Exploring total media wear

Exploring total media wear P. Radziszewski Mechanical Engineering Department, McGill University, 817 Sherbrooke Str. West, Montr�eeal, Canada H3A 2K6 Received 28 December 2001; accepted 20 September 2002 Abstract The goal of this paper was to explore total media wear by defining a total media wear model incorporating abrasive, corrosive and impact wear mechanisms, develop three ore–metal–environment specific laboratory tests to determine model parameters, and calibrate and verify model with real system data. The development is based on the possibility of estimating energy dissipated in impact and abrasion by using a discrete element charge motion model for mill simulation. The results show, for the cases studied, an improvement in the predictive ability of this methodology as compared with the Bond abrasion test. Further work is needed in order to improve test procedure. � 2002 Elsevier Science Ltd. All rights reserved. Keywords: Comminution; Grinding; Modelling; Mineral processing; Simulation 1. Introduction Typical mining operating costs can be divided be- tween extraction (30–70%), comminution (30–50%) and separation (5–20%). Comminution process costs, re- presenting an important contribution to mining operat- ing costs, can themselves be divided roughly between energy (50%) and liner/charge wear (50%). With respect to wear, world-wide steel consumption as grinding media is estimated at over 600,000 tonnes per annum (Malghan, 1982). As such, developing the ability of predicting mill wear will allow a more accurate estima- tion of wear costs. Charge media wear prediction is actually estimated using the Bond abrasion test (Weiss, 1985). From Bond abrasion index tests, it is possible to determine a wear rate using the following function: Wear=energy ¼ 0:159ðAi � 0:015Þ0:33 ðkg=kWhÞ ð1Þ From a number of different ores, the resulting wear/ energy values can be compared with that observed as shown in Fig. 1. For the results shown, the average error is )73% with a standard deviation of 192.5%. These differences can be explained in many ways, the principle one being that the abrasion test checks only abrasion wear in conditions atypical of cascade type mills. Total media wear in a given ball mill grinding process is a product of three recognised wear mecha- nisms – abrasion, corrosion and impact (Rajagopal and Iwasaki, 1992). Furthermore, the contribution to total media wear of each of these wear mechanisms has not been well established (Yelloji Rao and Natarajan, 1991). Based on these observations, as well as the impor- tance of wear in milling costs, total media wear predic- tion could very well be improved by integrating impact/ abrasion/corrosion wear mechanisms in a total media wear model. The goal of this paper is to explore the possibility of such a model. Essentially, the paper will address three objectives (Radziszewski, 1997): ii(i) propose a total wear model incorporating abrasive, corrosive and impact wear mechanisms; i(ii) develop three ore–metal–environment specific labo- ratory tests to determine model parameters; (iii) calibrate and verify model with real system data. 2. Background A tumbling mill, whether it be autogenous, semi- autogenous, ball or rod, is a system composed of a number of interrelated and interactive elements that work together in order to grind a given ore. This comminution process is achieved by individual balls that constitute the actual ball mill element which brings about ore breakage. Together, these balls form the mill ball charge which, during ball mill operation, typically has a charge profile as found in Fig. 2. 0892-6875/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved. PII: S0892-6875 (02 )00228-5 Minerals Engineering 15 (2002) 1073–1087 This article is also available online at: www.elsevier.com/locate/mineng Note that the charge profile shows three zones that are characterized by the type of breakage occurring there. The grinding zone is described by ball layers sliding over one another breaking the material trapped between them; the tumbling zone is described by balls rolling over one another and breaking the material in low-energy impact; the crushing zone is described by balls in flight re-entering the ball charge and crushing the material in high-energy impact. The form of the charge profile is directly dependent on the friction force existing between the charge and the ball mill wall. By the use of different liner profiles, the friction force can be changed and consequently affect the form of the mill charge as well. Currently, in comminution research, recent trends have been made to describe internal dynamics of mills using the discrete element method (DEM). Presently there exist at least eight efforts to apply the DEM to charge dynamics: • Mishra/Rajamani (MillSoft) (1994a,b), • Inoue/Okaya (tumbling mill software site on the In- ternet) (1996), • Cleary (CSIRO) (1998), • Mintek�s work in 3D DEM modelling of charge mo- tion [Hinde, 1998], • Wits University effort in modelling nutating mills us- ing DEM [Nesbit and Moys, 1998], • Powell/Nurick UCT (1996a,b,c) • Radziszewski agglomerated ball approach (Radziszewski, 1986; Radziszewski and Tarasiewicz, 1989; Tarasiewicz and Radziszewski, 1989; Rad- ziszewski and Morrell, 1998), • JKMRC contact model work of Zhang and Whiten (1998). Fig. 3 presents typical profiles for three of these ef- forts: Radziszewski, Powell/Nurick, Mishra/Rajamani (Radziszewski, 1999b; Radziszewski and Valery, 1999). Being able to simulate mill charge motion, it becomes possible to estimate power consumption (Fig. 4) as well as the energies dissipated in impact and abrasion as Nomenclature Ai Bond abrasion index (unity) Alball;Arball surface area of balls in lab mill and in real mill (m2) Eabr;Eimp energies dissipated in abrasion and impact (J) F force applied in abrasion (N) Fabr abrasion force (N) Fbatch batch mill abrasion forces (N) Hr media hardness (N/m2) f abrasion wear correction factor (unity) mabr;mimp mass of media worn in abrasion and in impact (g/s) _mmi wear rate of mechanism i (g/s) _mmabr; _mmimp; _mmcorr abrasion, impact and corrosion wear rates (g/s) _mmtotal; _mmbatch total and batch mill wear rates (g/s) nabr; nimp number of events in abrasion and impact at a given energy level (unity) _nnabr; _nnimp frequency of abrasive and impact events at a given energy level (1/s) x abrasion sliding distance (m) h; habr abrasive grain angle (degree) q media density (kg/m3) Fig. 2. Typical charge profile [14]. Fig. 1. Wear/energy results for the cases tested. 1074 P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 shown in Figs. 5 and 6. These energies can possibly be used to determine ore breakage and, with regards to the present work, mill liner and media wear. Moreover, as total media wear in a given ball mill grinding process is a product of three recognised wear mechanisms––impact, abrasion, and corrosion (Raja- gopal and Iwasaki, 1992)––it becomes possible to envi- sion defining a total media wear model by tying an impact and an abrasion wear model with the energies dissipated in impact and abrasion, as well as integrating a media corrosion wear model. 3. A total media wear model A total media wear model can be defined on the as- sumption that the effect of each wear mechanism can be independently determined which allows for a total media wear model to be defined as the summation of the wear result of each mechanism. _mmtotal ¼ X3 i¼1 _mmi ð2Þ where i ¼ 1; 2; 3 represents the abrasion, corrosion and impact wear mechanisms, respectively. It will be assumed that impact and abrasive media wear is a function of the energy dissipated in impact and abrasion as estimated by a charge motion simulation. Corrosive media wear is assumed to be a function of the media surface area present in a mill. Therefore, Eq. (2) applied to predict wear for a sim- ilar ore–metal–environment industrial context can be modified to: _mmtotal ¼ Xnabr i¼1 _mmabr iðEabr iÞ þ _mmcorrAlball Arball þ Xnimp j¼1 _mmimp j Eimp j � � ð3Þ In scaling from laboratory scale data to industrial scale for a specific ore–metal–environment condition experimented, the proportion that each mechanism plays in total wear product depends upon the impor- tance of the energies dissipated in impact and abrasion since corrosive wear, for similar environmental condi- tions, will be assumed to be the same per media surface Fig. 4. Observed vs predicted power (41 ball mills) (Radziszewski and Morrell, 1998). Fig. 5. Impact energy spectra for 4.75 m dia. Mill (45% filling, 12.5 cm top size ball, unit length). Fig. 6. Abrasion energy spectra for 4.75 m dia. Mill (45% filling, 12.5 cm top size ball, unit length). Fig. 3. Cadia 12 m SAG mill (75% critical speed, 20% charge volume, rectangular Hi-Lo lifters). P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 1075 area. It should be noted that the charge motion simu- lations used in the following development are those based on the model presented by Radziszewski and Morrell, 1998. 4. Three ore–metal–environment specific tests With respect to the proposed total media wear model, three ore–metal–environment specific wear tests are needed to determine the necessary wear models. The development of each wear test is outlined as follows (Radziszewski, 1999a). 