Techniques for the Health Assessment of Automotive 

Alternators

by Andrew J. Bayba, David N. Siegel, and Kwok Tom

ARL-TR-6041 June 2012

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Army Research Laboratory

Adelphi, MD 20783-1197

ARL-TR-6041 June 2012

Techniques for the Health Assessment of Automotive 

Alternators

Andrew J. Bayba, David N. Siegel, and Kwok Tom

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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Techniques for the Health Assessment of Automotive Alternators

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Andrew J. Bayba, David N. Siegel, and Kwok Tom

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14. ABSTRACT

Preliminary data analysis was performed on automotive alternators in common use in Army vehicles. This effort was an 

investigation on the feasibility of early fault detection using data analysis techniques. Using data acquired on a common 

military vehicle alternator, several analysis methods were employed to arrive at features expected to indicate anomalous 

behavior. This specific data analysis task supports the broader objective to investigate the feasibility of real-time condition 

monitoring and failure mode diagnostics in Army systems.

15. SUBJECT TERMS

Alternator health assessment, alternator health monitoring, alternator prognostics and diagnostics

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iii

Contents

List of Figures iv

List of Tables v

1. Introduction 1

2. PSU Experiment Description 2

3. Data 4

4. Signal Processing Techniques 4

4.1 Time Domain Waveform Analysis..................................................................................6

4.1.1 Time Domain Current Signals.............................................................................6

4.1.2 Time Domain Voltage Signals ............................................................................7

4.2 Frequency Domain Processing and Key Harmonics.......................................................8

4.3 Current and Voltage Spectra ...........................................................................................9

4.4 Vibration Spectra...........................................................................................................10

4.5 Time Synchronous Averaging.......................................................................................11

4.6 Residual and Regular Signal Processing.......................................................................12

4.7 Envelope Analysis.........................................................................................................12

4.8 Bearing Fault Analysis..................................................................................................12

4.9 Figures of Merit.............................................................................................................14

4.10 Feature Extraction and Selection...................................................................................15

5. Discussion 23

6. Conclusions and Recommendations 23

7. References 24

Appendix. Data Plots for Reference 27

List of Symbols, Abbreviations, and Acronyms 37

Distribution List 38
iv

List of Figures

Figure 1. Output current of alternators as a function of rotational speed. ......................................2

Figure 2. (a) Current signal of a new alternator and (b) alternator #5 just prior to failure.............7

Figure 3. (a) Current signal of a used alternator and (b) alternator #5 immediately after 

failure. ........................................................................................................................................7

Figure 4. (a) Voltage signal of a new alternator and (b) alternator #5 just prior to failure. ...........8

Figure 5. (a) Voltage signal of a used alternator and (b) alternator #5 immediately after 

failure. ........................................................................................................................................8

Figure 6. Typical voltage spectrum for a functional alternator. .....................................................9

Figure 7. Functional alternator spectrum showing the typical 36X peak. ....................................10

Figure 8. Y-direction spectrum of alternator #5 showing the 3X peak. .......................................11

Figure 9. Z-direction of alternator #5 showing high frequency content. ......................................11

Figure 10. 12X voltage peaks for all alternators tested as a function of shaft speed....................16

Figure 11. Current ripple standard deviation with the associated shaft speeds for all 

alternators.................................................................................................................................17

Figure 12. FOM_C1 with the associated shaft speed for all alternators.......................................18

Figure 13. 12X current peaks with the associated shaft speed for all alternators.........................19

Figure 14. 12X current peaks with the associated shaft speed for all alternators.........................20

Figure 15. Vibration 3X peak in the Y-direction with the associated shaft speed for all 

alternators.................................................................................................................................21

Figure 16. FOM_3-V with the associated shaft speed for all alternators. ....................................22

Figure 17. Kurtosis of the regular signal current with the associated shaft speed for all 

alternators.................................................................................................................................22

Figure A-1. Frequency spectra for the current output for the four alternator cases......................27

Figure A-2. Frequency spectra for the voltage signal for the four alternator cases......................28

Figure A-3. Vibration spectra for X-direction for the four alternator cases. ................................29

Figure A-4. Vibration spectra for Y-direction for the four alternator cases. ................................29

Figure A-5. Vibration spectra for Z-direction for the four alternator cases..................................30

Figure A-6. TSA current spectra for the four alternator cases......................................................30

Figure A-7. TSA voltage spectra for the four alternator cases. ....................................................31

Figure A-8. TSA X-direction vibration spectra for the four alternator cases. ..............................31

Figure A-9. TSA Y-direction vibration spectra for the four alternator cases. ..............................32

Figure A-10. TSA Z-direction vibration spectra for the four alternator cases..............................32
v

Figure A-11. Current residual for the four alternator cases. .........................................................33

Figure A-12. Voltage residual for the four alternator cases..........................................................33

Figure A-13. Current envelope signal for the four alternator cases..............................................34

Figure A-14. Voltage envelope signal for the four alternator cases. ............................................35

Figure A-15. Vibration envelope spectra (x-direction) showing BPFO. ......................................36

List of Tables

Table 1. Numbering and descriptions of alternators tested.............................................................3

Table 2. Method 1 operating set-points ..........................................................................................3

Table 3. Method 2 operating points. ...............................................................................................4

Table 4. Data collected. ..................................................................................................................4

Table 5. Recent work in alternator health monitoring. ...................................................................5

Table 6. Signal processing techniques employed in this report......................................................6

Table 7. Key harmonics to monitor. ...............................................................................................9

Table 8. Fault frequencies as a function of shaft frequency (order) and the special case of 

3500 RPM. ...............................................................................................................................13

Table 9. Features extracted. ..........................................................................................................15
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction

Automated prognostics and diagnostics (P&D) of the health of Army assets has become a top 

Department of Defense (DoD) priority. This is particularly true in the automotive field due to 

the sheer quantity of vehicles in service. The alternator has been identified as an item where 

P&D could have a significant impact. Alternator testing was performed by the Applied Research 

Laboratory at Pennsylvania State University (PSU) under contract from the U.S. Army Tank and 

Automotive Research, Development and Engineering Command (TARDEC). The testing 

performed by PSU was to characterize various alternators with the intention of conducting 

seeded fault testing. A limited number of alternators were characterized due to redirection of the 

PSU effort to another project. Six alternators were tested: three new and three used. The 

alternators are Leece-Neville 4000 Series, model number A0014827 JB 130A. Additional 

information can be found in the PSU Report of the testing (1). The used alternators had no 

obvious indication of damage. Curiously, one of the new alternators had a catastrophic failure 

during the course of testing. This failed alternator provided us the opportunity to search for 

precursor indicators of failure, in addition to developing characteristic baseline features for 

discriminating between new and used alternators.

