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Minerals Engineering 20 (2007) 84–91

Experimental analysis of charge dynamics in tumbling millsby vibration signature technique

B. Behera, B.K. Mishra *,1, C.V.R. Murty

Department of Materials and Metallurgical Engineering, Indian Institute of Technology, Kanpur, India

Received 2 February 2006; accepted 15 May 2006Available online 9 August 2006

Abstract

Up until now, real time identification of the dynamics of the charge in a tumbling mill has not been accomplished. This paper exam-ines the possibility of correlating the vibration signature of tumbling mills to characterize the motion of the charge and the state of grind-ing. Vibration signals were picked up using accelerometers mounted directly on the mill shaft of a 90-cm diameter mill. The time domainsignals were transformed to frequency domain by using fast Fourier transform (FFT). The Fourier spectra in the frequency domain weremethodically interpreted and correlated to establish the prevailing mode of the charge motion under any operating condition. The grind-ing behavior under dry as well as wet grinding conditions were analyzed by following the variations in the vibration signature as a func-tion of speed of the mill, volumetric filling, powder loading, and time of grinding.

Experimental results clearly show that the dominant peak in the FFT spectra is quite sensitive to the variations in any mill operatingparameter. This feature has been employed to detect undesirable operating conditions such as surging, mill over-load, etc. Finally, it isdemonstrated that by proper interpretation of the vibration signature of the mill, it is possible to predict the charge dynamics and esta-blish the state of grinding.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Ball mill; FFT technique; Vibration signature; Charge motion

1. Introduction

Characterization of the motion of the charge inside aball mill is one of the most important requirements for ana-lyzing the performance of the mill. The important charac-teristics of the charge motion are conventionally termedas (a) cascading, (b) cataracting, and (c) surging. Surgingof the charge may take place at all speeds and it is parti-cularly damaging at high speeds. If the motion of the grind-ing media were not controlled then a greater fraction ofenergy would be wasted in impacts, which do not breakparticles, or consumed in the generation of unwanted prod-uct sizes such as ultra-fines. Therefore, in order to improve

0892-6875/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mineng.2006.05.007

* Corresponding author.E-mail address: bk@iitk.ac.in (B.K. Mishra).

1 Currently Director, Regional Research Laboratory, Bhubaneswar.

the utilization of the energy, it is essential to have a goodunderstanding of the mechanics of the motion of the tum-bling charge.

A vast amount of research work has been done onmotion analysis of ball charge by visual means in smallermills. Among these, the work of Vermeulen et al. (1984)is noteworthy. These authors claim that the slip of thecharge in a rotary mill with smooth liners causes it to surge,while the grinding media adjacent to the mill shell do notever move counter to the mill shell. However, under low-ball fillings, surging may resemble the oscillating behaviorof the charge as first proposed by Rose and Sullivan(1958). In a very similar kind of approach, Agrawalaet al. (1997) have shown the surging behavior of the chargein a 90-cm diameter mill where they clearly identified theperiods of peak surge and subsequent charge collapse. Inlarger mills, obviously, motion analysis can only be carriedout by indirect means.

Fig. 1. Experimental set-up.

B. Behera et al. / Minerals Engineering 20 (2007) 84–91 85

Indirect assessments of the profile of the charge havebeen done in two ways: imbedding strain gauges and inte-grated circuitry inside the ball, or alternatively, imbeddingsensors on the mill shell. Rolf and Vongluekiet (1984)devised a measuring technique that consisted of tracer ballsthat are instrumented to record the number and intensity ofimpacts. Liddell and Moys (1988) studied the effect of millspeed and filling on the position of toe and shoulder ofthe ball charge. They used electrical conductivity probesthat are inserted in the liner to locate the angular positionof the toe and shoulder. More recently, Zeng and Forssberg(1993a,b, 1994) studied the mechanical vibration of tum-bling mills using accelerometers. They interpreted the vibra-tion data successfully to relate the change in the vibrationsignatures to several grinding parameters. Their results werebased on principal component analysis which is a techniqueused to reduce correlation between signal peaks. However,they maintained that the technique to interpret vibrationdata is difficult and it is not possible to quantify the differ-ence in signals by direct inspection. In contrast, we demon-strate a much simpler method to interpret vibration data.

