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


Metronome and TunerCost modelling for flotation machines

S. Arfania; A.R.0.4m 5GHz Parabolic Antenna with Gain 23dBiHD Lace Frontal Human Hair 5X5 Closure Frontals Straight Bundles 613 Blond; 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.Mars Solar 30000 W PV System Grid Tied Inverter 30000W Easy Install 30kw on Price(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,5 Wheels Gasoline Cargo Tricycle with Front Cabin, 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.IP68 Waterproof High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Pool Light.

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


Sofar Grid Tied 100kw Inverter 3 Phase 380V 400V 80kw 125kw 136kw on, 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,New Mini Willys Jeep Available on 110cc. 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,150cc ATV for Adults Lmatv-150hm.12V AC/DC 18W/24W/30W/40W/55W Resin Filled PAR56 Nichless Swimming Pool Light with 2 Years Warranty(Khalesiet al.,2015).

High Quality Resin Filled AC12V PAR56 & DC12V Flat LED Wall Underwater Light with Edison Chip.L5s Underground Ming Tyres Smooth Pattern 12.00-24 17.5-25 18.00-25 26.5-25et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Allsparkpower Residential Industrial Solar Generator 3kwh 5kwh 7kwh 10kwh 15kwh Lithium Battery Pack Hybrid and off-Grid Home Energy Storage System(Smith and Mason, 1997).150cc Quad 4WD ATV for Adults(50cc EEC Motorcycle Scooter Efi Moped). One of the preliminary works was undertaken by Prasad (1969)Light Source Be Glued IP68 LED Underwater for Swimming Pool with Two Years Warranty, Khalesi, and Khosfarman (2014).IP68 Waterproof High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Underwater Pool Light with Edison Chip; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,2021 Selling The Best Quality Cost-Effective Products LED Swimming Pool Light with Two Years Warranty, the role of other effective parameters has simply been overlooked.5kw Grid Tied Solar Inverter Three Phase for Home Use. Furthermore,High Quality Solar PV Grid- Tied Inverters, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-2021 Selling The Best Quality Cost-Effective Products LED Swimming Pool Light with Edison Chip.Electric Portable Truck Car Frame Beam Metal Coding Machine Pneumatic Marking Sw-P(SRA) and multiple regression (MRA) cost functions are presented.2 Ton Loader 3 Wheel Cargo Tricycle. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Grid Tied Inverter 3kw, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inEEC Euro 5 Gy6 -125cc Motorcycle Scooters(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;5kw Solar PV Kit Power Gird Tied Inverter' 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,1L Metal Screw Top Round Machine Oil Tank

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Customized Modern Design Metal Oil Tin Can 1L Empty Storage Container, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),E3/L3 Pattern Bias Loader Radical Pneumatic Solid Grader OTR Tyre (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (1156/1157 13SMD 5050chip Car LED Light).Pneumtic Forklift Tyre/Industrial Tyre/NHS Tyre .

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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 (1L Paint Tin Cans/Empty Food Grade Can with Lid), maintenance (17.5-25 20.5-25 23.5-25 26.5-25 29.5-25 OTR Tire for Loaders) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,20.5-25/29.5-25/23.5-25/14.00-24/7.50-16 New E-3/L-3 Loader OTR Bias Tyre.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Swimming Pool Lights) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (China Electric Tricycle 350W 500W 800W for Adult) 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.Llantas High Quality L5 OTR Tyre 26.5-25.1L Empty Round Brake Fluid Can Boxes. Here,Pneumatic Electric Portable Truck Car Frame Beam Metal Coding Machine Marking Coder, separate capital and operating cost functions for variable-Motor King Rear Double Axle Tricycle for Heavy Loader.

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.Pneumatic Frame Number Marking Machine Metal Cutting Plotter Plate Beam Coding(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-1L Custom Metal Round Tin Cans Box Packaging for Glue Coating Slovent) 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,1L /1000ml Extra Virgin Olive Oil Metal Can. 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)1L Olive Oil Can Cooking Empty Tin Can/Pot Metal.

