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Monitoring grinding parameters by vibration signal measurement - a primary application
Minerals Engineering, Vol. 7, No. 4, pp. 495-501, 7994 Copyright ~ 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0892---6875194 $6.00 +0.00
~ ) Pergamon 0892-6875(93)E0035-V
TECHNICAL NOTE MONITORING GRINDING PARAMETERS BY VIBRATION MEASUREMENT - A PRIMARY APPLICATION
SIGNAL
YIGEN ZENG and E. FORSSBERG Dept. of Chemical and Metallurgical Engineering, Lulet University of Technology, S-977 53, Lule~, Sweden (Received 24 March 1993; accepted 28 September 1993)
ABSTRACT Grinding plays an important role on energy consumption and subsequent separation stage in a mineral processing plant. To maintain higher grinding efficiency, the operating parameters must be continuously monitored and adjusted close to the setup of the optimal operating conditions. It is difficult amt expensive to trace the frequent variations of the grinding parameters by traditional methods in commercial scale operation. Since mechanical grinding emits strong vibration signals, it can be picked up by commercially available instrument in the form of time-domain waveform. The variations of the vibration signals were governed by the changes of the grinding state. A primary application was studied based on industrial scale measurements, where the mechanical vibration was picked up by an accelerometer and acoustic pressure changes by a microphone. The digitised time-domain source signals were processed by digital signal processing technique. The variable grinding parameters were the power draw, the feed rate, the pulp density, amt the particle sizes of the mill feed and ground product. By principal component analysis and parameter identification, the variations of the grinding parameters were related to the changes of the source vibration signals. By vibration measurement, a new alternative could be developed for monitoring the operating parameters in grinding. Keywords Ball grinding, Vibration analysis, Power spectrum estimation, Principal component, Multiple regression
INTRODUCTION Mechanical grinding emits strong vibration signals presented in the form of acoustic pressure variations and mechanical vibrations. An experienced grinding mill operator can assess the operating state by listening to the mill. The "decision making" follows the steps that the acoustic signal is first received by the ear of the human being and memorised in the brain (signal acquisition and storage), then deep thinking (signal processing and identification), and finally a decision is made based on the cumulative experiences. Similarly, all the source vibration signals from ball grinding could be picked up in the form of time-domain waveform by commercially available instrument. To evaluate a representative length of the signals, the time-domain waveforms of a certain length of grinding period must be considered and transformed into frequency-domain spectra. Since the variations of the vibration signals reflect the changes of grinding state so that a certain power spectral pattern of different peak energies will only correspond to one kind of grinding state [1]. After learning the particulars of the power spectra (hunting for "finger 495
496
Technical Note
prints') for some time, the variations of the measured power spectra to its "finger prints" spectrum could be related to the changes of the operating states of the ball mill. The advantages of using a computerised instrument over human beings are obvious: the instrument can be set to work 24 hours a day on-line and be tolerant to hazardous or tough working environments. Monitoring the operating parameters could provide an on-line information for the controlling and adjusting units.
EXPERIMENTAL Figure 1 shows the layout of grinding system and the instrumentation for signal acquisition and processing. The grinding system consisted of mainly a primary overflow ball mill, 4.2 m in diameter and 5.4 m in length, operated at LKAB, Malmberget, Sweden in an open circuit. The solid density of the free crushed iron ore (magnetite) was about 4.8 t/m3 and the particle size was < 10 ram. Under normal operation, the feed rate was about 255 t/h and the pulp density was 65 % solids by weight. The mill speed was 12.8 rpm (corresponding to 60% of the critical speed) and the charge volume was about 35%. The grinding charge originally consisted of 100 tons of steel balls. The balls of 60 and 40 mm in diameters, each accounting for 50 % by weight, were continuously added to the mill to maintain the power draw level at about 1130 kW. Under the whole testing period, the feed rate was set to be 60% of the normal operation by requirement. The additional water was directly injected into the ball mill to adjust the pulp density. The power draw and the feed rate were continuously recorded by built-in control units of the mill. Other grinding parameters were evaluated based on manual sampling after changing the operating parameters for about 30 minutes (the equilibrium operating state).