Mill load is an important operating parameter in a millcircuit. By its optimization, it is possible to achieve signifi-cant improvements in the production capacity and energyefficiency. Kolacz (1997) studied mill load (powder filling)variations by using a piezoelectric strain transducer. Thetransducer was installed midway along the length of the millon the mill shell. When the transducer reached the top posi-tion in one half of the rotation cycle, it measured compres-sion. When it reached the bottom, it measured tension. Bytaking the difference between the readings correspondingto compression and tension, it was possible to calculatethe total strain variations that are directly proportional tothe mill load.

Tumbling of balls inside a ball mill produces intensemechanical vibration. It is known that the mode of vibra-tion is related to the motion of the charge and variousother milling parameters (Rolf et al., 1982). Therefore, ifthe vibration signature of the mill in motion could berecorded and analyzed then it would become a very usefultool in establishing the charge profile of tumbling mills inoperating plants. Modern day instrumentation techniqueallows fast and accurate recording of the vibration signalby using sensitive accelerometers. The continuous timedomain data can be analyzed by the vibration signaturetechnique to yield frequency spectra characteristic ofcharge motion. Thus the main thrust of this paper is toexamine and correlate the vibration signatures obtainedfrom a laboratory scale ball mill to the prevailing chargedynamics and milling characteristic.

2. Vibration signature technique

It is a common knowledge in the field of mineral pro-cessing that mechanical grinding as in the ball mill pro-duces strong vibrations. The traditional way of observingthese signals is to view them in the time domain. The time

domain is a record of what happened to the amplitude ofvibration of the mill versus time. Since any waveform thatexists in the real world can be generated by adding up sinewaves in a very unique manner, these sine waves allow rep-resenting the complex wave form of the mill vibration sig-nal in the frequency domain. The relative amplitudes ofthese sine waves of different frequencies contain informa-tion directly related to the operating state of grinding (Zengand Forssberg, 1994). Thus, the time domain waveformsare transformed into frequency domain by fast Fouriertransform (FFT) technique.

In general, an acceleration signal wave can be repre-sented in the form

aðtÞ ¼ a0 þ a1 sin -1t þ a2 sin -2t þ � � �where a0, a1, a2, etc., are amplitudes corresponding to fre-quencies 0, -1, -2, etc. The Fourier amplitude spectrum isa plot of the amplitudes ai as a function of frequencies -i.Mathematically, the Fourier amplitude A(f) correspondingto frequency f of the signal a(t) can be obtained as

Aðf Þ ¼Z 1

�1aðtÞe�j2ipftdt

where j is simplyp�1. With this analysis, it is possible to

correlate the variations in the characteristics of the vibra-tion signals to the different charge profiles in the mill.

3. Experimental

The grinding system consists of a laboratory size ballmill of 900 mm diameter and 150 mm long which is drivenby a three-phase motor (5 HP, 1400 rpm). The criticalspeed of this mill is about 45 rpm. The mill is connectedto a shaft that rests on two plumber blocks. Fig. 1 showsthe layout of the experimental set-up. The speed of themotor is controlled by a Toshiba-make inverter and a gearbox system. The mill is fitted with 16 equally spaced lifterbars (length 150 mm, height 18 mm, and width 28 mm).Two doors are cut on the mill shell for the addition andremoval of the balls and grinding material. The mill oper-

0

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0 500 1000 1500 2000 2500 3000 3500 4000

Frequency (Hz)

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plit

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e (m

/s2 )

-10

-5

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5

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/s2 )

Fig. 2. A typical FFT and time series data (insert); mill speed = 40 rpm;ball load = 140 kg; powder weight = 15 kg.

86 B. Behera et al. / Minerals Engineering 20 (2007) 84–91

ates with a combination of four different diameter balls: 18,24, 34, and 40 mm. The mill is also equipped with a torquesensor (M/s Sensor Technology, UK) that picks up thepower draft and the speed of the mill. Considerable effortwas made to properly align the drive motor, gear box, tor-que sensor and the mill shaft.

