Acoustic emissions simulation of tumbling mills using charge dynamics

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<ul><li><p>grtin</p><p>Can</p><p>Process instrumentationMineral processingSAG milling</p><p>varihethethodme</p><p>the internal surface of the mill and the acoustic signal measured on the outer surface is measured exper-</p><p>minutiof theandingd the d</p><p>ics of the mill; however, DEM simulations still lack in accuracy. Inaddition, there are ongoing challenges for DEM simulations of tum-bling mills, such as shortcomings in simulating the ne progenyand behaviour of the slurry (Morrison and Cleary, 2008).</p><p>It is known that ball mills undergo strongmechanical vibrations,caused by the impacts and collisions. As a result, they generate aloud noise. Though noise and vibration may be harmful, from the</p><p>1997; Spencer et al., 1999; Tang et al., 2010; Watson, 1985; Zengand Forssberg, 1993). Moreover, there are some dynamic valueswhich play an important role in optimizing the mill performanceand mill design. The shoulder and toe angles are two such exam-ples. Correlating the acoustic/vibration signal with these dynamicfeatures has been much less studied than the relation betweenoperating parameter and the mill sound (Huang et al., 2009;Martins et al., 2006). Considering that the use of acoustic/vibrationsignal is a non-invasive, low cost tool of studying comminutionmachines, there remains room for more studies, specically forindustrial applications.</p><p> Corresponding author.</p><p>Minerals Engineering 24 (2011) 14401447</p><p>Contents lists availab</p><p>n</p><p>elsE-mail address: poorya.hosseini@mail.mcgill.ca (P. Hosseini).can potentially lead to signicant energy savings. Due to the harshenvironment inside the mills, as well as severe chargecharge andcharge-liner impacts, the use of on-line sensors presents somepractical problems (Martins et al., 2008). An alternative solutionis the use of discrete element models (DEM) to simulate internalmill dynamics and the charge motion (Cleary, 2001; Cleary et al.,2003; Mishra, 2003; Mishra and Rajamani, 1992; Powell andNurick, 1996). Signicant advances in computer technology havehad a role in the growing interest in using DEM to simulate dynam-</p><p>generated sound. The measurement of the sound of the mill bymeans of instrumentation has the benet of full-time on-line oper-ation, increased precision, while having a greater tolerance to per-ilous or harsh working environments (Zeng and Forssberg, 1993).Over recent decades, different studies have been conducted on lab-oratory and industrial scale mills to correlate the acoustic/vibrationsignal with the operating parameters of the mill such as powerdraw, feed rate, mill load, pulp density, ore type and particles sizedistribution (Aldrich and Theron, 2000; Das et al., 2010; Kolacz,1. Introduction</p><p>Tumbling mills are a class of comquently used for the size reductioncessing industry. Better understmechanism of energy utilization, an0892-6875/$ - see front matter 2011 Elsevier Ltd. Adoi:10.1016/j.mineng.2011.07.002imentally. Given this transfer function and the force distribution obtained from the DEM simulation, andassuming a linear time-invariant response, the on-the-shell acoustic of a laboratory scale ball mill hasbeen simulated. Comparison of this simulated signal with the signal measured experimentally can beused as a criterion to judge the validity of the DEM simulations, and as a tool for enhancing our under-standing of both DEM simulations and the use of acoustics within the context of mineral processing. Theresults derived from preliminary experiments on a laboratory scale mill shows satisfactory agreementbetween the actual measurement and the simulated acoustic signal.</p><p> 2011 Elsevier Ltd. All rights reserved.</p><p>on devices, and are fre-ore in the mineral pro-of the mode and</p><p>ynamics of the charge</p><p>viewpoint of a human operator, and are a waste of the energy, theycan serve as a useful tool in studying the operation of the mills. Theacoustic/vibration signal contains information directly related tothe operating state of the mill and the mill charge dynamics. Anec-dotal evidence has long suggested that a skilled grinding mill oper-ator can evaluate the operating state of the mill by listening to theKeywords:Discreet element modellingSimulation</p><p>odology is developed to simulate on-the-shell acoustic signal emitted from tumbling mills using theinformation extracted from a DEM simulator. The transfer function which links the forces exerted onAcoustic emissions simulation of tumblin</p><p>Poorya Hosseini a,, Sudarshan Martins a, Tristan MaaDepartment of Mechanical Engineering, McGill University, Montreal, Quebec, CanadabDpartement de gnie informatique et gnie logiciel, cole Polytechnique de Montral,</p><p>a r t i c l e i n f o</p><p>Article history:Received 26 January 2011Accepted 4 July 2011Available online 4 August 2011</p><p>a b s t r a c t</p><p>Knowledge of the internalthe mill, notwithstanding tTo overcome this problem,invasive measurement meAlternatively, virtual instru</p><p>Minerals E</p><p>journal homepage: www.ll rights reserved.mills using charge dynamicsb, Peter