- Email: [email protected]
Simulation and Detection of Faulty Behaviors in the Milling Process
Copyright (Q IFAC Information Control in Manufacturing, Nancy - Metz, France, 1998
SIMULATION AND DETECTION OF FAULTY BEHAVIORS IN THE MILLING PROCESS Mohamed Ben Lazrak and Philippe Charbonnaud
Laboratoire Genie de Production - Ecole Nationale d']ngenieurs de Tarbes BP 1629 - 65016 Tarbes Cedex - FRANCE Tel: (33) 05624427 34 - Fax: (33) 0562442708 E-mails:blazrak@enit·frandcharb@enit·fr
Abstract: This paper proposes a method to tune a real time detection test of machining process faulty behaviors. An evaluation of the test to detect efficiently quick faults for an application to milling process is described. The case of slow faults detection is also discussed. The detection and diagnosis of defects rest on a sequential test applied to statistical indicators built from an infonnation provided by existing sensors. The simulation program is validated by experiments. It allows to simulate defects defined according to the process knowledge as determinist and stochastic behavioral laws for physical parameters. Its easy implementation in a monitoring module is a good way to improve finished part quality and industrial and human safety. Copyright © J998 IFAC Keywords: Safety, machining, fault, detection, diagnosis.
Various models have been proposed to predict the order of magnitude of forces. Kim and Ehamann (1993) have represented static and dynamic cutting forces. Teitenberg et aI, (1992) have developed a model of tool-wear based on an analytical cutting mode. Parameters variation leads to an increasing force, to bad roughness of the finished part or to quick tool wear with a consequence on machine vibrations during cutting operation (Papazafiriou and Elbestawi, 1989), (Yao and Yu, 1991).
1. INTRODUCTION Reactive manufacturing systems increase product quality and industrial process safety. As a consequence, the cutting process must be better controlled to achieve a high reactivity degree (Kolarits and Devries, 1991), (El be stawi, Mohamed and Liu, 1990). The complexity of the milling process depends on the various and numerous cutting parameters, (Sridhar, Hohn and Long, 1968). An efficient controlled system must monitor the materialtool set (Charbonnaud and Ben Lazrak, 1995). In our approach, indicators are derived from the cutting forces, feed-rate and feed. Others works are based on the spindle current approach to diagnose defects on the work-piece or on the tool (Altintas, 1992).
Detection of tool defects could be based on various techniques. Residues based method is usual to localize defects (J aume and Verge, 1990). For tool breakage detection, the use of discrete Fourier transform on sliding window is an alternative approach (Nolzen, 1994). Estimation techniques and
963
cinematic chain (Verge et aI, 1993). thickness. The geometry of cutter is defined by: r!:
statistical tests are also required to diagnose In this work, an efficient tool to compute the normal functioning modes and the faulty behaviors of the milling process is presented. The simulator allows to tune a real time detection test of machining process. The quality of the finished part depends on the tuning of the detection test.
r p:
the radial cutting angle,
X
the axial cutting angle,
: the setting angle. The instantaneous static forces
r
components in a referential linked to the machine are given respectively by:
In the second, third and fourth sections, the cutting and machining process modeling are described as components of the simulation algorithm validated by experiments. So, faulty behaviors can be simulated. Sections 5 and 6 present the detection method and the performance of quick fault detection. Section 7 evaluates its extension to slow defects diagnosis.
= F, (i,t/J). cosYp . cosy!
FT (i,t/J)
(1)
+ Fr (i, qJ)' sin K r . sin r! + Fa (i, tfJ) . sin K r . sin r p
=-Ft (i,cfJ)' cos Y
FR (i,cp)
p •
sin y!
(2)
+ Fr(i,tfJ)'sin K r ·cosy! -Fa(i,(/J)'cos K r ·cosy!
= -F, (i,Cp)' sin yp
FA (i,t/J)
(3)
+ Fr (i,cp)' cos K r + Fa (i,cfJ)' sin K r . cosy p
2. CUTTING PROCESS MODELING
where: The geometry of the cutting relations depends on which way the tool rotates and the direction of the feed. The force exerted on the material by an i-th can be split up into three forces (FT' FR , FA) in the coordinate system linked to the tooth (figure 1).
. F(z,t/J)= t
k T • Ai (cp) Fr (.1,'t' th) - k F (. th) r ' t 1,'t' cosy! ,cosr p
Fa (i,t/J) = k a · F,(i,l/J)
(4)
These equations can be represented by:
Chip removal generates an F resulting force, exerted by the tool on the work-piece, which is obtained by projecting the elementary forces in a referential linked to the tool. F x is the feed force which goes the same way than the feed movement, F y is the transverse force perpendicular to the feed movement in the cutting plane, and F z is the axial force, perpendicular to the cutting plane (Smith and Tlusty, 1991).
FT(i,t/J»)
[al + /31 . kr + A, .k
Q
FR(~,t/J) = kr .a
Q
(8; (t/J}) . h(8;(f/)}}'
1F,..(l,t/J) where:
(Xl
= 1, 0.
