 6(c) and (d) shows that only Spindle T2 shows noticeable wespecially due to defects on the outer race of the front bearTherefore, Spindle T2 has greater wear due to its use in productdespite the ISO metric suggesting otherwise. The reason for

greater vibrations and ISO metric for Spindle T1 is seen in Fig. 6the dynamics function, G[f], for Spindle T1 is significantly grethan that for Spindle T2 for frequencies below 2.5 kHz, which leto greater vibrations for Spindle T1 compared to Spindle T2.

The NIST method, however, accounts for vibration differendue to system dynamics. The spindle defect metric is almostsame for both spindles, as seen in Table 1. In order to verify

result, a round brass test piece was turned on the two turnspindles at 1200 rpm, the same speed used for Fig. 6(a) and

Finally, the roundness profiles were measured. Fig. 7 shows tha

101

102

0

0.5

1

ρ met

ric (

um)

New (< 30 0 hours)

Used (< 5 000 hours)

Worn (< 16 000 hours)

Fig. 4. rrms(CPRcr) for numerous machine tool spindles.

0 2 4 6 8 10 12 14 160

10

20metriclinear fitmetric

linear �it

Table 1Metrics for conditions of two turning spindles.

Spindle T1 T2

Total operation time (h) 120 22

ISO metric (mm/s RMS)a 0.155 0.0

Spindle defect metric (mm) 2.51 2.4a Long term spindle condition metric from ISO/TR 17243-1 [2].

Fig. 6. (a and b) Typical vibration data and (c and d) defect function for two tur

spindles with different total operation times of 120 h or 2210 h; (e) dyna

function for spindles.

Fig. 5. Spindle defect metric for numerous spindles.

Fig. 7. Roundness data for part turned at 1200 rpm on (a) Spindle T1 and (b) Spindle T2.

3. Example of two turning spindles

The advantage of the metric in Eq. (11) over existing metrics canbe illustrated for two turning spindles (‘T1’ and ‘T2’), which are onmachines of the same model and configuration but with differentoperation histories. Spindle T1 is relatively new with only 120 h oftotal operation time, and Spindle T2 was used in production for2210 h. Table 1 shows that, according to ISO/TR 17243-1, Spindle

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G.W. Vogl, M.A. Donmez / CIRP Annals - Manufacturing Technology 64 (2015) 377–380380

ort of the NIST method, the spindles have similar peak-to- magnitudes in roundness variations.

xample of two milling spindles

nother example using two milling spindles (‘M1’ and ‘M2’)trates the advantages of the new method for spindlenostics. Similar to the turning spindle example, the twoing spindles are on machines of the same model andguration but with different operation histories. As seen in

e 2, ISO/TR 17243-1 [2] indicates that the condition of Spindleis about 16 times worse than the condition of Spindle M1.8(a) shows that the ISO metric estimates that Spindle M2 is inred ‘D’ zone, while Spindle M1 is in the green ‘A’ zone.

owever, the ISO metric values in Table 2 are not consistent other operational information. Both spindles have been usedore than 14 000 h of production, so Spindle M1 is not ‘newly

missioned’, per Zone A [2]. On the other hand, both spindlesproduce acceptable parts, without any indication of a ‘criticalition’ for Spindle M2, per Zone D [2].ontrary to the ISO metric and yet more consistent with otherrmation, the spindle defect metric indicates that the twoing spindles are in ‘used’ conditions with more similar levels ofadation and Spindle M1 having a condition that is worse thandle M2.hus, the significant difference between the two ISO metrices in Table 2 appears to be a result of the influence of systemamics. Due to this possibility, the ISO method allows for theusion of 10 percent of data near resonances. For the two millingdles, Fig. 8(b) and (c) shows typical acceleration signals for

attributed to the differences in dynamic behaviors of the twospindles.

5. Conclusions

A new method and device were developed for estimation ofmachine tool spindle condition. The method separates systemdynamics from defect geometry, and based on this method, aspindle defect metric relying only on defect geometry wasproposed. The metric includes effects due to rolling elements,inner races, and outer races. Therefore, the metric is not corruptedby resonances and other unwanted system dynamics.

