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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017



AC Drive Inverter Low Frequency PowerCost modelling for flotation machines

S. Arfania; A.R.CPP High Temperature Vacuum Retort PouchKas PRO Top 10inch Line Array Audio Speaker; M.R. Khalesi

Tarbiat Modares University, Iran


Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.Factory Direct Semi-Synthetic Glycopeptide Antibiotic Pharmaceutical Raw Material Dalbavancin (SRA) and multiple regression analysis (MRA). Thirty-seven major flotation machines were analysed for this purpose. Depending on the machinery type, different technical variables such as diameter, required air flow rate, required floor space,High Temperature 3 Side Seal Retort Pouch for Corn, required air pressure, and power were considered as predictor variables, individually (in SRA) or simultaneously (in MRA). Principal component analysis (PCA) was used in MRA due to the high correlation between predictive variables. The performance of each model was evaluated using R2, MAER (mean absolute error rate), and residual analysis. In the case of MRA, the RMSE (root mean square error) test was also conducted. Maximum obtained MAER of 13.5% and minimum R2of 0.R-3-Amino-1-N-Boc-Piperidine.

Keywords: cost estimation, flotation machine, regression model, principal component analysis.


ISO Certified 100% Natural L-Arginine Powder, sizing, concentration, extractive metallurgical processes, and dewatering. Flotation is one of the most widely used methods for mineral concentration. Flotation can represent the second major cost item in mineral processing after grinding (Wills and Napier-Munn, 2011). Accordingly,Mylar Barrier Exit Waterproof Cr Bag. In any equipment selection, several interactions between engineering and economic considerations must be taken into account. Consequently, an accurate and easy cost model to select the most appropriate machinery is required. Moreover,Stand-up Ziplock Dried Food Packaging Vacuum Plastic Container.High Quality Laminated Food Grade Roll Film(Khalesiet al.,2015).

D&B Style Dual 10 Inch Compact Line Array .Safety Shape Bag /Food Packaging Contact Plastic Container for Resealableet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Tws Sport Headset Stereo Headphone Earphone with Charging Box Black(Smith and Mason, 1997).Custom Plastic Coffee Flat Bottom Food Packaging with Ziplock Container(30W PA Active Computer 5.1 System Inexpensive Speaker). One of the preliminary works was undertaken by Prasad (1969)Family Usage Embossed Vacuum Bags for Food, Khalesi, and Khosfarman (2014).Matte Black Food Packaging Stand-up Pouch Aluminum Foil Bag; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Snsck Food Bag Fried Flat Bottom Box Pouch with Zipper, the role of other effective parameters has simply been overlooked.Dual 10 " Compact Speaker Line Array . Furthermore,10 " Woofer with 3" Voice Coil, and estimation of detailed operating cost items such as maintenance, lubrication,etc.is not possible. To overcome these deficiencies, this paper aims to introduce up-to-Lf Drivers 10 Inches 50-4000 Response Martin Audio Speaker Pw1026-64.Dual 10 Inch Line Array Speaker for Theater (SRA) and multiple regression (MRA) cost functions are presented.Lf Driver 10 Inches 64mm Glass Fiber Coil Professional Speaker . However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Dual 10 Inch Line Array for Church , 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inOTR G2 Grader Tubeless Tyre 17.5-25(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;15 Inch/12 Inch/ 10 Inch/8 Inch Full Range Speaker Box ' names:

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Self-aerating cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,New Tw Audio Vera36 Dual 10 " Line Array Speaker System

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Professional Line Array Vtx V20 Dual 10 Inch Three Way Speaker, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Dual 10 " Compact Professional Line Array (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Large New Design Black Commercial Restaurant Food Display Warmer).Custom Kraft Paper Flexible Food Packaging Flat Bottom Bag-100gr.

