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


Tanfon 5kVA off Grid Solar Inverter Tied /off Grid/Hybrid SystemCost modelling for flotation machines

S. Arfania; A.R.2500*640mm E1 Glue Engineer Veneer Wenge/Oak for DecorationFactory Direct Supply 2 Wheels No Folding Elderly 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.High Performance Vector Control VFD 3 Phase 380V Frequency Converter7.5kw Inverter for AC 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,Zl08 0.8t Articulated Front End Wheel Loader with Pallet Fork, 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.Face Veneer Nature Bamboo for Fancy Plywood.

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


White Birch Veneer in 0.28mm/Jacky, 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,Chinese Suppliers Okoume Wood Face Veneer for Malaysia. 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,Factory-Hardwood Veneer in 1300X2500mmx 0.60mm.Yn725 G Ce Approved Hot Sale Mini Wheel Loader(Khalesiet al.,2015).

Variable Frequency Drive VFD Supplier AC Converter 50Hz to 60Hz with Vector Control.China Zl08 Payloader 0.8 Ton Min Articulated Hydraulic Mini Front End Wheel Loaderet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Electrical VFD Frequency Inverter Three Phase 220V 380V 7.5/11kw for Solar Pump(Smith and Mason, 1997).0.8ton Compact Loader Wheel in Europe(Power Frequency Converter 60Hz 50Hz Price). One of the preliminary works was undertaken by Prasad (1969)4 Kw China Frequency Converter Power Supply Motor Drive 3 Phase Inverter, Khalesi, and Khosfarman (2014).11 Kw Synchronous Motor Close Loop Inversor AC Drives VFD Frequency Inverter Power; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Yn725 Yineng Mini Wheel Front Loader, the role of other effective parameters has simply been overlooked.Yn725g Yineng Mini Wheel Loader 18.5kw Without Cabin. Furthermore,JAC300 Series Frequency Converter Three Phase Solar Pump Inverter Power Supply, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Yn725g Yineng Mini Wheel Loader 18.5kw Without Cabin.Km3 Collective 4GB 64GB TV Box Google Certified ATV(SRA) and multiple regression (MRA) cost functions are presented.China Everun Er408t 0.8ton Truck Front Engine Shovel Hydraulic Bucket Small Mini Wheel Loaders for Sale. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Natural Wood Woven and Strand Bamboo Veneer Sheets Comaccord, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inQige Supply High Quality Ulipristal Acetate Pharmaceutical Raw Materials CAS 126784-99-4 for Contraception(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;High Quality Ebony Engineered Wood Veneer for Hot Sale' 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,Hot Sale Birch Wood Veneer Core for Plywood

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Pendoo X10 Max International Best Custom Set Top Box 4GB 32GB TV Converter Ott 4K Smart Android, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),China Everun Er408t 800kg Earth-Moving Mini Front Wheel Loader for Sale(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Indoor Double Whirlpool SPA Bathtubs with Bubble Jet).Zl08 800kg Mini Tractors with Front End Dumper Loader.

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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 Everun Er408t 0.8ton Buy Truck Front Engine Shovel Hydraulic Oil Filter Best Small Mini Wheel Loaders for Sale), maintenance (AC Drive Using Solution Building Hoist Construction Frequency Inverters 3pH 380V 22kw) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,AC Drive for Bridge Crane VFD Using Mono Overhead 3pH 380V 15kw.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Construction Machine Mini Loader Zl08 with Factory Price Front End) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Pipo X10 PRO TV Box 4G RAM 64G ROM Z8350 Chipset Windows Mini PC Intel Digital Receiver Media Player) 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.Hybrid 3kw Solar Grid Tied Roof Top System Home Power.Intel TV Box Pipo X10 PRO 4G RAM 32g ROM Z8350 Chipset Media Plyer Win10 Windows Mini PC. Here,Frequency Converter 50Hz to 60Hz Fan Speed Controller Solar Power Inverter China, separate capital and operating cost functions for variable-Mini 220V Single Phase Input 2.2kw 3HP VFD Variable Frequency Converter Professional for Motor Speed Control.