2
= tan y ! ' sin K cOS'Y p
tan'Y cos 'Y p
tool
Q
~+/33·kr+~·kQ
~I=-_r'~2=-_r,
tan r p • sin Kr
Al
]
a 2 + /32 .k, + A.:z . k (5)
cosy!
'
~
_
f1v 2
-
(X3
f3 3=
cos K r cosy p
=
tanyp cosy! cos Kr
cos r p • cos r! , A,3
sin Kr =-_. cosy!
K b Kr, K n are detennined by identification. Superimposing all active cutting edges the resultants of instantaneous static force components in a referential linked to the machine are given respectively by :
FA(i,cp)
.. f:feed
FXUP)) z rC~s8,(ljl) sin8,(ljl) 0]1 FT(i,f/»)) (6) Fy(f/») = ~86;lsm8;(t/J) -cos8;(f/») 0 FR(i,t/J) Fz{t/J) ,1 0 0 1 F,.. (i,t/J)
!
with:
06i {
=1
siI ~ ei ~ <1'2
otherwise 06 = 0 j
tool
and
,lp2: exit angle of
work-piece. The cutting model is encapsulated in the simulation algorithm.
~z
Fig. 1. Cutting forces on the i-th tooth
3. MACHINING PROCESS MODELING
The static tangential components FT (i, t/J ) is function of the geometry of machining and cutting edge. The geometry of machining is represented by the area of
Figure 2 shows the general diagram of the process. The three loops of current, feed-rate and feed define the cinematic of the actuator.
964
Se t UP
Se t 1 P
1)1
~~~ )/
JL ~
The actuator is submitted to a reference feed and generates the feed-rate to the cutting process from which the force Fe results. The modeling of actuator cinematic can be expressed in state variables modelisation as:
x=
-
~~~;
_[Om] I
F ,,£ = lr U
coui
J'" f".."
1\
Cpn ~c le~
..
I
1
It'-o ~trplJed
Oil
1
)
,
.,
,
j
Fig. 4. Feed regulation (a) Feed-rate regulation (b).
(7)
1 0L
]
'1\ ,
where, !.,-
(p)
0
A reference feed law is generated for the machining
[~o] .e J . . x + 1.
!£.]
-K -R [- - - L L
11
~~.
Fig. 2. Bloc diagram of the machining process
- F. J.
,
to
I
r
~
(;~)
.~
and v=sgn (
n ) m
process to perform the process planning. Figure 4.(b) shows the feed law with three functioning phases: entry in work-piece, machining at constant feed-rate and exit of work-piece.
(8)
4. FAULTY BEHAVIORS AND SIMULAnON
with the following notations: R, L : motor armature resistance and inductance. Kc : motor torque. FcouJ, Fg : table coulomb friction and global viscous friction. J g : motor global inertia. I, U : m : motor motor armature current and voltage.
Very often, abnormal behaviors of the cutting process are quick wear of the tool when the material tool parameters are not optimized, or chip sticking which depends on the material and on the operation.
n
speed. The simulation parameters are : - DC motor parameters
Many other faulty behaviors can be observed. The problem is to represent their various causes to diagnose and to take them into account in the monitoring system. Abnormal behaviors to be tested can be classified in two subsets: the quick and slow defects.
= 0,OO3m.N.s/ rd, J m = 0,017kg.m 2 Kc = 0,47m.N / A, R = 0,610, L = 0,OO19H - Screw and reduction parameters J v =0,OI2kg.m2 , P=O,Olm, R r =0,5, /=0,01 - Table parameters F, =5000N.s / m, M t = 81 Okg, F'coul =.02N - Cutting process parameters D = 63mm, Z = 5, aa = 1,5mm, ar =50mm , Vc = 150m/ mn, Ke ll = 1500N / mm 2 , me = 0,25, K r = 45° , fz = 0.2 mm/tooth. Fm
The control of the current and the feed-rate is ensured by two cascade loops with a PI controller determined by a pole placement method. Time
(5)
Fig. 5. Force with and without tool wear An example of slow defects is given on figure 5. The cutting force increases slowly up to the acceptable wear limit. Without monitoring, the force increases quickly up to the edge rupture.
Fig. 3. Feed-rate and current regulations
The bad quality of a finished part can also be induced by a faulty actuator. The brush wear c~use. ~n increasing value of R, (DC motor). A short CirCUIt In the motor armature induces a decrease of Rand L. A flux variation has a consequence on Kc value. A
A numerical regulator of proportional type allows to control the feed. Figure 4.(a) confirms the main phases produced by the cutting tool during machining.
965
The test is evolving between two boundaries which are estimated during a learning phase when it is sure that the process works in normal conditions. During the learning phase, a simplified model gives a reference behavior indicator monitoring the milling process.
motor superheat leads to a simultaneous change of R and Kc. 5. DETECTION METHOD The machining process can be simulated in normal functioning modes and with various types of defects. In this study, the cutting force supplies significant information. The resultant of cutting force is processed through a likelihood ratio method based on a variance and mean indicators (Basseville and Nikiforov, 1993).
