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Neural network approach for diagnosis of grinding operation by acoustic emission and power signals
Journal of Materials Processing Technology 147 (2004) 65–71
Neural network approach for diagnosis of grinding operation by acoustic emission and power signals Jae-Seob Kwak∗ , Man-Kyung Ha School of Mechanical Engineering, Pukyong National University, Busan 608-739, South Korea Received 20 May 2002; received in revised form 11 November 2002; accepted 18 November 2003
Abstract In this study, a neural network technique has been used to achieve an intelligent diagnosis for chatter vibration and burning phenomena on grinding operation. Acoustic emission and power signals were experimentally obtained by means of a multi-sensor method with acoustic emission sensor and power meter. By signal processing methods, signal parameters that influence the grinding state were determined from the acoustic emission and the power. Static power and dynamic power were determined as power parameters, and also peak of RMS and peak of FFT were applied as acoustic emission parameters. These parameters were used as inputs of the neural network to diagnose the grinding faults. According to the substructure of the neural network, the diagnostic performance of the constructed neural network was examined. © 2003 Elsevier B.V. All rights reserved. Keywords: Neural network; Diagnosis of grinding operation; Acoustic emission signals; Power signals
1. Introduction Nowadays, one of the important things in grinding researches is the fault diagnosis. But the grinding process, as compared with other cutting processes, has unique characteristics quite different to the cutting tool and the cutting mechanism. Grinding wheel consist of many abrasives randomly spaced. The grinding process includes, therefore, many factors that may bring a malfunction to the grinding. These factors are qualitatively interlinked and interactions between these factors cannot be clear yet [1]. A burning phenomenon of a workpiece is one of grinding faults that happen many times to the ground surface. The grinding burn is a discoloration phenomenon according to the thickness of oxide layer on the ground surface. The maximum temperature on the cutting zone affected the thickness of these oxide layers [2]. These layers in the case of the ferrous material are mainly composed of Fe2 O3 , Fe3 O4 , and FeO layers from free surface. At the onset of grinding burn, a grinding force and a wheel wear rate increase sharply, and a surface roughness deteriorates. The burn phenomenon often occurs, especially with ductile materials. Metals adhering between voids within a grinding wheel block up a machining action. This state is called the wheel loading. There-
∗
Corresponding author.
0924-0136/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2003.11.016
fore, the grinding process will be an abnormal state and the grinding temperature is rapidly arisen about 1000 ◦ C [3]. Another trouble is chatter vibration, which is a relative and an irregular movement between the grinding wheel and the workpiece during the operation [4]. When the chatter vibration is generated, the grinding process is under unstable state. Chatter marks normal to the grinding direction may be easily seen on the ground surface and a deterioration of the surface roughness is evident. It is, therefore, necessary to diagnose these fault phenomena. The grinding power has been used as a way for monitoring the grinding process. Chen et al. [5] reported that the effect of grinding conditions on the grinding force and the power was related to the idealized chip thickness. It was found that the grinding force and the power could be related to the dressing operation by considering the effective density of cutting edges on the wheel surface. The semi-empirical model developed in this paper could be used to predict the variation of the grinding power at the wheel life. Inasaki [6] introduced a monitoring and controlling system for the cylindrical grinding process with an experimental verification. His system used the acoustic emission (AE) sensor. According to his assertion, most of the problems generated in the grinding process could be detected and furthermore, the grinding cycle could be automatically optimized by the AE signal. Govekar et al. [7] proposed empirical modeling for estimation of tool sharpness in a turning operation
66
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
on a lathe and determination of the roughness of a surface generated by external grinding of cylindrical workpieces using AE signal and neural network. But, he did not mention the detection of chatter vibration and burning phenomena, and also he used only AE sensor. This paper proposes the diagnostic scheme of a grinding state by the neural network using the power signal and the AE signal from the multi-sensor method. This scheme utilizes the static and dynamic components from power signals and also the root mean square (RMS) and fast Fourier transform (FFT) components from AE signals as inputs of the neural network. The relationship between the change of signal parameters and the grinding faults was also discussed. Fig. 2. Percentage of influential factors to chatter vibration [8].
