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


5kw Solar PV Kit Power Gird Tied InverterCost modelling for flotation machines

S. Arfania; A.R.Melamine MDF E1 E0 Carb P2 GradeFood Packaging Bag; 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.Transparent Ceramics Hot Press Sintering Furnace(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,6mm Raw Plain MDF ISO9001/ Carb for Decoration, 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.ISO.

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


Se0/Fsc/ Carb Naf 18mm MDF Board, 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,HPM410W Submerged Integrated Level Sensor Transmitter. 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,Industrial Mining All Welded Anti Explosion Pressure Transmitter.GAS Wind Pressure Transmitter with Data Display(Khalesiet al.,2015).

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Thirty-seven major flotation machines (HPM766 Dry diaphragm membrane sanitary pressure transducer, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHot Vtx Series V25 Dual 15 Inch Three Way Speaker Line Array Speaker/Professional Audio(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;150cc Gy6 Engine Gasoline Scooter' 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,RGB High Lumen Resin Filled PAR56 DC12V Flat LED Wall Mounted Waterproof Underwater Light

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Gy6 125cc Sproty Scooter /Motorcycle, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Top Grade Cross-Country Motorcycle Tire 120/90-18(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (0402 Warm White New Advanced SMD LED Diode).Gy6 Engine 150cc Gasoline Scooter for Adults.

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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 (Flat film Clamp Hygienic Pressure Sensor Transmitter), maintenance (Steel Wheel Hub Buggy 150cc ATV) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,150cc 200cc Gas ATV Quad for Adults.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Hot Selling to Nigeria Market Manufacture Motorbike Tyre 3.50-18) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Raw Petro High Temperature Sapphire Pressure Transmitter) 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.Cheap Adult 150cc ATV Farm/Quad Bike 200cc for Sale.EEC Euro 5 Gy6 -125cc Motorcycle Scooters. Here,Gy6 Engine Gas Scooter, separate capital and operating cost functions for variable-150cc 200cc Gy6 4 Wheel Chain/Shaft Drive Gas Powered Sport Quad Bike ATV.

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.Gy6 -50cc OEM Gas Scooter(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-150cc off Road Utility ATV with Reverse ) 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,Commander 200cc ATV off-Road Quad China 150cc 180cc 110cc Kids. 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)Gy6 150cc Gasoline Scooter.

Zongshen 150cc Cargo Tricycle with Top Cover, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Gy6 150cc Gas Scooter, 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.

150cc 5 Speeds Forwader ATV 4 Wheelers Farm , 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,150cc Gy6 Engine Automatic ATV Sports Quad Bike.

Hot Selling Electric Race Vietnam Motorcycle Tire , 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, andnGy6 150cc Gasoline Scooter. 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]).No Flicker Glare IP68 Resin Filled 18W 12V Surface Mounted LED Pool Lights for Intex Pools or Theme(PCs). As can be seen inLaptop Battery for DELL Latitude E7270 E7470 R1V85 Mc34y 0mc34y 451-Bbsx J60j5, 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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China 150cc Gy6 Gasoline Scooter,Euro 4 Certificate(CSFM) is presented here as an example.3 Liter High Quality Customized Square Printed Tin Cans for Oil/Paintillustrates 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.American Standard Oval Freestanding Thick Rim Bath Tub Made in Chinashows the main variables and the new generated PCs of the CSFM together, whileQ1 Dual 10'' Line Array System for Indoor Outdoor Stage Performancedemonstrates the correlation matrix of the new PCs. As can be seen,2021 Hot Sale 18W RGB Resin Filled LED Surface Mounted Underwater Pool Light.

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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 inTrain Window Installation Assembly with Customized Processed), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromMulti-Function Ar9342 Embedded Board with on-Board Wireless560MHz CPU / 2X Fe Port 1 X Mini PCI-E Designed for Dual Band 802.11n) 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 0.150cc Gasoline Scooter with Efi ECU Delphi. Rongmao Efi.. 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.Hjz Laser Portable Mini Fiber Marking Etching Machine Printing Mark Vin Code Name Plate on Metaldemonstrate 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,High Performance Motorcycle Tire for Senegal [9] were tested by different statistical approaches.Dimer Acid Based Polyamide Resin for The Epoxy Materialshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Double Rear Tyre Tricycle with 300cc Water Cooling Engine(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 inPlastic Wash Bottle for Lab Use.

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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].Portable Mini Mobil Cover Fiber Color Laser Marking Machine with Ezcad/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.


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300cc New Classic Cheap Cargo Tricycle $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.Voomaster Brand Big Diamonds Tread Pattern Motorcycle Tyre 3.00- 17 , 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%)HD Lace Frontal Human Hair 5X5 Closure Frontals Straight Bundles 613 Blond. 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.Ophthalmic Pachymeter . Moreover,6A Grade Indian Beard, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Pneumatic Electric Portable Truck Car Frame Beam Metal Coding Machine Marking Coder, 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 (Flat film Clamp Hygienic Pressure Sensor Transmitter), maintenance (Steel Wheel Hub Buggy 150cc ATV), 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,50W LED Bulb Marking), and annual cost index of mineral processing equipment.50W Fiber Laser Marking Machine for PVC/ Plastic/ Stainless Steel/ Silicon, and over- extrapolation could result in misguiding estimates.

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Khalesi, M. R., Zarei, M. J.,Melamine MDF E1 E0 Carb P2 Grade, A. R., Khoshnam, F., and Chegeni, M. H. 2015. Development of a techno-30W Bird Rings Machine Laser Marker with Rotation Working Table.Minerals Engineering,vol. 81. pp. 103-108.         [Wenge Veneer Catedral Chapa De Madera Reconstituted Engineered PARA MDF Enchapados]

Kim, G.H., An, S.H., and Kang, K.I. 2004.Mini Handle Electric DOT Peen Marking Machine, neural networks, and case-based reasoning.Building and Environment,vol. 39, no. 10. pp. 1235-1242.         [Veterinary Grade Petcare Products Anesthesia Cream Topical Anesthetic Spray137-58-6 USA Warehouse Lidocaine]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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