1~
ffi j
where n =2m + 1 is the size of the sliding window. The variance is processed on sliding window with the following recursive equation:
er
2 2 ~ =~-l
I
F + Fj
n Abrupt change of parameter have been introduced, to observe the detection test (figures 6&7).
MHo
(9)
L (Fe (J) - Fo)I>
MH 1
(10)
2
!~l
(15)
11-+m -I1-m-l r + 1)EI~I +(n -1) El+m - ")nn'\] I 2 -t.
o L(Fe{J)-Fo) <0' .lnA+k.-.
(14)
n j=-m
For an increase of the mean value, a fault is defined by a significant increase p% of the mean from Fo to F I , assuming that the variance (J2 is kept constant. Fo and (12 are estimated during a normal behaviour when it is sure that the process works in normal conditions. So, the test can be performed to detect either an increase or a decrease of the mean value. The formulation of the test to detect an increase of the mean is given by: j=k
=- ..2./'i+j
2
j=k
.
I
j=l
2 (f
Fo+Fj .1nB + k . - 2
where: k is the number of samples, Time
I-PM
B =-- .
PF
PF and PM are respectively the probability
Fig. 6. Test on mean force for tool breaking
of wrong alarm and the missed fault probability. There is no decision when:
I~'
I
Fo + I) 2 .In A < £.J(Fc(J)-Fo)
2
j=1
The
test
aims
at
(11)
2
calculating
the
sum
j=k
L (F (j) - Fo) at checking in which area delimited c
j=I
by two boundaries those values converge. For an increase of the variance value, we define a fault by a significant increase of the variance value from 0'0 to 0'1. The formulation of the test to detect an increase of the variance value is given by:
j=k
L
2
(F (j) -
j=1
Fo)
2 0 1 2 e lnB+kln-2< - - I--1....;;0_0,;;.-
0
L
(F (j) -
Fo>
0.'
0.'
0.7
0.'
0.'
Fig. 7. Test on variance of force for tool breaking The objective is to analyze the effect of parameters adjustment in order to reduce the detection late time and the wrong alarm probability.
(12) 6. QUICK FAULTS DETECTION PERFORMANCE
-2--2 00 01 2
0..
T im e
C
j=k j=l
VHo
o.~
2
1
2 e In A + kIn -2-
> - - I--I""';o---=-.O
VH 1
The performance of the test and the delay of decision are optimized by studying the effect of the window size 'n', variance ci and mean m. values variation I
(13)
C
-2--2 00 01
I
966
revolution spindle length. The test gives good results for the mean force.
'p'. The detection procedure allows to compare the perturbed force and the normal force on sliding window by using the test described above.
For quick defects with short duration, the detection based on variance gives a better wrong alarm probability than the one based on mean. The test is well tuned for p = 0.001 and n = 0.5 revolution.
Figure 7 shows the test results with the following coefficients: PF=O.OO 1, PM=O.OO 1. The test is adjusted for a detection of 1% increase of variance value. The window size is equal to the number of samples per tooth in order to be able to monitor the tool state. The test detects a fault with a late of 2 samples. The advantage by comparison to a reference signal is to "eliminate" the wrong alarm.
Some quick defects cause non-reversing bad functioning modes and then cause the safety stop of machines. In the case of tool breaking, the detection late time is always low for p>O.OI, (figurel0) but the wrong alann probability increases. Then, a compromise leads to p = 1%. Tool beakina case
~.: _Vari~ce ~ ~~~t~~ ~~.e ~~f!l~
Mean ----..:.-.' . .. - .' . .'.
. Variance' :Faul~ dis~earing:tim~ ; . " . ",. ' " .- " . " .. " .. , ,Mean' , . , , ,
\
..
","
~
.
,
.•
,
,
,
0.01~
0.018
001.
::-"'~-_.':":-=-:..:.: , ,
. "
~
0.0tlZ
0.0lM
0.0llll
0.0llll
0.01
0.012
0.02
.'0 .r----.-----.-......... .........,.--r---r--,---r"-~__.
• a1~e.a1~rm:pr~~~·~~·~.
4Z .- - .'. ,
2
0~~~=:±:=Z::~:::::=.J 0._ 0._ 0
,
-
•
--Vanance··,· . ., .. •• - Mean . I
•
•
,
OI-.:;;~-.I_~~_.....I....----L._.......----1.._~--'
0._
;' 011
-
,
o
0.002
o.OlM
0.0llll
o.Ollll
0.01
0.012
0.01~
0.011
0.018
0.02
a~-r-~-..,.--~-~--r---,r---"""T'""'"""""""'----'
:I: Varianc~
/ ,Mean
.
NJis~ed. f~ult prob~ilitY.