2. Grinding faults The grinding operation has been used as the final step for finishing a product because of their ability of a miniature cutting and because of the satisfaction of strict requirements on the surface roughness. If the grinding fault is generated, an allowable range of the surface roughness could not be maintained. Grinding faults are affected by many influential factors that are mainly classified into the grinding condition, the grinding wheel, the dressing condition and the coolant. Fig. 1 describes a percentage of influential factors about the grinding burn. This result is obtained from replies submitted to a questionnaire. It is seen that the grinding condition more affects the burning phenomenon than others. Fig. 2 shows a percentage of influential factors about the chatter vibration. The grinding condition and the dressing condition dominantly affects the chatter vibration. This is known that if an adequate dressing was not conducted before the grinding, the chatter vibration is easily generated. Moreover, a correct selection of the grinding condition is more important to avoid fault phenomena. Fig. 3 is a good example showing how much the grinding faults deteriorate the surface roughness. According to the number of machined pieces, the values of the surface rough-
Fig. 3. Relationship between a surface roughness and the number of machined pieces.
ness are slightly increased in normal state of grinding, but rapidly increased when fault phenomena generate. It can be seen in order to produce a satisfactory product that fault phenomena, such as the burning and the chatter vibration, must be diagnosed in early stage and avoided as much as possible.
3. Preliminary experimentation and results 3.1. Experimental setup
Fig. 1. Percentage of influential factors to grinding burn [8].
An experimental setup is shown in Fig. 4. A series of grinding tests were conducted on a cylindrical grinder with a 228 mm diameter WA60LmV wheel that is mostly occupied with a general purpose in workshop. STD11 specimen was tested. Acquired signals from a power monitor and an AE sensor applied to this technique. The power monitor with 10 kHz sampling frequency was used to measure power signals during the grinding process. The power signal incoming the power monitor was induced from the main spindle motor in the grinding machine. Signals outrunning the power monitor were converted analog to digital. Digitalized signals stored in a personal computer.
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
67
Fig. 4. Experimental setup for acquiring signals from an AE sensor and a power monitor. Fig. 5. Variation behavior of power parameters: (a) static power; (b) dynamic power.
The AE sensor with a frequency response of wide bands was attached to the dead center of the grinding machine. To avoid signal attenuation during the transportation from the sensor to a computer, a pre-amplifier was connected. The raw AE signals were digitized using an A/D converter and stored using a personal computer for later analysis. An oscilloscope visualized power and AE signals. To maintain a constant in-feed rate, a stepping motor was attached in machine and a computer controlled the motor. Experimental conditions used in measuring power signals were listed in Table 1. 3.2. Experimental results and parameter selection 3.2.1. In power signals The obtained grinding power signal consists of static and dynamic power. Normally, the static power remains a conTable 1 Experimental specifications and conditions Items
Specifications and conditions
Grinding wheel Workpiece Wheel speed Workpiece speed In-feed rate Cutting fluid Dressing conditions
Type: WA60LmV, size: 228 mm × 24 mm Material: STD11, hardness: HRC 45–47 Vs = 27.1 m/s (1800 rpm) Vw = 0.20–0.40 m/s 0.5, 1.0, 2.0 mm/min Dry cut Depth of cut: 0.015 mm, lead: 0.020 mm/rev
stant magnitude with a small variation, but in many times, when a fault generates, its level happens to change. At the chatter vibration and the burn, static and dynamic powers have a magnitude significantly different than the aspects of the stable state. Therefore, grinding states can be detected with monitoring static and dynamic powers. The static power Ps is the power magnitude from the starting point to the settling point according to the vertical axis and presents an absolute level of the power generated in the grinding zone. The dynamic power Pflu is a power component of the high frequency and it fluctuates around the static power level. In the calculation of the dynamic power, it was defined as a standard deviation of the forty sampled data on the mid-point of a total grinding time. As shown in Fig. 5, these parameters increase or decrease dramatically in generation of not only the chatter vibration but also the burn of a workpiece. If these parameters are used for detecting fault phenomena of a grinding process, it will be more effective. 3.2.2. In AE signals Fig. 6(a) shows the typical AE signal obtained from the grinding operation. As other metal cutting processes, the raw signal forms are continuous types and sharply fluctuate with grinding time. The amplitude of raw signals increases according to the number of machined workpiece, but because
68
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
sensitive of the grinding state. The result of the frequency analysis of the raw signal is drawn in Fig. 6(c). The FFT amplitude is evident, especially when the frequency ranges reach about 1.8 and 15 kHz. In these frequencies, the FFT peak were so sensitivity in the grinding fault. Fig. 7(a) shows the peak values of AE RMS. It was found that the more the in-feed rates are applied, the higher the level of the RMS peak became. At the time of a fault generation, the RMS peak was increased rapidly. Fig. 7(b) presents the peak values of AE FFT. The FFT level was maintained to a particular piece, as an example, the 20th piece with 2.0 mm/min in-feed rate, and after the 20th piece, the peak level increased suddenly. It was seen that the AE parameters were increased in the fault generation.
