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ASI’s 20th Annual Symposium

Robust Engineering

TOOL-CONDITION MONITORING FROM DEGRADATION SIGNALS USING MAHALANOBIS-TAGUCHI SYSTEM ANALYSIS

Ratna Babu Chinnam Wayne State University Detroit, MI Bharatendra Rai Wayne State University Detroit, MI Nanua Singh Wayne State University Detroit, MI

ABSTRACT Drilling is a widely used machining process. With every hole drilled, a drill-bit gradually degrades until it breaks. In certain special applications replacing a drill-bit after it's breakage can be costly. In such cases degradation signals are often used to make a decision whether or not to replace the tool. However, very often the requirement of making a decision online, leads to online collection of data on the degradation signals of interest. From such data appropriate features are identified that help to arrive at a decision for the tool replacement before it breaks. In this paper we study two degradation signals viz., thrust force and torque using Mahalanobis-Taguchi System analysis. The study includes ten features (five features per degradation signal) and obtains Mahalanobis distance values based on data from holes with 'normal' degradation levels. Data from the last drilled hole prior to the tool breakage, representing 'abnormal' degradation level, are used for the validation of the measurement scale. Subsequently, the useful features out of the ten under study are identified using the orthogonal arrays and signal-to-noise ratios.

343

ASI’s 20th Annual Symposium

Robust Engineering

INTRODUCTION Of the cutting operations performed in mechanical industries, drilling operations contribute approximately 40% (El-Wardany et al. 1996). A drill-bit failure during the drilling operation can be costly in certain special applications. Such applications call for methods that can predict drill-bit failures in advance. Automated drilling operations too require reliable methods for online tool-condition monitoring. Several tool-condition monitoring methods that mainly use degradation signals have been reported in literature. El-Wardany et al. (1996) found monitoring of the kurtosis value obtained from the traverse and thrust vibrations to be effective for online detection of the drill-bit breakage. Dimla and Lister (2000) applied multi-layer perceptron neural network for tool-state classification using online data on cutting forces and vibration, and reported achieving approximately 90% accuracy in tool-state classification. Chinnam (2002) used general polynomial regression models to develop a rigorous degradation signal forecasting model for a similar application. Chinnam and Mohan (2002) develop a model based on neural networks and wavelets for online tool-condition monitoring. In this paper we study multiple features obtained from the degradation data simultaneously and provide a methodology for tool-condition monitoring using Mahalanobis-Taguchi System.

DRILL-BIT DEGRADATION DATA The experimentation for this study involves 12 drill-bits for which data on thrust force and torque were recorded online till the tool breakage. The number of holes drilled before its breakage is shown for each drill-bit in Figure-1. Figure 1. Number of holes drilled per drill-bit # of holes drilled before breakage

30 25

24

22 18

20

15

13

15 10

10

8

7

17

16

14

9

5 0 DB-1

DB-2

DB-3

DB-4

DB-5

DB-6 DB-7 Drill-bit #

344

DB-8

DB-9 DB-10 DB-11 DB-12

ASI’s 20th Annual Symposium

Robust Engineering

It is observed from the Figure-1 that the number of holes drilled varies from 7 for the drill-bit #4 to 24 for the drill-bit #8. The total number of holes for which data is collected across 12 drill-bits constitutes 173 holes. For each drilled hole, approximately 400 data points are recorded for both thrust force and torque at 250KHz. The data points are condensed to 24 root-mean-square (RMS) values per hole. The RMS values of thrust force and torque for different holes drilled before the drill-bit #2 breakage is shown as an example in Figure-2.

8

3000

7

2500

6

3

Data Sequence

397

361

325

289

253

217

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419

381

343

305

267

229

191

153

77

115

0

1

1

0

145

2

500

73

1000

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109

1500

5

37

2000

1

RMS (Torque)

3500

39

RMS (Thrust Force)

Figure 2. Degradation Data for Drill-bit #12 (a) Thrust Force, (b) Torque

Data Sequence

(a)

(b)

It is observed from Figure-2(a) that the RMS values for the thrust force show gradual increase before the drill-bit breakage takes place after the last hole drilled. A similar pattern is observed for RMS values obtained for torque. It is important to capture the inherent trends from the data for each hole using features that enable prediction of drillbit breakage. Towards this the 24 RMS values of thrust force and torque are further numerically summarized into five features each viz., maximum, average, standard deviation, third quartile, and coefficient of variation, leading to overall ten features considered for the study.

