- Email: [email protected]
Machine Tool-Wear Sensing Aided by a Stochastic Global Optimizer
MACHINE TOOL-WEAR SENSING AIDED BY A STOCHASTIC GLOBAL OPTIMIZER
M. A. Zohdy and B. Adamczyk Center for Robotics and Advanced Automation Oakland University Rochester, MI 48309
Abstract This paper presents an approach to the problem of on-line machine tool-wear sensing and monitoring. Ultrasonic energy acoustic emission signals are used in the diagnostic system. The real-time situation is simulated by using a linear combination of periodic waves superimposed on a random noise. The peaking pauern of the acoustic waves is keyed in as an indicator of tool-wear and is continuously monitored to predict tool failure or fracture. A new SlOChastic global optimization is used to generate the data set that best represents archetypes of machine-wear characteristics. Keywords. Tool-wear sensing; failure detection; global optimization; system diagnostics. ACOUSTIC EMISSION ANALYSIS INTRODUCTION This study concentrates on acoustic emission signals as the principal measured variables for online tool-wear monitoring. Acoustic emission analysis has been successfully used in the fields of non-destructive material testing and the estimation of structural integrity of the materials (Lee el al., 1987; Hayashi et al., 1988). Acoustic emission refers to the elastic stress waves generated as a result of a rapid release of strain energy within a material due to rearrangement of its internal structure. The stress waves generated by the structural rearrangement can produce displacements on the surface of the material which are detected by converting them into electrical signals. High levels of acoustic emission signals are observed when the failure of the cutting tool takes place. The level of acoustic emission signal is closely related to the size of the fracture surface of the tool.
The rapidly developing flexible manufacturing systems demand continuous on-line monitoring to predict tool-wear and breakage. On-line sensing of tool-wear forms an essential part of any realistic adaptive optimization scheme and is particularly important in efficient scheduling of machine downtime for tool changing. The method suggested in this paper points to the use of acoustic emission signal dynamic patterns as principal features . Acoustic emission signals prove to be a reliable approach for long term system operation, and leads to the economical and efficient manufacturing system. Data sets that best represent machine-wear characteristics are generated using a new stochastic global optimizer. The data are classified into recognized classes based on the "distance" between the prototype data set and the test set. Prototype set is obtained by minimizing the cost function associated with the tool-wear training data set. The approximate value of the global minimum is found by using a special transformation, where a function of only one variable may be investigated instead of the multivariable function at hand.
Three common methods of tool-wear analysis are set point, signature, and pauern recognition. They are used to link the desired decision with the measured variables. The set point technique assumes that the desired value can be based on the violation of a predetermined boundary by the measured signal. The pattern recognition method analyses key process parameters and tries to match them to a dynamic sequence of events that are known to be uniquely indicative of a broken or worn machine tool.
The measured acoustic signals pass through a bank of proper delay elements that can recognize a dynamic sequence of data, rather than an individual measurement, thus allowing a dynamic wear-pattern to be detected.
This study uses combined signature analysis and 216
We made the following assumptions. (1) It is sufficient to detect a sequence of consecutive peaks in order to identify it as a signal. (2) Sign of the peak amplitude changes randomly, negative values are ignored. (3) The following combination of conditions indicates the fault: (a) detection of the peak voltage signal after a period of 't J milliseconds; (b) detection of the peak voltage after a period of't2 millisecond; (c) present detection of the peak voltage signal.
pauern recogmuon technique. Deviation of the signature of the operating tool characteristics indicates a process of change which is interpreted as a worn-tool condition.
EQUIPMENT SETUP A sketch of the experimental equipment setup is shown in Fig. 1. It includes the machine tool, dynarnometer, and AE pin transducer. The AE pin transducer output is first amplilie..1 and then fIltered through successive hi-pass and low-pass filters. Then, it is amplilied once more before it is fed to the data acquisition system (DAS). The outputs for the force dynamometer are also amplified and fed into DAS to provide context to the acoustic emission.
The time delays built into the network allow the examination of the presence of these conditions. The network converts the serial events occurring in real-time to a set of parallel events which can be examined logically. The failure detection procedure is as follows. Initially the parameters for the periodic wave vs. amplitude A and frequency f are fed into the computer. Periodic wave is superimposed on a random noise wave effectively producing a nonperiodic acoustic emission signal with randomly peaking amplitudes at each cycle. The peak signal is calculated and compared with the peak amplitude. The first peaking amplitude is detected and an indication of a possible incoming failure is given. Next, time delay is set to first to 't J and then to 't2, and the search for the same peaking amplitude is conducted. If peaking amplitudes are detected at the respective time delays, then the critical point i.e., tool-failure point is identified.