., .. ~~;~_~~ce
'
, , , . , ."~' Missed' fault·probabilitY :
1
P (0/0)
0.6I-----'-_..L.....---'-_L.---L-
o
0.0tlZ
o.OlM
0.0llll
o.OCI
0.01
·:-M~
1.---L--.l_...L---J 0.012 0.014 0.018 0.01'
P (%)
Fig. 8. 'p' influence on detection parameters
Fig. 10. 'p' influence on detection parameters For the chip-sticking problem, the immunity to missed defects is good and the wrong a1ann probability increase with 'p' (figure 8). The values of detection late time is low for p> 1% with Rtet = 2 samples and Rtes = 2 samples. Chip stickinQ case
....
late ime
_v- :.---
..
For a small sliding window, mean and variance indicators are more sensible to random variations, which induce wrong detection. When the window size is too large, detection is slower. So, the risk to ignore significant variations is more important.
I
,"o~n
~
.-- ~ Var ·anc e_
ean
~--
Vr:.
u ... I......
Hr:.nl~A
Fal ~It d esal ~ear nQ ime
~
Fal e alarm prol abi 'ty
~~
'--
IM,:uln -1--
...
,.,.
...
~
• Fallse c larnle probe bilit~
'1----+--+--I---I---+-+-...-1
Va ~an( e "
-
_
_
,
V ria!1.~
Size of the sliding window
Size of the sliding window
Fig. 9. 'n' influence on detection parameters
Fig. 11. 'n' influence on detection parameters
The larger the window is, the more important missed defects probability and the more detection late time are (figure 9). The better size for the window is a half
967
.
7. EXTENSION TO SLOW DEFECTS DIAGNOSIS
The future work aims at implementing the previous recommendations.
The tool wear is a slow defect represented on figure 5. The detection late time is about 200 samples. In this case, wrong alarm and missed fault probability are very important. Figure 12 gives only the influence on the test of 'n' for p = 0.01. This kind of defect is not detected by the test on the variance. For tool wear, the recommended indicator is the mean force processed on a great number of samples.
REFERENCES Altintas, Y. (1992). Prediction of cutting forces and tool breakage in milling from feed drive current measurements. Transactions of the ASME, Vol. 114, 386-392. Basseville, M. and I. V. Nikiforov (1993). Detection of abrupt changes: theory and application. 528 pages, Prentice Hall. Charbonnaud, P. and M. Ben Lazrak (1995). Skill and knowledge integration for milling monitoring. INRIAIIEEE Conference on Emerging Technologies and Factory Automation, Vol. 1, 619-628. Elbestawi, M. A., Y. Mohamed and L. Liu (1990). Application of some parameter adaptive control algorithms in machining. Journal of Dynamic Systems, Measurement and Control, vol. 112, 611-616. Jaume, D. and M. Verge (1990). A model based diagnosis in machine tolols: application to the milling process. Annals of the Cirp, Vol. 39, 443446. Kim, H. S. and K. F. Ehman (1993). A cutting force model for face milling. operations. Int. .1. Tools Manufact., Vol. 33, 651-673. Kolarits, F. M. and W. R. Devries (1991). A mechanistic dYnamic model of end milling for process controller simulation. Transactions of the ASME, vol. 113, 176-183. Nolzen, H. (1994). Fault diagnosis and wear detection in the control loop of a milling machine. Safeprocess, Vol. 2, 463-468. Papazafiriou, T. A. and M. A. Elbestawi (1989). Flank wear modeling in milling. Journal of Mechanical Working Technology, 93-104. Smith, S. and 1. Tlusty (1991). An overview of modeling and simulation of the milling process. Journal of Engineering of Industry, Vol. 113, 169-175. Sridhar R., R. E. Hohn and G. W. Long (1968). A general formulation of the milling process equation. Journal of Engineering of Industry, 317324. Teitenberg Tony, M., A. E. Bayoumi and G. Yucesan (1992). Tool wear modeling through an analytic mechanistic model of milling process. Wear 154, 287-304. Verge, M., D. Jaume and D. Bernede (1993). Machine tools kinematic chains diagnosis. Tooldiag'93, 332-339. Yao-Qun Lin, and Yu-Hwa Wang (1991). Stick-Slip vibration of drill strings. Transaction of the ASME, Vol. 113,38-43.
Taiv.ear~
~
./
..
et
.m
\
\ \ n""---_:---.....~..-L--.~_J...____'____I'__...J_...__L._..L...___J o
,
02
\.
IV ....... 1""1
"
ca
O.
.,.
.
1:<41 1111
. ...
.
.., l
[,.tre n-ea
~ r-- t----_
n n
SUe et tIE slicq \\Uxb.v Fig. 12. 'n' influence on detection parameters
8. CONCLUSION The performance evaluation of the real-time detection test on the mean and variance indicators shows that a great number of defects is well detected. The simulation shows that the tuning parameters p = 0.01 and n = 0.5 revolution are adapted to quick defects. Slow defects detection of the cutting process is also possible with n = 1 revolution. The detection procedure to integrate in the supervision system must be based on statistical approach for the cutting process and also based on parameter estimation in order to detect actuators faults. After the diagnosis, the decision algorithm must be designed and implemented in an integrated architecture of supervision-control. The consequences of quick defects with short duration can be compensated by an additional loop of control which should allow for a better quality of the finished part and an improved machine safety. For irreversible defects such as tool defects, the safety stop and restart must be more formalized before being taken into account in the architecture.