A-A
F
P ion
Control
Fig. 1 Layout of grinding system and instrumentation for signal acquisition and processing The instrumentation sector consisted of two types of signal sensors and their corresponding pre-amplifiers, a DAT recorder and an IBM compatible personal computer (Figure 1). The vibration sensor - an accelerometer - was vertically screwed on the top surface of the supporting bearing for the pinion axis. The amplified mechanical vibration signal was stored in L-channel of the DAT recorder. To pick up the acoustic pressure variations, an acoustic microphone was placed outside the impact zone, 200 mm away from the mill shell (the cross section of the mill centre was illustrated in Figure 1). The acoustic vibration signal was amplified and transmitted to R-channel on the DAT recorder. To avoid alias by non-interested high frequencies, the sampling frequency of the AID converter was set at least 2.5 times the highest frequency of interest [2]. According to the primary studies that the important information for describing the grinding state lies in the frequency band of 0-2500 Hz, therefore a 4-cascade lowpass filter group (each with a cutoff in -24 dB/oetave) at a cutoff frequency of 3 kHz was installed before data acquisition unit. The digitised time-domain waveform signals were loaded into an IBM compatible personal computer for signal processing and identification.
Technical Note
497
The time-domain waveforms, were transformed into the frequency-domain power spectra by Welch's method [3]. The whole waveform was divided into sections of 4096 points in length. Each section was multiplied with the Harming window before power spectral estimation. To compensate the voids among the waveforms caused by the digital window, each new section included 60% of previous section of the waveforrn data (the overlapping process [4]). The power spectrum for each signal sample were therefore an average of 24 waveform sections (about 10 seconds in real grinding period). The number of frequency elements on the spectrum was much larger than the number of practical measurements under the current resolution. Since the peak energies on the spectrum were linearly correlated, principal component analysis (PCA) was therefore a suitable method to reduce a large number of original variables into a few new "latent" variables [5,6]. The relationship between the grinding parameters and the latent variables could be established by stepwise multiple regression. The data management, signal processing and parameter identification were fulfilled with an analytical computer software (DSP4ME toolbox) developed by the author.
RESULTS AND DISCUSSION To implement the modem digital signal processing technique on vibration analysis, the source continuous time-domain waveform signals were digitised into discrete time-domain waveforms. To ensure that the source signals were representative for one setup grinding condition, five signal samples were taken during a valid testing period. Figure 2 shows a short waveform sections in 0.2 second from an example measurement. The waveform picked up by the acoustic microphone is more complicated than by the aeeelerometer. 0,4
0
!
I
-0.| Aco~tic pressurechanges " 0.41,0 I -0.4
1.1
1.15
1.2
1.25
1.3
Progress time (See) Fig.2 Example section waveforms of mechanical and acoustic vibration signals The primary analysis shows that the most informative frequency band to characterise the variations of the spectra was 0-600 Hz. Figure 3 shows the average power spectra for full length mechanical and acoustic vibration signals with the identical measurement as used in Figure 2. The basic frequencies of the bearings, 57, 114 and 171 Hz, were found on both type of spectra. The spectrum of the mechanical vibration signal was simpler than the acoustic signal. The dominant peaks were clearly distinguishable on the vibration spectrum because the accelerometer was directly situated on the bearings. The major differences between those two spectra lie in the frequency band of 200-400 Hz. On the mechanical vibration spectrum, it contains mainly three peaks at 228, 286 and 341 Hz, however many small peaks covering all the frequency band were presented on the acoustic vibration spectrum.
498
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Frequency (Hz) Fig.3 Example power spectra of mechanical and acoustic vibration signals A waterfall diagram is commonly used to illustrate a number of similar spectra for comparison [1]. Figures 4 and 5 show the spectra of the mechanical and acoustic vibration signals respectively. To make the whole spectrum visible in waterfall plot, the decibel scale (Y-axis) was used to measure the peak energies. Each waterfall plot consisted of six curves representing six individual testing conditions. Each curve on the spectral plot denotes an average spectra of five signal samples under identical pre-set operating condition. Since the power spectra mainly reflect the "finger prints" of a specified ball mill, therefore, the power spectra of identical signal type on different grinding conditions are similar at the current resolution. The fingerprints spectrum is sensitive to the factors either impossible to control or lack of comparison base in practise, e.g. the machine assembly, therefore the most important information for the further analysis are the variations on the spectra instead Of the finger prints spectrum itself. The comparison base was set to the average of 30 peak energies at the corresponding frequency bands.