4.1. Impact test development Earlier, from a materials science point of view, three- body opened high stress wear is considered as abrasive and associated with the tumbling and free falling grinding media (Yelloji Rao and Natarajan, 1991). This tumbling and free falling grinding media better describe the phenomena of impact associated with the energies dissipated in the tumbling and crushing zones of the ball charge motion profile (Fig. 2). Impact wear can possibly be characterized as shown in Fig. 7 (Rajagopal and Iwasaki, 1992; Yelloji Rao and Natarajan, 1991; Blickensderfer and Tylczak, 1989). As such, most studies concerning impact wear have been limited to laboratory scale mill testing methods where impact does not play a significant role (Yelloji Rao and Natarajan, 1991); however, a couple of studies (Gangopadhyay and Moore, 1987; Xu et al., 1991; Radziszewski and Tarasiewicz, 1993; Scieszka and Dutkiewicz, 1991) have addressed this subject. In addition, three impact testers found in the litera- ture (Blickensderfer and Tylczak, 1989; Xu et al., 1991; Scieszka and Dutkiewicz, 1991) present interesting as- pects for determining grinding media impact wear. Of these, the impact principle shown by the Scieszka and Dutkiewicz (1991) tester (Fig. 8) presents the most flexibility for obtaining impact wear/impact energy re- sults for different ore–metal–environment contexts. As presented by Scieszka and Dutkiewicz (1991), ‘‘the proposed method, which simulates the impact action in the tube mill, involves the use of an electromagnetic vibrator (EMV) and chamber with two balls inside’’. Using this orientation, an Eriez 40A magnetic drive and controller were appropriately modified allowing vibra- tion frequency variation and installed in a vertical po- sition (Fig. 9). The impact chamber was assembled with the bottom being formed of a cut steel (or chrome) ball as shown in Fig. 9. Thus, it is possible to test ball on ball impact using balls of the same composition and hard- ness. Preliminary tests were completed with four media types A, B, C, D from three mine sites, I, II, III. It should be noted that media type B contained 12% chrome. The tests at 50 Hz frequency ran for 2.75 h each with four balls per media type and two tests per ball. As for the 225 and 400 Hz frequency tests, they were run for 6 hours each with one ball per media type and two tests per ball. The average wear rates for these tests as a function of impact frequency can be found in Fig. 10. The impact chamber test provides, for a given ball type, a wear product as a function of the energy used in impact. Even though the impact chamber was designed with flexibility in mind, it is necessary to determine the energies involved in impact as both a validation of the starting hypothesis (Radziszewski, 1998) and as a step toFig. 7. Classification of impact wear (Misra and Finnie, 1980). Fig. 8. Simulative tribo-testing of phenomena inside the tumbling mill (Scieszka and Dutkiewicz, 1991). Fig. 9. Impact chamber test installation. 1076 P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 translate chamber agitation frequencies with actual ball impact energies. Simulating this same context using WorkingModel (see Fig. 11), it is possible to estimate the impact energies and impact frequencies in the chamber. With this in- formation, the wear product per the estimated energy level is determined by dividing the change in mass by the number of impacts that occurred over the test period. With an impact wear product for a range of energies, a relationship can be determined that describes the rela- tionship between impact wear and impact energy. The impact chamber vibration motion was defined so as to simulate the agitation motion found in the real case. Due to simplicity, the vibration drive overlapped the desired frequency into the electric current frequency of 50 Hz. This resulted in a frequency pattern for 400 Hz vibration as shown in Fig. 12. Kinetic energy is calculated with respect to the chamber that gives a distribution for 400 Hz as shown in Fig. 13. It is, of course, difficult to determine what is the en- ergy at the moment of impact. However, if the moment of contact is determined, one can then determine the energies involved in impact. As such, the contact force is also tracked during the simulation and gives a distri- bution as shown in Fig. 14. Being able to determine the energies involved in im- pact, the average impact energy is determined for the impact as well as the impact frequency. These results are presented in Table 1. Fig. 12. Chamber motion for 400 Hz. Fig. 13. Kinetic energy with respect to the impact chamber for 400 Hz. Fig. 11. WorkingModel representation of the impact chamber. Fig. 10. Impact wear as a function of impact chamber frequency. 