968
SIMULATION AND DETECTION OF FAULTY BEHAVIORS IN THE MILLING PROCESS Mohamed Ben Lazrak and Philippe Charbonnaud
Laboratoire Genie de Production - Ecole Nationale d']ngenieurs de Tarbes BP 1629 - 65016 Tarbes Cedex - FRANCE Tel: (33) 05624427 34 - Fax: (33) 0562442708 E-mails:blazrak@enit·frandcharb@enit·fr
Abstract: This paper proposes a method to tune a real time detection test of machining process faulty behaviors. An evaluation of the test to detect efficiently quick faults for an application to milling process is described. The case of slow faults detection is also discussed. The detection and diagnosis of defects rest on a sequential test applied to statistical indicators built from an infonnation provided by existing sensors. The simulation program is validated by experiments. It allows to simulate defects defined according to the process knowledge as determinist and stochastic behavioral laws for physical parameters. Its easy implementation in a monitoring module is a good way to improve finished part quality and industrial and human safety. Copyright © J998 IFAC Keywords: Safety, machining, fault, detection, diagnosis.
Various models have been proposed to predict the order of magnitude of forces. Kim and Ehamann (1993) have represented static and dynamic cutting forces. Teitenberg et aI, (1992) have developed a model of tool-wear based on an analytical cutting mode. Parameters variation leads to an increasing force, to bad roughness of the finished part or to quick tool wear with a consequence on machine vibrations during cutting operation (Papazafiriou and Elbestawi, 1989), (Yao and Yu, 1991).
1. INTRODUCTION Reactive manufacturing systems increase product quality and industrial process safety. As a consequence, the cutting process must be better controlled to achieve a high reactivity degree (Kolarits and Devries, 1991), (El be stawi, Mohamed and Liu, 1990). The complexity of the milling process depends on the various and numerous cutting parameters, (Sridhar, Hohn and Long, 1968). An efficient controlled system must monitor the materialtool set (Charbonnaud and Ben Lazrak, 1995). In our approach, indicators are derived from the cutting forces, feed-rate and feed. Others works are based on the spindle current approach to diagnose defects on the work-piece or on the tool (Altintas, 1992).
Detection of tool defects could be based on various techniques. Residues based method is usual to localize defects (J aume and Verge, 1990). For tool breakage detection, the use of discrete Fourier transform on sliding window is an alternative approach (Nolzen, 1994). Estimation techniques and
963
cinematic chain (Verge et aI, 1993). thickness. The geometry of cutter is defined by: r!:
statistical tests are also required to diagnose In this work, an efficient tool to compute the normal functioning modes and the faulty behaviors of the milling process is presented. The simulator allows to tune a real time detection test of machining process. The quality of the finished part depends on the tuning of the detection test.
r p:
the radial cutting angle,
X
the axial cutting angle,
: the setting angle. The instantaneous static forces
r
components in a referential linked to the machine are given respectively by:
In the second, third and fourth sections, the cutting and machining process modeling are described as components of the simulation algorithm validated by experiments. So, faulty behaviors can be simulated. Sections 5 and 6 present the detection method and the performance of quick fault detection. Section 7 evaluates its extension to slow defects diagnosis.
= F, (i,t/J). cosYp . cosy!
FT (i,t/J)
(1)
+ Fr (i, qJ)' sin K r . sin r! + Fa (i, tfJ) . sin K r . sin r p
=-Ft (i,cfJ)' cos Y
FR (i,cp)
p •
sin y!
(2)
+ Fr(i,tfJ)'sin K r ·cosy! -Fa(i,(/J)'cos K r ·cosy!
= -F, (i,Cp)' sin yp
FA (i,t/J)
(3)
+ Fr (i,cp)' cos K r + Fa (i,cfJ)' sin K r . cosy p
2. CUTTING PROCESS MODELING
where: The geometry of the cutting relations depends on which way the tool rotates and the direction of the feed. The force exerted on the material by an i-th can be split up into three forces (FT' FR , FA) in the coordinate system linked to the tooth (figure 1).
. F(z,t/J)= t
k T • Ai (cp) Fr (.1,'t' th) - k F (. th) r ' t 1,'t' cosy! ,cosr p
Fa (i,t/J) = k a · F,(i,l/J)
(4)
These equations can be represented by:
Chip removal generates an F resulting force, exerted by the tool on the work-piece, which is obtained by projecting the elementary forces in a referential linked to the tool. F x is the feed force which goes the same way than the feed movement, F y is the transverse force perpendicular to the feed movement in the cutting plane, and F z is the axial force, perpendicular to the cutting plane (Smith and Tlusty, 1991).
FT(i,t/J»)
[al + /31 . kr + A, .k
Q
FR(~,t/J) = kr .a
Q
(8; (t/J}) . h(8;(f/)}}'
1F,..(l,t/J) where:
(Xl
= 1, 0.