The signal acquisition and processing is very critical tothe present investigation. A highly sensitive accelerometer(M/s Summit Instruments, USA) and a data acquisitioncard (M/s National Instrument Inc., USA) are used to col-lect vibration signature of the mill. The amplitude and thefrequency range of the accelerometer is in the range of ±2g

and 0–5000 Hz respectively. The purpose of the accelerom-eter is to record the vertical vibration of the mill. Since theaccelerometer had to be fitted on the mill shaft that rotates,a separate bearing wheel was inserted between the plumberblock and the front endplate of the mill (see Fig. 1). Theaccelerometer was vertically screwed on the surface of thebearing wheel (slip ring) that remains stationary even whenthe mill rotates. The accelerometer and the torque sensorare connected to the data acquisition card. The data acqui-sition is governed by the LabVIEW� programmingenvironment.

LabView� (National Instruments, Austin, TX, USA) isa software development package designed specifically forinstrument control and measurement. The essence of thisdesign concept is based around a programming methodol-ogy in which virtual instruments (VIs) are built graphicallyusing icon-based software modules instead of a text-basedprogramming language. LabView� based computer pro-gram not only controls the rate of acquisition of the databut also displays the data on a continuous basis. This pro-gram is also used to convert the time domain data to fre-quency domain. The conversion is done by utilizingLabVIEW�’s inbuilt FFT module.

3.1. Interpretation and tuning of vibration signals

The mechanical vibration of the mill during operationwas continuously collected from the surface of the millshaft using the accelerometer whose output was sent tothe data acquisition system. The time domain data wereprocessed using a Hanning window before applying FFT.Hanning window was used to reduce the spreading or leak-age of the spectral components away from the frequency ofinterest. It acts like a predefined, narrowband, and low passfilter. The computer program developed using LabVIEW�

takes three key input parameters such as sampling fre-quency, mill speed in rpm, and the number of blocks ofdata over which averaging is done. The output of the com-puter program is a graphical display that shows the vibra-tion signal in time as well as frequency scales.

Several tests were carried out at different speeds rangingfrom 20 to 60 rpm with different ball loads ranging from140 to 220 kg to calibrate and test the functioning of thesoftware as well as the hardware system. During these exper-iments, it was realized that the success of data acquisition

lies in positioning of the accelerometers on the mill shaft.Several positions were tried and finally it was decided thatthe accelerometer be positioned on the shaft as close to themill as possible. Shifting the accelerometer very close tothe mill along the mill shaft significantly improved the qual-ity of data and thereby meaningful results were obtained.

To avoid any error in measurement, determination ofthe sampling frequency is crucial. Several experiments werecarried out at different values of sampling frequenciesbetween 300 and 4000 Hz. The mill was operated at40 rpm and with 140 kg ball and 15 kg of clay powder. Itwas observed that at sampling frequency of 300 Hz, thereis no evidence of any dominant peak in the FFT spectrum.This is the case of under sampling; the mill heaves up anddown at a frequency near 450 Hz which is directly relatedto the natural frequency of the mill-ball charge system.However, at higher values of sampling frequency (greaterthan 1000 and less than 3000 Hz), the first dominant peakwas obtained. But in this case, it was not possible to cap-ture the complete information contained in the original sig-nal. By increasing the sampling frequency up to 4000 Hz itwas possible to capture all peaks of the signal; the secondand third dominant peaks became pronounced. At highervalues of sampling rate (more that 4000 Hz), no changewas detected and the positions and peak amplitude valuesof the dominant peaks did not change. Finally, it wasdecided to use a sampling rate of 4000 Hz in all subsequentexperimental work.