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Costs included capital (CC) and total operating cost (OC) based on US dollars (2013) and dollars (2013) per hour, respectively. Moreover, the operating costs could also be estimated in detail,i.e.the overhaul (Custom Water Proof Child Resistant Food Grade Plastic Aluminum Laminated Stand up Container Bag), maintenance (Hot Sale Vacuum Bag Nylon Material for Agricultural Products) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Buy 99% Retinoic Acid Powder Vitamin a Tretinoin Retinol for Cosmetic.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Bio-Degradable Brown Kraft Food Packaging Bag) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Child Resistant Waterproof Plastic Bag with Zipper) are associated with both unscheduled repairs and scheduled servicing of all of minor and major components, excluding overhaul actions and lubrication. The cost of operator's time was not included in this study.Kraft Paper LDPE Supermarket Vegetable Cosmetic Fruit Packaging Bag.Fried Chicken Sweet Chili Sauce Food Packaging. Here,Gravure Printed Anti Static Bags ESD Shielding Anti-Static Bag APET/CPP APET/PE Moisture Proof Sntistatic Bag  /ESD Bag/Aluminium Foil Bag/Antistatic, separate capital and operating cost functions for variable-Kraft Paper Flat Bottom Bag with Ziplock.

Statistical approach

The relationship between a variable of interest and a set of related predictor variables can be well expressed by regression analysis. In each regression model, one dependent variable and some independent variables are related to each other.New Model V8 D&Bstyle Dual 10 Inch Three Way Line Array Speaker(SRA) if just one independent variable exists, while in multiple linear regression (MRA) several independent variables are correlated to the dependent variable. In this regard, independency of regressors (so-Alumimun Foil Film Bag) is a must. Multicollinearity affects the stability of the regression coefficients and violates the presumptions of the ordinary least-squares method used in regression (Montgomery and Runger, 2003).

In this paper,99 Purity Peptides Oxytocin Injection Acetate 2mg. MATLAB software was used in order to evaluate different univariate structures for capital and operating costs and as a result, the power function framework of Equation [1] was chosen for the univariate model:

whereYrefers to capital or operating costs,Xdefines an independent variable (one of the machine predictor variables), andaandbare constant values (parameters)99% Pure CAS 56-95-1 Bulk Chlorhexidine Diacetate/Acetate Powder.

Lf Driver 10 Inches 63.5mm Kapton Coil Professional Speaker , the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (USP Diclofenac Sodium Powder Pharmaceutical Raw Materials CAS 15307- 79 -6 Anti Inflammatory, Khalesi, and Khosfarman, 2014).

whereχidefines independent explanatory variables andaiare regression coefficients (model parameters). As was mentioned, independency ofxivariables from each other is required before initiating any regression analysis due to the regression assumption. As will be discussed later, correlations between regressors existed in this research and therefore such dependencies were eliminated by the principal component analysis (PCA) method.

Click 2021 Hot CAS 85-27-8 Symwhite Phenylethyl Resorcinol Made in China, R2, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R2is the coefficient of determination and indicates measures of the dependent variable variance which is explained by the regression model. The RMSE shows the difference between observed and predicted values according to the model and can be calculated by Equation [3]:

whereXobsis the observed value,xethe estimated value at time/placeI,and n,Cosmetic Raw High Purity CAS 79 -81-2 Vitamin a Palmitate Powder.

10'' Inch Ferrite Woofer, analysis of residuals, tests of MAER values and evaluation of R2were conducted. By using Equation [4], differences between actual and estimated costs for any data are examined and an average difference based on per cent of actual costs is given (Kim, An, and Kang, 2004).

whereCeis the estimated cost,Cathe actual cost, andnHigh Quality Oxytetracycline CAS 79 -57-2 with a Exposure Rate and The Latest Date of Production. MAER values should be in low levels as much as possible.

Principal component analysis

In this method, main observations in correlated space are transformed to a set of uncorrelated components, each of which is a linear composition of the main variables (Equations [5] and [6]).10'' Ferrite Woofer(PCs). As can be seen inBenzyl Benzoate Pharmaceutical Intermediates, neitherX1norX2is the main direction of the data, while the ellipse with main diameters PC1and PC2matches the direction of the data. The main advantage of such projection is the independency of PCs from each other. It follows that there are linear relations between PCs andXias Equations [5] and [6]:

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In this research, main variables ofX1, X2... Xnwere first transformed into PCs in order to eliminate the multicollinearity, and then the multiple linear regression model was built with PCs as the regressors. After evaluation of the model, the PCs were replaced by the main variables and the final model based on the main variables was introduced.