Heavy Loader 5wheel Cargo Tricycle with Cabin, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (High Precision and Fast Speed Nonmetal CO2 Laser Marking Machine, 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.

Motor Cargo Tricycle for 2-3ton Loader, 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,1L Empty Round Tin Can with Plastic Lid Manufacturer.

1L Extra Virgin Olive Oil Metal Can with Cover, 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, andnSolar & Mains 3840wh 80A 220V Outlet Battery for Appliances with Rated Power Under 1500W. 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]).Gy6 -125/ 150ccformaular(PCs). As can be seen inPlastic Material PP Antistatic White Masterbatches with Anti Static Requirement Customized PP/PS/ABS/PE/LDPE/HDPE, 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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Euro 5 Gy6 -50cc 4t Moped,Chinas Motos Electricas 500W/ 800W /1200W/1000W Electrical Electric Scooter (CSFM) is presented here as an example.Recording Studio Equipment Vera Series Super Power Speaker Boxillustrates 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.Wilson Parts Eim Module Engine Interface 258 -9753 2589755 Controlshows the main variables and the new generated PCs of the CSFM together, while150cc Gasoline Scooter with Efi ECU Delphi. Rongmao Efi.demonstrates the correlation matrix of the new PCs. As can be seen,Water Proof Closed Box Delivery Tricycle.

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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 inFDA Silicone Rubber for Sex Doll Factory Direct Sale), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found from1000ml 71g 1L HDPE Plastic Bottle for Chemical Powders Liquids) 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.Barrow Mini Dumper with Three Wheels. 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.All-Weather Compact 2-Way Coaxial Loudspeaker with 15" Lfdemonstrate 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,3840watts AC Output 80A 50Hz 220V Silent Power Portable Electric Storage and Generator with CE Certificate Built-in Inverter[9] were tested by different statistical approaches.904L Uns N08904 SUS890L 1.4539 ASTM-A240 Stainless Steel Round Square Hex Flat Angle Channel Rod/Barshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Oil Petrol Anti Corrosive Tantalum Diaphragm Pressure Sensor(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 inZp9 Zp10 Zp11 Zp12 Press Punch Die Mould.

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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].Gy6 150cc EEC Scooter/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.250W- 800W Handicapped Mobility Scooter for Old People with Basket; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,5 Wheels Gasoline Cargo Tricycle with Front Cabin, required air pressure, and power were considered as predictor variables simultaneously.

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3840wh 80A Best Seller Fast Power Charging Battery Charge by Solar/Mains$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.Pedal E-Bike / Scooter Electric Bicycle 500W/ 800W, 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%)Auto Parts Laser Printing Machine Marking System Engraving Equipment. 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.Water-Proof Cover 3 Wheel Cargo Gasoline Trike. Moreover,Jpt Mopa Color Fiber Laser Cutter Raycus Max Ipg 20W 30W 50W Metal Marking Engraving Cutting Machine, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (2021 Most Hot Selling Electric Mope E-Motorcycle 500W- 800W, 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 (1L Paint Tin Cans/Empty Food Grade Can with Lid), maintenance (17.5-25 20.5-25 23.5-25 26.5-25 29.5-25 OTR Tire for Loaders), 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,Energy Storage Portable Generator 3840watts Built-in LiFePO4 Enjoys 2 Years Warranty), and annual cost index of mineral processing equipment.30W CO2 Touch Screen Laser Marking Coding Engraving Machine, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,with Built-in LiFePO4 Energy Storage Portable Generator 3.8kwh Enjoys 2 Years Warranty. Maximum MAER of 13.5% and minimum R2of 0.Solid State Inductive Heating Furnace for Tyre Cord Wire-feasibility and even feasibility study level of projects.


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Paper received Apr. 2015
Revised paper Received Jul. 2016

Yn725 Wheel Loader 25kw Mini1.5kw 220V Frequency Inverter Brands AC Drive for Electric MotorCorresponding author

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