Application for various milling and turning spindles shows thatthe new approach is robust for diagnosing the machine tool spindlecondition. Hence, a spindle condition estimation device could beused within a time-based maintenance schedule for monitoringspindle degradation. The metric could be tracked and outputtedto the user as a diagnostic based on thresholds (e.g., ‘new’ to‘unacceptable’), and the trend of the metric could be used topredict remaining useful life (RUL) for maintenance planning.

Acknowledgements

The authors thank Brian Pries (NIST) and Hardinge Inc. (Elmira,NY, USA) for their generous and pivotal help with data collection.This work was also served by invaluable discussions with JohannesSoons (NIST) and assistance from Taeweon Gim (Doosan Infracore,South Korea). Finally, the authors thank ISO Technical Committee39, Subcommittee 2 (ISO/TC39/SC2) for its stimulation regardingspindle condition research.

References

[1] Abele E, Altintas Y, Brecher C (2010) Machine Tool Spindle Units. CIRP Annals –Manufacturing Technology 59(2):781–802.

[2] International Organization for Standardization (2014) ISO/TR 17243-1: MachineTool Spindles – Evaluation of Spindle Vibrations by Measurements on Non-RotatingParts – Part 1: Motor Spindles Measured at Speeds between 600 min�1 and30 000 min�1 Supplied with Rolling Element Bearings, ISO, Geneva, Switzerland.

[3] McFadden PD, Smith JD (1984) Vibration Monitoring of Rolling ElementBearings by the High-Frequency Resonance Technique – A Review. TribologyInternational 17(1):3–10.

[4] Patel VN, Tandon N, Pandey RK (2012) Defect Detection in Deep Groove BallBearing in Presence of External Vibration Using Envelope Analysis and DuffingOscillator. Measurement: Journal of the International Measurement Confedera-tion 45(5):960–970.

[5] Liu J (2012) Shannon Wavelet Spectrum Analysis on Truncated VibrationSignals for Machine Incipient Fault Detection. Measurement Science and Tech-nology 23(5):055604.

[6] Wulandhari LA, Wibowo A, Desa MI (2015) Condition Diagnosis of MultipleBearings Using Adaptive Operator Probabilities in Genetic Algorithms and BackPropagation Neural Networks. Neural Computing and Applications 26(1):57–65.

[7] Luo H, Qiu H, Ghanime G, Hirz M, van der Merwe G (2010) SynthesizedSynchronous Sampling Technique for Differential Bearing Damage Detection.Journal of Engineering for Gas Turbines and Power 132(7):072501.

[8] Tomovic R, Miltenovic V, Banic M, Miltenovic A (2010) Vibration Response ofRigid Rotor in Unloaded Rolling Element Bearing. International Journal ofMechanical Sciences 52(9):1176–1185.

[9] Sheen Y-T, Liu Y-H (2012) A Quantified Index for Bearing Vibration AnalysisBased on the Resonance Modes of Mechanical System. Journal of IntelligentManufacturing 23(2):189–203.

[10] Elasha F, Ruiz-Carcel C, Mba D, Chandra P (2014) A Comparative Study of theEffectiveness of Adaptive Filter Algorithms, Spectral Kurtosis and LinearPrediction in Detection of a Naturally Degraded Bearing in a Gearbox. Journalof Failure Analysis and Prevention 14(5):623–636.

[11] Hoshi T (2006) Damage Monitoring of Ball Bearing. CIRP Annals – Manufactur-ing Technology 55(1):427–430.

[12] Vafaei S, Rahnejat H, Aini R (2002) Vibration Monitoring of High Speed

2ics for conditions of two milling spindles.

ndle M1 M2

al operation time (h) 14 200 14 700

metric (mm/s RMS)a 0.522 8.71

ndle defect metric (mm) 16.7 7.02

ong term spindle condition metric from ISO/TR 17243-1 [2].

. (a) Long term spindle condition metric from ISO/TR 17243-1 [2] and vibration

for two milling spindles with similar total operation times of (b) 14 200 h for

nd (c) 14 700 h for M2.

dle speeds remaining after data exclusion. For this case, therent discrepancy in the accelerations within Fig. 8(b) and (c) is

Spindles Using Spectral Analysis Techniques. International Journal of MachineTools and Manufacture 42(11):1223–1234.