This study provides valuable information on the relevance of various analysis techniques for the 

assessment of alternator health and significant observations regarding key features in the 

processed data. However, development of algorithms for P&D of alternator health would require 

additional data. By its nature, the PSU test data set does not lend itself to thorough diagnostic 

analysis, such as health assessment, and prognostics such as remaining useful life. This data set 

was only a baseline characterization of a subset of alternators available; the project was 

redirected prior to its completion and controlled fault testing never initiated. For proper 

diagnostic and prognostic algorithm development the alternators would require multiple runs at 

an operating set point, and runs for longer durations (some until failure). The PSU data set is 

lacking in both of these categories. However, we believe that our analysis of the data at hand is 

still very useful as various analysis techniques are examined and recommendations are presented 

for future work.

As a general note on performance of the alternators, all closely matched the expected 

relationship with output current and rotational speed according to the manufacturer’s data sheet 

(2), as shown in figure 1. Alternator #5 measurements are prior to its failure.
2

Figure 1. Output current of alternators as a function of rotational speed.

2. PSU Experiment Description

PSU performed two different series of experiments, hereafter referred to as Method 1 and 

Method 2. In Method 1, the current, rotational speed and ambient temperature were varied. In 

Method 2, the alternators were run at a given rotational speed at their maximum output current. 

Six alternators were tested in Method 1; the same alternators were testing in Method 2, except 

for #13. The reason for the exclusion of alternator #13 from Method 2 testing is unknown.

Identification numbers were assigned to the alternators by PSU, and for clarity, the same 

designations have been retained here. Alternator numbers, condition, and comments are provided 

in table 1.

1000 1500 2000 2500 3000 3500 4000 4500 5000

50

60

70

80

90

100

110

120

130

Rotational Speed (rpm) Output Current (A)

Alternator Output Curve

#15

#30

20

22

5
3

Table 1. Numbering and descriptions of alternators tested.

Alternator 

Identifier

Starting 

Condition Comments

# 5 New Failed during Run # 67 Method 2 test; output current and 

voltage dropped to near zero

# 13 New Was not tested during the second set of tests (Method 2)

# 15 New —

# 20 Used —

# 22 Used —

# 30 Used —

1. In Method 1, the current, rotational speed and ambient temperature were varied; operating 

at specific set-points for each of the alternators, as shown in table 2. From table 2, one can 

calculate that each alternator was tested under 75 different operating points (5 current setpoints, 5 speed set-points, and 3 temperature set-points). This produced 75 data files 

collected for each alternator. Since there were 6 alternators tested, a total of 450 data files

were generated.

Table 2. Method 1 operating set-points

Current Setting

(Amps)

Rotational Speed

(RPM)

Ambient Temperature

(°C)

10 1500 50

40 3000 100

70 4500 150

100 6000

130 7500

2. In the second set of experiments, Method 2, the alternators were operated at a given 

rotational speed in order to obtain the maximum output current for a given speed, as shown 

in table 3. This was essentially running the alternator at its output current set-points. Again, 

the same alternators were tested with the Method 2 procedure with the exception of 

alternator #13. During testing with Method 2, alternator #5 failed at some point in the 

second day of operation.
4

Table 3. Method 2 operating points.

Current Output

(Amps)

Rotational Speed 

(RPM)

60 1500

95 2500

107 3000

115 3500

120 4000

125 4500

3. Data

Output current, output voltage, and the signals from the three axes of a tri-axial accelerometer

comprised the measured data, as shown in table 4. The data were sampled at 102.4 KHz for all 

five channels. There is no tachometer signal; however, alternative methods were used to 

synthesize a tach signal so that certain analysis techniques could be employed. Measurement of 

the individual phase voltages and currents was not acquired, but would be very useful if future 

studies are conducted. 

Table 4. Data collected.

Signal Signal 

Description

Comments

1 Vibration - x From tri-axis accelerometer

2 Vibration – y From tri-axis accelerometer

3 Vibration – z From tri-axis accelerometer

4 Output Current From current transducer on the 28-V terminal

5 Output Voltage Voltage signal from 28-V terminal

4. Signal Processing Techniques 

The approach taken was to evaluate various signal processing techniques as to their applicability 

of identifying anomalies associated with degradation, health assessment, and prediction.
5

We first consider recent automotive alternator condition monitoring work to get an idea of what 

the primary faults are and what approaches are being used (table 5). It appears that the common 

alternator failure modes are diode faults, stator winding faults, belt slippage, and bearing faults. 

The two patents that employ the root-mean-square (RMS) ratio between phase currents should be 

noted. Their implementation appears to have significant potential due to the ease and low cost of 

insertion and the relative simplicity of processing. Unfortunately, we could not pursue this area

since individual phase currents were not recorded. 

Table 5. Recent work in alternator health monitoring.

Company/University/

Research Center Methods Comments

Caterpillar (3)

RMS ratio between each of 

the three phase currents 

This patent precedes the C. E.

Niehoff patent 

C. E. Niehoff (4)

RMS ratio between phase 

currents also includes control 

aspects for handling the 

degraded situation. 

They are an Original 

Equipment Manufacturer of 

alternators, so they could 

potentially embed the 

intelligence into the 

component. 

General Motors R&D, 

also includes Wright 

State University (5–7)

Data driven Principal 

Component Analysis and 

various residual model based 

algorithms 

Focused on belt slippage and 

diode problems. 

AMSSA and Applied 

Research Lab at Penn. 

State University (8)

Current and vibration time 

and frequency domain 

analysis, and feature 

extraction techniques 

Seeded fault test with stator 

winding short and bearing 

faults showed promise 

Clemson University (9)

Model-based residual 

method, automatically set 

thresholds using their 

approach

For detecting belt slippage, 

diode, and regular problems, 

the paper shows simulation 

results 

There are many signal processing techniques that can be employed on the alternator data set in 

order to generate features that might be useful for condition monitoring. Extracting features or 

condition indicators from the vibration, voltage, and current sensor measurements provides 

deeper comprehension of the alternator operational condition. Basic statistical conversion of the 

measured sensor data provides a means of reducing and summarizing the sensor output to a few 

parameters. Some of the other techniques enhance the signal quality through noise reduction or 

filtering. Analysis is also conducted in the frequency domain, where certain physical 

characteristics of the alternator can be easily recognized. These along with the rationale are 

presented in table 6.
6

Table 6. Signal processing techniques employed in this report.

Technique Rationale

Time Domain Analysis Voltage waveform has various signatures related 

to stator or diode faults (10, 11). 

Frequency Domain Analysis

Harmonics (36X/stator slot frequency); sub 

harmonics (12X or 18X), and sidebands could be 

important (12). 

Time Synchronous Averaging

Improve signal to noise ratio for harmonics 

synchronous with shaft (18X, 36X, 72X, etc.) 