CONSTRUCTION OF THE MEASUREMENT SCALE An operational definition for the 'normal group' is arrived to develop a reference point for the measurement scale to enable tool-condition classification. The data from drilled holes excluding the last five holes for each drill-bit are defined to come from 'normal' degradation levels. Thus a 'normal group' consists of data on 113 drilled holes out of the total 173 holes. The ten features are obtained from the data on these 113 holes. The data on each feature is subsequently normalized using the mean and the standard deviation obtained from the 113 holes. The Mahalanois distance (MD) based on 10 features is then obtained for each of the 113 holes in the 'normal group' using (Taguchi and Jugulum 2002), MD j = D 2j = Z ij' C −1 Z ij

(1)

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ASI’s 20th Annual Symposium

Robust Engineering

where, j = Number of data points in the normal group (1 to 113) k = Number of features (1 to 10) Z ij = ( z1 j , z 2 j ,..., z kj ) = Standardized vector

C −1 = Inverse of the correlation matrix. The scaled MD is obtained as, MD j =

1 ' −1 Z ij C Z ij k

(2)

VALIDATION OF THE MEASUREMENT SCALE Data from last but one hole are treated as coming from 'abnormal' degradation levels. Thus for each of the ten features under study, there are ten drilled holes with abnormal degradation levels. The last but one hole is chosen so as to enable prediction of tool breakage before the last hole can be drilled as degradation levels are unusually higher in the last drilled holes leading to other quality related problems. The data from abnormal conditions are normalized using mean and standard deviation obtained from the 'normal group'. The MDs are obtained for the abnormal group using the correlation matrix of 'normal group' in Eq. (2). The scaled MDs for both 'normal' and 'abnormal' group thus obtained are shown in Figure-3. Figure 3. MDs for the normal and abnormal group (a) Normal scale, (b) Log-scale 1000

(a)

111

89

100

Hole #

78

45

34

111

100

89

78

67

56

45

34

0.1 23

20 0 12

1

1

60 40

23

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MD

MD

100 80

Hole #

Abnormal Group

100

67

Abnormal Group

140 120

Normal Group

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Normal Group

1

180 160

(b)

Figure-3(a) shows MDs for normal and abnormal group on a normal scale. Figure-3(b) shows the same data on a log-scale which brings out the distinction between the normal and abnormal groups more clearly. The average MD for the normal group is approximately 0.991 as compared to 26.794 for the abnormal group. The higher values of MDs for the abnormal group validate the accuracy of the measurement scale. 346

ASI’s 20th Annual Symposium

Robust Engineering

IDENTIFICATION OF THE USEFUL FEATURES FOR THE TOOL CONDITION MONITORING The useful features among the ten under study that help to accurately discriminate between degradation levels are identified using orthogonal arrays (OA) and signal-tonoise ratio. The ten features under study are assigned to the first ten columns of orthogonal array L12(211) (Taguchi 1987). Level-1 in the orthogonal array column represents the presence of a feature and level-2 represents the absence of that feature. Table-1 shows the L12(211) orthogonal array and the assignment of the ten features to the first ten columns. Table 1. Column Assignments of the Ten Features in OA L12(211) Ex TF-max TF-Avg TF-sd TF-Q3 TF-CV Tq-max Tq-Avg Tq-sd Tq-Q3 Tq-CV 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 2 2 3 1 1 2 2 2 1 1 1 2 2 4 1 2 1 2 2 1 2 2 1 1 5 1 2 2 1 2 2 1 2 1 2 6 1 2 2 2 1 2 2 1 2 1 7 2 1 2 2 1 1 2 2 1 2 8 2 1 2 1 2 2 2 1 1 1 9 2 1 1 2 2 2 1 2 2 1 10 2 2 2 1 1 1 1 2 2 1 11 2 2 1 2 1 2 1 1 1 2 12 2 2 1 1 2 1 2 1 2 2

Using the feature combinations as given in Table-1, ten MD values for the abnormal group is obtained using Eq. (2). From the MDs, a larger-the-better signal to noise ratio is obtained for the qth run using (Taguchi and Jugulum 2002, Jugulum 2000),

1 t 1   ∑  t i =1 MD j 

η q = −10 log 

(3)

where 't' is number of features present for a given combination of the experimental run. An average S/N ratio at level-1 and level-2 is obtained for each feature. Subsequently, gain in S/N ratio values is obtained as, Gain = (Avg. S/N Ratio)Level-1 - (Avg. S/N Ratio)Level-2

(4)

The gain in average S/N ratio values obtained for the ten features under study using Eq. (4) is shown in Figure-4.

347

ASI’s 20th Annual Symposium

Robust Engineering

Figure-4 shows positive gain values for maximum, average, and standard deviation of thrust force degradation signals and average, standard deviation, and coefficient of variation from torque degradation signals. These six features with positive gain are identified as useful in discriminating the degradation signals for predicting drill-bit breakage. Figure 4. Average Gain in SNR for Each Feature

0.6

Tq-CV

Tq-Q3

Tq-sd

Tq-Avg

Tq-max

TF-sd

TF-CV

-0.2

TF-Avg

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TF-max

Avg. Gain in SNR

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Feature

-0.4

A confirmation run was conducted with the six useful features identified. MDs corresponding to the abnormal group were obtained using Eq. (2). A comparison of average MD for normal and abnormal group is given in Table-2. Table 2. Comparison After Confirmatory Trial Group Normal Abnormal (10 features) Abnormal (6 features identified as useful)

Avg. MD 0.991 26.794 27.158

It can be observed from the table-2 that a higher value for average MD based on the abnormal group is obtained with only six features identified as useful as compared to that obtained from all the ten features originally used.