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Fig.4 Waterfall plot of mechanical vibration spectra under six operating conditions
T~icalNote
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Fig.5 Waterfall plot of acoustic vibration spectra under six operating conditions The principal component analysis is a useful technique for reducing the number of original correlated variables in a data set by finding linear combinations of these variables that explain most of the variability [6]. About 245 frequency elements were found at the current frequency resolution over 0-600 Hz. Before making principal component analysis, the original power spectral data must be subtracted by the mean of all observations for the originals variable - obtaining the variations of the spectra. By performing the principal component analysis on the mechanical vibration signal, it was found that the first, second, third and fourth principal components account for 81.8, 10.1, 4.9 and 1.2% of the total variations of peak energies respectively. The first two principal components for the vibration signal account for 91.9% of the total variations. The most important frequencies for the first and second principal components are 114 and 286 Hz respectively. Similarly for the acoustic vibration signal, the first six principal components account for 27.8, 11.6, 8.4, 5.8, 4.4 and 4.0% of the total variations of the peak energies of the frequencies respectively. Much random noise were involved in the acoustic signal at the current sensor location. The correlation coefficients of the principal components indicates that the first three principal components are most effective for the original acoustic vibration signal. The first principal component is mainly affected by the frequencies at 72 and 57 Hz, and the second one by the frequency at 72 Hz. By principal component analysis, the original variables for characterising the spectra were reduced to 3-4 latent variables for the mechanical vibration signal and 5-6 latent variables for the acoustic vibration signal. When the loading of the principal components and the observed spectra were known, the scores for the corresponding principal components could be derived. The scores for the mechanical and acoustic vibration signals were described by Svi and Smi respectively, where i denotes the score on the i-th principal component of the spectra. By multiple regression analysis on 30 signal measurements, the grinding parameters were related to scores of the significant principal components, yields: P = 1102.1 + 8.33Svl -6.94Sv2 + 21.98Sv3 + 27.34Sv4 + 41.23Sm5
(1)
Q = 158.2- 2.12Svl - 19.65Sml - 14.69Sm2
(2)
C = 67.15 + 5.58Sv3 + 19.65S,rd - 15.38Sm4 + 24.93Sm5
(3)
500
Technical Note
Kf = 79.63 - 3.02Svl - 9.52Sml - 39.45Sm3 - 31.84Sm5
(4)
Kp = 48.03 + 1.15Svl + 2.42Sv2- 2.52Sv3 + 2.65Sml
(5)
where P denotes the power draw (kW), Q the feed rate (t/h), C the pulp density (% solids by weight), and Kfand Kp the particle sizes of the mill feed (%-1.7 nun) and product (%-0.105 ram) reapectively. Equations (1-5) account for 78.6, 70.1, 56.2, 82.5 and 82.7 % of the corresponding measurements. The valid prediction ranges of the grinding parameters are: the power draw (1080-1130 kW), the feed rate (145-165 t/h), the pulp density (59-72% of solid), the mill feed size (70-89% -1.7 ram) and the mill product size (45-50% -0.105 ram). The power draw and the product size were mainly related to the principal components of the mechanical vibration signal spectra and the other three parameters to the acoustic vibration signals. Figure 6 shows the relative errors of the grinding parameters predicted by these equations. It is found that most of the relative prediction errors were within -t-5%. The errors for predicting the mill feed rate and the pulp density are larger than the others, because of the lack of information on the natural variation of the mill feeding material. The first principal component plays the major role on the prediction. Particularly, the mechanical vibration signal has more effects on the power draw and the product size, and the acoustic signal on the others. Both the mechanical and acoustic vibration signals have described some of the particulars in the changes of the grinding state. Therefore a combination of both forms of signals can make the prediction closer to the observed grinding parameters.
