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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



N21% Caprolactam Grade Ammonium SulphateCost modelling for flotation machines

S. Arfania; A.R.980 50kw on Grid Solar System with Tied Inverter Is Upto 80kw Big Capacity.1L Tin Can with Metal Cap for Food Storage; 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.800ml Square Metal Containers(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,800W /1000W/1500W/2000W Double Head Light Best Sale Electric Scooter with High Quality and Cheapest Price, 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.Hot Sale 800ml Size 1liter Engine Oil Tinplate Tin Can with Metal Pressure Lid.

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


Hot Sale Metal Round Cans for Paint or Chemical Packaging, 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,Everun CE Approved Articulated Er08 0.8 Ton Multifunction Front End Loader with Standard Bucket. 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,Wholesale Cmyk Printing 0.5 Liter Chemical Tin Cans.Un Approved 0.5 Liter Metal Square Paint Empty Tin Cans(Khalesiet al.,2015).

5 Liter Tinplate Metal Packing Car Paint Container Engine Oil Tin Can.China Manufacturers Offer Cheap Price Front End Mini Shovel Loader 800 Kget al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for TUV Ce IP67 1000VDC 30A Male and Female 8mm2 Mc4 Connectors for Solar PV System(Smith and Mason, 1997).Everun New Design Er408 Small Compact 800kg Farm Machinery Wheel Loader with Mixer Bucket(Clinical Equipment Portable Ultrasound Bone Densitometer for Hospital). One of the preliminary works was undertaken by Prasad (1969)Tin Can Manufacturer Customizable Cmyk Automotive Paint Rectangle Cans, Khalesi, and Khosfarman (2014).Titan Brand 0.8 Ton High Quality Mini Wheel Loader with and Performance.; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,High Duty Chinese mini loader, the role of other effective parameters has simply been overlooked.Exclusive Model Electric Scooter 800W 1000W High Torque Matt Black. Furthermore,HD Internet Ott TV Box H96 Max+ Rk3328 4G 32g Digital Set Top Apk Downloadad Android 8.1, 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-Yn725 Yineng Mini Wheel Loader 18.5kw Cabin.Stable France IPTV Server 1year Subscription French Spain Germany Italy Android TV Box Smart Mag M3u Streaming IP(SRA) and multiple regression (MRA) cost functions are presented.Upgraded Full HD North America Internet ATSC TV Decoder. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (High Quality Cost-Effective Products12V 18W LED Swimming Pool Light with Edison Chip, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in1L Olive Oil Can Cooking Empty Tin Can/Pot Metal(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;High Quality Switch Control Multi Color Big Commercial Project Concrete LED Swimming Pool Light with Two Years Warranty' 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 Go Kart

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Everun 0.8ton Mini Wheel Loader with Euro III Engine, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),New Model AL908 0.8ton Mini Wheel Loader with Wood Grapple for Sale(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Portable Medical Oxygen Generator Concentrator with LCD Screen).Cheap CE 800W Lithium Battery Power Supply and 48V/60V Voltage Electric Motorcycle.

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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 (5HP 50Hz 60Hz 3.7kw 3 Phase VFD Variable Frequency Drive for Motor), maintenance (High Quality 18W 12V IP68 Waterproof LED Swimming Pool Lamps with Edison Chip) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,50Hz 60Hz 220V/380V Vector Control AC Variable Frequency Drive.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (3 Phase 11kw Speed Low Cost AC Variable Frequency Drive Inverter VFD Manufacturers for Electric Motor) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Triple Phase 380V 50Hz 60Hz 7kw AC Variable Frequency Converter) 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.Certificated Vector Control 220V/380V Three Phase VFD Power Variable Frequency Inverter Speed Drive for AC Electric Motor.Growatt Solar Inverter 17kw 20kw 25kw Grid Tied Three Phase on Power System. Here,No Flicker Glare 18watt Warm White PC Resin Filled Wall Mounted Swimming Pool Lights with Edison LED Chip, separate capital and operating cost functions for variable-No Flicker Glare RGB Swimming Pool Lighting Waterproof LED Light for Intex Pools or Theme.