4. Diagnosis of fault phenomena 4.1. Neural network fundamentals Artificial neural networks have been studied for many years in the hope of achieving the human-like performance in the field of the speech, the image recognition and the pattern classification. These neural networks are composed of many non-linear computational elements operating in parallel. Neural networks, because of their massive nature, can perform computations at a higher rate. Because of their adaptive nature using the learning process, neural networks can adapt to changes in the data and learn the characteristics of the input signals. The ability to learn is a fundamental trait of the neural network. Although a precise definition of learning is difficult to formulate, the learning in a neural network means the finding an appropriate set of the weights that are connection strengths from the elements to the other layer elements. In this study, the back propagation algorithm of neural networks that is one of the various learning modes is used. This algorithm in the multi-layer perceptron has made networks the most popular among researchers and users of neural networks. For the purpose of a pattern classification, the squared error cost function, which has most frequently used in the neural network and which has proven to converge into a small error is defined as [9] p
Fig. 6. AE raw and post-processed signal forms: (a) raw signal form; (b) RMS signal form; (c) FFT signal form.
of the similitude in signals it is not always distinguished either the grinding state is stable or unstable from this raw signal form. Therefore, other analytic parameters are needed to identify the grinding state. Fig. 6(b) presents the RMS signal of the raw signal shown in Fig. 6(a). The change in AE signal is easily verified by an AE RMS level and a distinctive type. It was seen that the peak value of the RMS signal was
1 (i) E= y − d (i) 2 2
(1)
j=1
where the subscript i is the ith input pattern. The y and the d are a calculated output and a desired output of this pattern. The back propagation algorithm is a gradient descent method to minimize the squared error cost function. The procedure of the learning in back propagation algorithm can be summarized as follows: • Step 1: Initialize the weights to small random values. • Step 2: Randomly choose an input pattern.
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
69
Fig. 7. Variation behavior of AE parameters: (a) RMS peak; (b) FFT peak.
• Step 3: Propagate the signal forward through the network. L • Step 4: Compute δL i in the output layer oi = yi L U L δL i = g (hi )[di − yi ]
(2)
where hL i represents the net input to the ith unit in the Lth layer, and g is the derivative of the activation function g. • Step 5: Compute the deltas for the preceding layers by propagating the errors backwards; j+1 L δL (3) wij δl+1 i = g (hi ) j j
for l = (L − 1), . . . , 1. • Step 6: Update weights using j
j−1
wji = ηδli yj
(4)
where η is a coefficient of the learning rate parameter. • Step 7: Go to step 2 and repeat for the next pattern until the error in the output layer is below a pre-specified threshold of a maximum number of iterations is reached.
4.2. Diagnostic results The performance of neural networks is widely different from others in accordance with the selection of the learning rate coefficient and the number of hidden layers. Therefore, it is necessary to select the adequate learning rate and the number of hidden layers. Through preliminary study, the coefficient of the learning rate coefficient was determined as 0.6. The number of hidden layers was composed of two layers. As shown in Fig. 8, the architecture of the neural network was used. Input units used were the Ps , Pflu , RMS peak and FFT peak. An output unit was occupied and it presented the grinding state. The output unit had interval values from 0 to 2. According to the value of the output unit, the neural network understood either the grinding state was a normal state or one of fault states. Table 2 lists learning patterns for the grinding state diagnosis. If the listed input patterns appear during the learning process, the neural network understands the grinding state from output values as normal (value 0), burning (value 1),
70
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
Fig. 8. Structure of the diagnostic neural network.