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Time series Fig.6 Relative prediction errors of grinding parameters by vibration measurements
CONCLUSIONS The vibration signal m~urements were performed on an industrial scale ball mill at LKAB, Malmberget, Sweden. The mechanical vibration signal of the grinding system was picked up by an aceelerometer and the acoustic vibration signal outside the impacting zone was sensed with a microphone. After signal processing and parameter identification, the relationships bntwoe.n the grinding parameters and the signal characteristics have been established by multiple regression. Most of the relative prediction errors were within 5:5%.
Technical Note
501
The power draw and the product size from the ball mill were mainly related to the mechanical vibration signal, and the others to the acoustic vibration signal. Both the vibration signals were important in monitoring the grinding state, so that a combination of these two types of signals may give a better predictions for the grinding parameters. By measuring and processing the mechanical and acoustic vibration signals, the grinding parameters could be monitored for the industrial scale ball mill. Vibration signal measurement provides a new alternative for developing an automatic monitoring system in grinding.
ACKNOWLEDGEMENT This work was partially sponsored by the Norrbotten's Research Board and LKAB, Sweden. The authors thank Kent Tano and Jan-Ch/ister GY~rde for their assistance during the industrial scale measurements.
REFERENCES .
2. 3. 4.
5. 6.
Zeng, Y. & Forssberg, E., Effects of operating parameters on vibration signal under laboratory scale ball grinding conditions, Intern. J. of Mineral Processing, 35, 273-290 (1992). Thomas, D.E.W., Vehicle sounds and recognition. Pattern Recognition: Idea in Practice. (ed. by Batchelor), Plenum Press. 333-339 (1978). Welch, P.D., The use of fast Fourier transform for the estimation of power spectra. IEEE Trans. Audio Electro-acoustics. 6, AU-15:70-73. (1967). DeFatta, D.J., Lucas, LG. & Hodgkiss, W.S., Digital Signal Processing: A System Design Approach. John Wiley & Sons. 29, 394-401 (1988). Kresta, J.V., MacGregor, J.F. & Marlin,T.S., Multivariate statistical monitoring of process operating performance. Canadian Journal of Chemical Engineering, 69, 35-47. (Feb. 1991). Wold, S. Esbensen, K. & Geladi, P., Principal component analysis. Chemometrics and Intelligent Laboratosy @stems. 2, 37-52 (1987).
~ ) Pergamon 0892-6875(93)E0035-V
TECHNICAL NOTE MONITORING GRINDING PARAMETERS BY VIBRATION MEASUREMENT - A PRIMARY APPLICATION
SIGNAL
YIGEN ZENG and E. FORSSBERG Dept. of Chemical and Metallurgical Engineering, Lulet University of Technology, S-977 53, Lule~, Sweden (Received 24 March 1993; accepted 28 September 1993)
ABSTRACT Grinding plays an important role on energy consumption and subsequent separation stage in a mineral processing plant. To maintain higher grinding efficiency, the operating parameters must be continuously monitored and adjusted close to the setup of the optimal operating conditions. It is difficult amt expensive to trace the frequent variations of the grinding parameters by traditional methods in commercial scale operation. Since mechanical grinding emits strong vibration signals, it can be picked up by commercially available instrument in the form of time-domain waveform. The variations of the vibration signals were governed by the changes of the grinding state. A primary application was studied based on industrial scale measurements, where the mechanical vibration was picked up by an accelerometer and acoustic pressure changes by a microphone. The digitised time-domain source signals were processed by digital signal processing technique. The variable grinding parameters were the power draw, the feed rate, the pulp density, amt the particle sizes of the mill feed and ground product. By principal component analysis and parameter identification, the variations of the grinding parameters were related to the changes of the source vibration signals. By vibration measurement, a new alternative could be developed for monitoring the operating parameters in grinding. Keywords Ball grinding, Vibration analysis, Power spectrum estimation, Principal component, Multiple regression
INTRODUCTION Mechanical grinding emits strong vibration signals presented in the form of acoustic pressure variations and mechanical vibrations. An experienced grinding mill operator can assess the operating state by listening to the mill. The "decision making" follows the steps that the acoustic signal is first received by the ear of the human being and memorised in the brain (signal acquisition and storage), then deep thinking (signal processing and identification), and finally a decision is made based on the cumulative experiences. Similarly, all the source vibration signals from ball grinding could be picked up in the form of time-domain waveform by commercially available instrument. To evaluate a representative length of the signals, the time-domain waveforms of a certain length of grinding period must be considered and transformed into frequency-domain spectra. Since the variations of the vibration signals reflect the changes of grinding state so that a certain power spectral pattern of different peak energies will only correspond to one kind of grinding state [1]. After learning the particulars of the power spectra (hunting for "finger 495
496
Technical Note
prints') for some time, the variations of the measured power spectra to its "finger prints" spectrum could be related to the changes of the operating states of the ball mill. The advantages of using a computerised instrument over human beings are obvious: the instrument can be set to work 24 hours a day on-line and be tolerant to hazardous or tough working environments. Monitoring the operating parameters could provide an on-line information for the controlling and adjusting units.
