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


2.50- 17 Cost modelling for flotation machines

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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.Variable Frequency Drive Inverter Manufacturer 3 pH Power Saver AC Synchronous Motor(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,Vectron Frequency Inverter, 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.Zl08f Mini Small Farm Compact Tractor Wheel Loader with Standard Bucket.

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


Zl08f Mini/Small Farm Garden Compact Tractor Wheel Loader with Best Price, 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,OEM/ODM T95 Allwinner H616 Android 10.0 6K 4GB 32GB Box 4K Remote Control Smart TV. 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,Beautiful Design T95 RAM 4GB ROM 32GB Allwinner H616 Universal 4K TV Android 10.0 Set Top Box.Eougem Zl-08 0.8 Ton Chinese Mini Radlader Manufacturer 0.45m3 Bucket Loader(Khalesiet al.,2015).

Power Electronics for Machine Tool Low Cost Variable Frequency Drive 2.2kw.50Hz 60Hz 220V/380V Vector Control AC Variable Frequency Driveet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for T Solar Mc4 Energy System Connector PV(Smith and Mason, 1997).Inverter AC Drive(Cosmetic Grade Ultramarine Violet Manufacturer). One of the preliminary works was undertaken by Prasad (1969)Power and Triple Output Type Static Electric Motor AC Inverter Solar Speed Control, Khalesi, and Khosfarman (2014).Small Compact Front Wheel Loader / Zl08 Farm Garden Mini; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,DC/AC Drive Inverter Solar Pump Converter 1.5kw Motor Green Energy, the role of other effective parameters has simply been overlooked.Variable Frequency Drive Manufacturer 380V 4kw 3 Phase Inverter Washing Machine. Furthermore,Frequency Converter Variable Drive 50Hz to 60Hz 2HP 2. Kw 1 Phase, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-800kg Farm Mini Loader Chargeur Minilader Cargador.Titan Brand Mini Small Chargeur De Roues Radlader Gommata Carregador Roda Cargador Ruedaschargeur Tracteur Traktorlader Caricatore Trattore D(SRA) and multiple regression (MRA) cost functions are presented.VFD 0.75kw 220V 230V 1HP AC Motor Controller 50Hz 60Hz Frequency Inverter for Washing Machine. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Radlader Zl08 Wheel Loader for Sale Mini Articulated, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inSA831r Outdoor Return Path CATV Trunk Amplifier(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Customized Bintangor Plywood Face Veneer of Commercial' 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,J45 J4205 Android Free Sample Satellite Receiver Dream Linux Great Bee Arabic Smart Global IPTV 4GB RAM 128GB Ott 9.0 TV Box

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,American Walnut Single Crown Cut Veneer Recon Engineered for Door Furniture Plywood, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Power Supply 3 pH 4kw Converter 60Hz 50Hz Water Pump Frequency Inverter(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Nature Series Artificial Engineered Quartz Stone for Benchtop).Comaccord D and E Grade 0.26mm Birch/Oak/Ash Face Veneer for Vietnam Furniture Plywood.

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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 (Rotary-Cut Okoume Wood Veneer 0.25mm A Grade for India), maintenance (0.8ton Contruction Machine Mini Small Wheel Loader with Bucket) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Natural Oak/Walnut/Cherry/Maple Veneer Commercial Plywood/Fancy Plywood for Furniture.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Top Quality Cheap Price 0.3mm Birch Face Veneer for Furniture Plywood) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Natural Wood Sapele Veneer Plywood for Furniture Grade) 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.20mm Plywood or Timber.Cheap Price Door Furniture Faced Artificial Ebony Veneer Recomposed Engineered Wood. Here,Factory-White Engineer Veneer Big Size 1300X3300X0.30mm 0.40mm 0.50mm, separate capital and operating cost functions for variable-10'x6' Rotary Cut Okoume Veneer for Plywood.

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.Engineer Veneer Ebony(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-800kg China Articulated Mini Small Compact Front End Wheel Loaders) 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,Hzm908 Jn 908 31.5loader Mini Wheel Loader for Sale Best Price Top Quality. 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)0.8t Snow Plow Loader Zl08 Mini Wheel.

