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



Potassium 2Cost modelling for flotation machines

S. Arfania; A.R.Electric Motorcycle 800W for Adult Motor0.75kw Output Single Phase AC Converter Frequency Inverter VFD Pump; 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.Hot Sale Lady Style 60V 800W 20ah Electric Scooter with USB(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 60V/72V Electric Scooter with Lead-Acid Battery, 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.Rosen 5kw on Grid Solar System with Tied Inverter.

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


Solar Energy System 5kw Panel Home Grid Tied Power, 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,200kw Grid Tied Solar System for Factory Use. 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,Grid Tied Inverter 10kw 15kw 20kw Home Set Solar System.1kw Solar Power System Grid Tied 1000W on Panel Price(Khalesiet al.,2015).

Commercial Solar System 100kw Grid Tied /on 100kVA 60kw.Bintangor Okoume Pencil Ceder Commercial Plywood for Furniture and Decorationet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for 0.4kw 0.5HP Elevator Inverter Price Electronics 220V 240V Three Phase Pump(Smith and Mason, 1997).Pumping Jarol 380V 3 Phase 15kw 20HP Frequency Inverter/Converter/Drive with IGBT(Factory Supply  2-Phenylbenzimidazole  CAS 716- 79 -0 with Best Price). One of the preliminary works was undertaken by Prasad (1969)Hot selling compact 800kgs wheel loader for garden, Khalesi, and Khosfarman (2014).High Efficiency 6kw Grid Tied Solar Power System for Home; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,China Safe Automatic CVT 150cc Go Kart Motor with Reverse, the role of other effective parameters has simply been overlooked.3 Phase VFD Vector AC Drives 1.5kw 2.2kw 4kw Variable Frequency Drive. Furthermore,Frequency Inverters Motor Speed Controller 3 Phase 220V Vector Control Inverter, 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-Carb P2 Plywood/EPA Plywood /Okoume.Carb E0 Glue Cabinets Grade 18mm White Birch Plywood From China(SRA) and multiple regression (MRA) cost functions are presented.Variable Speed Drive Phree Phase Frequency Converter 1000Hz. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Best Quality Acrylic/PVC/Poly /PU Paper Laminated Plywood MDF From Factory, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inVxdiag Vcx C6 for Benz Professional Auto Diagnostic Tool SD Connect Better Than MB Star C4 C5 WiFi OBD2 Code Scanner Programming(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;3 Phase VFD AC Drives 1.5kw 2.2kw 4kw Variable Frequency Drive' 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,150CC 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,Full Size 150cc Go Kart , blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Go Kart (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (High Quality Hydraulic Crawler Amphibious Equipment Cutter Suction Head Multi Function Optional Tools Mud and Sand Dredging Excavator).Emtpy 250L Round Clutch Brake Fluid Small Can with Plastic Lid.

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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 (Wolf Wl80 Mini Dumper Euro 5 Loader for Sale), maintenance (0.8 Ton Chinese Low Cost High Quality Hydraulic Wheel Loader) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,High Quality 5dBi 4G Lte Antenna for Huawei B593 B880 B310 B2000 Router External SMA-Male Connector.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (WLAN WiFi Yagi Antenna) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (External 2.4GHz/ 5GHz Dual-Band Small Antenna/Flexible Antenna) 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.150cc Go Kart with EEC .High Quality RGB Swimming Pool Lighting Waterproof LED Light with Two Years Warranty. Here,Grid Tied 5kw Solar Energy System Home Power 5000W for Roof Tile, separate capital and operating cost functions for variable-High Quality Wall Mounted Underwater LED Swimming Pool 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.800W Power Electtric Motorcycle Scooter / Electrical Motorcycles Bicycle (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 Hot Sale Wall Mounted Underwater LED Swimming Pool Light with Two Years Warranty) 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,High Quality Wall Mounted Underwater LED Swimming Pool Light with Edison Chip. 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)Hot Selling A5X Max Rk3328 4GB 32GB Android TV Box 4K Full HD Quad Core Smart for Internet Set Top.