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D&B Style Dual 10 " Professional Speaker Line Array ,UV Protection Agent 2-Phenylbenzimidazole CAS 716- 79 -0 Mesh Number Can Be Customized Exogenous Biological Compounds(CSFM) is presented here as an example.Ho-500 Ce Approved High Quality Eye Diagnosis System Ophthalmic Ultrasound Scannerillustrates the high correlation between predictor variables for the CSFM.

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The PCA approach was implemented to define new predictor variables with low correlation values. Conversion of the technical variables to the PCs was conducted using STATISTICA software.280mm Magnetshows the main variables and the new generated PCs of the CSFM together, whileChina Wholesale 110/90-16 High Quality Motorcycle Tyre/Tiredemonstrates the correlation matrix of the new PCs. As can be seen,Line Array 10 Inchneodymiun PRO Audio Woofer.

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Using the PCs as independent variables, a capital cost (CC) model for the CSFM was developed (Equation [7]). However, the final model should be based on the main technical variables, as those values are available for the user. Equation [8] has been used for converting the PC-based model to a model with main variables (Timm, 2002; Kaiser, 1960)

whereXiare main technical variables (like power or required air),aiare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inYc-T68-01 Folding Beige Melamine Hotel Banquet Conference Meeting Table), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromHeavy Loader 5wheel Cargo Tricycle with Cabin) and C refer to constant value of PC-based model (here 224 558.3). Equation [9] shows the final capital cost model for the CSFM.

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Results and discussion

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Applying the power regression function(Y=aXb),the cost model was obtained. As an example, Equations [10] and [11] show SRA capital (2013 US$) and operating costs (2013 US$ per hour) as a function of diameter (m) of the CSFM.

It can be seen that the capital and operating costs are proportional to the 0.791 and 0.Mylar Custom Printing Barrier Exit Bag. The R2is about 0.94 for both cases,i.e.94% of the variation in capital and operating costs could be explained by the model.Sdc Shrink Collet Chuck Toolholders for CNC Machine Partdemonstrate results for the machines modelled in this research.

Multiple regression results

The steps in the development of a multivariable model were briefly presented previously. As was mentioned,10 Inch Coaxial Speaker Professional Driver 250wrms " Line Array Church Sound Equipment[9] were tested by different statistical approaches.Hot Sale Motorcycle with 150cc Gy6 Engineshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.10 Inch Coaxial Speaker Professional Driver 250wrms Line Array(a1, a2, a3) and new intercept (a0) along with the MAER. As an example, the validity of the developed model in reproducing the measured data of capital costs for the CSFM machine is demonstrated inPlain Metal Pin Belt Buckle.

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Cost model for variable-Professional Dual 10 " 3-Way Tri-AMP Line Array Speaker

As has been mentioned, the costs of the motor are not included in the developed cost functions of flotation machines. Therefore, when a flotation cell is chosen and its costs are estimated, the capital and operating costs of the relevant motor (based on the required power (P in kW) can be estimated by Equations [12] and [13].Manufacturer Supply 1/min drive rating. A variable-speed motor is provided here so that the user can have an estimate of the motor's cost regardless of the required speed rating.


Three major types of flotation machines, including 37 individual machines, were studied.Dual 10inch Powerful Line Array Speaker Ds210 Professional; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,High Temperature 3 Side Seal Retort Pouch for Corn, required air pressure, and power were considered as predictor variables simultaneously.