In this study, force measurements were made using three-component piezoelectric Kristler a dynamometer auached below the work piece. The outputs of the dynamometer were converted to voltage signals using a Kristler dual mode charge amplifiers.
WORKPIECE
The following signals were simulated: acoustic sine wave (Fig. 2) and acoustic cosine wave (Fig. 3). Sample outputs are presented in Table 1 for the sine wave and in Table 2 for the cosine wave. Zero entry in the last three columns corresponds to no-fault situation, whereas entry of one indicates the detection of a possible incoming failure. Notice that the first case corresponds to the normal i.e., no-failure situation, whereas in the second case a critical point is identified (three one's in the same row) indicating a tool-failure .
HP 9816 COMPUTER SYSTEM
•• In(2·pl· w·'' • n(l)
101--~--~-~------- ---------------- ,10
8
Fig. 1. Sketch of experimental equipment
-e
SIMULATION OF TIlE ACOUSTIC SIGNAL of----\
Simulation of the proposed system can be performed on a reduced scope without loss of generality. The sample fault selected for simulation is that of very dull cutter which has been reduced to a combination of a periodic wave superimposed with a random noise to produce the required nonperiodic acoustic emission signal with varying sequence of peak amplitudes.
-2 -4
time
a::::::>
Fig. 2. Acoustic sine wave
217
STOCHASTIC GLOBAL OPTIMIZER
ocoo(2·pl·w·tI· nIU 1 2 , - - - - - - - - - --
-
-
---,12
10
For a given tool, a representative prototype data set is generated using a stochastic global optimizer. A prototype set represents machine-wear characteristics and the real-time machining data are compared to this set The data are classified based on the "distance" between the prototype set and the test data set This distance may be thought of as a multivariable objective functionj(x) that we want to be minimized subject to some constraints.
10
r 8
I---r--+---~_,~-----, -~~~O
-2 -4
time
~
This stochastic optimization problem can be stated as follows . Find the global extremum of the nonlinear functionj(x), subject to Qjx) ~ Bi , where x E R". Bj • j = 1 .. .. .M are known constants and Q/x) are in general non linear constraining functions, and both the dependent and independent variables are corrupted by random disturbances.
Fig. 3. Acoustic cosine wave
TABLE 1 SINUSOIDAL WAVE ANALYSIS Input = A -sin(21twt) + N(I) Time [msec] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Amplitude 0 2.1916 3.8143 7.2913 7.7088 8.4436 6.2843 9.4597 4.9819 4.6819
0 0 0 0 0 0 1 0 0
This opumlzation problem is solved by transforming the objective functionj(x) into a new function C(I) by the means of the nonlinear operator P{f(x)} ~ C(t) where scalars I are obtained by Lebesgue's division of the objective function j(x)
Delay 1 msec 2 msec 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
in! j{x) '" to < tl < ... < t, <
The C-transformation and the construction of function C(I) can be carried out by calculating the multi-dimensional integral (Zohdy and Adamczyk, 1991). Analytical calculation of this integral may involve considerable difficulties. We present practical solution by the means of statistical tests utilizing least squares method (Adamczyk and Zohdy, 1992).
TABLE 2 COSINUSOIDAL WAVE ANALYSIS Input = A 'COS(21tWl ) + N(I) Time [msec] 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40
Amplitude 0 2.3939 2.7510 7.5426 8.9642 9.4436 9.5843 5.4597 4.2619 4.1829
0 0 0
1 0 0 0
To solve this optimization problem we execute the following procedure.
Delay 1 mscc 2 msec 0 0 0 0 1 1 0 0 0
(1)
... < tM '" sup j{x)
1. Generate N independent identically distributed random vectors (xJ •... ,x.) and check the constraints for each of them. 2. Evaluate j(x) for the vectors that satisfy the constraints. (say, s is the number of such vectors) . 3. Assume the least value of the function j(x) from step 2, to be the infinium of j(x), the biggest value to be the supremum . 4. Let IJ be some intermediate value of all j(x)'s such that in! j(x) < I J < sup j(x). 5. Determine the number p(s) of vectors for which f[(X) / ~ I J is satisfied. 6. Determine a point J4J of the function C(t) according to the formula
0 0 0 0 0 1
0 0 0
218
REFERENCES
l!.