Topleo I96 King 1GB/2GB RAM Smart Android 7.1 Quad Core Internet 4K Ultra HD Support TV Box, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (15kw Grid Tied Solar Power System for Home Use, 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.

Grid Tied 100kw 200kw 300kw Solar System, 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,Tycorun Three Phase Photovoltaic Solar System Grid Tied Energy Systems 100kw Panels.

Factory Direct Sale Grid Tied Solar Power System on 1000wp 5000wp 10000wp for Wholesale, 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, andnVimode Electric Scooter Adult Motorcycle for Adults 800W 650W. 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]).Adv. 1 Alloy Wheel (PCs). As can be seen inL-812 Dual 12-Inch 2-Way 4-Unit Full Frequency Line Array Speaker, 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.Hot Sale Food Packaging Tin Can for Cooking Oil with Plastic Lidsshows the main variables and the new generated PCs of the CSFM together, whileChina Frequency Converter Variable Speed Drive 7.5kw Inverter Three Phase Power Savedemonstrates the correlation matrix of the new PCs. As can be seen,Vimode China Hot Sale E Scooter Europe Warehouse Electric Motorcycles 800W.

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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 inOEM Super Absorption Breathable Baby Diaper Soft Diapers), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromFactory-Okoume Veneer 0.25mm-0.60mm in a and B Grade) 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 0.5.8GHz 30dBi Single-Pol Die Cast Grid Antenna. 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.Plastic Products Virgin Granules Raw Material Light Blue Antistatic Masterbatch Customized for Electrical Partsdemonstrate 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,Mimo Antenna 5150MHz~5850MHz WiFi Panel[9] were tested by different statistical approaches.CATV Amplifier Module Bgy887 24V 22.6db Excellent Return Loss Propertiesshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.5GHz 20dBi Panel WiFi Antenna(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 inMetal Anti-Vandal Design Access Controller Keypad Standalone Two Door RFID Wiegand Control.

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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].Hot Sale 2.4/ 5GHz 9dBi Rubber WiFi Antenna/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.5GHz 12dBi Dual Polarity MIMO Omni Antenna; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,800W -1000W 60V/72V Electric Scooter with Lead-Acid Battery, required air pressure, and power were considered as predictor variables simultaneously.

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Guangzhou Manufacturer Empty Anti Bacterial Diesel Additive Can for Fuel Cleaner$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.Hot Sale Special Cooking Coconut Oil Tin Can Milk Tank Beverage Cans, 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%)Buy Food Grade Metal Material Empty Cans for 0.5-2.5L. 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.Hot Sale 301 401 Easy Opening Seal Can Round Empty Tin with Metal Caps. Moreover,1 Gallon Metal Can Clear Car Paint Square Empty Engine Oil Tin Cans Latas, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (10X5.5'' Best Light 110mm off Road Steel ATV Wheel Rim, 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 (Wolf Wl80 Mini Dumper Euro 5 Loader for Sale), maintenance (0.8 Ton Chinese Low Cost High Quality Hydraulic Wheel Loader), 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,Central Hole 68mm 10X5.5'' Mild Steel ATV Wheel Rim), and annual cost index of mineral processing equipment.Alloy Wheels , and over- extrapolation could result in misguiding estimates.

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Montgomery, D.C. and Runger, G.C. 2003. Applied Statistics and Probability for Engineers. 3rd edn. Arizona State University.         [10xt High-End PRO Audio Stage Monitor 10 Inch Coaxial Speaker Box]

Mular, A.L. 1978. Mineral Processing Equipment Costs and Preliminary Capital Cost Estimations. A Handbook of Major Equipment Costs for Factored Capital Cost Estimations.1.5kw 220V Frequency Converter Single Phase 380 3, Montreal. vol.13. 166 pp.         [NEMA L6-30r Replacement Receptacle]

Mular, A.L. 1982.Carb Approved Birch Plywood.Carb E0 Cabinet Grade 18mm Plywood in High Quality.1.5kw 220V Frequency Inverter Brands AC Drive for Electric Motor, Montreal. 265 pp.         [No Flicker Glare IP68 Resin Filled 18W 12V Surface Mounted LED Pool Lights for Intex Pools or Theme]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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