2
= tan y ! ' sin K cOS'Y p
tan'Y cos 'Y p
tool
Q
~+/33·kr+~·kQ
~I=-_r'~2=-_r,
tan r p • sin Kr
Al
]
a 2 + /32 .k, + A.:z . k (5)
cosy!
'
~
_
f1v 2
-
(X3
f3 3=
cos K r cosy p
=
tanyp cosy! cos Kr
cos r p • cos r! , A,3
sin Kr =-_. cosy!
K b Kr, K n are detennined by identification. Superimposing all active cutting edges the resultants of instantaneous static force components in a referential linked to the machine are given respectively by :
FA(i,cp)
.. f:feed
FXUP)) z rC~s8,(ljl) sin8,(ljl) 0]1 FT(i,f/»)) (6) Fy(f/») = ~86;lsm8;(t/J) -cos8;(f/») 0 FR(i,t/J) Fz{t/J) ,1 0 0 1 F,.. (i,t/J)
!
with:
06i {
=1
si
otherwise 06 = 0 j
tool
and
,lp2: exit angle of
work-piece. The cutting model is encapsulated in the simulation algorithm.
~z
Fig. 1. Cutting forces on the i-th tooth
3. MACHINING PROCESS MODELING
The static tangential components FT (i, t/J ) is function of the geometry of machining and cutting edge. The geometry of machining is represented by the area of
Figure 2 shows the general diagram of the process. The three loops of current, feed-rate and feed define the cinematic of the actuator.
964
Se t UP
Se t 1 P
1)1
~~~ )/
JL ~
The actuator is submitted to a reference feed and generates the feed-rate to the cutting process from which the force Fe results. The modeling of actuator cinematic can be expressed in state variables modelisation as:
x=
-
~~~;
_[Om] I
F ,,£ = lr U
coui
J'" f".."
1\
Cpn ~c le~
..
I
1
It'-o ~trplJed
Oil
1
)
,
.,
,
j
Fig. 4. Feed regulation (a) Feed-rate regulation (b).
(7)
1 0L
]
'1\ ,
where, !.,-
(p)
0
A reference feed law is generated for the machining
[~o] .e J . . x + 1.
!£.]
-K -R [- - - L L
11
~~.
Fig. 2. Bloc diagram of the machining process
- F. J.
,
to
I
r
~
(;~)
.~
and v=sgn (
n ) m
process to perform the process planning. Figure 4.(b) shows the feed law with three functioning phases: entry in work-piece, machining at constant feed-rate and exit of work-piece.
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4. FAULTY BEHAVIORS AND SIMULAnON
with the following notations: R, L : motor armature resistance and inductance. Kc : motor torque. FcouJ, Fg : table coulomb friction and global viscous friction. J g : motor global inertia. I, U : m : motor motor armature current and voltage.
Very often, abnormal behaviors of the cutting process are quick wear of the tool when the material tool parameters are not optimized, or chip sticking which depends on the material and on the operation.
n
speed. The simulation parameters are : - DC motor parameters
Many other faulty behaviors can be observed. The problem is to represent their various causes to diagnose and to take them into account in the monitoring system. Abnormal behaviors to be tested can be classified in two subsets: the quick and slow defects.
= 0,OO3m.N.s/ rd, J m = 0,017kg.m 2 Kc = 0,47m.N / A, R = 0,610, L = 0,OO19H - Screw and reduction parameters J v =0,OI2kg.m2 , P=O,Olm, R r =0,5, /=0,01 - Table parameters F, =5000N.s / m, M t = 81 Okg, F'coul =.02N - Cutting process parameters D = 63mm, Z = 5, aa = 1,5mm, ar =50mm , Vc = 150m/ mn, Ke ll = 1500N / mm 2 , me = 0,25, K r = 45° , fz = 0.2 mm/tooth. Fm
The control of the current and the feed-rate is ensured by two cascade loops with a PI controller determined by a pole placement method. Time
(5)
Fig. 5. Force with and without tool wear An example of slow defects is given on figure 5. The cutting force increases slowly up to the acceptable wear limit. Without monitoring, the force increases quickly up to the edge rupture.
Fig. 3. Feed-rate and current regulations
The bad quality of a finished part can also be induced by a faulty actuator. The brush wear c~use. ~n increasing value of R, (DC motor). A short CirCUIt In the motor armature induces a decrease of Rand L. A flux variation has a consequence on Kc value. A
A numerical regulator of proportional type allows to control the feed. Figure 4.(a) confirms the main phases produced by the cutting tool during machining.
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The test is evolving between two boundaries which are estimated during a learning phase when it is sure that the process works in normal conditions. During the learning phase, a simplified model gives a reference behavior indicator monitoring the milling process.
motor superheat leads to a simultaneous change of R and Kc. 5. DETECTION METHOD The machining process can be simulated in normal functioning modes and with various types of defects. In this study, the cutting force supplies significant information. The resultant of cutting force is processed through a likelihood ratio method based on a variance and mean indicators (Basseville and Nikiforov, 1993).