(2)
s
Lee, M., S.R. , C.E. Thomas, and D.G. Wildes (1987). Prospects for In-Process Diagnosis of Metal Cutting by Monitoring Vibrations Signals. Mathematical Sciences J, 22, 3821.
7. Let ti+' = ti + !l.t. Repeat steps 5 and 6 until the condition /f(x)/ ~ ti+1 is no longer satisfied. 8. Extrapolate the function G(t) from the calculated points }4 and approximate it by a polynomial function R(I)
Hayashi, S.R., C.E. Thomas, and D.G. WiIdes (1988). Tool Break: Detection by Monitoring Ultrasonic Vibrations. Annals of the CIRP,.TI. 61-64.
9. Find the coefficients llo. a,. a2 using least squares approach described in detail in [xl. That is. solve
Zohdy, M.A., and B. Adamczyk (1991). Least Squares Approach to Constrained Global Optimization. Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, 945-946.
with the following assumptions Co = o1J • a:> 1. Cv =~/J' ~ > 0, and 11 , t2 • IJ are the last three t's for which condition /f(x) / ~ ti+1 was satisfied, and
Adamczyk, B., and M.A. Zohdy (1992). An Approach to Constrained Neural Global Optimization. 1992 American Control Conference, Chicago, n, accepted for publication.
~ =
t; tl I}
ti
t2
t;
t3 1
1
Ill} Y = 112· 113
aa e=
01
(5)
Oz
10. Find the roots of R(I) = O. If llo < 0, then the largest root is equal to the global extremum of function f(x); if llo > 0, then either the least real root or the real part of the complex pair is equal to the extremum of I(x). CONCLUSION This study addressed the failure the tool-wear detection problem in the manufacturing process of cutting metals at high velocities. An acoustic emission based, on line monitoring scheme was proposed to detect tool-wear, tool-breakage and cutting conditions. Stochastic global optimization was utilized to generate the data set that best represents machine wear characteristics. A timedelayed monitoring scheme was presented for the fault monitoring. The simulated model of the acoustic emission signal can be used to predict tool failure for a specified duration of time leading to an economical and efficient manufacturing system.
Authors would like to thank Mr. Kamat P. Premanand for helping in preparation of this manuscript. 219
M. A. Zohdy and B. Adamczyk Center for Robotics and Advanced Automation Oakland University Rochester, MI 48309
Abstract This paper presents an approach to the problem of on-line machine tool-wear sensing and monitoring. Ultrasonic energy acoustic emission signals are used in the diagnostic system. The real-time situation is simulated by using a linear combination of periodic waves superimposed on a random noise. The peaking pauern of the acoustic waves is keyed in as an indicator of tool-wear and is continuously monitored to predict tool failure or fracture. A new SlOChastic global optimization is used to generate the data set that best represents archetypes of machine-wear characteristics. Keywords. Tool-wear sensing; failure detection; global optimization; system diagnostics. ACOUSTIC EMISSION ANALYSIS INTRODUCTION This study concentrates on acoustic emission signals as the principal measured variables for online tool-wear monitoring. Acoustic emission analysis has been successfully used in the fields of non-destructive material testing and the estimation of structural integrity of the materials (Lee el al., 1987; Hayashi et al., 1988). Acoustic emission refers to the elastic stress waves generated as a result of a rapid release of strain energy within a material due to rearrangement of its internal structure. The stress waves generated by the structural rearrangement can produce displacements on the surface of the material which are detected by converting them into electrical signals. High levels of acoustic emission signals are observed when the failure of the cutting tool takes place. The level of acoustic emission signal is closely related to the size of the fracture surface of the tool.
The rapidly developing flexible manufacturing systems demand continuous on-line monitoring to predict tool-wear and breakage. On-line sensing of tool-wear forms an essential part of any realistic adaptive optimization scheme and is particularly important in efficient scheduling of machine downtime for tool changing. The method suggested in this paper points to the use of acoustic emission signal dynamic patterns as principal features . Acoustic emission signals prove to be a reliable approach for long term system operation, and leads to the economical and efficient manufacturing system. Data sets that best represent machine-wear characteristics are generated using a new stochastic global optimizer. The data are classified into recognized classes based on the "distance" between the prototype data set and the test set. Prototype set is obtained by minimizing the cost function associated with the tool-wear training data set. The approximate value of the global minimum is found by using a special transformation, where a function of only one variable may be investigated instead of the multivariable function at hand.