EXPERIMENTAL Figure 1 shows the layout of grinding system and the instrumentation for signal acquisition and processing. The grinding system consisted of mainly a primary overflow ball mill, 4.2 m in diameter and 5.4 m in length, operated at LKAB, Malmberget, Sweden in an open circuit. The solid density of the free crushed iron ore (magnetite) was about 4.8 t/m3 and the particle size was < 10 ram. Under normal operation, the feed rate was about 255 t/h and the pulp density was 65 % solids by weight. The mill speed was 12.8 rpm (corresponding to 60% of the critical speed) and the charge volume was about 35%. The grinding charge originally consisted of 100 tons of steel balls. The balls of 60 and 40 mm in diameters, each accounting for 50 % by weight, were continuously added to the mill to maintain the power draw level at about 1130 kW. Under the whole testing period, the feed rate was set to be 60% of the normal operation by requirement. The additional water was directly injected into the ball mill to adjust the pulp density. The power draw and the feed rate were continuously recorded by built-in control units of the mill. Other grinding parameters were evaluated based on manual sampling after changing the operating parameters for about 30 minutes (the equilibrium operating state).
A-A
F
P ion
Control
Fig. 1 Layout of grinding system and instrumentation for signal acquisition and processing The instrumentation sector consisted of two types of signal sensors and their corresponding pre-amplifiers, a DAT recorder and an IBM compatible personal computer (Figure 1). The vibration sensor - an accelerometer - was vertically screwed on the top surface of the supporting bearing for the pinion axis. The amplified mechanical vibration signal was stored in L-channel of the DAT recorder. To pick up the acoustic pressure variations, an acoustic microphone was placed outside the impact zone, 200 mm away from the mill shell (the cross section of the mill centre was illustrated in Figure 1). The acoustic vibration signal was amplified and transmitted to R-channel on the DAT recorder. To avoid alias by non-interested high frequencies, the sampling frequency of the AID converter was set at least 2.5 times the highest frequency of interest [2]. According to the primary studies that the important information for describing the grinding state lies in the frequency band of 0-2500 Hz, therefore a 4-cascade lowpass filter group (each with a cutoff in -24 dB/oetave) at a cutoff frequency of 3 kHz was installed before data acquisition unit. The digitised time-domain waveform signals were loaded into an IBM compatible personal computer for signal processing and identification.
Technical Note
497
The time-domain waveforms, were transformed into the frequency-domain power spectra by Welch's method [3]. The whole waveform was divided into sections of 4096 points in length. Each section was multiplied with the Harming window before power spectral estimation. To compensate the voids among the waveforms caused by the digital window, each new section included 60% of previous section of the waveforrn data (the overlapping process [4]). The power spectrum for each signal sample were therefore an average of 24 waveform sections (about 10 seconds in real grinding period). The number of frequency elements on the spectrum was much larger than the number of practical measurements under the current resolution. Since the peak energies on the spectrum were linearly correlated, principal component analysis (PCA) was therefore a suitable method to reduce a large number of original variables into a few new "latent" variables [5,6]. The relationship between the grinding parameters and the latent variables could be established by stepwise multiple regression. The data management, signal processing and parameter identification were fulfilled with an analytical computer software (DSP4ME toolbox) developed by the author.