and chatter vibration (value 2). For the effective learning, the number of learning patterns was selected as 12 patterns. If more learning patterns were used, the learn error could not converge. The learning process was carried out successfully. Table 3 presents diagnostic results of new patterns that are not learned at the previous step. Because of pattern inTable 2 Learning patterns for grinding state diagnosis Input units
Output unit, o
Ps (W)
Pflu (W)
RMS (mV)
FFT (mV)
273 295 365 373 387 398 403 409 417 423 436 448
28 34 64 79 43 48 57 83 88 106 95 116
12 14 14 19 21 23 32 24 27 28 29 37
11 24 27 13 16 32 17 19 42 47 48 50
0 0 0 0 1 1 1 1 2 2 2 2
Table 3 Diagnostic results of new patterns Input units
Output unit
Ps (W)
Pflu (W)
RMS (mV)
FFT (mV)
o
Diagnosis
271 296 429 324 362 243 289 420 395 431 457
66 83 34 76 107 116 121 72 94 54 65
23 32 22 26 29 35 19 34 37 32 25
11 14 18 13 26 17 13 35 39 43 52
0.02 0.02 0.14 0.98 1.04 1.21 1.64 1.97 1.93 1.98 1.96
Normal (correct) Normal (correct) Normal (correct) Burning (correct) Burning (correct) Burning (correct) Chatter (incorrect) Chatter (correct) Chatter (correct) Chatter (correct) Chatter (correct)
Fig. 9. Successful diagnostic percentage in accordance with the variation of layer structures.
definiteness between the grinding burn and the chatter vibration, some erroneous diagnosis was made. Nevertheless, this diagnostic method using the power and the AE signals was available for grinding process. Fig. 9 presents the successful diagnostic percentage in accordance with the variation of layer structures. A few erroneously diagnostic results were made in the boundary between the grinding burn and the chatter vibration. As shown in Fig. 9, it is seen that the maximum successful diagnosis is about 95%. In view of the diagnostic results, this technique using the power signal and AE signal is able to diagnose the fault phenomena in grinding process.
5. Conclusions The technique of the fault diagnosis, such as the chatter vibration and the grinding burn, has been developed using the multi-sensor method with the AE sensor and the power meter for the grinding process. When fault phenomena occur, the values of the all AE parameters increase rapidly. The more the in-feed rates are applied, the higher the levels of AE parameters become. The FFT amplitude is especially evident when the frequency ranges reach about 1.8 and 15 kHz. In these frequencies, the FFT peak were so sensitivity in the grinding fault. Power parameters such as the static power and the dynamic power were sensitivity of fault phenomena. These parameters dramatically increased or decreased in generation of not only the chatter vibration but also the burn of a workpiece. In the learned neural network with power and AE parameters, the maximum successful diagnosis was about 95% when the learning rate coefficient was 0.6 and the number of hidden layers was 2.
References [1] Y.M. Ali, L. Zhang, A methodology for fuzzy modeling of engineering systems, Fuzzy Sets Syst. 118 (2) (2001) 181–197.
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71 [2] S. Kawamura, M. Mitsuhashi, Studies on the fundamental of grinding burn (3rd report)—oxidation rate law of workpiece, J. JSPE 47 (9) (1981) 106–111. [3] S. Malkin, Grinding Technology—Theory and Applications of Machining with Abrasives, Wiley, New York, 1989, p. 147. [4] Y.S. Liao, L.C. Shiang, Computer simulation of self-excited and forced vibrations in the external cylindrical plunge grinding process, Trans. ASME 113 (8) (1991) 297–304. [5] X. Chen, W. Rowe, D. Allanson, B. Mills, A grinding power model for selection of dressing and grinding conditions, Trans. ASME 121 (1999) 632–637.
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[6] I. Inasaki, Sensor fusion for monitoring and controlling grinding processes, Int. J. Adv. Manuf. Technol. 15 (10) (1999) 730– 736. [7] I. Govekar, E. Grabek, E. Susic, B. Antolovic, Monitoring manufacturing processes by utilizing empirical modeling, Ultrasonics 36 (1–5) (1998) 263–271. [8] G. Kim, Development of expert system for grinding operations, Ph.D. Dissertation, Keio University, 1995, p. 128. [9] J.A. Freeman, D.M. Skapura, Neural Networks—Algorithms, Applications, and Programming Techniques, Addison-Wesley, New York, 1991, p. 97.