1~
ffi j
where n =2m + 1 is the size of the sliding window. The variance is processed on sliding window with the following recursive equation:
er
2 2 ~ =~-l
I
F + Fj
n Abrupt change of parameter have been introduced, to observe the detection test (figures 6&7).
MHo
(9)
L (Fe (J) - Fo)I>
MH 1
(10)
2
!~l
(15)
11-+m -I1-m-l r + 1)EI~I +(n -1) El+m - ")nn'\] I 2 -t.
o L(Fe{J)-Fo) <0' .lnA+k.-.
(14)
n j=-m
For an increase of the mean value, a fault is defined by a significant increase p% of the mean from Fo to F I , assuming that the variance (J2 is kept constant. Fo and (12 are estimated during a normal behaviour when it is sure that the process works in normal conditions. So, the test can be performed to detect either an increase or a decrease of the mean value. The formulation of the test to detect an increase of the mean is given by: j=k
=- ..2./'i+j
2
j=k
.
I
j=l
2 (f
Fo+Fj .1nB + k . - 2
where: k is the number of samples, Time
I-PM
B =-- .
PF
PF and PM are respectively the probability
Fig. 6. Test on mean force for tool breaking
of wrong alarm and the missed fault probability. There is no decision when:
I~'
I
Fo + I) 2 .In A < £.J(Fc(J)-Fo)
2
j=1
The
test
aims
at
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2
calculating
the
sum
j=k
L (F (j) - Fo) at checking in which area delimited c
j=I
by two boundaries those values converge. For an increase of the variance value, we define a fault by a significant increase of the variance value from 0'0 to 0'1. The formulation of the test to detect an increase of the variance value is given by:
j=k
L
2
(F (j) -
j=1
Fo)
2 0 1 2 e lnB+kln-2< - - I--1....;;0_0,;;.-
0
L
(F (j) -
Fo>
0.'
0.'
0.7
0.'
0.'
Fig. 7. Test on variance of force for tool breaking The objective is to analyze the effect of parameters adjustment in order to reduce the detection late time and the wrong alarm probability.
(12) 6. QUICK FAULTS DETECTION PERFORMANCE
-2--2 00 01 2
0..
T im e
C
j=k j=l
VHo
o.~
2
1
2 e In A + kIn -2-
> - - I--I""';o---=-.O
VH 1
The performance of the test and the delay of decision are optimized by studying the effect of the window size 'n', variance ci and mean m. values variation I
(13)
C
-2--2 00 01
I
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revolution spindle length. The test gives good results for the mean force.
'p'. The detection procedure allows to compare the perturbed force and the normal force on sliding window by using the test described above.
For quick defects with short duration, the detection based on variance gives a better wrong alarm probability than the one based on mean. The test is well tuned for p = 0.001 and n = 0.5 revolution.
Figure 7 shows the test results with the following coefficients: PF=O.OO 1, PM=O.OO 1. The test is adjusted for a detection of 1% increase of variance value. The window size is equal to the number of samples per tooth in order to be able to monitor the tool state. The test detects a fault with a late of 2 samples. The advantage by comparison to a reference signal is to "eliminate" the wrong alarm.
Some quick defects cause non-reversing bad functioning modes and then cause the safety stop of machines. In the case of tool breaking, the detection late time is always low for p>O.OI, (figurel0) but the wrong alann probability increases. Then, a compromise leads to p = 1%. Tool beakina case
~.: _Vari~ce ~ ~~~t~~ ~~.e ~~f!l~
Mean ----..:.-.' . .. - .' . .'.
. Variance' :Faul~ dis~earing:tim~ ; . " . ",. ' " .- " . " .. " .. , ,Mean' , . , , ,
\
..
","
~
.
,
.•
,
,
,
0.01~
0.018
001.
::-"'~-_.':":-=-:..:.: , ,
. "
~
0.0tlZ
0.0lM
0.0llll
0.0llll
0.01
0.012
0.02
.'0 .r----.-----.-......... .........,.--r---r--,---r"-~__.
• a1~e.a1~rm:pr~~~·~~·~.
4Z .- - .'. ,
2
0~~~=:±:=Z::~:::::=.J 0._ 0._ 0
,
-
•
--Vanance··,· . ., .. •• - Mean . I
•
•
,
OI-.:;;~-.I_~~_.....I....----L._.......----1.._~--'
0._
;' 011
-
,
o
0.002
o.OlM
0.0llll
o.Ollll
0.01
0.012
0.01~
0.011
0.018
0.02
a~-r-~-..,.--~-~--r---,r---"""T'""'"""""""'----'
:I: Varianc~
/ ,Mean
.
NJis~ed. f~ult prob~ilitY.
., .. ~~;~_~~ce
'
, , , . , ."~' Missed' fault·probabilitY :
1
P (0/0)
0.6I-----'-_..L.....---'-_L.---L-
o
0.0tlZ
o.OlM
0.0llll
o.OCI
0.01
·:-M~
1.---L--.l_...L---J 0.012 0.014 0.018 0.01'
P (%)
Fig. 8. 'p' influence on detection parameters
Fig. 10. 'p' influence on detection parameters For the chip-sticking problem, the immunity to missed defects is good and the wrong a1ann probability increase with 'p' (figure 8). The values of detection late time is low for p> 1% with Rtet = 2 samples and Rtes = 2 samples. Chip stickinQ case
....
late ime
_v- :.---
..
