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25-1

25Fault Detectionand Diagnosis inMechatronic Systems

25.1 Introduction ......................................................................25-125.2 Model of the Metal-Cutting Process................................25-225.3 Fault Detection..................................................................25-4

Observer Model and Stability Analysis Model-Based Fault

Detection

25.4 Experimental Results.........................................................25-625.5 Conclusion.........................................................................25-8Acknowledgment .........................................................................25-8References..................................................................................... 25-8

Summary

Computer-numerical-control (CNC) machines used in automated manufacturing are mechatronic sys-

tems. In this chapter, a fault detection method is developed based on a state observer model for a milling

machine in a CNC machining center. The CNC machining center is treated as an uncertain linear system.

To obtain more information, a robust observer is designed based on the uncertain linear model. Subse-

quently, this model is used as a state (tool wear) estimator, and fault diagnosis is carried out using two-

variable information. The approach can be used for the detection of faults arising from the malfunction

of a sensor or an actuator.

25.1 Introduction

Computer-numerical-control (CNC) machines are commonly used in automated factories for producing

machined parts. A CNC machine, which consists of mechanical components, actuators, sensors, control-

lers, and interface hardware and software, is a mechatronic system. In a metal-cutting process using a

CNC milling machine, it is possible that a fault occurs during operation even though the process

parameters have been set properly. Faults in the cutting tools, which are frequently caused by tool wear,

can potentially damage the workpiece. Prevention of faults is therefore important to minimize possible

loss in manufacturing.

Before a fault occurs, parameters of the cutting process change beyond their normal values. By detectingthe unusual change of the parameters, it is possible to anticipate faults and take preventive or corrective

action. This possibility of preventing faults has made continuous monitoring of metal-cutting processes

and detection of the changes of parameters an important topic in the area of manufacturing automation

K.K. Tan

S. Huang

T.H. Lee

A.S. Putra

C.S. Teo

C.W. de Silva

2008 by Taylor & Francis Group, LLC

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25-2 Mechatronic Systems: Devices, Design, Control, Operation and Monitoring

and mechatronics. Successful monitoring systems can properly maintain the machine tools and delay the

occurrence of tool wear.

Various methods have been developed to detect the tool wear state. The application of statistical

algorithms to associate patterns in measurable signals with wear states is found in Reference [1]. Weck

[2] and Byrne et al. [3] use the signal of cutting force to monitor tool wear. By using inexpensive current

sensors, several intelligent tool-wear-monitoring systems have been developed [46]. Coker and Shin [7]

developed an in-process monitoring and control system for surface roughness during machining via

ultrasonic sensing. In Reference [8] an acoustic emission sensor and accelerometers are used to monitor

progressive stages of flank wear on carbide tool tips. An alternative approach to tool-wear monitoring is

to apply system-theoretic ideas to estimate the wear states during the cutting process. In Reference [9] a

linear model is built to detect the tool wear and breakage in the drilling process. In References [10,11]

another linearization model is used to design an adaptive observer for online tool-wear estimation in a

turning operation.

The aim of tool-wear detection is to find the loss of the original functioning or capability of the tool

to detect an abnormal state. The methods of tool-wear diagnosis have focused on the development of

signal processing techniques on the measurements such as cutting force, vibration, and spindle motor

current. However, a tool signal from a single measurement may make a misjudgment because of the

complicated dynamic characteristics of the cutting process and sensor noise. To prevent this, a multisensor

approach has been presented in References [12,13]. This requires a higher hardware device supplied for

simultaneously treating increased amounts of information.

This chapter presents a method of model-based process supervision with fault detection and diagnosis.

The model is built based on the data collection from a practical manufacturing plant. Unlike the results

of References [911], the method developed in this chapter is focused on a milling machine (see Section 25.2).

Note that in general the dynamic model of a milling operation is different from drilling or turning

operations, as used in References [911]. The method is also different from what is presented in References

[12,13], in that the sufficient observer information (software) is used to make decisions so as to enhance

the reliability of tool wear, as opposed to using a multisensor (hardware) technique.

The approach presented in this chapter can be summarized in the following steps. First, multiple linear

models are identified based on different working conditions, and a dominant model is obtained from

the models. The used model is the dominant model plus an uncertainty model with bounded signals.

Second, an observer is built based on the identified model. Third, tool-wear signatures are detected by

using two signal processing methods: the estimated wear rate based on the observer and the error between

the observer and actual cutting force.

25.2 Model of the Metal-Cutting ProcessA milling machining process is considered in this chapter. Milling is the process of cutting away material

of a workpiece by feeding a material stock against a rotating tool/cutter. The workpiece to be machined

may have several combinations of shape, such as flat, angular, curved, or tubular surfaces. The process

of milling is executed by a milling machinea mechatronic systemwhose construction and working

mechanism allow it to perform a variety of operations, including machining processes that are normally

performed by specifically designed machines (e.g., drilling, turning, and shaping). This makes the milling

machine among the most versatile machines in manufacturing.