0 500 1000 1500 2000 2500 3000 3500 0,E+00 2,E+05 4,E+05 6,E+05 Time [micro - s] Im pa ct F or ce [N ] Fig. 14. Contact force distribution for 400 Hz. P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 1077 Having thus described the energies involved in im- pact, it is possible to present the experimental results as a function of these energies as shown in Fig. 15. Even though the results are sparse, one can propose an exponential function to approximate each set of data. These equations constitute an empirical approximation for an impact wear model describing wear mimp as a function of impact energy Eimp. In other words, these equations describe the wear product of an individual impact as a function of the energy involved in that im- pact. For media type B, the resulting exponential func- tion is: Media B : mimp ¼ 0:0479e�8:8387Eimp ð4Þ 4.2. Abrasion test development Several authors have studied the mechanisms of abrasion (Blickensderfer and Tylczak, 1989; Durman, 1988; Eyre, 1976; Gangopadhyay and Moore, 1985; Garrison, 1987; Huard et al., 1987; Iwasaki et al., 1985a,b; Iwasaki et al., 1988; Jang and Iwasaki, 1992; Khruschov, 1974; Meulendyke and Purdue, 1989; Misra and Finnie, 1980, 1981a,b, 1983; Moore, 1974; Norman, 1980; Norman and Loeb, 1948; Perez, 1982; Pitt et al., 1988; Prasad and Kosel, 1984; Sailors, 1989; Scieszka, 1989; Zum Gahr, 1979; Zum Gahr and Eldis, 1980. Generally, from a materials science point of view, these studies fall into the classification found in Fig. 16. As applied to the ball media wear context (Yelloji Rao and Natarajan, 1991), abrasive three-body opened high stress wear is considered to be associated with tumbling and free falling grinding media while abrasive three-body opened low stress wear is considered to be associated with slippage and partial falling of balls or rods. However, with regards to the previous description of charge motion, the abrasive wear mechanism, as de- fined as the removal of surface material by rubbing or grinding down surfaces (Yelloji Rao and Natarajan, 1991), is assumed to be associated with the energy dis- sipated in the grinding zone where ball layers slide over one another. This effectively describes grinding zone abrasion as three-body open low stress wear which can be studied using three-body abrasion testers. Of the few found in the literature (Misra and Finnie, 1980), the abrasion wheel (Fig. 17) seems to be the most easily modifiable for the needs of determining the abrasive wear characteristics of grinding media. Here, abrasive wear, or the volume of material removed, and energy, a function of the applied force F and the distance slid x (rotation speed � wheel circumference � time worn), is described using an abrasive grain represented by angle h illustrated using Fig. 18. The relationship between wear and energy, can be described using the following relationship: the abrasion wheel test determines abrasive wear as a function of the weight (applied force F ), the test specimen (hardness Hr, metal density q), the abrasive used (abrasion grain angle h) and the distance slid (x ¼ rotation speed � Table 1 Average impact energy and frequency Impact chamber frequency (Hz) 50 225 400 Maximum impact energy (J) 0.0063 0.0334 0.1924 Number of impacts 26 11 12 Average impact (J) 0.0024 0.0146 0.0634 Impact frequency (1/s) 104.4177 42.1779 25.1362 Fig. 16. Abrasive wear classification (Misra and Finnie, 1980). Fig. 15. Impact wear as a function of impact energy. Fig. 17. Abrasion wheel general set-up (Misra and Finnie, 1980). 1078 P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 wheel circumference �time worn) described as a func- tion of the energy dissipated in abrasion, Eabr, abrasion grain angle h, hardness Hr and metal density q (Rabi- nowicz, 1996): mabr ¼ q tanðhÞpHr Eabr ð5Þ where mabr represents metal loss per ball, the energy Eabr is dissipated in grinding on one ball and Hr, q are metal hardness and density, respectively. Increasing energy dissipated on a ball increases metal loss independently of ball size. In other words, for the same energy dissipated in abrasion on two balls of dif- ferent diameter, metal loss would be the same, which for a large ball would represent a smaller diameter change than for a small ball. Initial test conditions are summarized in Table 2 and the abrasion test results as a function of energy are shown in Figs. 19 and 20. When running the abrasion wheel test, it was ob- served that as the abrasive ore grains passed between the steel wheel and the media specimen, a number of abra- sive grains were broken. This grain breakage was ac- companied by distinct breakage noises which increased in number with increased applied force on the abrasion wheel. Although no