(13). 

Analysis of the Residual 

Signal 

Analogous to gear signals, stator slot frequency 

vibration and current information (36X) can be 

removed and residual signal can offer diagnostic 

information. 

Envelope Demodulation Demodulation around 36X can reveal sidebands 

and amplitude modulation effects. 

Bearing High Frequency 

Response Technique (HFRT)-

Envelope Analysis

Most established method for bearing condition 

monitoring (14). 

4.1 Time Domain Waveform Analysis

Time domain waveform analysis is the easiest to perform and is potentially sufficient for 

diagnostics and prognostics. Statistical features such as RMS, peak to peak, and kurtosis are easy 

to calculate, making them amenable to real-time application, and in many cases, are good 

indicators of degradation. Samples of the raw signal data are presented below since several 

characteristics of interest are clearly visible.

4.1.1 Time Domain Current Signals

Figures 2 and 3 show sample plots of current time signals for two new alternators; figure 3 is 

immediately prior to failure of alternator #5. As seen in the figures, the signals distinctly show a 

clear ripple frequency of 36 times the alternator shaft speed (36X). The plots are shown for a 

single period with the alternator rotating at a nominal rate of 3500 rpm and an electrical load in 

the range of 120–130 A. This ripple frequency is based on their being six pole pairs, three

phases, and the rectification of each phase by the diodes producing 36 “ripples” for each rotation 

(3 x 6 x 2). Even though figure 3 is right before the failure of alternator #5, there is very little 

visual difference in the time domain between the signals of the two figures.
7

Figure 2. (a) Current signal of a new alternator and (b) alternator #5 just prior to failure.

Figure 3. (a) Current signal of a used alternator and (b) alternator #5 immediately after failure.

The current signal for a used alternator is shown in figure 3a and from alternator #5 immediately 

after failure in figure 3b. The used alternator shows the 36X ripple frequency along with 

amplitude modulation, in which the modulation frequency is approximately 6X. One can observe 

in figure 3b that the output of the alternator that failed is only at 1A output current. It still retains

a frequency of 36X.

4.1.2 Time Domain Voltage Signals

The voltage signal also shows a characteristic ripple frequency for new alternators (#13 and #5 

just prior to failure), as is seen in figures 4a and b. Visually, there is not a substantial difference 

in the two time signals. 

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

100

105

110

115

120

125

130

135

140

Time (s)

Current (A)

Current Time Signature for File: Method 2 and File # 8, Alternator #15

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

100

105

110

115

120

125

130

135

140

Time (s)

Current (A)

Current Time Signature for File: Method 2 and File # 66, Alternator #5

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

100

105

110

115

120

125

130

135

140

Time (s)

Current (A)

Current Time Signature for File: Method 2 and File # 18, Alternator #30

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time (s)

Current (A)

Current Time Signature for File: Method 2 and File # 67, Alternator #5
8

Figure 4. (a) Voltage signal of a new alternator and (b) alternator #5 just prior to failure.

The used alternator shows a visually similar voltage time signal (figure 5a) compared to a new 

alternator. Figure 5b is the voltage signal of the failed alternator and as seen, the failure signature 

is very obvious; not only is the voltage output much lower, a clear 6× frequency can be observed.

Figure 5. (a) Voltage signal of a used alternator and (b) alternator #5 immediately after failure.

4.2 Frequency Domain Processing and Key Harmonics

In this category, there are specific frequencies (key harmonics) to monitor and additional 

frequency domain information that can be examined. The key harmonics to be monitored are 

listed in table 7, where X is a multiple (order) of the shaft frequency. Other spectral components 

are related to the physical configuration of the alternator and briefly explained. Each individual 

phase voltage and current signal prior to rectification has a fundamental frequency of 6 times the 

shaft speed. Also, shaft vibration at 1X the shaft speed due to unbalance or 2X due to 

misalignment could also be present, as well as harmonics. Finally, there are several frequencies 

of interest related to bearing tones, which are discussed in more detail in section 4.8.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

25

26

27

28

29

30

31

Time (s)

Voltage (V)

Voltage Time Signature for File: Method 2 and File # 8, Alternator #15

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

25

26

27

28

29

30

31

Time (s)

Voltage (V)

Voltage Time Signature for File: Method 2 and File # 66, Alternator #5

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

25

26

27

28

29

30

31

Time (s)

Voltage (V)

Voltage Time Signature for File: Method 2 and File # 18, Alternator #30

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Voltage (V)

Voltage Time Signature for File: Method 2 and File # 67, Alternator #5
9

Table 7. Key harmonics to monitor.

Signal Frequency (Orders) Comments

Current 36X* and harmonics Ripple frequency, due to 6 poles, 3 phases, 

and rectification. 

Voltage 36X* and harmonics Ripple frequency, due to 6 poles, 3 phases, 

and rectification. 

Vibration 36X* and harmonics Stator slot frequency, 36 stator slots and each 

pass generates a magnetic force.

4.3 Current and Voltage Spectra

The current and voltage spectra are presented for new, used, and pre- and post-failure alternators 

in figures A-1 and A-2 of the appendix. The current and voltage spectra have a very similar 

structure for all cases and the following observations apply to both. The frequency spectra show

clear peaks at the ripple frequency, 36X, and its harmonics (up to 180X) for all the cases. An 

example plot of a new alternator is presented in figure 6, displaying the 36X peak and harmonics. 

A visual inspection of the current and voltage spectra (in the appendix) revealed some interesting 

observations. The spectra are very much similar for all the operational alternators. A 36X 

component is easily observed. Even the failed alternator has peaks at 36X and its harmonics;

however, the magnitudes are much, much lower than the other cases. The used alternator has a 

peak at 12X, which is not observed for any of the new alternators.

Figure 6. Typical voltage spectrum for a functional alternator.

0 20 40 60 80 100 120 140 160 180 200

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

X: 36.33

Y: 0.1713

Frequency (Order)

Voltage Magnitude (V)

Voltage Spectrum for File: Method 2 and File # 8, Alternator #15
10

4.4 Vibration Spectra

X, Y, and Z-direction accelerometer spectra are presented for a new, used, and pre- and postfailure alternator (#5) in figures A-3, A-4, and A-5 of the appendix. In comparing the spectra of a 

new alternator, the pre-failure alternator and a used alternator spectra, one can see a clear peak at 

the stator slot frequency (36X) in all cases and that the 36X peaks are reasonably close in 

magnitude. The difference in magnitude of these sample plots was later seen to be within the 

variation of all the alternators (pre-failure). The failed alternator has no frequency content at 36X 

or harmonics of 36X. One curious result in the Y-direction is that for both the pre- and postfailure alternators, there is a significant peak at 3X; this may be due to shaft-related problems 

such as misalignment or imbalance. The Z-direction accelerometer spectrum contains isolated

high frequency content as broadband responses between orders 50 and 60 (near 3000 Hz) and 

also between orders 100 and 120 (near 6000 Hz). The failed alternator also contains the high 

frequency content indicating that this phenomenon is related to structural resonances and not due

to the magnetic forces from the rotor passing each stator slot. Example plots of interest are 

included here for reference. Figure 7 shows the distinct 36X peak present in all pre-failure 

alternators, figure 8 shows the 3X peak in alternator #5 in the Y-direction, and figure 9 shows the 

high frequency broadband responses in the Z-direction.