A typical FFT spectrum of the mill vibration is pre-sented in Fig. 2. The corresponding time series data is alsopresented in Fig. 2 as an insert which shows a pattern cor-responding to the charge dynamics. Clearly much more canbe learnt from the FFT spectrum than the time series plot.The data were collected when the mill was running at40 rpm (88.88% of critical speed) with 140 kg ball loadand 15 kg clay powder. In most of the experiments claypowder was used to reduce the level of noise. Since the millis in circular motion, it is expected to generate vibrationwith certain periodicity. In fact, the time series data alwayscontains some degree of periodicity. In the frequency

B. Behera et al. / Minerals Engineering 20 (2007) 84–91 87

domain, the data shows three significant peaks. However,the amplitude of the first peak (450 Hz) is one order ofmagnitude higher than the other two. Thus, the amplitudeof the first peak which turns out to be the dominant peakwas considered to establish a relation between the vibrationsignature with various operating parameters of the mill.

4. Results and discussion

The results of experiments are analyzed in two parts. Inthe first part, the mill vibration is studied without any ref-erence to grinding. In all the experiments, unless it is specif-ically mentioned, clay powder was used as a dampingmedia to reduce the level of noise. In the second part, millvibration is correlated with progress of grinding.

4.1. Effect of mill speed

Mill speed has a profound effect on the overall dynamicsof the ball charge and the mill performance. Industrial millsare typically equipped with variable speed drive system.From time to time, the mill speed is adjusted such thatthe performance of the mill is maintained at its peak. How-ever, a correlation between mill speed and charge dynamicsin an operating mill is required to be established. Clearly,various other operating parameters complicate the situa-tion. Therefore, it was decided to investigate the vibrationsignature of the mill as a function of mill speed but withonly one of the other parameters changed at a time.

To examine the effect of mill speed the mill was operatedwith 140 kg ball load and 15 kg clay powder. At differentmill speeds the vibration signal was obtained. The firstdominant peaks in the FFT spectra at different mill speedsare placed together on one axis in Fig. 3. It is clear from thefigure that, the amplitude of the first dominant peakincreases with mill speed up to 40 rpm and then decreasesat higher mill speeds. This happens because at low speedscascading motion prevails. This produces mechanicalvibration of lesser intensity. As the mill speed increasesballs begin to cataract. At 40 rpm (88.88% critical speed),

Fig. 3. Variation in the amplitude of the first dominant peaks with millspeed (ball load = 140 kg, clay powder = 15 kg).

the charge mass moves to a longer distance along the millshell and at some point a portion of the charge collapseforming a cascading pattern and another portion take aparabolic path. The portion of the ball charge that takesthe parabolic path off the mill shell constitutes the cataract-ing charge profile where a large number of direct collisionsbetween ball and mill shell take place. The overall colli-sional effect produces a strong mechanical vibration.Beyond the critical speed (at 50 and 60 rpm) charge masscentrifuges and hence the balls lie against the mill shellthroughout the cycle of rotation. Practically, very less num-ber of collisions takes place and hence the intensity ofvibration produced is quite less.

The frequency spectra presented in Fig. 3 shows a wideband around the peak value. It becomes difficult to identifythe peak amplitude of the vibration signature and the cor-responding frequency. To avoid this difficulty a sixth orderpolynomial trend line was fitted to the scattered data(amplitude versus frequency) and the peak value was readfrom the trend line (see Fig. 2). The variation in the ampli-tude of the first dominant peaks with mill speed is shown inFig. 4. From this figure, it is very clear that a strongmechanical vibration is produced when the mill is operatedat about 40 rpm (88.88% of the critical speed). The levelnoise was also at its highest at this speed. It is expected thata significant portion of the charge mass at this speed cata-ract. At higher speeds the noise level decreases significantlyand so does the vibration. The amplitude of vibrationbeyond the critical speed is almost half compared to themill vibration at 50% critical speed.

As evident from Fig. 4, the amplitude of vibration is at itsmaximum at about 40 rpm and it decrease when the millspeed is either increased or decreased. Not surprisingly,therefore, the amplitude of vibration is approximately samewhen the mill operates at 30 and 50 rpm. In this situation itis not possible to predict the charge dynamics from thevibration signature by simply analyzing the FFT spectra.This ambiguous situation was overcome by analyzing thecorresponding time series data which is shown in Fig. 5. Itis clear from the figure that at 30 rpm a relatively widerband in the signal is present signifying a higher intensity

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Fig. 4. Variation in the intensity of vibration with mill speed (ballload = 140 kg, clay powder = 15 kg).