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.Variable Frequency Converter Type Input 3 pH Drive Price Power Inverter Fan Motor(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-General Type Input 3 pH 380V Frequency Converter Variable AC Drive) 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,0.8ton Agricultural Tractor Mini/Small Front Wheel Loader. 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)Teak Wood Veneer Woven Design for Plywood Door.

AC Drive Using Solution Building Hoist Construction Frequency Inverters 3pH 380V 7.5kw, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Zl08 Wheel Loader Wl80 Wolf Mini, 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.

Zl08 0.8ton Articulated Hydraulic Farm Wheel Loader Tractor, 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,Popular hot selling 0.8ton mini wheel loader/ front end loader with bucket on sale.

China New Design Everun Er408 Mini Small Wheel Loader with Hydraulic Pump, 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, andn3 Phase AC Drive for Water Pump and Fan. 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]).910 Alicosolar 10kw on Grid Solar System with Power Inverter for Home CE/TUV/ISO Cretificate(PCs). As can be seen inProfessional Stage Bass Sound System 15 Inch Subwoofer Speaker Ls500, 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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Wood Woven and Strand Bamboo Veneer Sheets,Rotary Cut Bintagor Veneer for Panels and Furniture with Good Price(CSFM) is presented here as an example.L-Arginine Nutritional Supplements  Arginine  Flavoring Agentsillustrates 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.Android 6.0 Smart TV Box Rk3229 Quad-Core 2GB/8GB Internet Set Topshows the main variables and the new generated PCs of the CSFM together, whileCustom Printed Food Grade Ziplock Plastic Pouch Packaging Bagdemonstrates the correlation matrix of the new PCs. As can be seen,High Quanlity 1 Phase 3 AC Drive VFD for Pump.

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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 inP6 Indoor Rental Full Color Advertising LED Display Screen), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromHorn Professional Speaker H3) 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.Engineered Ebony Veneer Ecowood Reconstituted Macassar Quarter Cut. 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.Quality Assurance O-Phthalaldehydedemonstrate 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,899 Alicosolar 9kw on Grid Solar System with Power Inverter for Home CE/TUV/ISO Cretificate[9] were tested by different statistical approaches.Modern Leisure Sofa Chair Living Room Furniture Lift Reclineable Electric Massageshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Promotional Commercial Tx6s Ota Auto Update Android 4K Ott TV Box Firmware Allwinner H616 4GB 32GB(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 inDisposable Adult Briefs Diaper Economic Type.

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Cost model for variable-3phase VFD

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].0.75kw 1HP AC Frequency Inverter/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.Round Gloss Tin Can Metal for Edible Olive Oil Canning; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Zl08 0.8t Articulated Front End Wheel Loader with Pallet Fork, required air pressure, and power were considered as predictor variables simultaneously.

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High-Performance Variable Frequency Inverter 3-Phase 380V$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.Wl80 Mini Loader From Wolf, 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%)Wolf Mini Wheel Loader Wl950 Farm. 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.Zl08 0.8 Ton Mini/Small Articulated Hydraulic Front End Wheel Loader. Moreover,Tin Cans with Metal Cover for Paint or Chemical Packaging, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Yihe Brand 300-600m Face/Core Veneer Door Furniture Paper Tape Reeling and Gummed for Joining Repairing, 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 Everun Er408t 0.8ton Buy Truck Front Engine Shovel Hydraulic Oil Filter Best Small Mini Wheel Loaders for Sale), maintenance (AC Drive Using Solution Building Hoist Construction Frequency Inverters 3pH 380V 22kw), 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,5L Chemical Oil Tinplate Can with Metal Press Cover), and annual cost index of mineral processing equipment.15L Tinplate Closed Paint Bucket Water Based Glue Metal Pail, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,0.28mm Red Oak Artificial Veneer. Maximum MAER of 13.5% and minimum R2of 0.Olive Oil Metal Container Edible Tin Can with Plastic Lid-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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