Figure 7. Functional alternator spectrum showing the typical 36X peak.

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

X: 36.19

Y: 3.258

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ax Vibration Spectrum for File: Method 2 and File # 66, Alternator #5
11

Figure 8. Y-direction spectrum of alternator #5 showing the 3X peak.

Figure 9. Z-direction of alternator #5 showing high frequency content.

4.5 Time Synchronous Averaging

As the name implies, time synchronous averaging (TSA) averages multiple blocks of data and is 

done in order to improve the signal-to-noise ratio. In order to employ this method, blocks of data 

must be synchronized. This is commonly done by synchronizing the start of each data block with 

a tachometer (tach) pulse. However, in this experiment a tach pulse was not recorded. Since the 

nominal speed of the shaft is known, we can use the data itself to derive a precise speed because 

of the presence of the 36X frequency component. With a precise speed, we can synthesize a tach 

pulse, which will serve as our synchronization mechanism. The steps for the aforementioned 

operation were previously described for gear meshing (15) and are detailed as follows:

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

6

X: 36.19

Y: 1.765

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ay Vibration Spectrum for File: Method 2 and File # 66, Alternator #5

X: 3.017

Y: 2.893

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

X: 36.33

Y: 1.225

Frequency (Order)

Vibration Magnitude (m/s

2

)

Az Vibration Spectrum for File: Method 2 and File # 8, Alternator #15
12

1. Bandpass filter the input signal around the 36X peak.

2. Take the Hilbert Transform of the filtered signal.

3. Calculate the phase of the analytic signal and unwrap the phase.

4. Take the modulus of the unwrapped phase signal over 2P.

With this synchronization technique, it is now possible to apply the standard TSA methodology.

In this technique, we find the zero crossings of the tach signal, interpolating the signal of interest 

at N equally spaced samples for each shaft revolution and ensemble averaging the re-sampled 

signal. Example spectra of the synchronous averages are provided in the appendix (figures A-6

through A-10) and show that most of the spectral lines are distinct order harmonics. Also, the 

36X peak has a noticeably higher magnitude ratio to other spectral lines compared to the nonaveraged signal.

4.6 Residual and Regular Signal Processing

These methods employ the concept that the synchronous signal can be divided into components,

which can be further analyzed. As shown in equation 1, the signal can be divided into xregular(t),

whose content is always present irrespective of the alternator condition or operating point and 

includes 36X and harmonics; xresidual(t), which possesses only the sidebands and sub-harmonics 

of the ripple frequency; and xshaft(t), which is the content related to shaft vibration unrelated to 

sidebands or sub-harmonics. Since these components contain particular information of the signal,

it allows for the extraction of unique and potentially useful features associated with that

component. The component xshaft(t) is expected to be unrelated to the alternator degradation and 

is not considered further in this study. Figures A-11 and A-12 in the appendix show residual 

signals for the current and voltage, respectively, for the four alternator cases.

x (t)

synchronous 

x (t) x (t) x (t) regular  residual  shaft

(1)

4.7 Envelope Analysis

The concept is to refine the examination of amplitude modulation affects around the ripple 

frequency/stator slot frequency. The processing steps include filtering around the 36X peak and 

using the Hilbert Transform to extract the envelope signal. Statistics of the envelope signal can 

then be processed in addition to examining the spectra. The rationale for including this method is 

that information related to sidebands, as well as amplitude modulation, can be captured. Sample 

plots for the current and voltage envelope signals are presented in the appendix (figures A-13

and A-14, respectively).

4.8 Bearing Fault Analysis

Bearing defects/damage is always an important consideration when analyzing rotating 

machinery. Bearing health is assessed by analysis involving the bearing characteristic 
13

frequencies, commonly referred to as fault frequencies. The bearing fault frequencies were 

calculated using the standard equations given in equations 2–5: The resulting orders/frequencies

are listed in table 8. It is important to note that the frequencies presented assume no slipping, 

while in reality, the actual values will vary slightly.

 

 

 

 

 

 

 (2)

 

 

 

 

 

 

 (3)

 

 

 

 

 

 

 (4)

 

 

 

 

 

 (5)

where

BPFI = the ball pass frequency of the outer race

BPFO = the ball pass frequency of the outer race and corresponds to a defect on the outer race

FTF = the fundamental train frequency

BSF = the ball spin frequency

f = the shaft frequency

n = number of balls

BD = ball diameter

PD = pitch diameter

θ = contact angle

Table 8. Fault frequencies as a function of shaft frequency (order) and the special case of 3500 RPM.

Bearing Fault 

Frequency Order Frequency at 3500 RPM (Order * Shaft Frequency)

BPFO 2.61 152.05 Hz

BPFI 4.39 256.28 Hz

BSF 1.83 106.82 Hz

FTF 0.37 21.72 Hz

Usually for incipient bearing damage, it is difficult to see bearing fault frequency peaks in the 

traditional spectrum (14). A very effective method to look for the fault frequencies is to perform 

envelope analysis; this method is well established for bearing condition monitoring. The 

procedure here is the same as that used previously for envelope analysis; however, the frequency 
14

that is bandpassed around is the natural or resonance frequency instead of the ripple frequency.

The bearing incipient fault is easier to detect at the resonance frequency band due to the 

amplification in this band over the noise corruption resident in the low frequency band. A 

bandpass filter centered around 3000 Hz was used, since there was a distinct natural frequency 

excited in this frequency range. The magnitudes of the fault frequencies are then recorded as 

features, as well as statistical information. Example plots of envelope vibration spectra are 

provide in figure A-15 in the appendix.

4.9 Figures of Merit

Certain features were calculated from combinations of other features based on their potential to 

provide better indicators of degradation; these metrics were termed figures of merit (FOMs).

These same set of FOMs are calculated for both the voltage and current signal. The vibration 

signal includes the first three, but replaces the last one with a ratio between the HFRT envelope 

RMS and the RMS of the raw signal.

