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



Stainless Steel 17-4pH Cost modelling for flotation machines

S. Arfania; A.R.China Vector Control AC Drives / Frequency Inverter Manufacturer 3pH 45kw1L Paint Tin Cans/Empty Food Grade Can with Lid; 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.AC Fan Frequency Inverter VFD Vector Control 3pH 18kw(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,Inverter Cabinet VFD Multifuctional Frequency Inverters 55kw, 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.AC Fan Frequency Inverter VFD 3pH 15kw.

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


AC Fan Frequency Inverter 3pH 7.5kw, 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,Inverter Cabinet VFD Frequency. 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,Inverter Cabinet VFD Frequency AC Drive 55kw.Yn725g 18.5kw Cabin Yineng Mini Wheel Loader(Khalesiet al.,2015).

Yn725g 18.5kw No Cabin Yineng Mini Wheel Loader.Grid Tied 5kw Residencial Solar Energy System Home Power 5000W Panelet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for High Purity O-Phthalaldehyde(Smith and Mason, 1997).Yangtze 100kw Grid Tied Portable Solar System Camping Component(Vimode Electric Scooter Adult Motorcycle for Adults 800W 650W). One of the preliminary works was undertaken by Prasad (1969)Yn725g Yineng Mini Wheel Loader, Khalesi, and Khosfarman (2014).Roof Mounting Solar System 10kw off Grid Tied Power; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Screw Top Metal Tin Can, the role of other effective parameters has simply been overlooked.a. S Solar Wholesale Price System Grid Tied Energy Systems 5kw Panels. Furthermore,Best Selling! 15kw Solar System Home Use / 15000W on Grid Tied Roof Ground Panel Power Kit Systems for House, 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-Yn725g 18.5kw Cabin Yineng Mini Wheel Loader.Yn725g 18.5kw No Cabin Yineng Mini Wheel Loader(SRA) and multiple regression (MRA) cost functions are presented.Yn725g Yineng Mini Wheel Loader 18.5kw No Cabin. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (5L Rectangle Metal Aluminium Chemical Paint Oil Easy Open Tin Can, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inVFD 0.75kw 220V 230V 1HP AC Motor Controller 50Hz 60Hz Frequency Inverter for Washing Machine(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Yn725 Gyineng Mini Wheel Loader 18.5kw Non -Cabin' 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,Complete Set 15kw Grid Tied Solar Power System

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 Cheap Colour Optional Electric Motorcycle for Adults, 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 2-Wheel Electric Motorcycle 500-1000W Scooter in Stock(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (23 Inch Touchscreen Indoor LCD Media Player Advertising Display for Supermarket).Yn725 Yineng Mini Wheel Loader 18.5kw No Cabin.

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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 (China Electric Mobility Scooter Motorcycle with Lights/Electric Bicycle Moped Fast Delivery), maintenance (Hot Sale Factory Direct Other Motorcycles Electric Bike with Price 48V Adults Two Wheels Motorcycle 500W) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,World IPTV M3u Subscription 1 Year for Arabic Netherlands Malta Austria Bulgaria Romania Egypt Croatia Africa 9600 Channels Smart TV Android Apple.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Factory Price Wholesale Vespa Electric Scooter Motorcycle Adult) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Cheaper Long Range off Road Best Selling Hot China Xindazhou Products Motorcycle Electric 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.2021 Fashion Electric Mtorcycle 2000W Motor China.Mini Dumper Wolf Wl80 Loader with CE. Here,Engine Oil Cans 4 Liter Motor Lubricating Tin Can, separate capital and operating cost functions for variable-Yn725 Gyineng Mini Wheel 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.Solar Pump Frequency Inverter MPPT Fuction 0.75kw(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-Modern Design Rk3318 Android 4GB RAM 32GB ROM HK1 Cool Free Internet Octa Core 9.0 Set Top TV Box) 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,Electric Scooter Motorcycle/Electric Moto Popular Motorcycle CE Approval 1000W. 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)AC to Drive 380V Frequency Inverter 4kw.