The typical feed system of a milling machine consists of the following basic components: cutting tool

and tool post, table, saddle, bearings, ball screw, feed box, and feed motor. Figure 25.1 illustrates the

typical feed-drive system of a horizontal milling machine.

Models for the cutting process have been studied in References [1416]. For example, Lauderbaugh

and Ulsoy [14] have proposed the following model:

(25.1)F F F K f n n s s+ + = 2 ,


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Fault Detection and Diagnosis in Mechatronic Systems 25-3

where is the cutting force and is the output of the system, is the feed rate, and the parameters ,

and depend on the depth of cut spindle speed and feed rate This equation can be rewrit-

ten in the statespace form as

(25.2)

with , and

(25.3)

The model is weakly nonlinear and has significant process parameter variations [14]. Now, consider

an uncertain linear model given by

(25.4)

where and are the nominal matrices (system matrix and the input gain matrix, respectively) of the

system, and

(25.5)

where and are the perturbation parameters of and respectively, and

is the bounded disturbance. It is seen that this model can include more classes than that of Reference [14].

In tool-wear detection, it is well known that the tool life can be divided into three phases characterizedby three different wear processes: (1) break-in, (2) normal wear, and (3) abnormal or catastrophic wear.

The present objective is to detect the rise in the tool wear and to diagnose the fault types so that a tool

replacement decision could be made. Because fault accommodation is not addressed in this chapter, we

can make the standard assumption that the control and the state vector remain bounded prior to

and after the occurrence of a fault.

FIGURE 25.1 A feed-drive system of a horizontal milling machine.

Feed box

Feed motor

Shaft Bearings

Bearings

Ball screw

Table

Saddle

Workpiece Cutting tool

F fs

n , Ks d, v, fs .

x Ax b

C xT

= +

=

u,

y ,

x F F T= [ ] , u fs=

A b C =

=

=0 1 0

1 02

n n s

T

K, , [ ]

x A A x b b

C xT

= + + + +

=

( ) ( )u d,

y ,

A b

=

=

A b0 1 0

1 2 1a t a t ,

b (t)( ) ( )

,

a t1( ), a t2( ), b t1( ) n2 , n , Ks ,

d

u x


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Assumption 1

There exist compact sets such that and for all

25.3 Fault Detection

Having obtained the model for the cutting process, the proposed method of fault detection and its

constituent components are now discussed in detail according to the following steps. First, an observer

model is presented for estimating the states. Second, the stability of the process is discussed based on the

Lyapunov theory. Third, the fault detection strategy is proposed based on the observer.

25.3.1 Observer Model and Stability Analysis

Consider the uncertain plant (25.4). The dominant model in (25.4) can be identified in an offline or

online manner. For the model represented in (25.4), the cutting force can be measured, whereas the other

state is not available (one cannot use the derivative of to represent because has strong noise).

However, the state variablex can be estimated by an observer.

An observer for the estimation of the states in (25.4) are given by

(25.6)

where denotes the estimate of the state and is the observer gain vector. Only

the output is assumed to be measurable.

Define the state and output estimate errors as and respectively. Thus, the error

dynamics is given by

(25.7)

(25.8)

Theorem 1

Consider the nonlinear system described by (25.4) and the observer by (25.6). If Assumption 1

holds, . Then, all of the signals are bounded and the state estimate still remains in the compactset . In addition, a small error of may be achieved by selecting gain .

25.3.2 Model-Based Fault Detection

For a practical cutting process, the tool wear can be formulated by

, (25.9)

where w is the tool wear level, w0 is the initial tool wear level, is the wear rate, and is the cutting

time. In the normal phase, the wear rate is constant. However, a sudden rise in the wear rate can beobserved in an abnormal phase. Our objective is to monitor the rise in the wear rate to give a warning

to the operators so that they can determine whether to replace the tool or to take some other action. It

is observed that the tool wear is related to the cutting force [5]. One may represent this by

, (25.10)

x R2 , u R , x x u t 0.

F x2 F

x Ax b K C x

C x

T

T

= + +

=

u y ,

y ,

( )

x x K =[ ]k k knT

1 2

y x x x = y y y = ,

x A K x Ax bT= + + +( C ) u d,

y x= CT .

x x0

x = || ||x Q xx | x x B ,x{ } || ||x K

= +0 t

t

F F L= +0


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where is the cutting force arising under identical cutting conditions, but with an unworn cutting tool,

and is a parameter dependent on the cutting speed, feed rate, and depth of cut. Substituting (25.9)

into (25.10) yields

. (25.11)

The following wear rate is derived in Reference [5]

(25.12)

where and are the differences of and respectively. Unfortunately, the measured cutting force is

noisy and this causes difficulty in the calculation of (25.12) in reality.

On the other hand, from (25.10) it follows that

. (25.13)

This implies that can be used to estimate the wear rate. Although cannot be computed due to

noise, its observer is available without the need of differentiation. When the observer is designed to

satisfy the stability requirement, one can use in place of In order to monitor the tool wear, a time

interval is defined as . This interval can be computed by

(25.14)

where is the reference distance that is determined by the user, is the feed rate (given in unit length

per minutes, which is a machining parameter), and 60 is one minute in seconds. The sampling points

can be calculated by , where is the sampling time. Thus, an estimate of during the interval

is given by

(25.15)

The threshold value is given by

(25.16)

where is a constant that is determined by experiments.