Radziszewski a, Francois-Raymond Boyer b</p><p>ada</p><p>ables of a mill is of importance in design and performance optimization ofdifculty in measuring these variables within the harsh mill environment.research has focused on measuring the internal parameters through non-s such as the use of the vibration/acoustic signal obtained from the mill.nts, such as discrete element methods (DEM), are employed. Here, a meth-</p><p>le at ScienceDirect</p><p>gineering</p><p>evier .com/ locate/mineng</p></li><li><p>Nomenclature</p><p>p acoustic pressurei impact forceh impulse responseft tangential component of contact forcefn normal component of contact forceK spring coefcient in contact modeldn relative normal displacement at contact~v translational velocity at contactm mass of particlef viscous damping ratio in contact modell sliding friction coefcient~n unit normal vector at the contact pointR radius of particle</p><p>f impact on mill shellF total force acting on mill shelld dirac delta functionG greens FunctionA displacement of mill shellr position vectorrm position vector of microphoneh angular position of impacthm angular position of microphoneu angular difference between impact position and micro-</p><p>phone positiont time</p><p>P. Hosseini et al. /Minerals Engineering 24 (2011) 14401447 1441Through the simulation of the charge motion inside tumblingmills, DEM models calculate distribution and magnitude of forcesand impacts. These forces and impacts engender the vibrations ofthe structure, and are the main cause of the sound signal generatedby the mill. If the relation between these impacts and the acoustic/vibration signal emitted from the mill is known, the vibration/acoustic signal can be simulated using the distribution of impactsextracted from the DEM simulator; such a simulation of acoustic/vibration signal was held to be unworkable in the past (McElroyet al., 2009). Replacement of surface vibration with DEMmodellingallows the implementation of DEMs for soft-sensors design ap-proaches, with the objective of measuring the internal variablesof the mill (McElroy et al., 2009). Furthermore, the comparison be-tween the simulated signal and the signalmeasured experimentallycan be used as a criterion for evaluating validity of DEM simula-tions, and as tool for enhancing our understanding of the dynamicsof the mill. If the inverse approach is taken, it may be possible todetermine dynamic values currently obtained from other methods,such as impacts inside the mill, using only the acoustic/vibrationsignal. Implementing such an approach for a similar application a vibratory ball mill containing a single ball produced promisingresult in the prediction of impact force using the vibration signal(Huang et al., 1997). These so-called inverse techniques have beenextensively used to predict features of mechanical systems whichare difcult or impossible to measure directly. A categorization ofthese techniques for force-prediction models, various appliedexamples and the required theoretical background has been pre-</p><p>sented by Wang (2002). Acoustic signal and vibration signal of</p><p>Fig. 1. Schematic of the labFor the experiment, a laboratory-scale ball mill featuring a camdrive is used, as illustrated in Fig. 1. A large diameter aluminiumdisc is xed to a shaft mounted on a bearing. The aluminium dischas two functions. Firstly, the followers for the cam drive are xedto its face. Secondly, the mill drum (or shell) is bolted to the disc. Atransparent Plexiglas face closes the mill at the free end of thedrum, allowing for the observation of the charge. The drum con-sists of a steel cylinder, with a diameter of 1.524 m and a lengthA brief description of the laboratory-scale ball mill used in theexperiments, the experimental setup used to capture the acousticsignal and to measure impact forces as well as the methodologyimplemented to process the primary measurements are presentedin this section.</p><p>2.1. The laboratory-scale ball millthe mill are highly correlated; however, the acoustic signal is moreof interest, since its measurement is more practical and has the po-tential of being captured through sensors which are not necessarilyattached to the structure. In this paper, as mentioned earlier, it isdemonstrated that an acoustic signal can be calculated from DEMmodels. This simulated acoustic signal will be shown to be compa-rable to the measured acoustic signal.</p><p>2. Experimental setupof 0.3048 m. A set of twelve plates are xed to the inner surface</p><p>oratory scale ball mill.</p></li><li><p>of the shell. These plates are called lifters. Their role is to furtherpromote the tumbling action of the charge, as induced by the rota-tion of the mill. The birch balls, which form the charge, have anaverage diameter of 5.1 cm and an average mass of 43 g.</p><p>2.2. Impulse response measurement</p><p>This section describes the method by which the relationship be-tween a single impact, inside the mill shell, at a specic positionand the corresponding acoustic signal captured on the mill shellis established. Impact force and the resulting acoustic signal aremeasured using an impact hammer with embedded forcetransducer and a pressure-eld microphone, respectively. A mul-ti-channel data acquisition system is used to concurrently amplifyand digitize both signals and to stream the resulting signals to acomputer. Fig. 2 shows a sample of the impact force signal alongwith the resulting acoustic pressure signal.