The first, FOM_0, is given in equation 6, and provides the percentage of the signal comprised of 

36X and harmonics compared distinct with the total signal content synchronous with the shaft 

(values of 0.9 or above were typical):

 

2

Re

















TSASignal

gularSignal

RMS

RMS

(6)

The second, FOM_1, given in equation 7 provides a percentage of the signal is left if one 

removes the frequency content to due to ripple signal and harmonics (36X):

 

2

Re

















TSASignal

sidualSignal

RMS

RMS

(7)

The third, FOM_2, given in equation 8 is the ratio between the 18X peak and 36X peak. Prior 

work by PSU suggested this metric (8).

 















X Peak

X Peak

36 _

18 _

(8)

Finally, FOM_3, given in equation 9 provides a normalization of the ripple magnitude by the 

36X peak; both are known to increase with RPM and electrical load.

 















X Peak

Ripple Magnitude

36 _

_

(9)
15

4.10 Feature Extraction and Selection

In an effort to capture any changes in the signal, features were extracted for analysis. As can be 

seen in table 9, statistical features that are commonly used as indicators of degradation were

extracted for time domain signals, specific frequency peaks were extracted from the frequency

domain, and there are a few special features such as the FOMs. 

Table 9. Features extracted.

# Signal Processing 

Method Features #Features

1 Raw Signal Time Domain RMS, peak to 

peak, kurtosis 

15

(3 for each signal)

2 Time Synchronous Signal Time Domain RMS, peak to 

peak, kurtosis 

15

(3 for each signal)

3 Regular Signal Time Domain RMS, peak to 

peak, kurtosis 

15

(3 for each signal)

4 Residual Signal Time Domain RMS, peak to 

peak, kurtosis 

15

(3 for each signal)

5 Envelope Signal Time Domain RMS, peak to 

peak, kurtosis 

15

(3 for each signal)

6 Vibration HFRT Envelope Signal Time Domain RMS, peak to 

peak, kurtosis 9 (3 for each vibration channel)

7 Ripple Feature Calculation - Mean, STDEV 4 (2 for current and voltage 

signal)

8 Envelope Signal Frequency 

Domain

Peaks at 1X 

and 6X 10 (2 for each signal) 

9 Time Synchronous Signal Frequency 

Domain

1X-3X, 

6X,12X...108

X 

105 (21 for each signal) 

10 Raw Signal Frequency 

Domain

BPFO, BPFI, 

BSF, FTF, and 

harmonics 

24 (8 for each vibration signal)

11 HFRT Envelope Signal Frequency 

Domain

BPFO, BPFI, 

BSF, FTF, and 

harmonics 

24 (8 for each vibration signal)

12 Figure of Merit Features - - 20 (4 for each signal)

From the large array of extracted features, it is common practice to use algorithms to downselect 

features that show correlation or trending as a function of degradation, which may then be use to 

determine the state of health of the system. However, this feature set is not amenable to this type 
16

of the analysis. The primary reason is that there are many data files but only a few at each 

operating point. This makes it difficult to use common feature selection ranking methods such as 

the fisher criterion, since the number of data samples in each class for a given operating point is 

small (16). In addition, the feature selection method is usually tuned for a specific aspect, such as 

classification. Considering these points, a visual screening of the features was done in order to 

examine which, if any, of the features were of interest. Figures 10–17 show plots of features that 

were deemed promising for future work. Discussion is incorporated with the figures. Note that 

figure 10 is from Method 1 testing and that figures 11 through 17 are from Method 2. Also, that 

in figures 11–17 that the plotting order on each graph starts with the new alternator #15, then the 

three used alternators #30, #20, and #22, and finally the new alternator that failed (#5)

As shown in figure 10, all the used alternators have a much higher 12X voltage peak than the 

new alternators. In the used alternators, a clear linear relationship with alternator speed can also 

be seen.

Figure 10. 12X voltage peaks for all alternators tested as a function of shaft speed.

Figure 11 shows the standard deviation in the current ripple. Both the new alternators (#5 and 

#15) show less variation in the ripple compared to the used alternators. In particular used 

alternator #30 has significantly higher variation. Note that all that is known about the used 

2000 3000 4000 5000 6000 7000 8000

0

0.02

0.04

0.06

0.08

0.1

0.12

Shaft Rotational Speed (RPM)

Voltage 12X Peak

Feature Plot (Set Point 100A and 100oC Ambient): Voltage 12X Peak

#15

#30

#20

#22

#13

#5
17

alternators is that they had been in operation on vehicles. No knowledge of how “used” they 

were is known. This could explain the difference between #30 and the other used alternators.

Figure 11. Current ripple standard deviation with the associated shaft speeds for all alternators.

Figure 12 shows the current FOM, FOM_C1, the ratio between the residual current RMS and the 

TSA current RMS. For the used alternators, the magnitude of this feature is higher and also there 

appears to be a more noticeable relationship with the increase in shaft speed.

0 10 20 30 40 50 60 70

0

0.5

1

1.5

2

Run #

Current Ripple STDEV

Feature Plot: Current Ripple STDEV

#15

#30

#20

#22

#5

0 10 20 30 40 50 60 70

1000

2000

3000

4000

5000

Run # Alternator RPM

Alternator RPM

#15

#30

#20

#22

#5
18

Figure 12. FOM_C1 with the associated shaft speed for all alternators.

Further examination of the results seen in figure 12 was done by looking at the 12X current peak

shown in figure 13. Based on the results shown in figure 11, the FOM_C1 behavior is attributed 

to the 12X current peak. Note that for the used alternators, the 12X current peak is larger in 

magnitude and exhibits a clearer relationship with shaft speed. Also significant in the current plot 

is the difference in the frequency dependence of new and used alternators; the new alternators 

appear to be decreasing with speed as opposed to the used alternators which are clearly 

increasing, both in a nonlinear fashion.

0 10 20 30 40 50 60 70

0

0.05

0.1

0.15

0.2

Run # FOM C1

Feature Plot: FOM C1

0 10 20 30 40 50 60 70

1000

2000

3000

4000

5000

Run # Alternator RPM

Alternator RPM

#15

#30

#20

#22

#5

#15

#30

#20

#22

#5
19

Figure 13. 12X current peaks with the associated shaft speed for all alternators.

The 12X voltage peak shows a similar pattern as the current peaks, as can be seen in figure 14. 

The peaks are clearly larger for the used alternators. Again, the strong dependence of the 12X 

peak on speed for the used alternators is noted.

0 10 20 30 40 50 60 70

0

0.5

1

1.5

2

2.5

Run # Current 12X Peak

Feature Plot: Current 12X Peak

#15

#30

#20

#22

#5

0 10 20 30 40 50 60 70

1000

2000

3000

4000

5000

Run # Alternator RPM

Alternator RPM

#15

#30

#20

#22

#5
20

Figure 14. 12X current peaks with the associated shaft speed for all alternators.