Neural network approach for diagnosis of grinding operation by acoustic emission and power signals Jae-Seob Kwak∗ , Man-Kyung Ha School of Mechanical Engineering, Pukyong National University, Busan 608-739, South Korea Received 20 May 2002; received in revised form 11 November 2002; accepted 18 November 2003
Abstract In this study, a neural network technique has been used to achieve an intelligent diagnosis for chatter vibration and burning phenomena on grinding operation. Acoustic emission and power signals were experimentally obtained by means of a multi-sensor method with acoustic emission sensor and power meter. By signal processing methods, signal parameters that influence the grinding state were determined from the acoustic emission and the power. Static power and dynamic power were determined as power parameters, and also peak of RMS and peak of FFT were applied as acoustic emission parameters. These parameters were used as inputs of the neural network to diagnose the grinding faults. According to the substructure of the neural network, the diagnostic performance of the constructed neural network was examined. © 2003 Elsevier B.V. All rights reserved. Keywords: Neural network; Diagnosis of grinding operation; Acoustic emission signals; Power signals
1. Introduction Nowadays, one of the important things in grinding researches is the fault diagnosis. But the grinding process, as compared with other cutting processes, has unique characteristics quite different to the cutting tool and the cutting mechanism. Grinding wheel consist of many abrasives randomly spaced. The grinding process includes, therefore, many factors that may bring a malfunction to the grinding. These factors are qualitatively interlinked and interactions between these factors cannot be clear yet [1]. A burning phenomenon of a workpiece is one of grinding faults that happen many times to the ground surface. The grinding burn is a discoloration phenomenon according to the thickness of oxide layer on the ground surface. The maximum temperature on the cutting zone affected the thickness of these oxide layers [2]. These layers in the case of the ferrous material are mainly composed of Fe2 O3 , Fe3 O4 , and FeO layers from free surface. At the onset of grinding burn, a grinding force and a wheel wear rate increase sharply, and a surface roughness deteriorates. The burn phenomenon often occurs, especially with ductile materials. Metals adhering between voids within a grinding wheel block up a machining action. This state is called the wheel loading. There-
∗
Corresponding author.
0924-0136/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2003.11.016
fore, the grinding process will be an abnormal state and the grinding temperature is rapidly arisen about 1000 ◦ C [3]. Another trouble is chatter vibration, which is a relative and an irregular movement between the grinding wheel and the workpiece during the operation [4]. When the chatter vibration is generated, the grinding process is under unstable state. Chatter marks normal to the grinding direction may be easily seen on the ground surface and a deterioration of the surface roughness is evident. It is, therefore, necessary to diagnose these fault phenomena. The grinding power has been used as a way for monitoring the grinding process. Chen et al. [5] reported that the effect of grinding conditions on the grinding force and the power was related to the idealized chip thickness. It was found that the grinding force and the power could be related to the dressing operation by considering the effective density of cutting edges on the wheel surface. The semi-empirical model developed in this paper could be used to predict the variation of the grinding power at the wheel life. Inasaki [6] introduced a monitoring and controlling system for the cylindrical grinding process with an experimental verification. His system used the acoustic emission (AE) sensor. According to his assertion, most of the problems generated in the grinding process could be detected and furthermore, the grinding cycle could be automatically optimized by the AE signal. Govekar et al. [7] proposed empirical modeling for estimation of tool sharpness in a turning operation
66
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
on a lathe and determination of the roughness of a surface generated by external grinding of cylindrical workpieces using AE signal and neural network. But, he did not mention the detection of chatter vibration and burning phenomena, and also he used only AE sensor. This paper proposes the diagnostic scheme of a grinding state by the neural network using the power signal and the AE signal from the multi-sensor method. This scheme utilizes the static and dynamic components from power signals and also the root mean square (RMS) and fast Fourier transform (FFT) components from AE signals as inputs of the neural network. The relationship between the change of signal parameters and the grinding faults was also discussed. Fig. 2. Percentage of influential factors to chatter vibration [8].