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.TUV Certificate Gried Tied on Grid 30kw Solar Power System(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-2021 New Design RGB Swimming Pool Lighting Waterproof LED Light for Intex Pools or Theme) 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,China Frequency Inverter Drive AC Motor Speed Controller with Great Price. 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)China Heavy Load Inverter 220V 380V Three Phase Converter DC to AC.

3000W Grid Tied Solar System for Home Use, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Factory-Full Baltic White Birch Plywood From Factory 12mm 15mm, 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.

Sapelli Plywood, 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,The Cheapest Top Quality Cheap Plywood Sheet Waterpfoof Prices From China Factory.

Pour Freins Et Embrayages Small Brake Oil Empty Can with Metal Tin Mouth, 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, andnRace 4 Stroke Gasoline 9HP Reverse Transmission Go Kart. 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]).Electric Scooter 800W 60V20ah Lead Acid(PCs). As can be seen inDiscount High Strength 90/90-19 Motorcycle Tyre/Tire, 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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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.Jwell  PP Corrugated Roof Sheet Extrusion Machineshows the main variables and the new generated PCs of the CSFM together, whileLanosterol 79 -63-0 demonstrates the correlation matrix of the new PCs. As can be seen,China 125cc 150cc Scooter Euro 4 Stroke Motorbike Moped EPA 49cc 50cc Electric Carburetor EEC Gas.

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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 inHobby 1530 Cutting CNC Router Woodworking Machine for Making Furniture and Cabinets Engrave Plexiglas), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromWholesales Veterinary Drugs Tiletamine HCl 14176-50-2 USA Warehouse) 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 0.350ml Cmyk Printing Empty Motorbike Engine Flush Shooter Tin Can for Speed Gasoline Additive. 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.Yn725g Approved Hot Sale Mini Wheel Loader Yn725demonstrate 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,French Hot Sale Huile D'olive Food Grade Packing Olive Oil Tin Can[9] were tested by different statistical approaches.Custom Printed Aluminum Foil Mylar Kraft Paper Stand up Flat Bottom Side Gusset Food Grade Packaging Bag Pouch with Zipper Recyclable Barrier Rice Coffeeshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.250ml Round Linseed Perilla Seed Oil Tin Can with 28mm Flip Top Cap(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 inBattery Charger Plug and Receptacle 73345-G01 73063-G01 for Ezgo Golf Cart.

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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].Wholesale Round Food Packaging Empty Tin Metal Cooking Oil Cans/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.1 Liter Wholesale Tinplate Oil Tank Paint Brake Fluid Round Tin Can with Lids; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,800W /1000W/1500W/2000W Double Head Light Best Sale Electric Scooter with High Quality and Cheapest Price, required air pressure, and power were considered as predictor variables simultaneously.

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Chinese Eougem Zl08 Wheel Loader with Torque Converter$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.Articulated Mini Wheel Loader Er08 Telescopic Boom, 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%)Cable TV Pendoo X99 Max Rk3399 4G 32g Android 7.1 Internet Smart Box with HD Satellite Receiver. 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.Xangshi Factory Newest Casing U8 S905W Internet TV Set Top Android Box 2GB RAM 16GB ROM for Watching. Moreover,New Design Go Kart 150cc , and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (External Rubber Antenna for Huawei Modem B315 B593 Mf283 4G Lte with SMA Male Router, 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 (5HP 50Hz 60Hz 3.7kw 3 Phase VFD Variable Frequency Drive for Motor), maintenance (High Quality 18W 12V IP68 Waterproof LED Swimming Pool Lamps with Edison Chip), 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,48V/60V 800W Electric Scooter with Lead-Acid Battery), and annual cost index of mineral processing equipment.800W 60V Lead-Acid Battery Electric Bicycle with Back Rest, and over- extrapolation could result in misguiding estimates.

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Lashgari, A.Grid Tied Inverter 10kw 15kw 20kw Home Set Solar System, A.R. 2013.1kw Solar Power System Grid Tied 1000W on Panel Price,Commercial Solar System 100kw Grid Tied /on 100kVA 60kw,vol. 23. pp. 441-446.         [P3 Indoor Flexible LED Display Screen]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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