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


NBR Nitril 80 Duro Rubber X Ring /QuadCost modelling for flotation machines

S. Arfania; A.R.18L Square Metal Tin Cans with Handle and Lid for Oil800W Color Fashion Electric Motorcycle; 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.Glue Tin Can with Plastic Lid / Square Metal Paint Sizes(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,Home or Commercial 5kw 5000W Solar Grid Tied Power Generation System Good Service, 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.Grid Tied 30kw Solar PV System for Shingle Roof.

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


Good Quality Empty 1 Litre Metal Tin Paint Cans with Handle for Sale, 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,Pinergy Grid Tied Solar Panel System 6kw Energy 110V Single Phase. 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,off Grid 5kw 10kw Solar Power System.Pinergy 9kw on- Grid Tied Solar Power System for Home or Industrial Roof(Khalesiet al.,2015).

2013 Popular Electric Motorcycle 90km with Pedal CE .Chinese Zl08f Wheel Loader 0.8ton Mini with Quick Hitch for Saleet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Frequency Converter 60Hz 50Hz 60HP(Smith and Mason, 1997).Wolf Loader Wl80 Radlader Without Cabin(Line Array PA Speaker System Stage 12inch Monitor PRO Audio). One of the preliminary works was undertaken by Prasad (1969)Yn725g Approved Hot Sale Mini Wheel Loader Yn725, Khalesi, and Khosfarman (2014).Er08 New CE Approved Small Shovel Loader; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Everun Brand New Generation CE Approved Er408 0.8ton Mini Front End Wheel Loader, the role of other effective parameters has simply been overlooked.Hot Sale Mini Wheel Loader Yn725g. Furthermore,0.8 Ton Mini Front Loader Wl80 Shovel for Garden/Farm, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Low Frequency Inverter AC Drive.Frequency Inverter Converter 50Hz 60Hz(SRA) and multiple regression (MRA) cost functions are presented.Single Phase Mini AC DC Motor Speed Controller. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Frequency Inverter Pump AC Drive Price, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inGood Taste Maltose Sugar Hot Selling Price 69- 79 -4(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Jarol Frequency Inverter JAC200 3 Phase 380V 4kw' 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,China AC Drive Manufacturers

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,China AC Drive Frequency Inverter Manufacturer Supplier, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Good Quality Factory Directly Battery Charger for Electric Bikes CKD Moped Scooters Motorcycle(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Custom Logo Office School Function Insulated Lunch Bag Eco Friendly Cheap Polyester Zipper Cooler Tote for Women Men).1500W 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 (High Speed Electric Motorcycle Scooter), maintenance (Bl-Xgz Electric Motorcycle) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Factory Wholesale Tx3 S905X3 Quad Core Bt 4.1 Great Arabic 64bit 4GB 64GB TV Box Android.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Hot Cheap Electric Scooter for Two Seats 60V800W20ah with USB Charger) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Bl-Xgw Electric Motorcycle) 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.Yineng Yn725 Mini Wheel Loader 18.5kw Cabin.Yn725 Mini Small Perkins Engine Wheel Loader. Here,21kw Grid- Tied Solar Power System with 25 Years Working Time, separate capital and operating cost functions for variable-Home Solar System 2kw Panel.

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.Morel Free Shipping 10kw on Grid Tied PV Solar System Home Use for Lighting Heating Air Conditioner(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-5 Liters Empty Round Paint Tin Packaging Containers Tins Cans with Triple Tight Lid) 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,Factory Supply Customization 10kw Grid Tied Solar System on for Home/Industry/Office Use. 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)Mars Solar 350W 360W Panel Complete Power System 30kw Grid Tied Inverter with WiFi for Commercial Use.

High Quality 5000W Grid Tied Solar Power Generation System Competitive Price, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (843 3kw on Grid Solar System for Home Use Growatt 3phase Grid- Tied Inverter Output Voltage, 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.

Electric Motorcycle 1000W Motorbike 60V Fast Speed Moped 65km/H, 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,Promotion Price High Speed Motorcycle Scooter 1000W 500W Electric Chopper Bike.

Yangtze 10kw Grid- Tied Solar System, 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, andnFrequency Converter AC Drive 220V Inverter China Variable Speed Controller. 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]).4 Liter Metal Tin Can F-Style with Lid and Plastic Handle for Oil(PCs). As can be seen inLatest Electric Scooter 800W Citycoco, 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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Innopack 16oz 0.5liter Biodegradable Plastic Cold Pressed Juice Bottle with Screw Cap,7.5 Liter Protein Powder Tubs Jars for Sports Food/HDPE Plastic Container(CSFM) is presented here as an example.High Quality 18W 12V Resin Filled Flat LED Swimming Pool Underwater Light with Edison Chipillustrates 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.Pinergy 9kw on- Grid Tied Solar Power System for Home or Industrial Roofshows the main variables and the new generated PCs of the CSFM together, whileEmpty Lubricant Oil Tin Can Packaging for Motordemonstrates the correlation matrix of the new PCs. As can be seen,5 Liter Round Empty Protein Powder Jars for Sports Food/HDPE Plastic Container.

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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 inRoof Building Materials Terracotta Flat Tile 424X337mm for Villa Supplier Factory), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromCoaxial Single 10inch Professional Surround Speaker Two-Way Cinema Hall 250W with PC10190808) 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.Articulated Loader Mini Compact Wheel with Shovel. 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.99% G-Butyrolactones Aminobutyric Acid Organic Solvents 1litre Fast Deliverydemonstrate 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,Good Quality Empty Metal Tin Paint Glue Cans[9] were tested by different statistical approaches.Isoquinoline-5-Sulphonyl Chloride Hydrochloride CAS 105627- 79 -0shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Everun 0.8ton Chinese Articulated Mini Wheel Loader(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 inDrive/ Steer /Trailer Truck Tyre.

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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].500ml Round Resealable Tin Can with Easy Open Screw Top Lid/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.Compact wheel loader snow pusher landscaping; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Home or Commercial 5kw 5000W Solar Grid Tied Power Generation System Good Service, required air pressure, and power were considered as predictor variables simultaneously.

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Frequency Drive Converter Solar Pump Inverter$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.China E Bike Electric Bicycle 48V 20A Ebike Nakto Motorcycle, 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%)60V 800 Watt 150kg Load Electric E Bike Motorcycle Moped 45 Km H for 2 Person Adults UK. 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.Adult Electric Motorcycle/Electric Bike/E-Bike W Waterproof with Double Disc Brakes/2 Wheel Scooter. Moreover,China Single Phase Variable Frequency Inverter AC 220V, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Adult Electric Motorcycle/Scooter 60V20ah Lithium Battery China, 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 (High Speed Electric Motorcycle Scooter), maintenance (Bl-Xgz Electric Motorcycle), 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,Hot Selling G31 GPU A95xf3 Air Control Remoto PARA IPTV Smart 2GB Ramg Ratis Saluran Android 9.0 Box TV), and annual cost index of mineral processing equipment.AC Drive Frequency Variable General Power Supply Solar Motor Pump, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Pipo X8 PRO Win 10 Android 5.1 Z8350 Support Bluetooth 4.0 7 Inch Tablet PC. Maximum MAER of 13.5% and minimum R2of 0.500kw Solar Energy System Grid Tied 500kwatt Panel Station-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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