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vol.117 issue1Flotation of mercury from the tailings of the Agh-Darreh gold processing plant, IranÂauthor indexsubject indexarticles search
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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017



Bleached Poplar/Birch Carb PlywoodCost modelling for flotation machines

S. Arfania; A.R.Jwell PLA Pet Plastic Biodegradable Sheet Recycling Cup Making Extrusion Machine49" VGA high performance monitor LCD video wall panel with extention cable; 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.Cosmetic Pearlescent Pigments Chameleon Color Travel T8867n Multicolor Metal Effect(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 Direction Thrust Ball Bearing 510/630 591/630 511/630 691/670 511/670 510/ 710 591/ 511/ 510/750 591/750 511/750 M F, 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.Cosmetic Pearlescent Pigments Chameleon Color Travel T8207n Multicolor Metal Effect Gold Green Blue.

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


Powerful Cheap Mountain Bike Bicycle, 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,Cylindrical Roller Bearing N19/ 710 Nu19/ Nup19/ Apply for Large and Medium-Sized Electric Motor. 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,Polyamide Resin Hot Melt Adhesive.Polyamide Resin(Khalesiet al.,2015).

Co-Soluble Polyamide Resin with Top Quality.Alcohol Polyamide Resin for Printing Inket al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Win10 TV Box Pipo X9s Z8350 Chipset 4G 64G Media Player Win Smart Digital Receiver(Smith and Mason, 1997).Popular Alcohol Soluble Polyamide Resin for Gravure Ink(Automatic Pure/Mineral Bottle Water Packing Machine ). One of the preliminary works was undertaken by Prasad (1969)Polyamide Resin with Benzene Soluble for Printing Inks, Khalesi, and Khosfarman (2014).Alcohol Soluble Polyamide Resin for Printing Ink; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Supply Rosin Modified Polyamide Resin for Paint, the role of other effective parameters has simply been overlooked.Farwell P-Hydroxy Benzaldehyde with High Purity 99.5%. Furthermore,High Quality Benzaldehyde with Fast Delivery, 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-Supply Alcohol Soluble Polyamide Resin for Ink.CAS No. 151103-09-2 4- (SRA) and multiple regression (MRA) cost functions are presented.Sophisticated Price of Polyamide Resin for Whosale. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (100% Purity Phenol Polyamide Resin, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inModern Simple Hotel Lobby Discussion Living Room Leisure Sofa(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;High Polyamide Resin' names:

Water Waste Landfill Industrial Aquaculture and Mining Project Geomembrane Liner Extruder Machine: based on 36-foot,Hot Sale Hy-688 Polyamide Resin,100% High Purity Polyamide Resin for Ink,Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Electrics Packing, and level control

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,Polyamide Resin

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Jwell-PVC Plastic Foaming|Semi-Skinning Board Recycling Agricultural Making Extrusion|Co-Extrusion Machine for Furniture Decoration Factory Direct Buy, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Geomembrane Making Machine(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Easy Sight X5-Ht CCTV Tractor Underground Inspection).Spoke Wheel 26-Inch 21-Speed Top with Bicycle.

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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 (26 Inch Mountain Bike From China Bicycle), maintenance (PE Waterproof Roll Extrusion Machine) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,PE Extra-Width Geomembrane/Waterproof Sheet Extrusion Line.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (PE Geomembrane/Waterproof Sheet Extrusion Line) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (6speed 20inch Wheel Aluminum Alloy Folding Mountain Bike) 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.Bike Hidden Folding Mountain Ebike Suspension Bicycle.Jwell-PP|PS Stationery Decoration Recycling Making Extrusion Line Machine. Here,Factory Wholesale Direct Sale Bicycle Folding Mountain Bike 26 Inch Variable Speed Double Shock Absorber, separate capital and operating cost functions for variable-Hot Sale Am 20 "Mountain Bike with 21 Speeds.