2. Grinding faults The grinding operation has been used as the final step for finishing a product because of their ability of a miniature cutting and because of the satisfaction of strict requirements on the surface roughness. If the grinding fault is generated, an allowable range of the surface roughness could not be maintained. Grinding faults are affected by many influential factors that are mainly classified into the grinding condition, the grinding wheel, the dressing condition and the coolant. Fig. 1 describes a percentage of influential factors about the grinding burn. This result is obtained from replies submitted to a questionnaire. It is seen that the grinding condition more affects the burning phenomenon than others. Fig. 2 shows a percentage of influential factors about the chatter vibration. The grinding condition and the dressing condition dominantly affects the chatter vibration. This is known that if an adequate dressing was not conducted before the grinding, the chatter vibration is easily generated. Moreover, a correct selection of the grinding condition is more important to avoid fault phenomena. Fig. 3 is a good example showing how much the grinding faults deteriorate the surface roughness. According to the number of machined pieces, the values of the surface rough-
Fig. 3. Relationship between a surface roughness and the number of machined pieces.
ness are slightly increased in normal state of grinding, but rapidly increased when fault phenomena generate. It can be seen in order to produce a satisfactory product that fault phenomena, such as the burning and the chatter vibration, must be diagnosed in early stage and avoided as much as possible.
3. Preliminary experimentation and results 3.1. Experimental setup
Fig. 1. Percentage of influential factors to grinding burn [8].
An experimental setup is shown in Fig. 4. A series of grinding tests were conducted on a cylindrical grinder with a 228 mm diameter WA60LmV wheel that is mostly occupied with a general purpose in workshop. STD11 specimen was tested. Acquired signals from a power monitor and an AE sensor applied to this technique. The power monitor with 10 kHz sampling frequency was used to measure power signals during the grinding process. The power signal incoming the power monitor was induced from the main spindle motor in the grinding machine. Signals outrunning the power monitor were converted analog to digital. Digitalized signals stored in a personal computer.
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
67
Fig. 4. Experimental setup for acquiring signals from an AE sensor and a power monitor. Fig. 5. Variation behavior of power parameters: (a) static power; (b) dynamic power.
The AE sensor with a frequency response of wide bands was attached to the dead center of the grinding machine. To avoid signal attenuation during the transportation from the sensor to a computer, a pre-amplifier was connected. The raw AE signals were digitized using an A/D converter and stored using a personal computer for later analysis. An oscilloscope visualized power and AE signals. To maintain a constant in-feed rate, a stepping motor was attached in machine and a computer controlled the motor. Experimental conditions used in measuring power signals were listed in Table 1. 3.2. Experimental results and parameter selection 3.2.1. In power signals The obtained grinding power signal consists of static and dynamic power. Normally, the static power remains a conTable 1 Experimental specifications and conditions Items
Specifications and conditions
Grinding wheel Workpiece Wheel speed Workpiece speed In-feed rate Cutting fluid Dressing conditions
Type: WA60LmV, size: 228 mm × 24 mm Material: STD11, hardness: HRC 45–47 Vs = 27.1 m/s (1800 rpm) Vw = 0.20–0.40 m/s 0.5, 1.0, 2.0 mm/min Dry cut Depth of cut: 0.015 mm, lead: 0.020 mm/rev
stant magnitude with a small variation, but in many times, when a fault generates, its level happens to change. At the chatter vibration and the burn, static and dynamic powers have a magnitude significantly different than the aspects of the stable state. Therefore, grinding states can be detected with monitoring static and dynamic powers. The static power Ps is the power magnitude from the starting point to the settling point according to the vertical axis and presents an absolute level of the power generated in the grinding zone. The dynamic power Pflu is a power component of the high frequency and it fluctuates around the static power level. In the calculation of the dynamic power, it was defined as a standard deviation of the forty sampled data on the mid-point of a total grinding time. As shown in Fig. 5, these parameters increase or decrease dramatically in generation of not only the chatter vibration but also the burn of a workpiece. If these parameters are used for detecting fault phenomena of a grinding process, it will be more effective. 3.2.2. In AE signals Fig. 6(a) shows the typical AE signal obtained from the grinding operation. As other metal cutting processes, the raw signal forms are continuous types and sharply fluctuate with grinding time. The amplitude of raw signals increases according to the number of machined workpiece, but because
68
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
sensitive of the grinding state. The result of the frequency analysis of the raw signal is drawn in Fig. 6(c). The FFT amplitude is evident, especially when the frequency ranges reach about 1.8 and 15 kHz. In these frequencies, the FFT peak were so sensitivity in the grinding fault. Fig. 7(a) shows the peak values of AE RMS. It was found that the more the in-feed rates are applied, the higher the level of the RMS peak became. At the time of a fault generation, the RMS peak was increased rapidly. Fig. 7(b) presents the peak values of AE FFT. The FFT level was maintained to a particular piece, as an example, the 20th piece with 2.0 mm/min in-feed rate, and after the 20th piece, the peak level increased suddenly. It was seen that the AE parameters were increased in the fault generation.