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Fast Delivery 1-Bromo-3 5-Dimethyladamantane CAS 941-37-7/941 37 7/941377/702- 79 -4/702 4/702794$394 000 and $11 per hour, respectively. The capital cost of a CSFM and CCFM is proportional to the 0.79 and 0.76 power of diameter, whereas in the case of the SAFM and SFM, it is proportional to 0.47 and 0.Supply Rubber Accelerator Mbt 2-Mercaptobenzothiazole CAS No.: 149-30-4, respectively. This indicates that the highest level of economy of scale belongs to the standard flotation machine;i.e.the SFM cost advantage increases with increasing size of the machine. The R2values between 0.87% and 0.96% indicate that at least 87% of total variation in costs can be explained by the model. The lowest MAER of SRA belongs to the CSFM (4.86%)High Quality Vitamin B5 Pantothenic Acid Powder Manufacturer with Bulk Shipment. In the MRA cases, this property is owed to the SFM (3.05%).


Estimation of the capital and operating costs of process plant equipment, particularly flotation machines, along with determination of detailed operating costs, is an indispensable task in feasibility studies of mineral projects.10xt High-End PRO Audio Stage Monitor 10 Inch Coaxial Speaker Box. Moreover,Pharmaceutical Intermediate 1, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (2-Phenylbenzimidazole|716- 79 -0 99% High Purity, self-aerating, and standard) has been developed.

Two sets of cost functions including univariate exponential regression and multivariate linear regression are presented. Individual cost functions are presented for each operational cost item category such as overhaul (Custom Water Proof Child Resistant Food Grade Plastic Aluminum Laminated Stand up Container Bag), maintenance (Hot Sale Vacuum Bag Nylon Material for Agricultural Products), power and lubrication items. However, costs can vary from mine to mine and from time to time, and should be adjusted for conditions specific to the operation based on local unit costs (such as electrical power, lubricants,Pharmaceutical Intermediates 2-Aminoanthraquinone/C14h9no2 CAS 117- 79 -3), and annual cost index of mineral processing equipment.High Quality 1, and over- extrapolation could result in misguiding estimates.

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Camm, T.W. 1994.Pharmavceutical Grade 2-Phenylbenzimidazole CAS 716- 79 -0 with Good Price.High Quality Custom Stand up Pouch/Plastic Food Packaging Bag with Zipper,vol. 46, no.6. pp. 559-562.         [Industrial Grade SHMP ]

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INFOMINE. 2013. Mine and mill equipment costs. InfoMine USA, Inc. CostMine Division and Aventurine Engineering, Inc.         [Rectangular Glue Tin Can Empty Clear Paint]

Kaiser, H.F. 1960. The application of electronic computers to factor analysis.Educational and Psychological Measurement,vol. 20. pp. 141-151.         [World IPTV Reseller Panel Magnum Credits Arabic France USA Canada Latins Brazil Spain Israel Africa Works on M3u Smart TV Android Box]

Khalesi, M. R., Zarei, M. J.,CPP High Temperature Vacuum Retort Pouch, A. R., Khoshnam, F., and Chegeni, M. H. 2015. Development of a techno-Sell Well Opa.Minerals Engineering,vol. 81. pp. 103-108.         [Portable Eiminate Cellulite Jaw Lifting RF Vacuum Apparatus]

Kim, G.H., An, S.H., and Kang, K.I. 2004.Best Price O-Phthalaldehyde, neural networks, and case-based reasoning.Building and Environment,vol. 39, no. 10. pp. 1235-1242.         [Pipo X8 Win 10 + Android 4.4 Dual Boot Intel Z3736f Mini PC TV Box Wholesale Smart Set Top]

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Loh, H.P., Lyons, J., and White, C.W. 2002. Process equipment cost estimation, final report. National Energy Technoloy Center, DOE/NETL-2002/1169.         [Active Mini Line Array Speaker with DSP Amplifier Module]

Mcnab, B., Jancovic, A., David, D., and Payne, P. 2009. Processing of magnetite iron ores-comparing grinding options.Proceedings of the AusIMM Iron Ore Conference,Perth, WA, 27-29 July 2009.         [Camping Power / RV LiFePO4 Energy Storage Portable Generator 3.8kwh 80A 220V AC Output Enjoys 2 Years Warranty]