Three common methods of tool-wear analysis are set point, signature, and pauern recognition. They are used to link the desired decision with the measured variables. The set point technique assumes that the desired value can be based on the violation of a predetermined boundary by the measured signal. The pattern recognition method analyses key process parameters and tries to match them to a dynamic sequence of events that are known to be uniquely indicative of a broken or worn machine tool.
The measured acoustic signals pass through a bank of proper delay elements that can recognize a dynamic sequence of data, rather than an individual measurement, thus allowing a dynamic wear-pattern to be detected.
This study uses combined signature analysis and 216
We made the following assumptions. (1) It is sufficient to detect a sequence of consecutive peaks in order to identify it as a signal. (2) Sign of the peak amplitude changes randomly, negative values are ignored. (3) The following combination of conditions indicates the fault: (a) detection of the peak voltage signal after a period of 't J milliseconds; (b) detection of the peak voltage after a period of't2 millisecond; (c) present detection of the peak voltage signal.
pauern recogmuon technique. Deviation of the signature of the operating tool characteristics indicates a process of change which is interpreted as a worn-tool condition.
EQUIPMENT SETUP A sketch of the experimental equipment setup is shown in Fig. 1. It includes the machine tool, dynarnometer, and AE pin transducer. The AE pin transducer output is first amplilie..1 and then fIltered through successive hi-pass and low-pass filters. Then, it is amplilied once more before it is fed to the data acquisition system (DAS). The outputs for the force dynamometer are also amplified and fed into DAS to provide context to the acoustic emission.
The time delays built into the network allow the examination of the presence of these conditions. The network converts the serial events occurring in real-time to a set of parallel events which can be examined logically. The failure detection procedure is as follows. Initially the parameters for the periodic wave vs. amplitude A and frequency f are fed into the computer. Periodic wave is superimposed on a random noise wave effectively producing a nonperiodic acoustic emission signal with randomly peaking amplitudes at each cycle. The peak signal is calculated and compared with the peak amplitude. The first peaking amplitude is detected and an indication of a possible incoming failure is given. Next, time delay is set to first to 't J and then to 't2, and the search for the same peaking amplitude is conducted. If peaking amplitudes are detected at the respective time delays, then the critical point i.e., tool-failure point is identified.
In this study, force measurements were made using three-component piezoelectric Kristler a dynamometer auached below the work piece. The outputs of the dynamometer were converted to voltage signals using a Kristler dual mode charge amplifiers.
WORKPIECE
The following signals were simulated: acoustic sine wave (Fig. 2) and acoustic cosine wave (Fig. 3). Sample outputs are presented in Table 1 for the sine wave and in Table 2 for the cosine wave. Zero entry in the last three columns corresponds to no-fault situation, whereas entry of one indicates the detection of a possible incoming failure. Notice that the first case corresponds to the normal i.e., no-failure situation, whereas in the second case a critical point is identified (three one's in the same row) indicating a tool-failure .
HP 9816 COMPUTER SYSTEM
•• In(2·pl· w·'' • n(l)
101--~--~-~------- ---------------- ,10
8
Fig. 1. Sketch of experimental equipment
-e
SIMULATION OF TIlE ACOUSTIC SIGNAL of----\
Simulation of the proposed system can be performed on a reduced scope without loss of generality. The sample fault selected for simulation is that of very dull cutter which has been reduced to a combination of a periodic wave superimposed with a random noise to produce the required nonperiodic acoustic emission signal with varying sequence of peak amplitudes.
-2 -4
time
a::::::>
Fig. 2. Acoustic sine wave
217
STOCHASTIC GLOBAL OPTIMIZER
ocoo(2·pl·w·tI· nIU 1 2 , - - - - - - - - - --
-
-
---,12
10
For a given tool, a representative prototype data set is generated using a stochastic global optimizer. A prototype set represents machine-wear characteristics and the real-time machining data are compared to this set The data are classified based on the "distance" between the prototype set and the test data set This distance may be thought of as a multivariable objective functionj(x) that we want to be minimized subject to some constraints.
10
r 8
I---r--+---~_,~-----, -~~~O
-2 -4
time
~
This stochastic optimization problem can be stated as follows . Find the global extremum of the nonlinear functionj(x), subject to Qjx) ~ Bi , where x E R". Bj • j = 1 .. .. .M are known constants and Q/x) are in general non linear constraining functions, and both the dependent and independent variables are corrupted by random disturbances.