before and after sizing on the abrasive ores used or measurement of the frequency of breakage noises were made, it was suspected that the breaking grains would affect the abrasion angle used in the wear model of Eq. (5). Therefore, it was decided to calculate the abrasion angle as a function of the applied force on the abrasion wheel. The results shown in Fig. 21 illustrate generally that the abrasion angle is a func- tion of the applied force and can not be considered a constant value. From these results, a number of exponential func- tions can be determined to describe the relationship between abrasion force and the resulting abrasion angle. The resulting equation for abrasion of media type B with an Au oxide ore gives Mine II : oxide�mediaC : habr ¼ 0:1012e�0:0168Fabr ð6Þ These relationships can now be used to determine abrasive wear using the following equation Table 2 Test specifications Ore Mine I: Pb/Zn, Cu ores, Mine II: oxide, sulphide Au ores Mine III: Au ore Sample size: all 100% )850 lm Media 5� 4 halves, media A (ave. hardness �62.1 HRC), 5� 4 halves, media B (ave. hardness �63.2 HRC), 5� 4 halves media C (ave. hardness �61.9 HRC), 5� 4 halves media D (ave. hardness �57.2 HRC), Abrasion wheel: 290 mm dia. mild steel wheel, Abrasion wheel rotation speed 214 rpm rotation speed, Wheel tangential velocity 2.57 m/s Applied abrasion wheel force range �20–140 N (2–14 kg) Test time per specimen 120 s Fig. 19. Abrasion test using Mine I ore. Fig. 20. Abrasion test using Mines II and III ores. Fig. 18. Abrasion wear description (Rabinowicz, 1996). P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 1079 mabr i Fabr ið Þ ¼ q tan hðFabr iÞð ÞpHr Fabr ix ð7Þ where x is the abrasion sliding distance is a product of the wheel circumference, the rotation speed and the wear test time. As applied to a given mill, the sliding distance is determined by the slippage speed between ball layers and the simulated time interval. 4.3. Corrosion test development Corrosive wear of metals in an aqueous solution can be characterized as (Dorlot et al., 1986, pp. 202–223): • electrochemical where equilibrium potential deter- mines the presence of corrosion; • corrosion current determines the corrosion rate and is a function of electrode polarisation; • polarisation has two mechanisms: activation and dif- fusion, where activation is dependent on the metals involved, the electrolyte and the temperature and dif- fusion is dependent on electrolyte agitation; • pacification by protective film growth can slow down if not stop corrosion and can lead to an asymp- totically time decreasing corrosion rate if the protec- tive film is not removed. This characterization can be explained graphically using Fig. 22 (Rabinowicz, 1996, pp. 212–213). With regards to the characteristics of corrosive wear, it will be assumed that for corrosive environments having similar metals, electrolytes, temperatures and agitation, corrosive wear per ball of like diameter will be the same. For balls of different diameter yet similar in ore–metal–environment context, wear per ball is pro- portional to surface area. Under comparable assumptions, several authors have studied the mechanisms of corrosion (Adam and Iwasaki, 1984; Adam et al., 1984; Austin and Klimpel, 1985; Baker et al., 1990; Briceno and Chander, 1988; Burton, 1966; Chander and Briceno, 1987; Dean et al., 1971; Forssberg and Subrahmanyan, 1993; Fuerstenau et al., 1985; Greef et al., 1985; Gundewar et al., 1990; Guy and Trahar, 1984; Hoey et al., 1977; Iwasaki et al., 1973; Iwasaki et al., 1985a,b; Jacobson et al., 1987; Katzer et al., 1981; Klimpel, 1982; Klimpel andManfroy, 1978; Learmont and Iwasaki, 1984; Martin et al., 1991; Moore et al., 1988; Narayanan et al., 1983; Natarajan, 1992; Natarajan, 1996; Natarajan and Iwasaki, 1984; Natarajan et al., 1984a; Natarajan et al., 1984b; Pazhi- anur et al., 1996; Pozzo et al., 1990; Senior et al., 1989; Shinozaki and Semma, 1981; Thorton, 1973; Vang et al., 1989; Vathsala and Natarajan, 1989; Wang and Xie, 1992; Yelloji Rao and Natarajan, 1988a,b,c, 1989a,b, 1990). Corrosion of ball mill media and its effect on flotation has generally been studied as ore–metal–envi- ronment specific as determined in laboratory batch mills. In laboratory scale tests, corrosion can represent anywhere from 25% to 75% of metal loss depending upon the ore–metal–environmental factors involved (Yelloji Rao and Natarajan, 1991). Furthermore, cor- rosion represents less than 10% of total metal loss in typical large diameter ball mills (Rajagopal and Iwasaki, 1992). This observation confirms, at least tentatively, that the corrosion rate for a similar ore–metal–envi- ronment context will be the same independent of mill size. Increasing mill size increases the energy dissipated in grinding, tumbling and crushing which in turn would increase metal loss through abrasive and impact wear. Corrosion wear investigation has followed similar de- velopment amongst several authors of which Gundewar et al. (1990) and Natarajan (1992) present a good de- scription of the experimental procedure used. Fig. 21. Abrasion angle as a function of abrasive force. 