348

ASI’s 20th Annual Symposium

Robust Engineering

TOOL CONDITION MONITORING WITH THE USEFUL VARIABLES A threshold value to predict drill-bit breakage is arrived by taking 99th percentile MD values based on the six useful features identified in the previous section. The threshold value and the MDs for each hole drilled using the 12 drill-bits studied are shown in Figure-5. It is seen from Figure-5 that the MDs combining six features into a single value and the threshold of 4.54, show a satisfactory performance. The performance obtained is further quantified and compared with individual performances of the six useful features identified. The comparisons are given in Table-3. Figure 5: MD Values for the 12 Drill-bits using the Six Features Identified as Useful 1000.00

100.00 Threshold = 4.54

MD

10.00

1.00

0.10

0.01 1

2 3

4

5 6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hole #

Table 3. Comparison of Results

Feature Mahalanobis Distance (six features) Thrust Force (Maximum) Thrust Force (Average) Thrust Force (s.d.) Torque (Average) Torque (s.d.) Torque (CV)

Threshold (99th percentile value based on % of holes drilled out of % of false signals to replace % drill-bit breakage the 'normal group') total 161 possible the drill-bit per hole not predicted 4.54

91.9%

0.6%

0.0%

2057

83.2%

0.0%

8.3%

1444

66.5%

1.2%

16.7%

687

77.6%

1.2%

8.3%

3.39

70.2%

1.2%

16.7%

1.68

23.6%

1.9%

75.0%

4.3%

1.9%

100.0%

53.84

349

ASI’s 20th Annual Symposium

Robust Engineering

Table-3 shows that, the threshold values for the MDs that combine six features into one and each of the six individual features are obtained as the 99th percentile value from the 'normal group'. The percentage of holes drilled out of the total 161 possible is obtained to understand the amount of total drill-bit life usage. The prediction of drill-bit breakage using MD allows approximately 91.9% usage of the total drill-bit life. Whereas when individual features are used for predicting drill-bit breakage, the life usage varies from 4.3% to 83.2%. The percentage of false signals to predict drill-bit breakage is minimum for 'thrust force maximum'. However, percentage of drill-bit breakage not predicted is minimum when MD is used and is worst for torque-CV. Thus, it is observed that MD with a threshold value of 4.54 provides a significantly better performance in predicting drill-bit breakage and at the same time utilizing the maximum tool life when compared to any of the individual features studied.

SUMMARY & CONCLUSIONS Drilling operations very often require prediction of drill-bit breakage due to cost considerations or automation. Degradation signals provide useful data for an online toolcondition monitoring. However, from the degradation signals suitable features need to be extracted to enable prediction of drill-bit breakage. This paper shows an application of Mahalanobis-Taguchi System analysis for feature selection and subsequent prediction of the drill-bit breakage. This study involved ten features from two degradation signals viz., thrust force and torque. A measurement scale was constructed by computing Mahalanobis Distance (MD) values using the ten features obtained from a 'normal group'. MDs obtained from 'abnormal' group were then compared to MDs from the 'normal group' to validate the measurement scale. The ten features were subsequently assigned to an orthogonal array with level-1 indicating presence and level-2 indicating absence of the feature. Using gain in signal-to-noise ratio values, six features were identified as useful for predicting drillbit breakage. A threshold value obtained as 99th percentile of the MDs from the 'normal group' showed significantly superior performance as compared to any of the individual features studied.

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REFERENCES Chinnam, R. B. and Mohan, P. 2002, “Online Reliability Estimation of Physical Systems Using Neural Networks and Wavelets.” Smart Engineering System Design, Vol. 4, 253264. Chinnam, R. B. 2002, “ Online Reliability Estimation for Individual Components using Statistical Degradation Signal Models.” Quality and Reliability Engineering International, Vol. 18, 53-73. Dimla, D. E. and Lister, P.M. 2000, “Online metal cutting tool condition monitoring. II: tool-state classification using multi-layer perceptron neural networks.” International Journal of Machine Tools and Manufacture Design, Research and Applications, Vol. 40, 769-781. El-Wardany, T. I., Gao, D., and Elbestawi. 1996, “Tool condition monitoring in drilling using vibration signature analysis.” International Journal of Machine Tools Manufacturing, Vol. 36, 687-711. Jugulum, R. 2000, “New Dimensions in Multivariate Diagnosis to Facilitate Decision Making Process.” Thesis, Wayne State University, Detroit, MI. Taguchi, G. and Jugulum, R. 2002, The Mahalanobis-Taguchi Strategy – A pattern technology system. John Wiley & Sons, New York. Taguchi, G. 1987, System of Experimental Design. Dearborn, Michigan, and White Plains, New York: ASI Press and UNIPUB-Kraus International Publications.

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