The 3X peak from the Y-direction accelerometer is shown in figure 15. It has a noticeable trend 

for the alternator which failed (#5). However, this is most likely related to shaft misalignment 

and a function of the test-rig and not the alternator condition.

0 10 20 30 40 50 60 70

0

0.02

0.04

0.06

0.08

0.1

Run #

Voltage 12X Peak

Feature Plot: Voltage 12X Peak

#15

#30

#20

#22

#5

0 10 20 30 40 50 60 70

1000

2000

3000

4000

5000

Run # Alternator RPM

Alternator RPM

#15

#30

#20

#22

#5
21

Figure 15. Vibration 3X peak in the Y-direction with the associated shaft speed for all alternators.

Figures 16 and 17 show FOM_3 voltage (FOM_V3) and the kurtosis feature of the regular 

current signal, respectively. As can be seen, both features are slightly higher for alternator #5

before failure. Whether the levels are significant enough to use as a precursor to failure is 

uncertain, since it is not possible to test for this given the limited data samples at each operating 

point.

0 10 20 30 40 50 60 70

0

5

10

15

Run #

Ay 3X Peak

Feature Plot: Ay 3X Peak

#15

#30

#20

#22

#5

0 10 20 30 40 50 60 70

1000

2000

3000

4000

5000

Run # Alternator RPM

Alternator RPM

#15

#30

#20

#22

#5
22

Figure 16. FOM_3-V with the associated shaft speed for all alternators.

Figure 17. Kurtosis of the regular signal current with the associated shaft speed for all alternators.

0 10 20 30 40 50 60 70

2

3

4

5

6

Run # FOM V3

Feature Plot: FOM V3

#15

#30

#20

#22

#5

0 10 20 30 40 50 60 70

1000

2000

3000

4000

5000

Run # Alternator RPM

Alternator RPM

#15

#30

#20

#22

#5

0 10 20 30 40 50 60 70

1.5

2

2.5

Run #

Current Reg Kurtosis

Feature Plot: Current Reg Kurtosis

#15

#30

#20

#22

#5

0 10 20 30 40 50 60 70

1000

2000

3000

4000

5000

Run # Alternator RPM

Alternator RPM

#15

#30

#20

#22

#5
23

5. Discussion

To develop automotive alternator health indicators, the need for additional testing has become 

apparent. The PSU test procedure was designed for characterization, which appropriately 

resulted in the data set being constructed of many operating points, unfortunately there were not 

many replications at a given condition. Several processing methods were applied to the data, and 

although distinct relationships between rotational speed and several features are observed, none 

of the methods can confidently provide an early indicator prior to alternator #5 failing. Likewise, 

although distinct differences in the used and new alternators are apparent, the construction of 

methodologies to assess state of health or predict remaining useful life is not possible.

6. Conclusions and Recommendations

Observations were made on the PSU alternator data using a wide variety of processing methods 

and it is believed that these will prove useful in future studies. Several features of interest were 

identified that have potential for use in the health assessment of automotive alternators given 

appropriate testing. We first point out that the current/speed output curves for the five alternators 

represented a normal shape when compared with the manufactures specifications sheet. Also, 

that the ripple voltage increased with alternator shaft speed, as expected. We note that the used 

alternators had a distinctly different magnitude for the 12X voltage and current peaks; they also 

showed a much different relationship with alternator shaft speed. Additionally, the Y-direction 

vibration 3X peak showed an increasing trend prior to the failure of alternator #5; however, this 

is likely due to an increasing misalignment or imbalance and not related to the electrical failure.

We suggest that to better understand the failure of #5, that the alternator be physically 

investigated.

Our strongest recommendation is to perform additional testing. Specifically, conducting a set of 

run-to-failure tests at a fixed operating point (perhaps 80% of rated load at 3000 or 4000 rpm) 

should provide insight on the signal characteristics/features and how they change over time prior 

to alternator failure. Also, any additional testing should include collecting the individual phase 

voltages and currents, since these have a high potential to offer insight on the alternator’s

condition.
24

7. References

1. Tactical Wheeled Vehicle Alternator Performance Characterization and Fault Detection 

Methodology Report, Prepared by The Pennsylvania State University – Applied Research 

Laboratory, July 1, 2010.

2. Performance Curve for A0014827JB – High Output Alternator Product Specifications, 

PrestoliteElectric. 

http://www.prestolite.com/productinfo/alternators/A0014827JB/A0014827JB_curve.jpg

(accessed August 2011).

3. Hendrickson, M.; Gottemoller, B. P. Method and Apparatus for Detecting Phase Current 

Imbalance in a Power Generator, U.S Patent, 20100066294 A1, March 18, 2010.

4. Becker, J.; Jabaji, I.; Patterson, C. System and Method for Generator Phase Signal 

Monitoring and Control of Electrical Current Distribution, U.S. Patent, 20100138071 A1, 

June 3, 2010.

5. Zhang, X.; Uliyar, H.; Farfan-Ramos, L.; Zhang, Y.; Salman, M. Fault Diagnosis of 

Automotive Electrical Power Generation and Storage Systems. 2010 IEEE International 

Conference on Control Applications, 2010.

6. Farfan Ramos, L. Real-time Fault Diagnosis of Automotive Electrical Power Generation and 

Storage System, Master Thesis, Wright State University, Dayton, OH, 2011.

7. Zhang, Y.; Rajagopalan, S.; Salman, M. A Practical Approach for Belt Slip Detection in 

Automotive Electric Power Generation and Storage System. IEEE 2010 Big Sky Aerospace 

Conference, pp. 1–7, 2010.

8. Banks, J.; Brought, M.; Estep, J.; Hines, J.; Hobbs, N. Health and Usage Monitoring for 

Military Ground Vehicles Power Generating Devices. IEEE 2011 Big Sky Aerospace 

Conference, pp. 1–17, 2011.

9. Ashemi, A.; Pisu, P. Adaptive Threshold-based Fault Detection and Isolation for 

Automotive Electrical Systems. World Congress on Intelligent Control and Automation, pp. 

1013–1018, 2011.

10. Thibedeau, D. G.; Faehnrich, R. J.; Brott, A. P.; Goetzellmann, A. D.; Willems, P. A 

Alternator Testing Method and System Using Ripple Detection, U.S. Patent, 6,806,727 B2, 

October 19, 2004.

11. Hamdan, M.; Holler, G.; Grolle, K.; Macnamara, J.; Thakkar, K. System and Method for 

Detecting Alternator Condition, U.S. Patent, 6,862,504 B2, March 1, 2005.
25

12. Wang, K. S.; Heyns, P. S. Application of Computer Order Tracking, Vold-Kalman Filtering 

and EMD in Rotating Machine Vibration. Mechanical Systems and Signal Processing 2011, 

25, 416–430.