RESULTS AND DISCUSSION To implement the modem digital signal processing technique on vibration analysis, the source continuous time-domain waveform signals were digitised into discrete time-domain waveforms. To ensure that the source signals were representative for one setup grinding condition, five signal samples were taken during a valid testing period. Figure 2 shows a short waveform sections in 0.2 second from an example measurement. The waveform picked up by the acoustic microphone is more complicated than by the aeeelerometer. 0,4
0
!
I
-0.| Aco~tic pressurechanges " 0.41,0 I -0.4
1.1
1.15
1.2
1.25
1.3
Progress time (See) Fig.2 Example section waveforms of mechanical and acoustic vibration signals The primary analysis shows that the most informative frequency band to characterise the variations of the spectra was 0-600 Hz. Figure 3 shows the average power spectra for full length mechanical and acoustic vibration signals with the identical measurement as used in Figure 2. The basic frequencies of the bearings, 57, 114 and 171 Hz, were found on both type of spectra. The spectrum of the mechanical vibration signal was simpler than the acoustic signal. The dominant peaks were clearly distinguishable on the vibration spectrum because the accelerometer was directly situated on the bearings. The major differences between those two spectra lie in the frequency band of 200-400 Hz. On the mechanical vibration spectrum, it contains mainly three peaks at 228, 286 and 341 Hz, however many small peaks covering all the frequency band were presented on the acoustic vibration spectrum.
498
Technical Note 4
l1411z
Mechanical vibration
3
I 2 1 0
$711z
1711tz
A
A
"t'mi~ ~ A
MIItI .
t~tm
0.4
^
A
A
.~.
Aeoustie preum'e changes
0.3 0.2 0.1 ~l"f"
'i " ~
I
I
I
100
200
300
I
400
I
500
600
Frequency (Hz) Fig.3 Example power spectra of mechanical and acoustic vibration signals A waterfall diagram is commonly used to illustrate a number of similar spectra for comparison [1]. Figures 4 and 5 show the spectra of the mechanical and acoustic vibration signals respectively. To make the whole spectrum visible in waterfall plot, the decibel scale (Y-axis) was used to measure the peak energies. Each waterfall plot consisted of six curves representing six individual testing conditions. Each curve on the spectral plot denotes an average spectra of five signal samples under identical pre-set operating condition. Since the power spectra mainly reflect the "finger prints" of a specified ball mill, therefore, the power spectra of identical signal type on different grinding conditions are similar at the current resolution. The fingerprints spectrum is sensitive to the factors either impossible to control or lack of comparison base in practise, e.g. the machine assembly, therefore the most important information for the further analysis are the variations on the spectra instead Of the finger prints spectrum itself. The comparison base was set to the average of 30 peak energies at the corresponding frequency bands.