Fig. 3. Acoustic cosine wave
TABLE 1 SINUSOIDAL WAVE ANALYSIS Input = A -sin(21twt) + N(I) Time [msec] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Amplitude 0 2.1916 3.8143 7.2913 7.7088 8.4436 6.2843 9.4597 4.9819 4.6819
0 0 0 0 0 0 1 0 0
This opumlzation problem is solved by transforming the objective functionj(x) into a new function C(I) by the means of the nonlinear operator P{f(x)} ~ C(t) where scalars I are obtained by Lebesgue's division of the objective function j(x)
Delay 1 msec 2 msec 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
in! j{x) '" to < tl < ... < t, <
The C-transformation and the construction of function C(I) can be carried out by calculating the multi-dimensional integral (Zohdy and Adamczyk, 1991). Analytical calculation of this integral may involve considerable difficulties. We present practical solution by the means of statistical tests utilizing least squares method (Adamczyk and Zohdy, 1992).
TABLE 2 COSINUSOIDAL WAVE ANALYSIS Input = A 'COS(21tWl ) + N(I) Time [msec] 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40
Amplitude 0 2.3939 2.7510 7.5426 8.9642 9.4436 9.5843 5.4597 4.2619 4.1829
0 0 0
1 0 0 0
To solve this optimization problem we execute the following procedure.
Delay 1 mscc 2 msec 0 0 0 0 1 1 0 0 0
(1)
... < tM '" sup j{x)
1. Generate N independent identically distributed random vectors (xJ •... ,x.) and check the constraints for each of them. 2. Evaluate j(x) for the vectors that satisfy the constraints. (say, s is the number of such vectors) . 3. Assume the least value of the function j(x) from step 2, to be the infinium of j(x), the biggest value to be the supremum . 4. Let IJ be some intermediate value of all j(x)'s such that in! j(x) < I J < sup j(x). 5. Determine the number p(s) of vectors for which f[(X) / ~ I J is satisfied. 6. Determine a point J4J of the function C(t) according to the formula
0 0 0 0 0 1
0 0 0
218
REFERENCES
l!.
(2)
s
Lee, M., S.R. , C.E. Thomas, and D.G. Wildes (1987). Prospects for In-Process Diagnosis of Metal Cutting by Monitoring Vibrations Signals. Mathematical Sciences J, 22, 3821.
7. Let ti+' = ti + !l.t. Repeat steps 5 and 6 until the condition /f(x)/ ~ ti+1 is no longer satisfied. 8. Extrapolate the function G(t) from the calculated points }4 and approximate it by a polynomial function R(I)
Hayashi, S.R., C.E. Thomas, and D.G. WiIdes (1988). Tool Break: Detection by Monitoring Ultrasonic Vibrations. Annals of the CIRP,.TI. 61-64.
9. Find the coefficients llo. a,. a2 using least squares approach described in detail in [xl. That is. solve
Zohdy, M.A., and B. Adamczyk (1991). Least Squares Approach to Constrained Global Optimization. Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, 945-946.
with the following assumptions Co = o1J • a:> 1. Cv =~/J' ~ > 0, and 11 , t2 • IJ are the last three t's for which condition /f(x) / ~ ti+1 was satisfied, and
Adamczyk, B., and M.A. Zohdy (1992). An Approach to Constrained Neural Global Optimization. 1992 American Control Conference, Chicago, n, accepted for publication.
~ =
t; tl I}
ti
t2
t;
t3 1
1
Ill} Y = 112· 113
aa e=
01
(5)
Oz
10. Find the roots of R(I) = O. If llo < 0, then the largest root is equal to the global extremum of function f(x); if llo > 0, then either the least real root or the real part of the complex pair is equal to the extremum of I(x). CONCLUSION This study addressed the failure the tool-wear detection problem in the manufacturing process of cutting metals at high velocities. An acoustic emission based, on line monitoring scheme was proposed to detect tool-wear, tool-breakage and cutting conditions. Stochastic global optimization was utilized to generate the data set that best represents machine wear characteristics. A timedelayed monitoring scheme was presented for the fault monitoring. The simulated model of the acoustic emission signal can be used to predict tool failure for a specified duration of time leading to an economical and efficient manufacturing system.
Authors would like to thank Mr. Kamat P. Premanand for helping in preparation of this manuscript. 219