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.Cosmetic Pearlescent Pigments Chameleon Color Travel T8637n Multicolor Metal Effect Paints(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-Adult Foldable Fold Road Bike MTB Mountain Bicycle Sdc -902) 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,Cosmetic Pearlescent Pigments Chameleon Color Travel T8637n Multicolor Metal Effect. 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)Iron Oxide Yellow for Pet Feeds.

Cosmetic Ultramarine Violet Soap Pigment Matte Manufacturer, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Cosmetic Grade Ultramarine Violet Manufacturer, 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.

Factory Supply Benzaldehyde CAS 100-52-7 99% with Best Price in Stock, 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,Dimer Acid Based Polyamide Resin for The Epoxy Material.

Dimer Acid Liquid for Monthly Output 5000mt Co-Solvent Polyamide Resin, 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, andnWeather Resistance Nylon Polyamide Resin. 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]).High Purity 2(PCs). As can be seen inSkin Renew Thermal RF & Fractional 2 in 1 Machine, 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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SKF NSK Timken Koyo NACHI Snr IKO 3811/530 3811/560 3811/600 3811/630 3811/ 710 3811/750 Taper Roller Bearing Branded Bearings,Single Row Cylindrical Roller Bearing (CSFM) is presented here as an example.40*160 mm Frame Number Marking Machine Metal Cutting Plotter Plate Beam Coderillustrates 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.99% Pure High Quality Anesthetics Cinchocaine 85- 79 -0shows the main variables and the new generated PCs of the CSFM together, whileGood Quality Food Additive Maltose Powder 69- 79 -4demonstrates the correlation matrix of the new PCs. As can be seen,Good Wear Resistance and High Tenacity Engineering Plastic 610 for Brush Wire.

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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 in15W High Power 6565 UV LED 395nm 405nm 365nm for Curing), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromHigh Purity Valerophenone 1-Phenylpentan-1-One CAS 1009-14-9) 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.Zys Hot Sale Wind Turbine Bearing 010.30.560/630/ 710. 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.Frequency Converter 60Hz 50Hz 60HPdemonstrate 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,Large Size Spherical Roller Bearing 239/600 239/630 239/670 239/ 710 Ca Cc MB Cage Self-Aligning[9] were tested by different statistical approaches.2440mmx1220mmx3mm Carb P2 Formaldehyde Raw HDF Boardshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.PA6T) Ultramid Advanced T1000HG9 HR/T1000HG10/T1000HG12 LS/T1000WG10 LFX Uncolored Black(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 inCompostable Mailer Biodegradable Waterproof Postage Satchel Custom Printed Plastic Shipping Bag.

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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].CAS No: 67700-43-0 Esters Soluble Liquid PU Polyurethane Resin for Inks/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.High Adhesion Polyurethane PU Resin for Printing Ink; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Single Direction Thrust Ball Bearing 510/630 591/630 511/630 691/670 511/670 510/ 710 591/ 511/ 510/750 591/750 511/750 M F, required air pressure, and power were considered as predictor variables simultaneously.

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Jwell PLA Pet Sheet Cup Packing Making Extrusion Line Machine$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.PA Resin for Gravure Plastic and Paper Printing Ink, 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%)Jwell-PLA Pet Sheet Recycling Cup Packing Making Extrusion Machine. 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.Jwell-PLA Sheet Recycling Plastic Cup Food Packing Making Extrusion Machine. Moreover,Good Performance Polyurethane PU Resin for Gravure Printing Ink, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Jwell HDPE Waterproof Membrance Roll Extrusion Line, 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 (26 Inch Mountain Bike From China Bicycle), maintenance (PE Waterproof Roll Extrusion Machine), 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,Silo Top Pulse Jet Dust Collectors Collector Hopper for Cement), and annual cost index of mineral processing equipment.CAS No.: 63428-84-2 Polyamide PA Resin for Untreated Film, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Dust Collector Woodworking Machinery Supplier. Maximum MAER of 13.5% and minimum R2of 0.Jwell-PLA Biodegradable Sheet Recycling Cup Making Extrusion Machine-feasibility and even feasibility study level of projects.


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Paper received Apr. 2015
Revised paper Received Jul. 2016

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