1080 P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 As the corrosion tests are performed in a ball mill, the resulting wear is a sum of both essentially abrasive and corrosive mechanisms. In order to isolate the contri- bution of corrosion wear, it becomes necessary to use the results of the previous abrasion test to determine abrasion wear as a function of the energy dissipated in abrasion and subtract it from the observed wear as follows: _mmcorr ¼ _mmbatch � _mmabr Fbatchð Þ ð8Þ The corrosion test apparatus consists of a stainless steel batch mill run at 70% critical speed with approxi- mately 40% filling (known media initial mass). The mill and associated media are preheated to 70 �C. After filling the mill with the media and ore, the mill process water, which was preheated to 70 �C, is added. The mill is bolted shut and run for 2 h. The mill is subsequently emptied after a temperature reading is taken, and the mill media is cleaned and dried using an acetone wash. Media mass is measured. The corrosion test results are found in Figs. 23–25. In order to determine the contribution of corrosion to total batch mill wear, it is necessary to determine the contribution of abrasion as shown in Eq. (8). Batch mill charge motion is therefore simulated, and abrasion forces are determined since wear by impact is considered negligible as compared to total batch mill wear. These results are presented in Figs. 26 and 27. Fig. 28 shows abrasive wear spectra for Mine I Cu ore and media A combination. Using this procedure, it is possible to determine batch mill abrasive wear for each metal-ore combination. Fig. 23. Corrosion test results using Mine I Cu and Pb/Zn ores with media types A and B. Fig. 24. Corrosion test results using Mine II ores with media types B and C. Fig. 25. Corrosion test results using Mine III Au ore, media D in bore and circuit water. Fig. 22. Accumulated corrosive wear process (Rabinowicz, 1996). P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 1081 Comparing the abrasion wear results with those of the batch wear, one notices that the abrasion wear result is greater in many cases than the batch wear result. This may be due to a number of factors, the principle being dry conditions during the abrasion wheel wear test. A correction factor is in order where the corrosive wear result would be determined as _mmcorr ¼ _mmbatch � f _mmabrðFbatchÞ ð9Þ Yelloji Rao and Natarajan (1991) observed that ‘‘. . . in laboratory tests, corrosion can represent anywhere from 25% to 75% of metal loss depending on the ore–metal– environmental factors involved’’. Based on this remark, a correction factor (f ) of 0.0235 was determined that for corrosion gave the average percentage of total batch wear of 60.3%. In order to determine a specific corrosion rate that can be used to determine total corrosion for any mill, the corrosion rate is divided by the surface area of the balls used in the batch mill. Results for Au oxide with media B can be found in Table 3. 5. Wear model verification Based on the assumption that total media mill wear can be determined using a de-coupled wear model (Eq. (3)), it was possible to experimentally identify, in the laboratory using ore, water and media samples from industry, impact, abrasive and corrosive wear as a func- tion of energies, forces and materials. However, in order to verify the promise of the above assumption, it now becomes necessary to determine if combining these ex- perimental results through the proposed total media wear model of Eq. (3) does indeed improve total media wear prediction. To this end, the following procedure is defined in order to determine the total media wear for the mills tested. iiii(i) Use impact wear test to determine relationships between impact energy and impact wear for differ- ent media compositions. iii(ii) Use abrasion wear test to determine relationships between abrasive force and abrasive angle for dif- ferent ore-media compositions. ii(iii) Use batch corrosion wear test as well as well as abrasion wear results to determine specific corro- Table 3 Specific corrosion wear from batch mill test: Au oxide and media B Ore/media Batch wear (g/s) Abrasion wear (g/s) Corrosion wear (g/s) % of Total batch Specific corrosion wear (g/m2 s) Mine II: Au oxide and media B 0.00091 0.018963 0.0004655 51.1 0.0018730 Fig. 26. Batch mill charge motion profile (dia.: 0.295 m, 70% crit. speed, 40% charge vol., length: 0.258 m). Fig. 27. Abrasion force spectra for a batch mill (dia.: 0.295 m, 70% crit. speed, 40% charge vol., length: 0.258 m). Fig. 28. Abrasion wear product spectra for a batch mill (Mine I Cu, media A) (dia.: 0.295 m, 70% crit. speed, 40% charge vol., length: 0.258 m). 