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30 rpm

Fig. 5. A typical time series data for the mill running at two different millspeeds with 140 kg of ball load and 15 kg clay powder.

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Fig. 6. Variation in the amplitude of the first dominant peak with powderfilling at various mill speeds (mill diameter = 0.9 m, ball load = 140 kg).

88 B. Behera et al. / Minerals Engineering 20 (2007) 84–91

of mill vibration compared to the mill vibration at 50 rpm.Moreover, at 30 rpm the characteristic of the charge is onethat of cascading-type, whereas at 50 rpm, it is of centrifug-ing-type. Thus, the amplitude of vibration is expected to behigher at 30 rpm compared to 50 rpm. To sum up, it is quiteevident that the mechanical vibration as captured by theaccelerometers mounted on the mill shaft is directly relatedto the dynamics of the charge.

4.2. Effect of powder filling

Presence of particles in the mill significantly reduces thenoise and impact forces generated due to collision of balls.The behavior of particles as a damping medium can beanalyzed by considering various energy dissipation mecha-nisms. These mechanisms involve complex physical pro-cesses and cannot be analyzed here. Here, the analysis isrestricted only to the extent that has particular relevanceto the milling practice. In practice, build up of particlesinside the mill—over-load condition, is undesirable as itmay lead to operational problems and poor energy utiliza-tion. In a continuously operating plant, it is of interest todetermine the onset of over-load condition.

To start with a series of experiments were conducted bysimply changing the particle load inside the mill to cover awide range of milling situations. These include no-powder-load to over-load condition. The former condition refers tomill operation with only steel balls. In contrast, the latercondition refers to the mill operation, where excess powderis present which is typically higher than the available totalvolume of all the interstices between the balls. To relate themill vibration to the level of powder filling, the mill wasoperated between 30 and 40 rpm and with 140 kg of balls.The variation in the peak amplitude at different powder

loading conditions starting from no-powder to 25 kg ofpowder filling was studied. From the frequency spectra,the peak amplitude value at each level of powder load atdifferent mill speeds was recorded. Fig. 6 shows a plot ofvariation in the peak amplitude of vibration with theamount powder present in the mill. At any given millspeed, the peak amplitude of vibration decreases with theamount of powder. It is only at very high powder loading(25 kg powder and more) mill vibration becomes insensi-tive to mill speed. It takes about 15 kg of powder to fillthe void space of a 140 kg ball charge in the mill. Thus,25 kg of powder clearly represents an over-load condition.Therefore, in the light of these experiments, the over-loadcondition could be identified when the vibration signal con-tinuously reduces at any given speed and ball load and sub-sequently becomes insensitive to mill speed.

4.3. Effect of ball load

The charge mass or the ball load inside the mill alsoinfluences the amplitude of the characteristic peaks of thevibration signals. To study the effect of mill filling on thevibration signature of tumbling mills, three experimentswere carried out at different ball loads: 140, 180 and220 kg corresponding to 45%, 58%, and 68% mill filling.The grinding media was composed of 18, 24, 34 and40 mm balls. Proportionate amount of clay powder of 15,20, and 25 kg was added to 140, 180 and 220 kg of ball loadrespectively. The mill was operated at various mill speedsranging from 20 to 60 rpm. Fig. 7 shows variation in theamplitude of vibration at various mill speeds. In all theexperiments it was found that the amplitude of vibrationincreases with mill speed and reaches a maximum valuecorresponding to a characteristic speed and subsequentlydecreases with further increase in the speed. The overallvariation of amplitude of vibration with mill speeds underdifferent loading conditions can be broadly analyzed aboveand below the critical speed.

At any given speed below 36 rpm (80% critical), theintensity of vibration increases as the ball load decreases,

0

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/s2 )

140 kg ball + 15 kg powder

180 kg ball + 20 kg powder220 kg ball + 25 kg powder

Fig. 7. Variations in the intensity of first dominant peaks at various ball-loading conditions with increasing amount of powder addition.