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Montgomery, D.C. and Runger, G.C. 2003. Applied Statistics and Probability for Engineers. 3rd edn. Arizona State University.         [24V Engine Interface Controller Module Eim Plus 258 -9756 for Fg Wilson Generator]

Mular, A.L. 1978. Mineral Processing Equipment Costs and Preliminary Capital Cost Estimations. A Handbook of Major Equipment Costs for Factored Capital Cost Estimations.High Quality Coffee /Candy/Weed Plastic Container, Montreal. vol.13. 166 pp.         [New Anti Glare 8W /15W/20W/30W Round Recessed Ceiling LED Spotlight]

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Mular, A.L. and Poulin, R. 1998. Capcosts 1998.10 Inch 2 Ways Self-Powered Active Column Speaker Box Line Array System.Two-Way Passive Line Array .Lmhf Audio Dual 10 Inch Passive Speaker Professional Line Array System Q210, Montreal. 319 pp.         [High Quality Nickel Alloy Monel 400 ]

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Noakes, M. and Lanz, T. 1993.Custom Printed Food Grade Aluminum Foil Plastic Packaging Weed Mylar Bag for Fine Powder Snacks.Foil Liquid Packaging Stand up Spout Pouch Food Bag, Carlton, victoria. 412 pp.         [Economic Professional Bjjcz Ezcad Mini Fiber Laser Marking Engraving Cutting Machine 20W 30W 50W Price with Sino Galvo Scan Head]

O'hara, T.A. 1980. Quick guide to the evaluation of ore bodies,CIM Bulletin,February. pp. 87-89.         [PVC Sheet Roll Flooring Waterproof Strong Quality China Floor Covering Goldenma Brand]

O'hara T. A. and Subolesk,i C.S. 1992. Costs and cost estimation.Smell Proof Waterproof Weed Bag Plastic Food Packaging Child Resistant.vol. 1.Custom Printing Child Resistant Zip Plastic Food Packaging Stand-up Pouch for Weed / Ca, Metallurgy and Exploration, Littleton, CO. Chapter 6.3, pp. 405-424.         [Best Price Creatinol-O-Phosphate ]

Pascoe, R.D. 1992. Capital and operating costs of minerals engineering plants:Mylar Child Resistant Waterproof Plastic Bag with Zipper.Minerals Engineering,vol. 5, no. 8. pp. 883-893.         [3kw Air-Cooled UHF Digital TV Transmitter DTV]

Prasad, L. 1969.Plastic Pouch Custom Water Proof Weed Packaging Food Pack Stand up Bag.Mylar Custom Printed Plastic Weed Bag Stand up Pouch with Zipper, Metallurgy and Petroleum, Montreal. pp. 3-15.         [Plastic Raw Materials Black Masterbatch for PP PE Plastics]

USP Diclofenac Sodium Powder Pharmaceutical Raw Materials CAS 15307- 79 -6 Anti Inflammatory, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-Globally Popular Glycolic Acid CAS Nmber 79 -14-1 with a High Exposure Rate and Favorable Price.Tunnelling and Underground Space Technology,vol. 27. pp.133-141.         [Outdoor Show Audio Lt12 Passive Line Array Speaker System]

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USP Diclofenac Sodium Powder Pharmaceutical Raw Materials CAS 15307- 79 -6 Anti Inflammatory, A.R., Khalesi, M.R., and Khosfarman, M. 2014. A parametric cost model for mineral grinding mills.Minerals Engineering,vol. 55. pp. 96-102.         [Dibucaine Hydrochloride CAS 61-12-1 for Pian Relieve Dibucaine/Nupercaine/Percaine/Sovcaine No Side Effect Local Anestheti]

Smith, A.E. and Mason, A.K. 1997. Cost estimation predictive modelling: Regression versus neural network.The Engineering Economist,vol. 42, no. 2. pp. 137-161.         [Farm Equipment 800kg Small Loader Payloader for Sale]

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Timm, N.H. 2002. Applied Multivariate Analysis. Springer-Verlag, New York.         [Grade AA Veneer Furniture Building Material Plywood to Dubai]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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