1082 P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 sion wear rates and abrasion wear correction fac- tor (see Eq. (9)). ii(iv) Use charge motion simulation to determine con- sumed power as well as the impact energy and abrasion force spectra. iii(v) Couple impact energy and abrasion force spectra with the relationships for wear and impact and wear and abrasion of points (i) and (ii) to deter- mine impact and abrasive wear rate. ii(vi) Determine media surface area and multiply with specific corrosion wear rates to determine mill cor- rosion wear. i(vii) Summate impact, abrasion and corrosion wear rates for total media wear rate estimation. (viii) Finally, divide the total media wear rate by the consumed power. Applying this procedure would produce results as il- lustrated by Eqs. (4) and (6) and corrosion results found in Table 3 for steps (i)–(iii). Total mill power is deter- mined as 7.61 kW. Step (iv) would produce for a given mill results such as those illustrated in Figs. 29–31. Step (v) is initiated by knowing the wear product of an individual impact as a function of the energy in- volved in that impact, Eimp j, and number of impacts at a given energy level, _nnimp j (Fig. 30), then the product of these two entities will give us the impact wear product over the energy spectra in the mill (Fig. 31): _mmimp jðEimp jÞ ¼ _nnimp jmimp jðEimp jÞ ð10Þ where j is a given impact energy interval. Similarly, knowing the wear product of an individual abrasion as a function of the force involved in that abrasion, Fabr i, and number of abrasions at a given force interval, _nnabr i, (Fig. 32) gives us the abrasive wear product at this force interval as shown in Fig. 33: _mmabr i ¼ f _nnabr imabr iðFabr iÞ ð11Þ where i is a given abrasion force interval and f is the correction factor determined in Eq. (9). Summing over the curve for both impact and abra- sion for the mill simulation in Fig. 29, gives the results found in Tables 4 and 5 and thus completing step (v). Steps (vi) and (vii) produce the results found in Table 6 for total media wear for the simulated mill. The resulting ratio of point (viii) can now be deter- mined. This ratio for the simulated mill is 0.0856 kg/kWh. Applied to all the media/ore/water/mills tested and then compared with results of the Bond abrasion test presented in Fig. 1, the above procedure gives the results Fig. 29. Charge motion profile (dia.: 1 m, 70% crit. speed, 35% charge vol., length: 1 m). Fig. 30. Impact energy spectra for a ball mill (dia.: 1 m, 70% crit. speed, 35% charge vol., length: 1 m). Fig. 31. Impact wear product spectra for a ball mill (Media A) (dia.: 1 m, 70% crit. speed, 35% charge vol., length: 1 m). Fig. 32. Abrasion force spectra for a ball mill (dia.: 1 m, 70% crit. speed, 35% charge vol., length: 1 m). P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 1083 presented in Fig. 34. As seen earlier, the overall average error for the Bond abrasion index results, as compared with the observed cases tested was )73% with a standard deviation of 192.5%. While for the total media wear model (Eq. (3)), the overall average error as compared with the observed cases is 0% with a standard deviation of 66.1%. 6. Discussion With regards to the impact test, WorkingModel al- lowed the simulation of the impact chamber. In order to improve this simulation, further experimentation will be needed. However, the simulation results show that the velocities involved in impact for chamber vibration of 400 Hz are in the order of 0.9 m/s which represent the impact velocity of a 4 cm drop. This is far from the drop heights that would be experienced in large diameter mills. However, this test technique illustrates well the energies involved in tumbling low energy impact. As for the abrasion test, the differentiation between wear rates using different media and ore types is signifi- cant and in the expected directions. The average corrosion wear proportion, for the cases studied in the corrosion test, has decreased from the batch mill case of 60.3–45.9%. This approaches the ‘‘. . . less than 10% of total metal loss in typical large diameter balls mills’’ (Rajagopal and Iwasaki, 1992). Media wear is sensitive to changes in media and ore type as well as make-up water and temperature. The model needed some calibration when simulating real cases. The correction factor was 0.0235 of Eq. (9) determined from the specific corrosion rate and used in the 1� 1 m2 test mill (Table 6). However, in order to obtain an average error of 0% over the tested mills, as found in Fig. 34, the correction factor was increased to 0.1668.Using this factor reduced the effect of corrosion for the mills tested from an average of 74.78% (f ¼ 0:0235) to an average of 40.63% (f ¼ 0:1668) which is not ‘‘. . . less than 10% of total metal loss in typical large diameter balls mills. . .’’ (Rajagopal and Iwasaki, 1992) but definitely converging to it. 7. Conclusions As presented in the introduction, the objectives of this paper were to explore the possibility of integrating im- pact/abrasion/corrosion wear mechanisms in a total media wear model by addressing three objectives ii(i) define a total wear model incorporating abrasive, corrosive and impact wear mechanisms; i(ii) develop three ore-metal-environment specific labo- ratory tests to determine model parameters; (iii) calibrate and verify model with real system data. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0 5 10 15 20 Bond Work Index Wi W ea r/E ne rg y [k g/ kW h] Wear Bond Rate Wear Real Rate Wear MB Rate Au oxide Au sulphide Au ore Cu ore Pb/Zn ore Fig. 34. Wear/energy results for the cases tested. Fig. 33. Abrasion wear product spectra for a ball mill (Mine I/Media A) (dia.: 1 m, 70% crit. speed, 35% charge vol., length: 1 m). Table 6 Total wear for the 1� 1 m2 simulated ball mill Ore/media Impact wear (g/s) (% total) Corrected abrasion wear (g/s) (% total) Corrosion wear (g/s) (% total) Total wear (g/s) Total wear (kg/day) Mine II: Au oxide and media B 0.0000635 (0.0004) 0.1067 (59.0) 0.0741 (41.0) 0.1810 15.6 Table 5 Total abrasion wear for a 1� 1 m2 ball mill Media Total corrected abrasion wear (g/s) Total abrasion wear (t/day) Mine II: Au oxide and media B 0.1067 9.218 Table 4 Total impact wear for a 1 m ball mill Media Total impact wear (g/s) Total impact wear (g/day) Media B 0.0000635 5.49 1084 P. Radziszewski / Minerals Engineering 15 (2002) 1073–1087 All three objectives were attained and can be de- scribed as follows. A total media wear model was defined incorporating abrasive, corrosive and impact wear mechanisms. The total media wear model is of a decoupled nature that permits the individual identification of each wear mech- anism. However, this decoupling experimentally as- sumes that such a decoupling is possible and will not greatly affect the resulting analysis. Three ore–metal–environment specific laboratory tests were developed in order to identify the model para- meters for this decoupled total media wear model. In the case of impact, the laboratory set-up did not attain the expected high impact energy levels. However, some experimental data was generated allowing the definition of an impact wear/impact energy relationship for different mill media. In the case of abrasion, the laboratory set-up per- formed as expected in the range of applied abrasion forces. However, these forces were greater than those experienced in a batch mill and less than those experi- enced in a real mill. This undoubtedly contributed to the use of different correction factors (0.0235 for the batch mill and 0.1688 for the real mills). In the case of corrosion, the stainless steel batch mill test also performed as expected. However, it is impor- tant to note that the specific corrosion rate calculation is based on the assumption that the decoupled model works and that the abrasion wear test data can be in- dependently determined. Model calibration and verification, of course, is de- pendent on the data obtained from industry. However, as these tests were of an exploratory nature, it can be said that this was achieved with a measure of success. The total media wear model is sensitive to changes in media, ore and environment, and illustrated total wear as a function of the proportions in impact, abrasion and corrosion wear. It is understood that abrasive and corrosive wear mechanisms, if present together, are a coupled phe- nomenon. One can therefore expect that proposing a total media wear model as a function of three decoupled wear models will not completely describe the wear en- vironment of a typical tumbling mill. 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Radziszewski / Minerals Engineering 15 (2002) 1073–1087 1087 Exploring total media wear Introduction Background A total media wear model Three ore-metal-environment specific tests Impact test development Abrasion test development Corrosion test development Wear model verification Discussion Conclusions Acknowledgements References