13. Decker, H. J.; Zakrajsek, J. J. Comparison of Interpolation Methods as Applied to Time 

Synchronous Averaging; Technical Memorandum, NASA/TM – 1999-209086, ARL-TR1960; U.S. Army Research Laboratory: Cleveland, OH, 1999.

14. Randall, R. B.; Antoni, J. Rolling Element Bearing Diagnostics – A Tutorial. Mechanical 

Systems and Signal Processing 2011, 25, 485–520.

15. Bechhoefer, E.; Kingsley, M. A Review of Time Synchronous Average Algorithms. Annual 

Conference of the Prognostics and Health Management Society, 2009.

16. Guyon, I.; Elisseeff, A. An Introduction to Variable and Feature Selection. The Journal of 

Machine Learning Research 2003, 3, 1157–1182.
26

INTENTIONALLY LEFT BLANK.
27

Appendix. Data Plots for Reference

Under each heading there are figures for the four alternator “cases” where first figure (top left) is 

for a new alternator, the figure to its right (top right) is for a used alternator, the third figure

(bottom left) is alternator #5 just prior to failure and figure (bottom right) is alternator #5 

immediately after failure.

A-1 Current Frequency Spectra (From Raw Signals)

Figure A-1. Frequency spectra for the current output for the four alternator cases.

0 20 40 60 80 100 120 140 160 180 200

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

X: 36.33 Y: 1.961

Frequency (Order)

Current Magnitude (A)

Current Spectrum for File: Method 2 and File # 8, Alternator #15

0 20 40 60 80 100 120 140 160 180 200

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

X: 36.02 Y: 1.601

Frequency (Order)

Current Magnitude (A)

Current Spectrum for File: Method 2 and File # 18, Alternator #30

X: 12 Y: 1.053

0 20 40 60 80 100 120 140 160 180 200

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

X: 36.19 Y: 1.986

Frequency (Order)

Current Magnitude (A)

CurrentSpectrum for File: Method 2 and File # 66, Alternator #5

0 20 40 60 80 100 120 140 160 180 200

0

0.01

0.02

0.03

0.04

0.05

0.06

X: 36.49 Y: 0.05617

Frequency (Order)

Current Magnitude (A)

Current Spectrum for File: Method 2 and File # 67, Alternator #5
28

A-2 Voltage Spectra (From Raw Signals)

Figure A-2. Frequency spectra for the voltage signal for the four alternator cases.

0 20 40 60 80 100 120 140 160 180 200

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

X: 36.33 Y: 0.1713

Frequency (Order)

Voltage Magnitude (V)

Voltage Spectrum for File: Method 2 and File # 8, Alternator #15

0 20 40 60 80 100 120 140 160 180 200

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

X: 36.02 Y: 0.1388

Frequency (Order)

Voltage Magnitude (V)

Voltage Spectrum for File: Method 2 and File # 18, Alternator #30

X: 12 Y: 0.03344

0 20 40 60 80 100 120 140 160 180 200

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

X: 36.19 Y: 0.1738

Frequency (Order)

Voltage Magnitude (V)

Voltage Spectrum for File: Method 2 and File # 66, Alternator #5

0 20 40 60 80 100 120 140 160 180 200

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

X: 36.49 Y: 0.004949

Frequency (Order)

Voltage Magnitude (V)

Voltage Spectrum for File: Method 2 and File # 67, Alternator #5

X: 5.654 Y: 0.03433
29

A-3 Vibration Spectra (From Raw Signals)

A-3.1 X-direction

Figure A-3. Vibration spectra for X-direction for the four alternator cases.

A-3.2 Y-direction

Figure A-4. Vibration spectra for Y-direction for the four alternator cases.

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

X: 36.33 Y: 3.1

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ax Vibration Spectrum for File: Method 2 and File # 8, Alternator #15

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

X: 36.02 Y: 0.5057

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ax Vibration Spectrum for File: Method 2 and File # 18, Alternator #30

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

X: 36.19 Y: 3.258

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ax Vibration Spectrum for File: Method 2 and File # 66, Alternator #5

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ax Vibration Spectrum for File: Method 2 and File # 67, Alternator #5

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

6

X: 36.33 Y: 3.582

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ay Vibration Spectrum for File: Method 2 and File # 8, Alternator #15

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

6

X: 36.19 Y: 1.765

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ay Vibration Spectrum for File: Method 2 and File # 66, Alternator #5

X: 3.017 Y: 2.893

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

6

X: 36.02 Y: 0.4342

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ay Vibration Spectrum for File: Method 2 and File # 18, Alternator #30

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3

4

5

6

X: 3.041 Y: 4.1

Frequency (Order)

Vibration Magnitude (m/s

2

)

Ay Vibration Spectrum for File: Method 2 and File # 67, Alternator #5
30

A-3.3 Z-direction

Figure A-5. Vibration spectra for Z-direction for the four alternator cases.

A-4 Time Synchronous Average 

A-4.1 Current Spectrum Plots

Figure A-6. TSA current spectra for the four alternator cases.

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

X: 36.33 Y: 1.225

Frequency (Order)

Vibration Magnitude (m/s

2

)

Az Vibration Spectrum for File: Method 2 and File # 8, Alternator #15

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

X: 36.02 Y: 0.41

Frequency (Order)

Vibration Magnitude (m/s

2

)

Az Vibration Spectrum for File: Method 2 and File # 18, Alternator #30

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

X: 36.19 Y: 1.468

Frequency (Order)

Vibration Magnitude (m/s

2

)

Az Vibration Spectrum for File: Method 2 and File # 66, Alternator #5

0 20 40 60 80 100 120 140 160 180 200

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Frequency (Order)

Vibration Magnitude (m/s

2

)

Az Vibration Spectrum for File: Method 2 and File # 67, Alternator #5

0 50 100 150 200

0

1

2

3

4

5

6

X: 36

Y: 5.61

Frequency Orders Current Magnitude (A)

TSA Spectrum for Current: Method 2 and File # 8 Alternator #15

0 50 100 150 200

0

1

2

3

4

5

6

X: 36

Y: 5.682

Frequency Orders Current Magnitude (A)

TSA Spectrum for Current: Method 2 and File # 18 Alternator #30

0 50 100 150 200

0

1

2

3

4

5

6

X: 36

Y: 5.479

Frequency Orders Current Magnitude (A)

TSA Spectrum for Current: Method 2 and File # 66 Alternator #5

0 50 100 150 200

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

X: 36

Y: 0.1351

Frequency Orders Current Magnitude (A) TSA Spectrum for Current: Method 2 and File # 67 Alternator #5
31

A-4.2 Voltage Spectrum Plots

Figure A-7. TSA voltage spectra for the four alternator cases.