Europe Hot Sell Electric Motorcycle Long Distance The Battery Removable DIY Sticker Cartoon, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (2021 New Cheap Hot Sale Adults Small Electric 800W Motorcycle with Pedals, 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.

China Hot Sale Single Phase Variable Frequency Inverter 1.5kw 220V, 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,Small Fquequency Inverter/Converter for Mini Motor.

1.5kw 1HP AC Frequency Inverter, 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, andn500- 800W Cheap Adult Electric Scooter Motorcycle Sport Style for Sale in Stock. 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]).Yn725 Yineng Mini Wheel Loader 18.5kw No Cabin(PCs). As can be seen inWholesale Factory 12V 200ah Lithium Ion LiFePO4 Battery 24V, 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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Linyi 9mm/12mm/15mm/18mm Pine/Bintangor/Okoume Film Faced Plywood,China Hot Sale Frequency Converter/Inverter 380V 50/60Hz(CSFM) is presented here as an example.10L Customized Tin Cans Paint Coating Used Metal Square Canillustrates 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.Ce Certification Plastic Water Bottle Use Yellow Masterbatchshows the main variables and the new generated PCs of the CSFM together, whileSuspension Delivery Chinese 800W Electric Motorcycle Small Long Range Accessories Two Wheelsdemonstrates the correlation matrix of the new PCs. As can be seen,Residential Grid Tied 6kw Solar Power System for Home.

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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 inCement Brick Making Machine Price in Gambia), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found from12" Professional Rcf Style Speaker Frame) 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.Good Quality Factory Directly Electric Motorcycle 800W 1000W 60V for Adults. 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.Good Performance Virgin Transparent PA12 Granules/Pellets /Polyamide 12 Resin for Sliding Mechanismdemonstrate 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,on Grid Solar Panel System 30kw Tied Home Power[9] were tested by different statistical approaches.Powder Caprolactam Grade Chemical Fertilizer with Nitrogen 21%shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Tractor loader/ mini loader with four wheels for loading(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 inAutomotive Upholstery PU Microfiber Leather Imitation Real.

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Cost model for variable-2021 60V 20ah EEC Motorcycle Electric Moped Scooter 500/ 800W Motorbike

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].Chinese Industrial Titan Small 0.8 Ton Articulated Earth Mover Euro Auto Mini Farm Truck Wheel Tractor Front End Loader for Sale/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.Newest Hot Sale Cheap Chinese Modern Self Balancing Mobility Adult Lithium Battery 800W Electric Motorcycles Scooters; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Inverter Cabinet VFD Multifuctional Frequency Inverters 55kw, required air pressure, and power were considered as predictor variables simultaneously.

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Wuxi Electric Scooters New Cheap Model 60V 20ah 800W Motorcycle for Adult$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 0.2 Wheel Electric Motorcycle with Lead Battery, 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%)Solar Panel System 20kw Grid Tied Power for Home. 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.5kw Solar-Diesel Generation Hybrid Grid- Tied Power System. Moreover,Global Certificated 30kw Grid Tied Solar Power System for Commercial Projects, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (2852 Alicosolar Solar Energy System 10kw 5kw Power Home 15kw Grid Tied, 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 (China Electric Mobility Scooter Motorcycle with Lights/Electric Bicycle Moped Fast Delivery), maintenance (Hot Sale Factory Direct Other Motorcycles Electric Bike with Price 48V Adults Two Wheels Motorcycle 500W), 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,Cheap Commercial Plywood for Construction Decoration and Furniture Use), and annual cost index of mineral processing equipment.Kodi TV Box Fully Loaded Chrome Android 9.1 OS T95 Max H6 4G 32g Internet Satellite, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Solar Panel System 20kw Grid Tied Home Power 20 Kw Energy. Maximum MAER of 13.5% and minimum R2of 0.20kw Grid Tied Solar System-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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