0.02

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Fig. 8. Variation of peak amplitude with time during continuous 1 h drygrinding operation (ball load = 140 kg, mill speed = 30 rpm).

B. Behera et al. / Minerals Engineering 20 (2007) 84–91 89

i.e., the mill loaded with 140 kg ball load (45% filling) givesthe maximum amplitude of vibration. This happensbecause up to 36 rpm, the effective circulating distance(the distance from the cascading surface and back) movedby the whole charge mass decreases as the mill fillingincreases. This reduces the intensity of vibration. As seenfrom Fig. 7, around 50 rpm (105% critical), a transitionin the vibration behavior of the mill takes place. Abovethe critical speed, intensity of vibration increases as the ballload increases. This can be explained by the fact that abovethe critical speed, a fraction of the charge always centri-fuges. The centrifuging balls do not contribute to vibration.It is also expected that for any given size of the mill, thefraction of balls that centrifuges, increase with decreasingmill filling. The remaining fraction of balls always cata-ract/cascade. By this argument, it appears that the catar-acting mass is more at 220 kg ball load compared to140 kg ball load. Hence, the amplitude of vibrationincreases with ball load above the critical speed.

4.4. Batch grinding under dry and wet conditions

The mill vibration is expected to respond to the changein the milling environment. Milling changes the fineness ofthe powder which in turn alters the collision spectra. Inorder to understand this aspect, it was decided to analyzethe vibration signals to determine the extent of grindingunder batch condition. The mill was operated at 30 rpmwith 140 kg ball load and14 kg of quartz particles. Thequartz particles were sieved and the fraction in the sizerange of 4 and 14 mesh was used for grinding. Vibrationdata were collected at various time intervals when the millwas operated continuously for a period of 1 h. The peakamplitude of the FFT spectra at various time intervalswas recorded. Fig. 8 shows the variation in the amplitudeof the dominant peak with time. It is observed from thisfigure that initially the amplitude of vibration increases ata faster rate. The rate of increase in the amplitude dimin-ishes after about 20 min and then it eventually plateaus

off after 30 min. These features of the vibration signaturecan be correlated to the grinding behavior by identifyingtwo distinct regimes. In one regime, say up to 30 min, par-ticles break and in the other regime beyond 30 min there isvery little breakage. The demarcation between theseregimes corresponds to the time when the amplitude ofvibration is at its peak.

The increase in the vibration in the early stages of mill-ing can be explained by considering the utilization of theenergy for the fracture and fragmentation of the particles.Initially, a larger fraction of the available energy is utilizedin grinding, but as the time passes, the particles becomefiner and the available impact energy is no longer suffi-cient for further breakage of particles. These impacts arewasted in collisions, which in turn, are responsible forincrease in the intensity of vibration of the ball mill.Towards the end, when the fineness of the material doesnot change the mill vibration stabilizes as evident fromthe figure.

It appears from Fig. 8, that most of the grinding opera-tion was over within about 25 min. When the grinding getsover and particles are in a powder state, the intensity ofvibration attains its peak value and then it stabilizes after-wards as grinding continues. In order to relate the ampli-tude of vibration with progress of grinding, severalsamples were collected at different stages during the 1-hgrinding period. The samples were analyzed by a combina-tion of sieving and laser particle size analyzer. The compos-ite grinding data is presented in Fig. 9. It is observed fromthe figure that the median size of the ground materialchanges from 1.5 mm to 105 lm as the grinding progressesfrom 1 min to 15 min. It eventually reaches a value of24 lm at the end of 1 h. This is very much in line with whathas been explained earlier with respect to variation in theamplitude of vibration during grinding.

To study the vibration response of the mill in wet grind-ing situation, the mill was operated under identical condi-tions as before except that 13 l of water was used.Vibration data were collected for a period of 1 h. Fig. 10shows a comparison between the peak vibration ampli-

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Cu

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mo

un

t pas

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g (%

)

1 Hr

15 min

1 min

d50 = 24 micron

d50 = 1500 micron

d50 = 105 micron

Fig. 9. Variation in the size distribution of the particles at different times.