</p><p>Assuming the vibrations of the shell is linear and time invariant,meaning different impact at the same position at different timesproduce the same response, the shell response to the impact forcecan be characterized through the system impulse response. Conse-</p><p>a constant amplitude in the frequency domain the denominator ofEq. (3) becomes constant and the impulse response, in this case, isequal to the acoustic pressure divided by a constant (the magnitudeof the impact). However, in this research deconvolution of the actualexcitation exerted by hammer is used for calculations rather thanthe ideal impact assumption. Fig. 3 shows a sample of the calculatedimpulse response in the time domain.</p><p>2.3. Acoustic signal of the mill</p><p>The same microphone and recording system described in Sec-tion 2.2 were used to capture the acoustic signal of the mill whilerotating with the charge. The microphone is mounted on the millshell and rotates with the mill. The position of the microphone istracked through adding a ngerprint to the acoustic signal everytime the microphone passes by a certain point. To detect the posi-tion of the microphone, a bber unit proximity sensor has beenused. At any time the sensor detects the microphone, a voltage isgenerated; this voltage becomes amplied and nally activates abuzzer. Since the frequency of the sound generated by this buzzeris unique, it can be distinguished from other sound sources in the</p><p>1442 P. Hosseini et al. /Minerals Engineering 24 (2011) 14401447quently, the relationship between acoustic pressure p(t) and im-pact force i(t) can be expressed using the convolution integral(Phillips et al., 2008):</p><p>pt it ht Z 11</p><p>isht s ds 1</p><p>where h(t) is the system impulse response to the impacts at a spe-cic position. By applying the Fourier transform to both sides of Eq.(1), the time domain convolution integral becomes a multiplicationin the frequency domain (Phillips et al., 2008):</p><p>Pjx Ijx Hjx 2where P(jx), I(jx) and H(jx) are Fourier Transforms of p(t), i(t) andh(t) respectively. To obtain the impulse response in time domain,the Inverse Fourier Transform, then, is applied to the Eq. (2),</p><p>ht F1 PjxIjx</p><p> 3</p><p>If the force exerted by impact hammer is assumed to be an ideal im-pact a perfect impulse that has an innitely small duration causingFig. 2. Excitation exerted by impact hammer inside the mill shell (top), and response tosignal. The sensor has been used during the whole measurement;however, once the location of the microphone is known at a spe-cic time, its position can be found thereafter using the mill rota-tion speed.</p><p>3. DEM simulation</p><p>The DEM simulator used in this work has been originally devel-oped for broader research purposes in comminution, includingbreakage efciency, and mill equipment design. DEM, in general,is a numerical iterative method which calculates the dynamics ofa discontinuous system of particles (Cundall and Strack, 1979). Inthe case of tumbling mills, it is the charge of the mill that is repre-sented by a collection of particles of dened properties. As shownin Fig. 4, at each cycle or time step, the calculator initially resolvescollisions and calculates the corresponding forces generated bythese collisions. The collision forces along with external forces,such as gravity or electrostatic forces are subsequently applied tothe appropriate particles. By repeating this calculation cycle, thesimulator generates trajectories and forces of particles as athe excitation captured by a pressure microphone on the mill shell (bottom).</p></li><li><p>Fig. 3. A typical impulse response.</p><p>P. Hosseini et al. /Minerals Engineering 24 (2011) 14401447 1443function of time. The time step of the simulation, varying from 10to 100 microseconds, is dynamically adjusted to achieve the bestpossible compromise between precision and performance.</p><p>While different contact models may be used to describe thecontacts in DEM simulations (Zhu et al., 2007), here the softwareadopts the linear spring-dashpot contact model (Cundall andStrack, 1979; Martins, 2011; Xiang et al., 2009). The tangentialcomponent (ft) and normal component (fn) of interparticle contactforce in this model are calculated as below,</p><p>Fig. 4. Calculations steps of the DEM.</p><p>Fig. 5. Demonstration of charge motion obtainfn Kndn~n 2Knm</p><p>pfn~v ~n~nR p 4</p><p>Table 1Parameters of simulation and contact model.</p><p>Parameter Value</p><p>Drum, d l (cm) 152.4 30.5Normal viscous damping ratio 0.3Tangential viscous damping ratio 0.4Normal stiffness (N/m) 10,000Tangential stiffness (N/m) 20,000Particle diameter, D (mm) 50.6Particle density (g cm3) 0.49Sliding friction coefcient 0.5Filling percentage of the mill (%) 30Rotation speed of the mill (rpm) 24ft minflfn;Kt ~v dt 2 Ktm ft~v ~n ~ngwhere dn is the r...</p></li></ul>

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