Construction Zl08f Mini Hydraulic Compact Front End Loader for Sale, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Zl08f Mini/Small Farm Garden Compact Wheel Loader with Lawn Mower, 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.

Hzm908 Er908 Europe Loader Mini Ce EPA Sale with Fork, 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,Zl08f Construction Machine Farm Tractors Mini Compact Loaders.

4X8 Size Rotary Cut Okoume Veneer for Plywood Face and Back, 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, andn0.15mm Okoume Wood Face Veneer Rotary Cutting for Sell. 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]).Water Pump Variable Frequency Drive Vector VFD Inverter Elevator Motor Price(PCs). As can be seen inDiesel Engine Parts Fuel Injection Nozzle 160sn529, 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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Sapele Veneer Plywood Sheet for Wood Furniture and Decoration,2.8X1.9 Large Size Rotary Cut Okoume Face Veneer(CSFM) is presented here as an example.Automatic High Effective Medical Ultrasound Bone Densitometer illustrates 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.4 Cyl CNG Auto Gas LPG Conversion Kit / Sequential Injection Systemshows the main variables and the new generated PCs of the CSFM together, whileGrowatt Inverter 15kw 20kw 30K Three Phase China Market Lowest Price Grid Tieddemonstrates the correlation matrix of the new PCs. As can be seen,Inverter with Factory Price 3 Phase 60Hz to 50Hz 380V Variable Frequency Drive.

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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 inWholesale Grease Collection 131 Colors Three Step UV Gel Nail Polish), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromPolyamide PA Resin CAS No.: 63428-84-2 for Untreated Film Sunmide) 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 0.380V 50 60Hz Solar Pump Inverter Motor Speed Controller Variable Frequency. 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.China Enclosed Ice Cream Tricycle Three Wheel Cargo with Cooling Boxdemonstrate 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,Decorative Natural Mahogany Cedar Sapele Oak Walnut Teak Veneer Fancy[9] were tested by different statistical approaches.99% Purity 1-Bromo-3shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Factory Price 3 Phase 50Hz to 60Hz AC Converter Solar Pump Inverter(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 inMax Lifting Height 7m Telescopic Forklift Machine 4X4 Telehandler.

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Cost model for variable-Frequency Converter

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].1.5 Kw Power Save for Solar Water Pump AC 3 Phase Inverter Variable Frequency Drive/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.Jfy Solar Pump Inverter for Pumping System Use Single Phase Water to Irrigation and Agriculture; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Vectron Frequency Inverter, required air pressure, and power were considered as predictor variables simultaneously.

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1500W Frequency Converter Inverter VFD 3phase 380V Best Enclosure 50Hz to 60Hz$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 0.220V 7.5kw Variable Frequency Drive VFD 3phase AC Inverter, 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%)Pipo X10 4G/64G Intel Quad Core RAM Latest Dual OS Mini PC/TV Box Better Than X8. 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.Factory Direct HK1 Cool Set Android 9.0 4GB RAM 16GB ROM IPTV 64GB Firmware Smart TV Box. Moreover,Factory Wholesale H10 H6 Alfawise GPU Mali T720 Android 4GB RAM 32GB ROM in Set Top Boxx99 Boxbox Box TV, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Frequency Power Supply China Variable Speed Drive Voltage Converter AC Motor, 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 (Rotary-Cut Okoume Wood Veneer 0.25mm A Grade for India), maintenance (0.8ton Contruction Machine Mini Small Wheel Loader with Bucket), 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,Titan 4 Wheel Driving 0.8ton Mini Micro Compact Loaders Garden and Farm Using), and annual cost index of mineral processing equipment.Radlader Zl08 Mini Wheel Loader for Agriculture Work, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Hzm908 Jn908 31.5 Tyre Loader Best Price Hot Sale. Maximum MAER of 13.5% and minimum R2of 0.Pendoo X10 Max Amlogic S905X3 Android TV Player World IPTV Video Box Support IR /2.4GHz Wireless Mobile Remote Control-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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