A-4.3 Vibration Spectra, X-direction

Figure A-8. TSA X-direction vibration spectra for the four alternator cases.

0 50 100 150 200

0

0.1

0.2

0.3

0.4

0.5

X: 36

Y: 0.4899

Frequency Orders Voltage Magnitude (V) TSA Spectrum for Voltage: Method 2 and File # 8 Alternator #15

0 50 100 150 200

0

0.1

0.2

0.3

0.4

0.5

X: 12

Y: 0.06687

Frequency Orders Voltage Magnitude (V) TSA Spectrum for Voltage: Method 2 and File # 18 Alternator #30

X: 36

Y: 0.4923

0 50 100 150 200

0

0.1

0.2

0.3

0.4

0.5

X: 36

Y: 0.4796

Frequency Orders Voltage Magnitude (V) TSA Spectrum for Voltage: Method 2 and File # 66 Alternator #5

0 50 100 150 200

0

0.002

0.004

0.006

0.008

0.01

0.012

X: 36

Y: 0.01192

Frequency Orders Voltage Magnitude (V) TSA Spectrum for Voltage: Method 2 and File # 67 Alternator #5

0 50 100 150 200

0

2

4

6

8 X: 36

Y: 8.987

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Ax: Method 2 and File # 8 Alternator #15

0 50 100 150 200

0

2

4

6

8

X: 36

Y: 1.834

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Ax: Method 2 and File # 18 Alternator #30

0 50 100 150 200

0

2

4

6

8 X: 36

Y: 8.992

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Ax: Method 2 and File # 66 Alternator #5

0 50 100 150 200

0

2

4

6

8

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Ax: Method 2 and File # 67 Alternator #5
32

A-4.4 Vibration Spectra, Y-direction

Figure A-9. TSA Y-direction vibration spectra for the four alternator cases.

A-4.5 Vibration Spectra, Z-direction

Figure A-10. TSA Z-direction vibration spectra for the four alternator cases.

0 50 100 150 200

0

2

4

6

8

10

12

X: 36

Y: 10.3

Frequency Orders Vibration Magnitude (m/s

2

) TSA Spectrum for Ay: Method 2 and File # 8 Alternator #15

0 50 100 150 200

0

2

4

6

8

10

12

X: 36

Y: 1.513

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Ay: Method 2 and File # 18 Alternator #30

0 50 100 150 200

0

2

4

6

8

10

12

X: 36

Y: 4.869

Frequency Orders Vibration Magnitude (m/s

2

) TSA Spectrum for Ay: Method 2 and File # 66 Alternator #5

0 50 100 150 200

0

2

4

6

8

10

12

Frequency Orders Vibration Magnitude (m/s

2

) TSA Spectrum for Ay: Method 2 and File # 67 Alternator #5

0 50 100 150 200

0

1

2

3

4

5

6

X: 36

Y: 3.539

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Az: Method 2 and File # 8 Alternator #15

0 50 100 150 200

0

1

2

3

4

5

6

X: 36

Y: 1.401

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Az: Method 2 and File # 18 Alternator #30

0 50 100 150 200

0

1

2

3

4

5

6

X: 36

Y: 4.101

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Az: Method 2 and File # 66 Alternator #5

0 50 100 150 200

0

1

2

3

4

5

6

Frequency Orders Vibration Magnitude (m/s

2

)

TSA Spectrum for Az: Method 2 and File # 67 Alternator #5
33

A-5 Residual Signal

A-5.1 Current

Figure A-11. Current residual for the four alternator cases.

A-5.2 Voltage

Figure A-12. Voltage residual for the four alternator cases.
34

A-6 Envelope Signal

A-6.1 Current

Figure A-13. Current envelope signal for the four alternator cases.

5 5.005 5.01 5.015

5.7

5.75

5.8

5.85

5.9

5.95

6

Time (s) Current (A)

Current Envelope Time Signature for File: Method 2 and File # 8

5 5.005 5.01 5.015

5.7

5.75

5.8

5.85

5.9

5.95

6

Time (s) Current (A)

Current Envelope Time Signature for File: Method 2 and File # 18

5 5.005 5.01 5.015

5.3

5.4

5.5

5.6

5.7

Time (s) Current (A) Current Envelope Time Signature for File: Method 2 and File # 66

5 5.005 5.01 5.015

0.1

0.11

0.12

0.13

0.14

Time (s) Current (A)

Current Envelope Time Signature for File: Method 2 and File # 67
35

A-6.2 Voltage

Figure A-14. Voltage envelope signal for the four alternator cases.

5 5.005 5.01 5.015

0.48

0.49

0.5

0.51

0.52

Time (s) Voltage (V)

Voltage Envelope Time Signature for File: Method 2 and File # 8

5 5.005 5.01 5.015

0.48

0.49

0.5

0.51

0.52

Time (s) Voltage (V)

Voltage Envelope Time Signature for File: Method 2 and File # 18

5 5.005 5.01 5.015

0.47

0.48

0.49

0.5

0.51

0.52

Time (s) Voltage (V)

Voltage Envelope Time Signature for File: Method 2 and File # 66

5 5.005 5.01 5.015

0.01

0.011

0.012

0.013

0.014

0.015

Time (s) Voltage (V)

Voltage Envelope Time Signature for File: Method 2 and File # 67
36

A-7 Vibration HFRT Envelope Spectra (X-direction)

Figure A-15. Vibration envelope spectra (x-direction) showing BPFO.

0 100 200 300 400 500

0

0.05

0.1

0.15

0.2

X: 153.8

Y: 0.04328

Frequency (Hz) Vibration Magnitude (m/s

2

)

Vibration Ax Envelope Spectrum for File: Method 2 and File # 8

0 100 200 300 400 500

0

0.05

0.1

0.15

0.2

X: 149.5

Y: 0.02823

Frequency (Hz) Vibration Magnitude (m/s

2

) Vibration Ax Envelope Spectrum for File: Method 2 and File # 18

0 100 200 300 400 500

0

0.05

0.1

0.15

0.2

X: 154.1

Y: 0.05546

Frequency (Order) Vibration Magnitude (m/s

2

) Vibration Ax Envelope Spectrum for File: Method 2 and File # 66

0 100 200 300 400 500

0

0.05

0.1

0.15

0.2

Frequency (Hz) Vibration Magnitude (m/s

2

) Vibration Ax Envelope Spectrum for File: Method 2 and File # 67

X: 152

Y: 0.05185
37

List of Symbols, Abbreviations, and Acronyms

DoD Department of Defense 

FOMs figures of merit

HFRT High Frequency Response Technique

P&D prognostics and diagnostics

PSU Pennsylvania State University

RMS root-mean-square 

TARDEC U.S. Army Tank and Automotive Research, Development and Engineering 

Command

TSA time synchronous averaging
38

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