For a small sliding window, mean and variance indicators are more sensible to random variations, which induce wrong detection. When the window size is too large, detection is slower. So, the risk to ignore significant variations is more important.
I
,"o~n
~
.-- ~ Var ·anc e_
ean
~--
Vr:.
u ... I......
Hr:.nl~A
Fal ~It d esal ~ear nQ ime
~
Fal e alarm prol abi 'ty
~~
'--
IM,:uln -1--
...
,.,.
...
~
• Fallse c larnle probe bilit~
'1----+--+--I---I---+-+-...-1
Va ~an( e "
-
_
_
,
V ria!1.~
Size of the sliding window
Size of the sliding window
Fig. 9. 'n' influence on detection parameters
Fig. 11. 'n' influence on detection parameters
The larger the window is, the more important missed defects probability and the more detection late time are (figure 9). The better size for the window is a half
967
.
7. EXTENSION TO SLOW DEFECTS DIAGNOSIS
The future work aims at implementing the previous recommendations.
The tool wear is a slow defect represented on figure 5. The detection late time is about 200 samples. In this case, wrong alarm and missed fault probability are very important. Figure 12 gives only the influence on the test of 'n' for p = 0.01. This kind of defect is not detected by the test on the variance. For tool wear, the recommended indicator is the mean force processed on a great number of samples.
REFERENCES Altintas, Y. (1992). Prediction of cutting forces and tool breakage in milling from feed drive current measurements. Transactions of the ASME, Vol. 114, 386-392. Basseville, M. and I. V. Nikiforov (1993). Detection of abrupt changes: theory and application. 528 pages, Prentice Hall. Charbonnaud, P. and M. Ben Lazrak (1995). Skill and knowledge integration for milling monitoring. INRIAIIEEE Conference on Emerging Technologies and Factory Automation, Vol. 1, 619-628. Elbestawi, M. A., Y. Mohamed and L. Liu (1990). Application of some parameter adaptive control algorithms in machining. Journal of Dynamic Systems, Measurement and Control, vol. 112, 611-616. Jaume, D. and M. Verge (1990). A model based diagnosis in machine tolols: application to the milling process. Annals of the Cirp, Vol. 39, 443446. Kim, H. S. and K. F. Ehman (1993). A cutting force model for face milling. operations. Int. .1. Tools Manufact., Vol. 33, 651-673. Kolarits, F. M. and W. R. Devries (1991). A mechanistic dYnamic model of end milling for process controller simulation. Transactions of the ASME, vol. 113, 176-183. Nolzen, H. (1994). Fault diagnosis and wear detection in the control loop of a milling machine. Safeprocess, Vol. 2, 463-468. Papazafiriou, T. A. and M. A. Elbestawi (1989). Flank wear modeling in milling. Journal of Mechanical Working Technology, 93-104. Smith, S. and 1. Tlusty (1991). An overview of modeling and simulation of the milling process. Journal of Engineering of Industry, Vol. 113, 169-175. Sridhar R., R. E. Hohn and G. W. Long (1968). A general formulation of the milling process equation. Journal of Engineering of Industry, 317324. Teitenberg Tony, M., A. E. Bayoumi and G. Yucesan (1992). Tool wear modeling through an analytic mechanistic model of milling process. Wear 154, 287-304. Verge, M., D. Jaume and D. Bernede (1993). Machine tools kinematic chains diagnosis. Tooldiag'93, 332-339. Yao-Qun Lin, and Yu-Hwa Wang (1991). Stick-Slip vibration of drill strings. Transaction of the ASME, Vol. 113,38-43.
Taiv.ear~
~
./
..
et
.m
\
\ \ n""---_:---.....~..-L--.~_J...____'____I'__...J_...__L._..L...___J o
,
02
\.
IV ....... 1""1
"
ca
O.
.,.
.
1:<41 1111
. ...
.
.., l
[,.tre n-ea
~ r-- t----_
n n
SUe et tIE slicq \\Uxb.v Fig. 12. 'n' influence on detection parameters
8. CONCLUSION The performance evaluation of the real-time detection test on the mean and variance indicators shows that a great number of defects is well detected. The simulation shows that the tuning parameters p = 0.01 and n = 0.5 revolution are adapted to quick defects. Slow defects detection of the cutting process is also possible with n = 1 revolution. The detection procedure to integrate in the supervision system must be based on statistical approach for the cutting process and also based on parameter estimation in order to detect actuators faults. After the diagnosis, the decision algorithm must be designed and implemented in an integrated architecture of supervision-control. The consequences of quick defects with short duration can be compensated by an additional loop of control which should allow for a better quality of the finished part and an improved machine safety. For irreversible defects such as tool defects, the safety stop and restart must be more formalized before being taken into account in the architecture.
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