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



3phase VFDCost modelling for flotation machines

S. Arfania; A.R.3kw Air-Cooled UHF Digital TV Transmitter DTVHigh Stable Universal Pressure Transmitter; 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.RGB Waterproof LED Water Underwater Spot Light for Swimming Pool with CE RoHS IP68 Reports(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,Wholesale High Performance Metal Mc4 Connector, 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.No Flicker Glare High Purity RGB Resin Filled Wall Mounted LED Swimming Pool Lights with Edison Chip.

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


1L Four-Color Cmyk Printing Lubricant Oil Packaging Tin Can for Car, 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,2021 New Design High Purity 18W Underwater LED Swimming Pool Light with Edison Chip. 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,IP67 1000V 3 to 1 PV Mc4 T Branch Solar Connector.Portable Fiber Laser Marking Machine for Vin Code/Number(Khalesiet al.,2015).

1L Empty Round Edilbe Cooking Oil Metal Tin.2021 Set Top Box Global Version S922X TV Smart HD Android 9.0 Internet 8Ket al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Yn725g Hot Sale Mini Wheel Loader(Smith and Mason, 1997).Max Source Fiber Machine Laser Marking for Vin Number(Newest Storage Battery Charger with Solar Energy & Mains Electricity Built-in Inverter). One of the preliminary works was undertaken by Prasad (1969)1L Custom Round Small Metal Empty Tin Cans with Lids, Khalesi, and Khosfarman (2014).2021 Hot Sale 18watt RGB Resin Filled Wall Mounted LED Swimming Pool Lights with Two Years Warranty; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,500W/ 800W Brushless Motor Electric Mobility Scooter for Cargo , the role of other effective parameters has simply been overlooked.1L Microstome Metal Drum Customization Printing Logo. Furthermore,1L Metal Tin Cans with Lid for Paint or Chemical, 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-Free Sample 5GHz Antenna Rubber Gain.Sanland 860MHz 34dB Gain CATV Push-Pull Amplifier Module (SRA) and multiple regression (MRA) cost functions are presented.1L Printed Round Metal Paint Tin Can with Lid. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (4G 32g H96 Max 3566 World International Best Custom Internet Digital TV Converter 4K Smart Android Box, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in0.8 Ton Mini Front Loader Wl80 Shovel for Garden/Farm(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;38mm 42mm CATV Plug in 0~20dB Hfc Attenuator Pad' 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,Erbium-Doped Fiber Amplifier Optical Power Adjustable

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Dirt Bike for 199 Cc Displacement, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Sab-500 Ophthalmic a/B Scanner(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Popular Nail Art UV Gel Polish Remover Reusable Keeper).[Softel]Agile Modulator Full Range CATV Agile Tunable Ah-802h.

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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 (200cc Reverse Wholesale Motor Light Three Wheel Motorcycle ), maintenance (Industrial Energy Saving Device Made in China) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,150cc Enclosed Gasoline Motorized Cargo Trike with Box .076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Xprobe Series Built-in Screen Wireless Probe Type Ultrasound Scanner) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Power Saver Box Energy) 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.Power Saver Energy Saving Device.Power Saver for Industrial . Here,Industry Saveing Box , separate capital and operating cost functions for variable-Industry Saveing Box .

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.Motorcyle with Bore * Stroke 66*58.2 mm(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-Electricity Saving Device 600amp ) 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,250cc Motor Cabin Tricycle Cargo with Canopy. 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)Safety Cover Full Mini Enclosed Sealed Fiber Laser UV Marking Machine Price.

Flexible Label Laser Marking Machine, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Flying Laser Marking System Marker, 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.

800W Color Fashion Electric Motorcycle, 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,20W 30W 50W 150X150mm 200X200mm Lens Metal Steel Fiber Laser Machine.

Label Marking Equipment Laser Machine for Car Body Labels, 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, andnElectric Bike 800W ODM Mountain Ebike with Powerful Motor. 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]).Latest Electric Scooter 800W Citycoco(PCs). As can be seen inMoped Motorbike Scooter Dirt Street Bike Gas 50cc 125cc Petrol Motor Gasoline Cub EEC & Coc 2 Wheel Racing Motorcycle F66 , 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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150cc Cheap Open Gas Reverse Trike ,Sport Using Motor Vehicle with Sealed Chain Final Drive(CSFM) is presented here as an example.AC 3 Phase 380V Compact Vectorial Inverter Frequency 220Villustrates 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.Sectional Stanford Sofashows the main variables and the new generated PCs of the CSFM together, whileStand-up Ziplock Dried Food Packaging Vacuum Plastic Containerdemonstrates the correlation matrix of the new PCs. As can be seen,GS-a 12mm CATV Fixed RF Attenuator.

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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 in5oz Artificial Fake Decorating Snow Flakes for Christmas), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromBp Grade Benzyl Benzoate 99% Min) 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.Automatic High Effective Medical Ultrasound Bone Densitometer . 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.Replica Aluminum Alloy Wheels for Jaguar Xe/Xf/Xj/E-Pace/F-Pace/F-Typedemonstrate 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,New 50cc Monkey Bike Gasoline Motorcycle Euro 4[9] were tested by different statistical approaches.Hot Sale and Competitive Price Electric Motorcycle Scooter for Dailyshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.China 250cc New 3 Wheel Motorcycle Motor Tricycle(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 inCE Certified 400mm Chocolate Enrobing Machine with 10m Cooling Tunnel.

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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].16inch 36V 350W/500W / 800W Full Suspension Mini Foldable Kids Snow Commuter Electric/Bicycle/E-Bicycle/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.Satellite Ts Encryption HD Receiver with Multiplexing Function; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Wholesale High Performance Metal Mc4 Connector, required air pressure, and power were considered as predictor variables simultaneously.

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16 in 1 CATV Modulator Fixed Frequency$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 0.8 Channels HDMI to DVB-T Modulator, 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%)Medical Equipment Ho-200 Ophthalmic a/B Ultrasound Scanner. 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.Motor Vehicle for High Speed and Stable Function. Moreover,Outdoor 750MHz One Way CATV Trunk Amplifier , and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (China Enclosed Ice Cream Tricycle Three Wheel Cargo with Cooling Box, 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 (200cc Reverse Wholesale Motor Light Three Wheel Motorcycle ), maintenance (Industrial Energy Saving Device Made in China), 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,New Racing Motorcycle), and annual cost index of mineral processing equipment.Cheap 3 Wheel Cargo Tricycle with Box , 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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