200 •
V6 150 "
V5 V4
loo V3 V2
50-
V1
Ws~tx/! st~p = 30 dB 0
260
Frequency 0H[z)
sbo
Fig.4 Waterfall plot of mechanical vibration spectra under six operating conditions
T~icalNote
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60 $0 40 M3
M
20 10 Waterfall step = 10 dB 100
-60
,mo Frequency (Hz)
Fig.5 Waterfall plot of acoustic vibration spectra under six operating conditions The principal component analysis is a useful technique for reducing the number of original correlated variables in a data set by finding linear combinations of these variables that explain most of the variability [6]. About 245 frequency elements were found at the current frequency resolution over 0-600 Hz. Before making principal component analysis, the original power spectral data must be subtracted by the mean of all observations for the originals variable - obtaining the variations of the spectra. By performing the principal component analysis on the mechanical vibration signal, it was found that the first, second, third and fourth principal components account for 81.8, 10.1, 4.9 and 1.2% of the total variations of peak energies respectively. The first two principal components for the vibration signal account for 91.9% of the total variations. The most important frequencies for the first and second principal components are 114 and 286 Hz respectively. Similarly for the acoustic vibration signal, the first six principal components account for 27.8, 11.6, 8.4, 5.8, 4.4 and 4.0% of the total variations of the peak energies of the frequencies respectively. Much random noise were involved in the acoustic signal at the current sensor location. The correlation coefficients of the principal components indicates that the first three principal components are most effective for the original acoustic vibration signal. The first principal component is mainly affected by the frequencies at 72 and 57 Hz, and the second one by the frequency at 72 Hz. By principal component analysis, the original variables for characterising the spectra were reduced to 3-4 latent variables for the mechanical vibration signal and 5-6 latent variables for the acoustic vibration signal. When the loading of the principal components and the observed spectra were known, the scores for the corresponding principal components could be derived. The scores for the mechanical and acoustic vibration signals were described by Svi and Smi respectively, where i denotes the score on the i-th principal component of the spectra. By multiple regression analysis on 30 signal measurements, the grinding parameters were related to scores of the significant principal components, yields: P = 1102.1 + 8.33Svl -6.94Sv2 + 21.98Sv3 + 27.34Sv4 + 41.23Sm5
(1)
Q = 158.2- 2.12Svl - 19.65Sml - 14.69Sm2
(2)
C = 67.15 + 5.58Sv3 + 19.65S,rd - 15.38Sm4 + 24.93Sm5
(3)
500
Technical Note
Kf = 79.63 - 3.02Svl - 9.52Sml - 39.45Sm3 - 31.84Sm5
(4)
Kp = 48.03 + 1.15Svl + 2.42Sv2- 2.52Sv3 + 2.65Sml
(5)
where P denotes the power draw (kW), Q the feed rate (t/h), C the pulp density (% solids by weight), and Kfand Kp the particle sizes of the mill feed (%-1.7 nun) and product (%-0.105 ram) reapectively. Equations (1-5) account for 78.6, 70.1, 56.2, 82.5 and 82.7 % of the corresponding measurements. The valid prediction ranges of the grinding parameters are: the power draw (1080-1130 kW), the feed rate (145-165 t/h), the pulp density (59-72% of solid), the mill feed size (70-89% -1.7 ram) and the mill product size (45-50% -0.105 ram). The power draw and the product size were mainly related to the principal components of the mechanical vibration signal spectra and the other three parameters to the acoustic vibration signals. Figure 6 shows the relative errors of the grinding parameters predicted by these equations. It is found that most of the relative prediction errors were within -t-5%. The errors for predicting the mill feed rate and the pulp density are larger than the others, because of the lack of information on the natural variation of the mill feeding material. The first principal component plays the major role on the prediction. Particularly, the mechanical vibration signal has more effects on the power draw and the product size, and the acoustic signal on the others. Both the mechanical and acoustic vibration signals have described some of the particulars in the changes of the grinding state. Therefore a combination of both forms of signals can make the prediction closer to the observed grinding parameters.
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Time series Fig.6 Relative prediction errors of grinding parameters by vibration measurements
CONCLUSIONS The vibration signal m~urements were performed on an industrial scale ball mill at LKAB, Malmberget, Sweden. The mechanical vibration signal of the grinding system was picked up by an aceelerometer and the acoustic vibration signal outside the impacting zone was sensed with a microphone. After signal processing and parameter identification, the relationships bntwoe.n the grinding parameters and the signal characteristics have been established by multiple regression. Most of the relative prediction errors were within 5:5%.
Technical Note
501
The power draw and the product size from the ball mill were mainly related to the mechanical vibration signal, and the others to the acoustic vibration signal. Both the vibration signals were important in monitoring the grinding state, so that a combination of these two types of signals may give a better predictions for the grinding parameters. By measuring and processing the mechanical and acoustic vibration signals, the grinding parameters could be monitored for the industrial scale ball mill. Vibration signal measurement provides a new alternative for developing an automatic monitoring system in grinding.
ACKNOWLEDGEMENT This work was partially sponsored by the Norrbotten's Research Board and LKAB, Sweden. The authors thank Kent Tano and Jan-Ch/ister GY~rde for their assistance during the industrial scale measurements.
REFERENCES .
2. 3. 4.
5. 6.
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