90 B. Behera et al. / Minerals Engineering 20 (2007) 84–91

tudes at different stages of grinding. The curve representingwet grinding lies below the corresponding curve for the drygrinding. This signifies that the amplitude of vibrationunder wet grinding condition is less than that of the drygrinding condition. This could be simply due to the pres-ence of water. However, it also appears that particle sizeof the product plays a role. This was confirmed by doingsize analysis of ground product obtained after 1 h grinding.It was observed that the product of dry grinding is coarseras compared to that of wet grinding. After about 30 min,the amplitude of vibration varies little with time undereither conditions of grinding. However, as observed fromFig. 10, even during this grinding period, wet grinding pro-duces less vibration compared to dry grinding. Theobserved lower vibration under weight condition after allgrinding action is presumably over, is due to the additionaldamping effect provided by the slurry. For benchmarkingpurpose, Fig. 10 also shows the amplitude of vibration ofthe mill in absence of any grinding material (particle) andwater where the peak amplitude of vibration is compara-tively quite high and remains steady during the entire per-iod of mill operation.

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Only Ball

Grinding Period

Fig. 10. Variation of peak amplitude with time under dry and wetgrinding conditions (ball load = 140 kg, mill speed = 30 rpm,water = 13 l).

5. Summary

From a practical standpoint, it is important to judge thedynamics of the charge as it influences, among other things,the efficiency of grinding and power draft. However, duringoperation, it is not easy to directly predict the chargedynamics as a function of various operating and designparameters. In this study, an attempt is made to correlatethe vibration signals of a laboratory mill to the overallcharge dynamics. The vibration signals are picked up fromthe mill shaft and processed to convert the signals from thetime domain to the frequency domain using the Lab-VIEW� software environment. The experimental datashow the frequency spectrum of the overall mill vibrationthat has been interpreted to predict the dynamics of thecharge and grinding behavior of the mill.

During dry grinding, variations in the vibration signa-tures are observed as a function of speed of the mill, volu-metric filling, powder loading, and time of grinding. It hasbeen found that, the amplitude of vibration graduallyincreases with mill speed up to the critical value (45 rpm)and beyond this speed the amplitude of vibration decreases.In addition to mill speed, mill filling is found to have a sig-nificant influence on the amplitude of vibration. Up to thecritical speed, as the ball load increases from 45% mill filling,the amplitude of vibration decreases. However, the trend isreversed when the mill speed exceeds the critical speed.

Several observations were made with respect to the pro-gress of grinding through the vibration signature analysis.Under batch milling condition, it has been found thatamplitude of vibration always increases with the progressof grinding and it peaks when the grinding is complete.These observations have been supported by simultaneousmeasurement of the vibration signal and size distributionof the ground product at different intervals of time. Underwet grinding situation, identical behavior is observed.However, the amplitude of vibration during any given per-iod under wet grinding condition is always lower than thatof the dry grinding condition. Thus, it is believed that bymeasuring and correctly processing the vibration signals,it should be possible to monitor the grinding parameterscontinuously for better mill operation.

6. Conclusions

Vibration signature of a 900-mm diameter ball mill isinvestigated. Through in-depth analysis of vibration dataon the time as well as frequency domain, characteristicsof the mill vibration is established. It has been found thatoptimal mill operation corresponds to a specific mill speedand ball load and these parameters can be identified fromthe variations in the vibration signature of the mill. It isalso possible to correlate the peak vibration amplitude withthe state of grinding. Last but not least, the vibration canbe interpreted to identify the mill over-load condition.

We believe that the simplicity of the vibration signaturemethod would make the approach very attractive as a diag-

B. Behera et al. / Minerals Engineering 20 (2007) 84–91 91

nostic tool. In fact, this work lays down an important foun-dation for further investigation into the industrial millvibration characteristics and design of suitable diagnosticstrategies for improved plant practice.

Acknowledgements

The authors wish to acknowledge the financial supportprovided by the Department of Science and Technology(DST) through the PAC of manufacturing and robotics.The authors would also like to thank the CARE committeeof IIT Kanpur for providing financial support to procurethe laser size analyzer.

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