Another variable to monitor is the error between the cutting force and its estimated value:

(25.17)

Similarly, the threshold value is given by

. (25.18)

F0L

F F L L t = + +0 0

=F

L t,

F t F t,

F L=

F Fx2

x2 F.

[ ]t ,tf0

t tl

f /f

f

r

=060

,

lf fr

Nt t

Tf=

0 T x2

| |

.xx (i)

Ni

N

2

21= =

F C xT = 1 2 ,

C1

e y= C xT .

E Ce(i)

NT

i

N

= =

21| |


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The fault detection problem consists of checking whether the following conditions hold:

. (25.19)

The fault detection based on multiple variables strengthens the reliability of the method.

25.4 Experimental Results

The model of the cutting process and the state observer for tool-wear detection as discussed in Section

25.2 and Section 25.3 have been implemented in an actual milling machine. The results of the imple-

mentation of the developed method are discussed now.

The machine used in the experiment was a horizontal milling machine, designed and manufactured

by MAKINO. The actual cutting force was measured by a force dynamometer at a sampling rate of 2000 Hz.

In order to estimate the tool wear, a camera system was mounted on the machining center.

For model identification, several cutting tests were conducted under various cutting conditions, asshown in Figure 25.2.

Utilizing the identification technique, the following models were obtained:

for test 1, (25.20)

for test 2, (25.21)

for test 3, (25.22)

for test 4, (25.23)

The nominal model was then constructed as

, (25.24)

. (25.25)

The observer gain is chosen as so that is stable (where the eigenvalues are100.4987 and 2155.7). By choosing , the Lyapunov equation can be computed, providing anerror estimation.

The cutting processes according to the aforementioned four tests were used to compare the estimated

results and the actual measurement. Figure 25.3 presents the comparisons. The estimated error was found

to be within 12 m, which validates the accuracy of the proposed method. It follows that the establishedobserver is suitable for use as a monitoring method to detect faults.

| | | |e E , x F T T> >2

G s.

s . s .1

3

2 3 3

1 633 10

3 9488 10 1 2247 10( ) =

+ +

G s.

s . s .

2

3

2 3 3

1 2034 10

1 7258 10 1 2584 10

( ) =

+ +

G s.

s . s .3 2 3

433 5270

1 2310 10 580 9918( ) =

+ +

G s.

s . s .4 2 3

699 6232

1 7190 10 996 5475( ) =

+ +

A =

0 1

1 0152 10 2 1562 103 3

1

. .

a (t)| | 4435 17932, a (t)| |

b =

0

992 38766421

., b (t)

K [ ]100 10

T

A-KCQ I= 2


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FIGURE 25.2 Cutting force obtained from CNC milling center: (a) SS = 800 rpm,fr = 150 mm/min, depth of cut =

1 mm; (b) SS = 1000 rpm,fr = 100 mm/min, depth of cut = 1 mm; (c) SS = 1000 rpm,fr = 200 mm/min, depth of

cut = 1 mm; (d) SS = 1200 rpm, and fr= 200 mm/min, depth of cut = 1 mm.

FIGURE 25.3 Comparison of actual and estimated cutting forces: (a) SS = 800 rpm,fr = 150 mm/min, depth of cut =

1 mm; (b) SS = 1000 rpm,fr = 100 mm/min, depth of cut = 1 mm; (c) SS = 1000 rpm,fr= 200 mm/min, depth of

cut = 1 mm; (d) SS = 1200 rpm, and fr = 200 mm/min, depth of cut = 1 mm.

250

200

150Cutting

force

Cu

tting

force

Cutting

force

Cutting

force

100

100

140

120

160

180

200

40

80

100

120

140

160

180

60

80

100

120

140

0 20 40 60

0 0 5 10 155 10 15 20

Time

(a)

Time

(c)

Time

(d)

0 20 40 60

Time

(b)

30

20

10

10

Errors

20

30

20

10

0

Errors

100 20 40

Time

(a)

60

0 5 10 15

Time

(c)

20 0 5 10

Time

(d)

15

0 20 40

Time

(b)

60

0

30

20

10

10

Errors

20

0

30

20

10

10

Errors

20

0

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25.5 Conclusion

CNC machines used in automated manufacturing are mechatronic systems. In this chapter, a fault

detection method was developed based on a state-observer model for a milling machine in a CNC

machining center. Specifically, a state-observer model of the cutting force was used to detect tool wear

in milling operations, with satisfactory results. In this method, only the cutting force was used for

monitoring the automated machining. The inexpensive technique based on the observer model was

applied to a CNC milling center. Experimental results showed that the proposed method would provide

robust performance and could be easily used to monitor tool wear.

Acknowledgment

The authors thank Dr. Wang Wenhui for his helpful suggestions and the effort in data collection.

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