4. Diagnosis of fault phenomena 4.1. Neural network fundamentals Artificial neural networks have been studied for many years in the hope of achieving the human-like performance in the field of the speech, the image recognition and the pattern classification. These neural networks are composed of many non-linear computational elements operating in parallel. Neural networks, because of their massive nature, can perform computations at a higher rate. Because of their adaptive nature using the learning process, neural networks can adapt to changes in the data and learn the characteristics of the input signals. The ability to learn is a fundamental trait of the neural network. Although a precise definition of learning is difficult to formulate, the learning in a neural network means the finding an appropriate set of the weights that are connection strengths from the elements to the other layer elements. In this study, the back propagation algorithm of neural networks that is one of the various learning modes is used. This algorithm in the multi-layer perceptron has made networks the most popular among researchers and users of neural networks. For the purpose of a pattern classification, the squared error cost function, which has most frequently used in the neural network and which has proven to converge into a small error is defined as [9] p
Fig. 6. AE raw and post-processed signal forms: (a) raw signal form; (b) RMS signal form; (c) FFT signal form.
of the similitude in signals it is not always distinguished either the grinding state is stable or unstable from this raw signal form. Therefore, other analytic parameters are needed to identify the grinding state. Fig. 6(b) presents the RMS signal of the raw signal shown in Fig. 6(a). The change in AE signal is easily verified by an AE RMS level and a distinctive type. It was seen that the peak value of the RMS signal was
1 (i) E= y − d (i) 2 2
(1)
j=1
where the subscript i is the ith input pattern. The y and the d are a calculated output and a desired output of this pattern. The back propagation algorithm is a gradient descent method to minimize the squared error cost function. The procedure of the learning in back propagation algorithm can be summarized as follows: • Step 1: Initialize the weights to small random values. • Step 2: Randomly choose an input pattern.
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
69
Fig. 7. Variation behavior of AE parameters: (a) RMS peak; (b) FFT peak.
• Step 3: Propagate the signal forward through the network. L • Step 4: Compute δL i in the output layer oi = yi L U L δL i = g (hi )[di − yi ]
(2)
where hL i represents the net input to the ith unit in the Lth layer, and g is the derivative of the activation function g. • Step 5: Compute the deltas for the preceding layers by propagating the errors backwards; j+1 L δL (3) wij δl+1 i = g (hi ) j j
for l = (L − 1), . . . , 1. • Step 6: Update weights using j
j−1
wji = ηδli yj
(4)
where η is a coefficient of the learning rate parameter. • Step 7: Go to step 2 and repeat for the next pattern until the error in the output layer is below a pre-specified threshold of a maximum number of iterations is reached.
4.2. Diagnostic results The performance of neural networks is widely different from others in accordance with the selection of the learning rate coefficient and the number of hidden layers. Therefore, it is necessary to select the adequate learning rate and the number of hidden layers. Through preliminary study, the coefficient of the learning rate coefficient was determined as 0.6. The number of hidden layers was composed of two layers. As shown in Fig. 8, the architecture of the neural network was used. Input units used were the Ps , Pflu , RMS peak and FFT peak. An output unit was occupied and it presented the grinding state. The output unit had interval values from 0 to 2. According to the value of the output unit, the neural network understood either the grinding state was a normal state or one of fault states. Table 2 lists learning patterns for the grinding state diagnosis. If the listed input patterns appear during the learning process, the neural network understands the grinding state from output values as normal (value 0), burning (value 1),
70
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71
Fig. 8. Structure of the diagnostic neural network.
