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



50 to 60 Hz Frequency ConverterCost modelling for flotation machines

S. Arfania; A.R.18" Die Cast P-Auido Style Aluminum FrameCarb Grade 18mm Commercial Plywood; 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.Professional Stage Active Line Array Speaker with DSP(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,Single 18" Subwoofer Speaker Box, 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.Wholesales Veterinary Drugs Tiletamine HCl 14176-50-2 USA Warehouse.

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


12" Professional Rcf Style Speaker Frame, 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,Horn Professional Speaker H3. 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,Coaxial Loudspeaker TD12.18'' Subwoofer Speaker Box Ls1200(Khalesiet al.,2015).

Dual 12" Subwoofer Speaker Box.DV Portable Speaker 12 Inch 1600W Subwoofer Box Audio Professionalet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for 5GHz 23dBi Dual Polarized Panel Antenna (Smith and Mason, 1997).Fast Delivery 1(Diesel Engine Parts Fuel Injection Nozzle 140s6655). One of the preliminary works was undertaken by Prasad (1969)Professional Speaker Box F12+, Khalesi, and Khosfarman (2014).Df B&C Trees Speaker Subwoofer Audio Professional; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,15'' Coaxial Speaker , the role of other effective parameters has simply been overlooked.Customs Guaranteed 1. Furthermore,China Factory Supply Ethylmagnesium Bromide CAS 925-90-6, 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-Ltk One 12" Woofers and 3" Driver Compact Coaxial Line Array Speaker.Manufacturer Supply Bdo Novel Intermediate 1(SRA) and multiple regression (MRA) cost functions are presented.Tetracaina HCl Tetracaine Base Depuracao Segura Mercado 100% Brasileiro. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (99% Pain Reliever Local Anesthetic Powder Tetracaine CAS 94-24-6, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inPE Dog Food Pouch with Hole(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;China Factoty Supply Levamisole HCl CAS16595-80-5 Hydrochloride Tetramisole' 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,Dare Dual 8" Neodymium Active Line Array Set PA 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,12" Die Cast Aluminum PA Speaker Frame, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),PA Speaker Dual 18" Subwoofer System(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Whirlpool Massage Small Bathroom Bathtub).PA Speaker with Line Array Tweeter Horn .

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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 (Active Mini Line Array Speaker with DSP Amplifier Module), maintenance (Quality Certified Product Ethyl 2-Phenylacetoacetate CAS: 5413-05-8 BMK Powder) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,High Quality Karaoke Loudspeaker with B&C Compression Driver.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (99% Tetracaine Hydrochloride/ HCl Powder CAS 136-47-0) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Factory Supply BMK Powder Glycidate CAS: 5413-05-8) 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.China Factory Supply CAS 99-93-4 4-Hydroxyacetophenone.Chinese Manufacturer Bulk Stock Pmk Intermediates16648-44-5 BMK White Powder. Here,99.9% High Purity Prilocaine Hydrochloride/Prilocaine HCl CAS 1786-81-8, separate capital and operating cost functions for variable-High Quality 4'-Hydroxyacetophenone CAS 99-93-4 4-Hydroxyacetophenone with Best Price.

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.Factory Bulk Stock Pmk Intermediates BMK White Powder CAS: 16648-44-5(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-99% BMK White Powder Glycidate Bulk Sales CAS: 16648-44-5) 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% 4'-Hydroxyacetophenone CAS 99-93-4 100% Pass Customs. 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)62442 Shiny and Non Phena Powder 62 44 2.

Quality Guaranteed BMK White Powder CAS: 16648-44-5 Glycidate, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Hair Loss Treatment Acetyl Tetrapeptide-3/Capixyl CAS 827306-88-7 Purity Min 99% Powder, 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.

100% Passing The Customs Europe Free Shipping BMK Glycidate 16648-44-5, 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,Trolley Large Audio Loudspeaker Box Professional Stage Active PA Speaker.

BMK White Powder Europe Free Shipping Pmk Glycidate CAS: 13605-48-6, 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, andnPortable 15inch PA Speaker F15+. 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]).Pharmaceutical Chemical CAS 236117-38-7(PCs). As can be seen inPendoo X10 Max International Best Custom Set Top Box 4GB 32GB TV Converter Ott 4K Smart Android, 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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Speaker Tcx- 10,PA Woofer Speaker T- 10 12 15(CSFM) is presented here as an example.3kwh LiFePO4 Battery System Energy Powerillustrates 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.Quilted Fabric Sofa Couch Bed Set Armchear Furnitureshows the main variables and the new generated PCs of the CSFM together, whileHot Sale Professional Loudspeaker PRO Audio demonstrates the correlation matrix of the new PCs. As can be seen,Passive Double 10 Inch Proal Audios Sound System Line Array Speakers for Direct Sale.

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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 inWomen Fashion Knitted Sweater with Long Sleeve), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromSwimming SPA Pool Hot Tub Combo) 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 0.10 " PRO Audio DJ Line Array Speaker Equipment System. 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.Modern Home Hotel Lesuire Corner Single Fabric Living Room Sofademonstrate 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,Wholesale Factory Price CAS: 16648-44-5 BMK Glycidate Powder[9] were tested by different statistical approaches.14"X5.0"J 14'x5.5'j 14X6.0j 14X7.0j Inch Steel Wheel for Sport Trailershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Buy Real Pharmaceutical Intermediates BMK Glycidate Powder 16648-44-5(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 in6W UV Gel Polish Curing LED Lamp with USB.

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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].Big Outdoor Sound Equipment Active Dual 8" Line Array Speaker/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.Professional Powered Line Array Selfpowered Speakers Active System; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Single 18" Subwoofer Speaker Box, required air pressure, and power were considered as predictor variables simultaneously.

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Self Powered Generator Double 8 Inch Outdoor Sound Indoor Line Array$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.Light and Durable Mixing Console Mg124cx Audio Mixer, 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%)Chassis/Dolphin/Powerful Speaker for Stadium. 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.Line Array with Accessories for PRO Audio. Moreover,Wholesales Aminobutyric Acid Organic Solvents 1litre Reagentplus T-Butyrolactone Fast Delivery, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Kara Line Array Speakers Double 8 Inch Concert, 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 (Active Mini Line Array Speaker with DSP Amplifier Module), maintenance (Quality Certified Product Ethyl 2-Phenylacetoacetate CAS: 5413-05-8 BMK Powder), 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,Top Quality Isopropyl Alcohol ), and annual cost index of mineral processing equipment.Disco Sound+ PA System Speaker, and over- extrapolation could result in misguiding estimates.

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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