and chatter vibration (value 2). For the effective learning, the number of learning patterns was selected as 12 patterns. If more learning patterns were used, the learn error could not converge. The learning process was carried out successfully. Table 3 presents diagnostic results of new patterns that are not learned at the previous step. Because of pattern inTable 2 Learning patterns for grinding state diagnosis Input units
Output unit, o
Ps (W)
Pflu (W)
RMS (mV)
FFT (mV)
273 295 365 373 387 398 403 409 417 423 436 448
28 34 64 79 43 48 57 83 88 106 95 116
12 14 14 19 21 23 32 24 27 28 29 37
11 24 27 13 16 32 17 19 42 47 48 50
0 0 0 0 1 1 1 1 2 2 2 2
Table 3 Diagnostic results of new patterns Input units
Output unit
Ps (W)
Pflu (W)
RMS (mV)
FFT (mV)
o
Diagnosis
271 296 429 324 362 243 289 420 395 431 457
66 83 34 76 107 116 121 72 94 54 65
23 32 22 26 29 35 19 34 37 32 25
11 14 18 13 26 17 13 35 39 43 52
0.02 0.02 0.14 0.98 1.04 1.21 1.64 1.97 1.93 1.98 1.96
Normal (correct) Normal (correct) Normal (correct) Burning (correct) Burning (correct) Burning (correct) Chatter (incorrect) Chatter (correct) Chatter (correct) Chatter (correct) Chatter (correct)
Fig. 9. Successful diagnostic percentage in accordance with the variation of layer structures.
definiteness between the grinding burn and the chatter vibration, some erroneous diagnosis was made. Nevertheless, this diagnostic method using the power and the AE signals was available for grinding process. Fig. 9 presents the successful diagnostic percentage in accordance with the variation of layer structures. A few erroneously diagnostic results were made in the boundary between the grinding burn and the chatter vibration. As shown in Fig. 9, it is seen that the maximum successful diagnosis is about 95%. In view of the diagnostic results, this technique using the power signal and AE signal is able to diagnose the fault phenomena in grinding process.
5. Conclusions The technique of the fault diagnosis, such as the chatter vibration and the grinding burn, has been developed using the multi-sensor method with the AE sensor and the power meter for the grinding process. When fault phenomena occur, the values of the all AE parameters increase rapidly. The more the in-feed rates are applied, the higher the levels of AE parameters become. The FFT amplitude is especially evident when the frequency ranges reach about 1.8 and 15 kHz. In these frequencies, the FFT peak were so sensitivity in the grinding fault. Power parameters such as the static power and the dynamic power were sensitivity of fault phenomena. These parameters dramatically increased or decreased in generation of not only the chatter vibration but also the burn of a workpiece. In the learned neural network with power and AE parameters, the maximum successful diagnosis was about 95% when the learning rate coefficient was 0.6 and the number of hidden layers was 2.
References [1] Y.M. Ali, L. Zhang, A methodology for fuzzy modeling of engineering systems, Fuzzy Sets Syst. 118 (2) (2001) 181–197.
J.-S. Kwak, M.-K. Ha / Journal of Materials Processing Technology 147 (2004) 65–71 [2] S. Kawamura, M. Mitsuhashi, Studies on the fundamental of grinding burn (3rd report)—oxidation rate law of workpiece, J. JSPE 47 (9) (1981) 106–111. [3] S. Malkin, Grinding Technology—Theory and Applications of Machining with Abrasives, Wiley, New York, 1989, p. 147. [4] Y.S. Liao, L.C. Shiang, Computer simulation of self-excited and forced vibrations in the external cylindrical plunge grinding process, Trans. ASME 113 (8) (1991) 297–304. [5] X. Chen, W. Rowe, D. Allanson, B. Mills, A grinding power model for selection of dressing and grinding conditions, Trans. ASME 121 (1999) 632–637.
71
[6] I. Inasaki, Sensor fusion for monitoring and controlling grinding processes, Int. J. Adv. Manuf. Technol. 15 (10) (1999) 730– 736. [7] I. Govekar, E. Grabek, E. Susic, B. Antolovic, Monitoring manufacturing processes by utilizing empirical modeling, Ultrasonics 36 (1–5) (1998) 263–271. [8] G. Kim, Development of expert system for grinding operations, Ph.D. Dissertation, Keio University, 1995, p. 128. [9] J.A. Freeman, D.M. Skapura, Neural Networks—Algorithms, Applications, and Programming Techniques, Addison-Wesley, New York, 1991, p. 97.